(next)
 
 
 
 
 
 
 
 
 

GUIDE TO THIS SECTION:

 (read me!)
  Links have been added to help pick out or refer to a few subjects of interest. Where calling up particular information is desired, using the links, may be helpful! However, on first reading, it will be simpler to read through to the end, without making any "side trips."

    (Begin at the "beginning")   (Perspective and Introduction)

    or

    (This way back to the "library index")   (home)

    or

    Subject Links

    Mission and Methods

    Perspective and Introduction

    diffraction  (Part 1)

    "The Great Debate"  (Part 2)   (Newtonian reflector versus refractor)

    achromat

    apochromat

    Brandon Refractor

    Vignetting  (Part 3)

    Shedding a Little Light  (Part 4)

    Schmidt-Cassegrain   (compound optical systems)

    modulation transfer function
    (Why do obstructed telescopes suffer more from turbulence than unobstructed telescopes?)
 

    (next)
 
 
 
 
 
 
 
 
 

.
    A Fourth Order Relationship  (Part 5)

    Eyepieces, Barlow Lenses and Filters  (Part 6)

    visual acuity

    eyepiece test results

    The Quest for a "Nailed" Image  (Part 7)

    The Proper Mind Set--What Every Observer Needs to Know!  (Part 8)

    Finishing Touches  (Part 9)

    * * *
 

    Addendum:
       Optical testing  (Lunar and planetary observing tips--testing for crispness
       and accuracy ("terminator test," "scintillation test" and "snap technique")
 
 

    Appendix:

       Terminology

       History

       Sources
 
 

    Links to:

    (Perspective and Introduction)

    (Return to the beginning of the "Guide")

    (Begin Part 1)

    (This way to the "library index")
 
 
 
 
 

Mission and Methods

Preliminary comments: The author is not an expert on optics or astronomical observing, more likely a student of behavior and how things work together. This document started out as a compilation of observing notes, with  (sometimes creative) conclusions and observations on the nature of optical systems. This is one man's take, a study of how things work, sometimes arrived at as an intuitive process. A few mistakes have been made along the way, and they continue to be corrected. (As of this edition, 12-06-06, an attempt has been made to mark (***) personal theories, assumptions, (points of view) and terminology, which may not otherwise be identified as original work, conclusions, and opinions, within the body of the copyrighted material. The content of Part 7 and Part 8 are almost entirely of the author's creation) There are sections on human physiology (i.e., from the book As Well As Nature Intended, by the author), and how the structure of the eye, and being in the peak of good health, can affect what is seen at the eyepiece. The eyepiece tests are original, and should work well with any type or size telescope. (Terminology was improvised or adapted to elaborate on and identify physical principles.) Generally, and as an extension of other work, some of the text (methods and explanations) is original ideas (i.e., creative property). This work was done, in stages, over a period, of 9 -1/2 years, and this is the third major edition, and the second major internet revision--12-06-06, the original version being undertaken March 20, 1997, updated through September 9, 1999, and the second formal release being May 12, 2000--as the first internet version.

(A work in progress: Because The Perfect Telescope covers a lot of ground, and because the information was accumulated and added to over a period of years, there is a tendency, to tie things together by repeating a point of interest, and adding a few new comments, something like an update. This makes the text redundant, at times, but with the intent of bringing out more information, or expressing a different point of view on the same subject. Another method is making up terminology to describe some effect--"science according to me." Sometimes it is good, and sometimes it is a work in progress.) (This identifying paragraph was added to the internet version 12-06-06, partly because of infringement problems. There is a supporting document at eyepiece.html. None of the included information came from the internet, and is protected by original copyright, beginning April 1997. See copyright notice at the front of this file, and on the home page at ALOBS.html. Other related work by the author: As Well As Nature Intended, A Collision of Two Infinities, Under Southern Skies: 1950 through 2000, Bloom's Nursery: A Dynasty in Orchids and Other Living Things.)

The author is committed to crediting sources, and wishes everyone respected the work of others both as an attributable source, and as copyrighted material (intellectual property). (If someone else's work is instructive, it adds credibility to any new work to acknowledge the source!)

   (Return to the beginning of the "Guide")
 

Perspective and Introduction
(Getting into a new hobby: Observational astronomy for the serious student.)

  One of the most common questions for the proud new telescope owner is, "how can I tell if the "seeing" conditions justify setting up my telescope?" Perhaps the more important question is, have we overlooked something in the excitement of our expectations, and let the process of acquiring equipment and signing checks begin before fully understanding the challenge. (This essay, a work in progress, is an effort to address as many of the practical and technical issues as possible!)

  In amateur astronomy, "telescope building" and "observational astronomy" are two entirely different but interacting pursuits, and they require different skills. The next question: What do I have to do to see what I thought I was going to see when I started this hobby? Once you have a working telescope, figure out how to set up and optimize the performance of its eyepieces and accessories, with regard to the advantages of different designs, and with consideration for the optimal power range for the aperture, on a given occasion. There are methods in Parts 7 and 8, for getting the most out of every observing outing. If you think in terms of setting things up, and using just the right eyepiece, intending to see the best possible image, for the conditions, and going easy on the expectations, you will be more successful. ("Satisfaction comes from being skilled at what you do, not from having your wishes fulfilled!")

  On the serious side, not developing and having an operational technique kills this hobby for many. On the less serious side, sometimes you just want to get set up and show friends and family whatever there is to see. This is not a "blood-sport," and there is a lot that can be done for less than $1,000!

  I sometimes forget there are other branches of this hobby, and that there are amateurs doing more advanced projects, not just looking through the eyepiece of a telescope. Some CCD enthusiasts and radio astronomers have technical backgrounds, and they are not particularly interested in visual astronomy. So, if visual astronomy isn't primary, this information may be of less interest.

  There is a rule of diminishing return with telescopes. With a small scope, power can be reduced in turbulent or murky skies and still see much of what is expected, but when observing with a larger telescope (one that is more than 6 or 8 inches in aperture) there may be a disconnect versus what is seen with the unaided eye. ("I cannot relate to what I am seeing," or, "all I can see is a swarm of rippling lights.") This is why a good pair of binoculars, or a 4" telescope, is always good to have, even, and especially, after gaining a little experience and expertise!

  The original question ("how can I tell if the "seeing" conditions justify setting up my telescope?"): When looking up at the night sky, the transparency of the atmosphere is difficult to determine. The sky can seem very clear and dark, to the unaided eye, but one look through the eyepiece of even a small telescope may reveal significant turbulence. In some locales, when the "seeing" is good, the air has a special "feel" to it. It may seem still and "close," as though you are "wearing the air!" It can be a motivating moment, when  recalling how remarkable telescopic images have been on similar nights in the past.

  It will feel different in other parts of the country (and world), depending on the topography and whether there is a large body of water near by, but a famous amateur astronomer lives near my observing site, and he has more success and has more good nights than anyone in the area. He lives on the bay, and I live three miles inland, and there is no comparison between his sky and mine. Here, there are only 5 or 6 really good nights a year, and the best nights are most likely to occur in October and November. (I have read, and believe, it is best in October no matter where the observing site is, but in most parts, farther north (USA), the winter is moving in by October, and the mixing of low and high pressure fronts gets the layers of air "rolling," and that is the worst possible situation for observing.)

  The conditions vary for sites closer to water, or at higher altitudes, or in the dessert. Mountains are a problem! In the Florida Keys, just meters and feet from the gentle waves of the mid Atlantic and the Gulfstream, there are so many good nights if you started to analyze and compare notes, with other amateurs, someone would say, "I came 1,500 miles to see this, and it looks good to me." (It may be useful (in the future) to take note of how the air "feels," on nights that turn out to be exceptional.)

 When it seems cool and dry and crisp, air cells move fast and the effect is devastating, in the eyepiece. Until a "feel" for the air on good nights is acquired, pointing the telescope at a bright star or planet and focusing, a little closer than infinity, will most likely reveal a swarm of ripples, at their worst, looking something like the "rapids on the Colorado." If the cells are all running together, and seem to be flying by at 200 miles per hour, they probably are, but if they look like a traffic jam on the freeway from three miles up that is a good sign. The field on "still nights" is slowed down enough to almost see what individual air cells actually look like. Whatever astronomical object is to be viewed has to get through the "canopy," and when the ripples are slow moving and less active, that is as good as it is going to be. The situation can be deceptive! On seemingly great nights, the majesty of the heavens is invigorating to take in, with the unaided eye, but the "blanket of turbulence" that brings the crispness, or a cool, pleasant feeling to the evening air, is not likely to be conducive to good telescopic viewing.

More on "seeing" conditions and eyepiece testing at:

eyepiece testing and observing techniques
 
 

Part 1
In the Beginning...
  With no particular expertise in the field, and while trying out a new telescope,
a 6-inch refractor, in an attempt to solve some of its optical problems, I came
across, and worked up, information that may help others engaged in a similar
struggle. The goal was to get the highest possible optical performance, from a
lens or mirror, with regard to contrast, stability, sharpness and maintainability.

  The most important factor affecting optical performance is diffraction, and less
diffraction is better. Diffraction cannot be eliminated, but it can be kept to a
minimum. If everything is precise and accurate, in the construction of a telescope,
there will still be diffraction related to the edge of any obstruction, lens or mirror.
Diffraction, as spikes of scattered light, forms at every boundary in the system
(i.e., where there is an uneven edge, scratch, deformity or obstruction. Any standard
or measure of performance must consider, and allow for, diffraction as an inherent
defect, because even in a flawless system (which there none of) there will always
be an edge. The Rayleigh criterion was devised with this in mind. (Lord Rayleigh
was the first scientist to establish a standard for the performance of an optical system.)
According to Rayleigh, a well made optic is said to be "diffraction limited" if it
has wavefront errors of 1/4 wave or less, in sodium light. For an instrument to
demonstrate "diffraction limited"performance, a clean and concentric pattern of
rings, of uniformly decreasing intensity, moving away from the center, should be
noted, while focusing the eyepiece on the Airy disc of a star, at 50x per inch of
aperture. (Diffraction limited means the only thing affecting performance is
(inherent) diffraction, related to aperture...there are no optical errors or defects.)

   (Return to the "Guide")   (diffraction)
 

  "There is no substitute for aperture," but for someone new to this hobby, it
will be difficult to prevail by just wanting more performance and purchasing
a larger telescope! Higher cost and diminishing return, versus the "seeing"
limits, go against the hope of pulling the theoretical performance, for a given
aperture, out of a storage case on a given evening. This is true for any
aperture, but success with a larger telescope requires more skill, patience
and determination.

  There are technical points having to do with performance that must be understood
before an informed purchase can be made. Most of it is the domain of the optician,
but going to star parties and talking to experienced amateurs is a good beginning.
Searching the "WEB," making long distance phone calls, and reading technical
articles and books on the subject, along with chance conversations with other
amateurs and going to star parties are all part of what it takes to find out what
works and what doesn't.

  To begin, the resolving power of a lens or mirror is determined by its clear aperture
or diameter. Surface accuracy and obstructions in the light path are important, but,
unless the imperfection is significant they will not have a noteworthy affect on
resolving power. However, their affect on resolution and contrast is another story.

  Decisions must be made as to affordability, carry-weight and bulkiness? Is it
transportable? Is it feasible to go to a "dark site" and wait several hours for a
large mirror or lens to cool down, and achieve its best figure? (Planning, loading,
transporting, unloading, setting up and hanging on until the "seeing" and the optics
are stable, or at their best, can consume most of the night!)

  As to the image presented to the eye or camera there are several fundamental and
largely uncontrollable considerations: If the "seeing" is poor, a large lens or mirror will
be more affected than a small one. Using a large aperture telescope can be rewarding:
You can see all the wondrous images shown in the books and magazines through
a telescope of 12 to 16 inches aperture. However, to see what you hope to see, it
may be necessary to visit a remote site, and risk the possibility of having traveled
many miles just to turn around and head home, because of poor atmospheric conditions.
(After purchasing a 6-inch refracting telescope, it took many months and many trips
to the backyard to find out what it could do. Even for telescopes as small as 5 or 6
inches, "seeing" conditions good enough to test the theoretical limits can be rare!
Because of this, some amateur astronomers, new to the hobby, give up and sell their
telescope without ever seeing what it is capable of.)

notes:
1) In the course of answering questions and coming up with solutions, an important
question keeps coming up...whether or not, subtle refinements, good for mid-sized
or small telescopes may be less useful above 10 or 12 inches of aperture, where
"seeing" conditions count as a much more important factor. An unavoidable limitation:
Big telescopes are affected more by turbulence and light pollution, and trying out
something done to improve performance, in a larger instrument, may have to wait
for another day, and better "seeing."

2) A change in viewing sites can provide a new perspective as to what high quality
eyepieces and other accessories can really do. That is, there may be a tangibly
different outcome, such as, some upgrade or improvement may be useful in the
city, and less important at a darker site, or any effect of changing to a better
eyepiece, may be less noticeable in poor "seeing," or in a bigger telescope, which
would be more affected by poor "seeing," so much so that using a better eyepiece,
with the given conditions may almost be inconsequential, or it may be a stunningly
satisfying surprise.

  A dark sky is not always what it seems! In light polluted locales, turbulence
often shows itself as increased "skyglow," surrounding relatively bright objects.
As the atmosphere becomes more steady, the "skyglow" diminishes. In fine
"seeing," most of the unwanted illumination can be traced to the optics. With very
clean optics, in a dark sky, the telltale "glow" may not be detected, but faint objects
that should be visible cannot be seen through the swarm of rapidly moving particles.
As turbulence varies, or momentarily subsides, "invisible stars wink on," only to
disappear again in a few seconds. (Light pollution and smog probably get more
than their share of the blame, when the effects of turbulence limit the "seeing"
conditions (i.e., transparence and stability.)

  (There was a rare moment of good "seeing" on November 11,  1997, the night before
an occultation of Saturn by the Moon. With the Moon nine days old, the edges of
eight or nine craterlets could be seen on the floor of Plato, using a six-inch telescope,
at 155x. Even with a thin layer of cirrus clouds, forming after 9:00 p.m., the customary
glow that usually appears around Jupiter and Saturn, most noticeable at high power,
did not show up, and the sky was dead calm. On this particular occasion, while
viewing from the downtown area, the sky appeared transparent and unusually dark,
even at 70x per inch of aperture.)

  Turbulence, fog and rain, cannot be controlled, but resolution can. ("Resolution
is the absence of diffraction," and diffraction is the scattering or "displacement
of light.) It can also be said that "resolution goes to contrast***," and that resolution
is affected by errors in surface smoothness (i.e., scratches and deformities), spherical
errors,  obstructions in the light path, centering of components, the perfection of
edges and collimation. Contrast is reduced by surface errors, marginal coatings,
internal reflections and obstructions in the light path. Even with a large telescope,
without good contrast, faint nebulae and galaxies will fade into the background!

  (In a telescope, construction interferes with perfection as a function of the limits of
technology and craftsmanship. In terms of what we see, and as a point of reference,
the purpose of all the hard work is to attain the highest possible contrast. In the
telescope, the same problems of execution in design affect both detail and contrast.
Resolution and contrast are thus inextricably interconnected. However, in the
way we prefer to think of it, contrast is one thing, and detail is another. This is
more about psychology and human behavior than about science and physical
properties.)

  "Resolution goes to contrast:" For this discussion, if, within an image, let's suppose
the color and the detail changes every one thousandth of an inch, and a given
eyepiece can see to half a thousandth of an inch, more or less, every detail and
every color will be seen, but another eyepiece that is less corrected, and less sharp,
may seem indistinct, or less crisp, as the threads of color run together, dulling
small-scale contrast (i.e., micro-contrast).*** (This explanation did not quite paint
the mental picture I wanted, so I eventually tried a different approach--next.)

  To the eyes, and in our way of thinking, a telescope "sees" points of light. If there
are scratches on the lens or mirror, the light bounces off scratches and imperfections
at angles, and overall sharpness is reduced, leaving no possibility for normal
(perfect is normal) contrast. When the lens is "perfect," each point of light arrives
at its exact designated position, relative to each of the other points in the field.
If a "point" is out of position because of errors in the lens it will "pile up" on
other points in the field, hence light scatter and poor contrast are the trademark
of an imperfect lens. If all the points of light are allowed to reach their proper
place at the image plane, everything appears crisp and contrasty. If the image
is imperfect, the scattered (out of place) points detract from definition and mix
colors together, reducing contrast. Therefore, "resolution goes to contrast"
means a "perfect optic" scatters no light!***

  (A 2-dimensional concept: Points in the field are measured "x" and "y," hence
what is measured, or studied, by the eye is detail, but what we see on first opening
our eyes, or on looking into the eyepiece, is changes in color and intensity,
something simpler (i.e., requiring less study) for the brain to respond to than detail.
Therefore, "everything is about contrast" (because large scale markings and changes
in intensity are seen at first glance), and "resolution goes to contrast," are consistent
statements. When first looking at Mars in a telescope (in the first instant), we see
changes in the surface as different colors. Then, in a few moments, after we have
more of a chance to process (become fully aware of) the structure of the image,
"detail comes into view," and there is an opportunity for more serious scrutiny.)

  Any change in contrast on the small scale, subsequent to an improvement in
resolution and sharpness, will be noted as some degree of enhancement (i.e., less
blurry). However, changes that "go to contrast," in terms of overall color and
intensity, depend on transparency, more than sharpness, and they are large scale
effects, light and dark, not minute dimensional effects. Of course, the best optic
will do all these things!

  Contrast affects imagery on the "macro" (i.e., large scale effects, like color and
intensity), while resolution affects contrast on the "micro" (i.e., in microns--small
scale effects), but only for the better, if everything else is ideal. Example: A fine
5 or 6-element eyepiece may be sharp, but it may have too many internal reflections
to provide good contrast. Conversely, a two or three element eyepiece may transmit
more light, but it may not be very sharp, or well corrected. One eyepiece is sharp,
with less than ideal contrast, the other has good contrast, but is not so sharp! The
rule is, "resolution goes to contrast," but in the real world, the result may not be good,
if other factors are less than ideal, such as when using a scope with a relatively large
secondary mirror obstruction (to be covered in Part 4), or if there are noteworthy
internal reflections.

  Most of the seven previous paragraphs are more important to, and more in
the parlance of, planetary observing. Originally, it was like a revelation that
"resolution goes to contrast." (One night, while at the eyepiece, it came to me,
and I began repeating it to other amateurs.) A few years later, when asked to
explain what I meant, I came up with these examples and explanations. (In the
idiom of planetary observers, "contrast is everything" or "everything is about
contrast," is axiomatic, and leads to "resolution goes to contrast.")

  How much is enough accuracy? Variations in the shape of the optical surface
are measured in ten thousandths of an inch (a.k.a., "fringes"), and the transmitted
image at the focal plane is represented in fractions of a wave of green light. For
the best result, optical centering and the perfection of finished edges, in and
bordering the light path, must be held to two or three thousandths of an inch.
(Think of optical edges as though they were part of a festoon on Jupiter. If the
edges are rough, the festoon will be less discernible! "Good edges produce
good images.") Other factors like focal ratio, tube overhang and baffling have an
indirect effect on image quality and on rejection of stray light (i.e., neighborhood
lights and skyglow).

  The focal ratio of a telescope affects its performance, and lower "f" numbers
need higher surface accuracy, precise assembly and exact collimation to perform
well at high power. Below f/6, analyzing the image is a more difficult job for most
eyepieces. That is, the angle of incidence makes the refractive index of the glass,
the coatings and anything that might promote or allow internal reflections more
critical. Also, with a short focal length mirror or lens, an eyepiece of higher
magnification is required to achieve the desired image size. As a result, the
residual errors and any contamination, that has collected on the surface of each
optical element, will be magnified a greater number of times, to achieve the same
image as would be yielded by a longer focal length instrument.

  Objectives and mirrors with long focal lengths work well with most of the simpler
eyepiece designs, and they have a greater range of focus and depth of field.
They are also less affected by stray light approaching at angles close to the line
of sight. All this is because the cone of light brought to the focal plane is "steeper"
(i.e., more nearly parallel). As a result, there are fewer problems related to refraction,
internal reflection, and losses in transmission and contrast, due to the angle of
incidence and the quality of the coatings. Simpler eyepiece designs, with fewer
elements, usually have difficulty dealing with such problems at focal lengths under
f7 or f8, while the sophisticated design of many wide-field, eyepieces is specifically
intended to accommodate low  "f"numbers, and the shallow incident angles that
accompany them.)

  With a longer focal length, reflector or refractor, more room for baffling and a
more ideal cone of light versus the weakness and simplicity (attributes) of the
eyepiece can improve performance enough to make the sky appear darker. Of
course, a telescope with a long tube may not be transportable, or easy to set up,
even at home. A compromise in length will usually have to be made if galaxies,
nebulae and trips to a dark site are part of the plan. (Regardless of design,
precise assembly and surface accuracy yield important dividends. This is
especially true with short tube optics.)

  To improve contrast, in reflecting telescopes, the edges of aluminized surfaces
are sometimes painted to attain a more perfect outside circle. Painting the edges
of objective lens and eyepieces is an even more common practice; however, for
both refracting and reflecting optical elements, this approach requires a precise
technique, and should only be attempted by those expertly qualified!

  (Return to the "Guide")   (Part 1)
 

Part 2
"The Great Debate"
  There has been a debate between advocates of Newtonian optical systems and
refractors for many years. One side says spectral shift and the number of optical
surfaces make a refractor inferior. The other side says any obstruction in the light
path reduces resolution and contrast, no matter what is done to enhance quality.
Arguments can be made to support both points of view!

  An obstructed telescope will have some degree of added diffraction. However,
for focal ratios of  f/6 or greater, a secondary mirror with a diameter equal to
about 20%, of the primary will have a nominal effect. That is, there is not much
difference between the effects of no obstruction and an obstruction with a diameter
of not more than 20% of the primary mirror. In fact, with painstaking attention given
to detailing all components in the light path, a small amount of added diffraction
may seem to improve contrast, with some objects. (The edges of contrasting
markings on the moon and planets may be intensified by the effects of diffraction
related to secondary obstruction. There is a section on this phenomenon--Part 7.)

Beyond the obvious advantages of reflecting telescopes (cost and
portability), refractors are too complex to allow any but a very few to figure
the lens and construct an optical tube assembly (OTA) from the ground up.
A note: Some short focus (f/6 to f/9), three-element, apochromatic lenses
(APOs) are designed and figured to an aspheric curve, appearing on a star
test to have an overcorrection of about 1/10 wave, at the center and at the edge.
Moving away from the center, the lens becomes slightly undercorrected then
reaches perfection at the 70% zone. (To be apochromatic, the maximum
variation from the focal plane of any wave length (color) cannot exceed 1/4
wave.)

  With an apochromat, an aspheric figure tends to prevent the spherical errors
common at low "f" numbers (f/6 to f/9). An aspheric apochromat may also
perform better at the peak visual null between 500 and 600 nm (i.e., between
green and yellow--the most sensitive visual range). Such designs should bring
the blue end of the spectrum closer to the focal plane, and it should also give
the image a better "edge," in less (stabilizing) time, after initial setup. (The
tendency, on first moving the telescope outside, given the sudden change in
temperature, usually being cooler outside, is toward under correction. While
the noteworthy thickness of the elements tends to increase the cool-down
time, the combination of under and overcorrection usually allows the lens to
stabilize and operate near its best in 20 to 30 minutes. However, stabilization
can take several hours, especially if there is a chill in the air.)

  APO versus everything else: The slightest color shift may be detected, or the
image may not quite snap in place the way it would with a Newtonian reflector,
or with an APO on the order of f/11, or higher. Such errors can cause the feeling
that something is not quite right, when using anything less than the most highly
corrected eyepieces. This will be more noticeable at moderately high power,
above 35x per inch. A note: A few 6.1 and 7.1-inch, f/9 APOs, available on
the used equipment market in the 1990s, exhibited what looked like some degree
of astigmatism at high power, and others were just smooth enough to test about
1/4 wave.)

   Color filters can reduce a lack of sharpness related to color error. The
limitations (e.g., the need for the best corrected eyepieces) of the APO may
seem minor to many observers, versus the advantages; however, many
amateurs accustomed to the virtues of the refractor have only used a long
focus achromat (f/11 to f/15), and may not be aware of the differences.
If you are really a "refractor person," a 5-inch to 7-inch lens, faster than
f/10, may produce surprises. For some, an f/12 achromat may yield images
more pleasing to the eye; however, while eyepiece selection is more critical
with an APO, the right color filter may help the achromat!

  (The design of short focus APO lenses is meant to reinforce the image at the
peak visual null (610 to 510nm--yellow/green). "Color softness" in an APO
or an achromat may be offset by using green (#56) or blue (#80A and #82A)
filters. A #11 green filter will also help, but some generic optical suppliers
have been known to substitute the #56 for the paler #11, and some do not stock
#11. (Ask for a name brand--no generic substitutes!) The #11 is fine on certain
planetary objects, especially Saturn, in that it tends to defeat skyglow and
turbulence, while putting a fine, almost three-dimensional, edge on the ring
system.)

  To the peril of the unsuspecting, the low "f" number and complexity of some
apochromatic designs can make choosing eyepieces a project by itself. Both
the moderate cost, narrow-field eyepieces, with few elements, and the more
complex and expensive, wide-field types, have unique advantages that make
having more than one set of eyepieces an idea worth considering! Caution:
You cannot be sure an eyepiece will do what you expect just because it is
expensive. Ask the opinion of someone who fully understands your application
and your expectations. (You cannot be too well informed for this class of
instrument, and while the results may be outstanding with a fine refractor, a
well finished, 8-inch, f/8 or f/9 Newtonian should, after cooling down, and in
good "seeing," equal or outperform an intermediate or short-focus, 6 or 7-inch
apochromat. Eyepieces are less critical with Newtonians, especially with optical
assemblies longer (i.e., "slower") than f/6, but the same rule, "the right eyepiece
for the telescope," always applies.)

  The exit pupil (i.e., ep), with mid to short-focus mirrors and lenses is more likely
to show errors as stress and deformity in the image--experienced as fatigue and a
not-nailed or not-quite-right feeling, and only the best corrected eyepieces, preferably
with high relief, will provide a relatively fatigue-free and satisfying image. (This
seems more of a problem for observers with imperfect sight (e.g., astigmatism) or
who need corrective glasses.)

  Observers with younger eyes, and those who are normal-sighted, may be more at
ease with fast reflectors and short focus apochromats, and any mismatch between
instrument and observer, due to vision defects, may be more troublesome when
viewing fine details, such as planetary markings! This seems not to be as likely
with longer lenses, f/10 and above. (There is more on dealing with astigmatism
and errors of the eye in Part 8.)

  Considering cost, convenience and performance, the most practical moderate
sized refractor may be a five-inch f/12 achromat (approx. $3,000 mounted, with
a clock drive), or, for those cramped for space, but more heavily cash-laden,
a carefully selected, five-inch, f/6 or f/8 APO ($4,000 and up). For those set
on a refractor, but with less space or a limited budget (a few hundred dollars),
some of the 80 and 90mm (i.e., 3.1 and 3.5-inch) f/10 to f/11 achromats,
while limited in light gain and resolving power, provide pleasing images
and good contrast, even when atmospheric conditions are relatively poor.

  Some amateurs find that having two or three telescopes, with one in the 80 to
106mm (3-4 inch) range, allows them to cover more situations, and, in fact, the
smaller instrument will probably spend more time under the stars than the others.
Many amateurs who sell or trade-off a small refractor, to move up to a larger
instrument may wish they had both when they see how detrimentally the "seeing"
conditions, on most occasions, affect larger apertures. (The cost of a high quality
fluorite or ED refractor in the 100mm range can be unbudgetable, while the lower
cost and better performance of a high quality f/11, achromat, in the same size
range (90 to 100mm), mark it as a superior value!) (Tips: Because the "seeing"
conditions are critical, when observing double and multiple stars, very often,
the most pleasing image will be had using the smallest aperture, that will readily
resolve the individual stars! Similarly, when observing the Moon and planets,
the most pleasing image will be had using the lowest power, that will reveal
the desired detail.)

  (Return to the "Guide")    (apochromat)   (Newtonian)
 

With achromats, the characteristic color shift can make the orange and red
hues slightly darker. While this makes the interpretation of color less accurate,
it may have a desirable affect on contrast. Whatever the exact reason, the
attributes of an f/15 achromat can be starkly beneficial on some objects,
especially the Moon and planets. The Great Red Spot can appear almost ruby
red at its core, engulfed by luminous aquamarine gas clouds. The surrounding
multicolored bands of hydrogen, ammonia and methane stand out in bold relief.
The arguments previously made concerning color error may seem in conflict
with this, but a shift toward the blue may be desirable--planetary surface
markings may tend to darken! (With a long focus achromat, the depth of field
and "tunnel of darkness" add a three-dimensional quality when viewing Saturn
and its rings, and objects like M 1 and NGC 205 are easier to pick out from
the background.)

 (Return to the "Guide")   (achromat)
 

On The Subject of the Brandon Refractor
(condensed from The Meridian the newsletter of the SFAAA)
 On Saturday night, 11-9-96, a group of us were at the park (limiting visual
magnitude 4.6), when another club member, showed up with a few of his
favorite eyepieces. Of particular note was a 40-mm König with a 60 degree
apparent field of view and 95% light transmission. (Because it has only 4
elements, this eyepiece is pleasingly transparent, and delivers remarkably
natural star images. Some of the wide-field, 7 and 8-element eyepieces, on
the market today, do not transmit light as clearly.) In the 6-inch f/15 refractor
(circa 1949), this eyepiece, and its 2-inch format, yields 57X and 1.1 degrees
of sky. This combination of telescope and eyepiece made it possible to, with
averted vision, just barely make out M 110/NGC 205, magnitude 10.8, when
it was nearly overhead, in a 4th magnitude sky.

  NGC 205, the faintest member of the famous Andromeda trio of galaxies, a
test for a long-focus 4-inch refractor under dark sky conditions, is difficult to
to detect given skyglow near the city and at the park. While this faint, structureless,
10' by 5' oval could be seen in the 6-inch refractor, neither the 13-inch Dobson
nor the C14 could pick it out. The turbulence and pollution, though not significant,
were too great an affront to the larger instruments to allow them to cut through
the skyglow. Of course, under better "seeing" conditions, the Dobson and the
C14 will reveal much fainter objects than the 6-inch refractor. (Contrary to the
success of this and similar instruments on Jupiter and on deep sky objects it and
other older achromatic refractors of larger size (i.e., 6-inch or greater), do not do
as well on Mars. The characteristic color error works against the achromat when
viewing the vague bluish gray and dull orange surface markings, cast against
the ruddy red background of the Martian landscape.

 There are so many factors affecting performance, the result will be a little
different for every tube assembly. For example: We can say that with a
Newtonian reflector, a large secondary obstruction, will have a more
deleterious effect on image quality than one that is small. However, as an
offsetting factor, concentrating efforts in other areas may allow the size of
the secondary to be fairly large, as a percentage of the diameter or aperture
of the telescope (i.e., 25-30%), without doing serious harm to the image.
By being precise, and with attention to the smallest detail, very good
performance can be achieved with secondary obstructions in the range
of 25% of the diameter of the primary!

  However, no matter what is done to improve performance, the finest
planetary markings and edges should still be more easily detected with
less or no obstruction! The word "should" is used because there are
exceptions. On a brilliant object like Mars, the light losses and "shrouding
effect" caused by a medium to small secondary obstruction (20%) seem
to be acceptable, even beneficial, somehow making surface markings easier
to see. (Such effects have a better chance of materializing where the quality
of the optical surfaces is optimal, and the aperture of the instrument is similar
to, or not very much greater than, the size of a single air cell, 3-5 inches.
Because of this relationship to air cells, small, high quality telescopes, up to
about 6 inches in aperture, have an advantage, when compared to larger
instruments.)

  Theoretically, diffraction as a function of the edge of the mirror or lens, will
affect resolving power and resolution equally. However, because there are
many factors working against achieving an ideal result, the two characteristics
usually drift apart, with resolving power being a mathematical function of
diameter, or clear aperture, and resolution being something less than the
ideal for the aperture.

  Efforts to perfect the edge of the primary reflective surface and the edge
of the obstruction presented by the secondary mirror, or its support, will
minimize image degradation, and ensure the best possible performance.
If the diameter of the optic is important, evenness and uniformity of all
edges is also important! (With any obstruction, a more perfect circle
will add less diffraction, and related optical errors, as errors in the image,
will be minimized!)

  If the minor axis of the secondary mirror is larger than the cone of light
at the point of incidence, imperfections in the edge of the aluminized area
cannot interact with the "cone" and become part of the image, and there
will be less likelihood of vignetting the field. However, the silhouette of the
secondary and its support must still be smooth, even and uniform. Any
obstruction in the light path having a ragged edge will be more detrimental
to contrast and resolution than one with a more perfect edge!

  (Return to the "Guide")    ("Great Debate," Brandon Refractor)
 

Part 3
Interaction and Vignetting in Obstructed Reflecting Telescopes
 Given that there are no truly perfect edges, and that near perfect will have to
do, and given that all other components in the system are of good quality, if
the edge of the primary surface or if the silhouette of any obstruction is rough
or less than ideal, the image at the eyepiece will be less perfect than it could be.
And if the secondary is critically small (approximately 18.5% or less for f/6),
the image could be degraded twice. (If the reflective surface of the secondary
mirror is the same size as, or smaller than, the light cone of the primary at the
point of incidence, any imperfection in the edge of the secondary's optical
surface will become part of the image. Such effects are usually slight, but should
be considered. Normally, a good quality secondary mirror, careful painting
of mirrored edges, and proper positioning, during assembly, will minimize
losses related to the edge. And as previously mentioned, with a secondary
mirror, the slightest bit larger than the cone of light, at the point of contact,
imperfections in the edge will not interact with the cone. The intent is to use
the smallest possible secondary, without interacting and degrading the image.
However, many experts say the benefit from using a small secondary is overrated,
and a more moderate approach should be sufficient!

  Comparing the performance for secondary mirrors of different sizes predicts
a slight decline in performance when the size of the secondary mirror reaches a
certain point. The net result for f/6 (with obstructions under 18%--interacting,
and over 18%--noninteracting) should yield a slightly better result at 19 or 20%
than at 16 or 17%. (Don't be mislead by what may appear to be improved results:
If the secondary is small enough to interact with and vignette the light cone, the
background may appear darker because of light losses related to an effective
reduction in aperture (i.e., vignetting), rather than because of improved contrast,
due to smaller obstruction!)

  If the focal ratio is greater than f/6, the interaction and vignetting will begin
at a lesser percentage of the primary mirror's diameter, but at f/5, it occurs at
22% of the primary diameter! (At 6 inches, and f/6, vignetting begins at 1.1
inches (18%). It seems best to avoid vignetting, and allow a little working room
by choosing a secondary with, for this example, f/6,  a minor axis of 1.2 or 1.3
inches. An 8-inch, f/6 would require a secondary with a minor axis of 1.5
inches, or slightly larger.) (To accommodate the smallest workable secondary,
a low profile focuser is best, but must be constructed and baffled to keep out
stray light!) (Low profile focusers are potentially more vulnerable to stray light
than standard focusers.)

  The optimal sized secondary for a given primary diameter and "f" number,
without vignetting, can be determined by drawing the light cone on a sheet
of paper. Scaling the dimensions down to fit the paper, converge the cone
down from the primary diameter to a 1/2-inch image at the point of focus.
Then measure the cross section of the cone where the secondary would sit
in the light path (i.e., the point of intersection). If a secondary mirror smaller
than this dimension is used there will be some vignetting of the field!

  There is another way to determine the smallest/optimal secondary size:
Divide the radius of the tube, plus the offset of the focuser, by the "f" number.
(The dimension arrived at by this method will be smaller than that taken
from a scale drawing, because it does not allow for the 1/2-inch image at the
eyepiece. Adding .2 inches to the resulting critically small number (i.e., the
quotient) will correct the shortfall and lessen the risk of losing illumination
near the edge of the field. If a low profile focuser is used, extending the
optical tube 1.5 times its diameter, forward of the secondary mirror position,
will help keep stray light out of the focal plane.)

  If the intent is to optimize the result for a 6 or 8-inch instrument, by
reducing the size of the secondary, consider refiguring the primary, and
increasing the "f" number to f/7, f/8, f/9 to further improve the result.
For 6 and 8-inch instruments, the choices of secondary sizes are limited--
most vendors do not offer much of a size selection for secondaries smaller
than 1.0 inches, but they are available. (f/6 is chosen for most of these
examples because most experts say it is the minimum usable "f" number
for good image quality, with a relatively wide field of view.)

  Assuming the optics are good, in the quest for more contrast, it is possible
to reduce the secondary too much, but the related effective loss in aperture
is not necessarily a bad thing. With an undersized secondary, the effective
aperture decreases (vignettes) and the "f" number increases. This may be
desirable with some eyepieces, on some objects, as it may provide better
rejection and less sensitivity to local street lights and skyglow. This can be
advantageous in the city, but performance at a dark site, with good "seeing,"
will be less than it should be!

  Using an undersized secondary, in this way, will be a better tactic than
trying to improve contrast and darken the field with an aperture mask, such
as would be used with a refractor in poor "seeing." An aperture mask will
reduce the "glow," but it will also increase diffraction by increasing the
ratio of the secondary diameter to the primary diameter. Another possible
advantage: With an undersized secondary, the light from the edge, usually
the least perfect part of the primary mirror, will not be able to reach the
eyepiece. Result: When the "seeing" is not good enough to use full aperture
or a low "f" number, an undersized secondary will only reflect light from
what is usually the most perfect part of the mirror, and not from the more
critical and potentially irregular area, near the edge. (In an f/10 to f/12
refractor, and where the "needs of civilization" and the "sodium demon"
reign supreme, having two aperture masks, with the edge finely cut and
finished at about 70% and 85% of full aperture, may provide better overall
imagery, and given less than perfect "seeing" conditions, may not affect fine
detail excessively. In an f/6 to f/9 apochromat, 5 to 7 inches in aperture,
one mask, 70% of aperture, should be sufficient to make the wavefront more
ideal. The resulting focal ratio will be approximately f/12, and the lesser
aperture should cut off about 50% of the skyglow and turbulence.)

  For anyone considering changing out a Newtonian secondary, the quality
of the replacement mirror vs the original, and the percentage of reduction
in size vs the original should be carefully weighed against whether the
quality of the primary mirror justifies the effort. Possibly, the primary should
be refigured before anything else is done. Unless all work is done to perfection,
and unless the size of the secondary is reduced significantly, say from 28%
down to 18%, there may be little or no noticeable improvement in sharpness
and contrast. (All optical surfaces should be finished or refinished to near
perfection or at least as good as what is being changed out, to get a worthwhile
result! Any reduction in the size of the secondary might loose rather than
gain performance, if the original secondary is more perfectly finished than
the replacement!)

  I tend to explore every possibility and consider every adjustment that might
yield some gain: If the primary mirror has defects near the edge, such as a
"turned edge," or is chipped or "dog biscuited," masking out that part of the
surface by using a secondary that will vignette the outer diameter by just 1/8th
or 1/4 inch, will use the best portion of the mirror, and reduce diffraction and
light scatter from the defective area, yielding the best result, given the defects
in the mirror.

  For example: With an 8" f/6 mirror, with noteworthy edge defects (i.e., worse
than 1/4 wave), where the calculation for an ideal primary/secondary combination
is 1.5," yielding an obstruction of 18.75%, a secondary of 1.35" inches, minor
axis (i.e., 16.9%), would vignette less than 1/4" (1/8" all the way around leaving
the effective aperture at 7.75") of the actual diameter of the primary mirror. It is
likely that a noticeable change, would require the vignetting be a little tighter
than 1.35," possibly a minor axis of 1.3" to get 1/4" of vignetting, and (maybe?)
a cleaner image. A 1.1 or 1.2 inch secondary would reduce the 8" mirror closer
to a 7-inch aperture (i.e., effective). If the damaged or defective area is greater,
more reduction of the minor axis would be needed, and at some point the mirror
may have to be reworked or discarded. (Whatever is done would have to be
centered to within 1/64 of an inch to get a good result.)

  Experimenting with a smaller than optimal secondary, where the primary has
an edge defect, may yield no useful benefit! "Turned edges" of 1/4 wave are
not uncommon, and are not usually noticeable in the eyepiece. To determine if
there is any difference in a vignetted combination and one that does not vignette,
two secondaries might have to be swapped and compared (side by side, so to
speak), and then a best guess, even in very good seeing conditions, as to which
combination is better (i.e., has a darker background or a crisper image), might
have to be made, and if you are hurried, or make a mistake, and drop something
down the tube, you will regret having been so picky! The risks tend to outweigh
the potential for gain, with minor defects and subtle changes! Experience guides
the "wary traveler," and there is always a chance, later on, to make adjustments.

  At lower "f" numbers, interaction occurs at a greater percentage of the primary
diameter. However, above f/6, better still above f/9 or f/10, the advantages of
less eyepiece magnification, needed to attain a given image size, and all the
advantages of the more parallel rays of light, mentioned in Part 1, come into play.
(Smaller may be better, but at ratios f/8 and greater, opting for a 16% or 18%
secondary (slightly greater than the calculated minimum) should yield very good
results, while accommodating the use of a variety of long focal length and wide-
field eyepieces, in a two- inch focuser. In fact, with most "f"numbers and most
ATMs (i.e., amateur telescope makers), staying just above the point of interaction
should have no downside, and it should be easier to work with--such as just
above 20% for f/5.6, 16.5% for f/7, 14.5% for f/8, and 13% for f/9. (Note:
With a small secondary, the edge of the field may lose some illumination, where
the field lens of the eyepiece is larger than the secondary mirror.)

  There is another way to avoid making a scale drawing. To determine the
optimal size diagonal, with no interaction, divide 1.15 by the "f" number,
and multiply the result by the diameter of the primary mirror. The result will
be the optimal minor axis dimension of the secondary. (Whichever method
you use, "round up," to allow for a margin of error. To use this number, it is
assumed the diagonal will be mounted up the tube or frame as close to the
focuser and eyepiece as reasonably possible. While a low-profile focuser is
not always necessary, it may be beneficial with low "f" numbers! And it
is always a good idea to extend the optical tube 1.5 times its inside diameter
forward of the secondary mirror's mounting position.)

  If a small secondary is to be used, precision assembly and holding extremely
close tolerances is important, but one thing always stands out! The accuracy
of optical surfaces is more important than any other consideration, including
subtle variations in the size of the secondary! Adjustments and improvements
can be made at any time, but the smoothest possible optics, preferably approaching
1/16th wave peak-to-valley, will provide a strong foundation to build on! (With
wavefront accuracies of 1/16th, or better, resolution and contrast will be so good
that it is difficult to quantify a visible advantage of a 16 or 17%  secondary over
one that is 22% or 23%, where the optimum is about 15%--f/8.)

  For most beginning and intermediate telescope makers, the decision as to how
small or how large the secondary should be, will be made arbitrarily. To achieve
optimum performance, the optical tube should be near perfect, or it will be
difficult to locate the optical path, and center the secondary mirror assembly
exactly in the middle of the reflected light cone of the primary mirror. This
will be so even with using a slightly oversized secondary mirror, hoping to
pick up all of the light from the primary mirror. Selecting a round and straight
tube, or constructing a truss structure that allows the primary and secondary
to be concentric is not easy, and any centering error will have much more
significant consequences than whether the minor axis of secondary is 16%
or 22% of the primary.

  For general visual use, especially with the first effort, it is probably best to
stay in the range of about 25% for primary mirrors f/5 to f/7. (Note: Few ATMs
have the experience, time and tools to build, align and operate a tube assembly
faster than f15 and get a good and readily maintainable result! Large diameter,
high performance reflectors, built by the most highly regarded telescope makers,
are usually in the range of f/5 to f/7.This is so even at apertures of 16 to
36 inches. What is more remarkable, visa vis the risk of going to small, the
secondaries in many of these telescopes are less than 15% of the primary,
and they provide extraordinary results both visually and with CCD imagers.)

  One of the drawbacks of most large (over 12.5"), fast systems, especially where
planetary viewing or high resolution is desired, is the need to "touch-up" the
collimation of the primary mirror. This may have to be done two or three times
during an evening of observing. Choosing the right eyepiece, and precision
assembly, are critical; however, persistent and skillful amateurs, relatively new
to the hobby, have found it reasonably easy to build good instruments at f/6
and above. And at the higher "f" numbers, touching up the collimation is
needed less frequently.

  It is good to have all this information, but making the decision as to what size
secondary to use should not become an obstacle to getting the job done! (Before
getting caught up in the quest for bigger and better toys be aware that, by far, the
most important factor in getting good images, especially at moderate to large apertures,
is the stability and transparency of the atmosphere.)

  When all the parts are in one place, and it is time to put the optical tube together,
concentrate on assembling and centering everything to a small fraction of an inch.
Experimenting with the size of the secondary mirror is something that can be done
later, after everything is together and working!

  (Return to the "Guide")   (vignetting)
 

Part 4
Shedding a Little Light
  There are several causes of what is generally identified as background illumination.
Sometimes it is from skyglow, and sometimes it is more appropriately identified
as spurious illumination of the visual field, related to optical defects. Thus, the effect
we call background illumination has multiple causes, and is also present in the
foreground. (For example: scattered light in the atmosphere (a.k.a. skyglow), and
scattered light in the telescope, can get between the eye of the observer and subtle
planetary markings, such as those on Mars and Jupiter.)

  (Every point in an optical system becomes part of the image that eventually
arrives at the focal plane, to be resolved (scanned) by a sensory mechanism
located in the center of the eye, the foveola, a part of the fovea centralis--"the
observer is part of the optic!")

  Once released from a point, waves of energy expand outward, declining in
strength exponentially, until they reach a boundary, no matter how, or in what
type of system, they are developed. In optics, the energy escaping from a point
will expand, or "ripple out," to the full aperture of the system. Therefore, we might
conclude that some level of illumination, however diminished, permeates the entire
visible field. However, once taken beyond five rings (a pattern, possibly no more
than 10 to 12 arc seconds across) the chance of any visible effect on the rest of the
field is reduced to an insignificant level. (With a 15% obstruction about .5% of the
total light, displaced from a point, is cast beyond the fifth ring. (A 25-30% secondary
would still displace less than 1%, beyond the fifth ring.) Therefore, it is highly unlikely
the eye could detect any effect on (i.e., illumination of) the surrounding field. However,
this relates to another interesting possibility--"peak flattening."

  While energy displaced into the diffraction rings, related to any effect of the
secondary, should not be a factor in any loss of large scale contrast (i.e., affecting
darkness of the field), its loss from the central spot of the Airy disc could reduce
small-scale contrast (i.e., "micro-contrast") and intensity. Any loss of energy at
the "tip" of the Airy disc (i.e., "peak flattening") could, by dulling points of light
(i.e., stars) in the field, make the background seem relatively brighter. This seems
more likely to have an effect if the net magnification is close to, but not quite sufficient
to, "open up," or expose, the interior of the Airy disc (i.e., 30x to 32x per inch), and
any demonstrable effect should be minimal, especially if the size of the secondary
is not excessive--preferably less than 25% of the primary mirror!

   An interesting experiment: By suspending a round disk of black art paper in the
center of the light path, using two crossing strands of sewing thread, a refractor can
be made to function somewhat like a four-vane, Newtonian reflector. Interestingly,
even the finest thread causes enough diffraction, to form a visible "line" of light,
similar to that seen with the vanes of the secondary support in a Newtonian reflector.
And when the obstruction is no larger than about 20% of the primary lens, image
quality on such delicately detailed objects as Jupiter's festoons, is only slightly
affected by the added diffraction, if at all. (The losses caused by the obstructions, in
this experiment, are similar to those encountered with a Newtonian reflector. In the
reflector, the "lines of light," caused by the secondary spider vanes, criss-cross the
field, spreading diffraction as they go. In this test, there was no discernible increase
in background illumination, with the paper disk and the threads in place.)

The smoother the primary lens or mirror, the more likely, the "lines of light,"
related to the "thread," or in the case of the Newtonian reflector, to spider vanes,
will be visible, and less likely to scatter, and "disappear," in the field. And to the good,
with a more prefect lens or mirror (esp. smoother), any such minor added diffraction
will seem to have a lesser net effect on resolution and contrast. This is because, fine
optics will have more "headroom" (i.e., reserve performance), beyond the ability of the
eye to detect any loss of detail, usually better than 1/8 wave P-V, net, for all aberrations.
That is, most of us can't tell 1/16 wave optics from 1/8 wave optics, because 1/8 wave
is very good. And the subjective differences in what each of us sees, make it difficult
to put image quality into words. (Marginal coatings contribute to spurious illumination,
and good coatings minimize it! A secondary mirror with a "minus-440" coating, yet to
be discussed, should diminish illumination of the visible field related to skyglow.)

  Rough or scratched surfaces, inadequate baffling and stray light can join in with
collimation problems, surface contamination, spider vanes and less than ideal
coatings to reduce performance and spuriously illuminate the field. The displacement
of energy (i.e., added diffraction and lost intensity) caused by a large (e.g., 30+%)
secondary mirror, and resulting in significant flattening of the peak of the Airy disc,
might make it seem there is an increase in background illumination. (Caution:
Cleaning contaminated surfaces can be risky, and consulting with experienced
"amateurs" is a good place to start. Some "amateurs" find it desirable (and go to
the trouble) of periodically returning eyepieces and objectives/mirrors to the factory
for cleaning.) (There is more on background illumination in Part 8, Issue 4.)

  (more "headroom" and visual acuity)

A 3-dimensional description of the image plane: An optical aperture
transmits, or forms, a field in which the light energy from stars could be
represented as tiny "terraced mountains," with the base of each "mountain"
tapering off into invisibility. Most of the terrain would seem to be flat land,
but, in fact, there would be an infinitely diminishing grade radiating away
from each point that does not stop until it reaches the edge of the primary
lens or mirror, or until it is disrupted by similar waves of energy radiating
from other points in the field. (One evening, a day or so after the Moon
reached first quarter, a personal experience with an 8-inch Schmidt-Cassegrain,
a high diffraction system, made this point dramatically clear! Observing  at
250x, the tips of mountain peaks, near the terminator, were "fuzzy." This
was most noticeable on the brightest and most pin-point-like outcroppings.
Closer examination of several of the "fuzzy" peaks, showed each resolving
into a central spot, or dot, surrounded by a single diffraction ring--an Airy
disc was formed.)

  This discussion can be carried on ad nauseam, by pointing out that any test is
tainted because there will always be diffraction related to the edge of the lens or
mirror, thus there can be no perfect standard to compare to. The background can
never be as dark as it would be in a "perfect telescope" (i.e., one with no edges)!
(Of course, any difference between very good, optics and the unattainable "perfect
telescope" should be slight!)

The results of "backyard testing" might seem to support the belief that a large
secondary causes more background illumination than a smaller secondary or than
no secondary, but related testing is often inexact or unbalanced. A large secondary
will cause slightly more diffraction than a small one, but any effect of increased
diffraction, across the field, is nonexistent. Example: With "skyglow" a problem
at the observing site, I had an opportunity to compare a 6-inch Newtonian, with a
1.5-inch (25%) secondary, to an 8-inch Schmidt-Cassegrain, with a 2.7-inch (34%)
secondary, two classic but very different configurations--not a fair comparison, but
it was an opportunity to collect useful information.

  The target for this test is the globular cluster, M 13, when positioned
approximately 60 degrees above the eastern horizon. The date is early April
1997, and the eyepieces being used are an ordinary 4-element design, yielding
about 100x from both scopes. The "seeing" conditions are typical of areas
near large cities, with the limiting visual magnitude of approximately 4.2. (When
the "horse and rider" are high in the sky, Alcor, "the rider," is just visible with
averted vision.) At this power, the Newtonian barely resolves the cluster, almost
to the center, while the Schmidt-Cassegrain shows a noticeably brighter but
mostly unresolved and hazier patch of light, on a noticeably illuminated (i.e.,
gray) background. (At higher power (above 17x per inch), the skyglow would
be somewhat diminished, especially in the larger scope, and any difference in the
background would be less noticeable.)

  (Schmidt-Cassegrain--more)

  In this test, there is a web of factors, including baffling, magnification of residual
errors, too much light gain for the conditions, high secondary diffraction, dirty
eyepieces, critical alignment, and an unbalanced test, that can and/or do contribute
to the difference in performance. (This test is lopsided because the two telescopes
are very different in design and size, but comparison of equipment of the same design
will produce a similar variation in performance with similar differences in aperture.
There is an example of this coming up, but there is a need to clarify a point about
background illumination before going further: Whatever glow or scatter is produced
by the optics and whatever comes from the sky overhead (i.e., the effect of dust and
water particles in the atmosphere), comes together as one at the eyepiece. Adding
to the frustration, another instrument nearby may seem to fare much better under
the same conditions!)

  Here is a more fair but still not ideal comparison of two telescopes of the same
design and manufacture, where the secondary sizes and the "f" numbers differ
only nominally: A 10-inch f/6 and an 8-inch f/7 Cave Newtonian reflector,
circa 1976 and 1977, respectively, were used for this test, in 1979. The
comparison was made in a dark sky, high overhead, with a visual limiting
magnitude of 5.6 or 5.7. Again the target was M 13, but this time, the sky (at
the same site as the previous example, but 18 years earlier, and with M 13
crossing the meridian, 10 degrees north of the zenith) was much darker, and
the instruments were more powerful (esp. in light gain). Again both instruments
employed similar magnification, this time, 120x.

  Both instruments presented the cluster in almost photographic detail, but the
8-inch f/7 provided a more pleasing view--the background in the 10-inch model
was noticeably brighter! Were the optical surfaces in the 8-inch model cleaner?
Was f/7 a better ratio for this test? Possibly the answer is "yes" in each case, but
the differences had to be small, and with such closeness in quality, design and
obstruction ratio, there could not be much if any difference in light scatter, versus
the brightness of the object in view, due to any effect of the secondary.

 In this test, the brighter background was probably largely due to the greater
light gain of the larger instrument, when used at the same net power, not the
same power per inch of aperture, as the smaller telescope, versus the atmospheric
threshold (i.e., turbulence and skyglow). The eye and the mind cannot compensate
for background illumination, whatever the cause, and there will usually be a sense
of disappointment when the field is not sufficiently dark! (If the light gain of the
telescope could be "turned-down" until the background appeared almost totally
dark, whatever is left should be the most pleasing image.)

  Differences in power per inch, design, surface cleanness and accuracy produce
differences in scatter and spurious illumination which might be misinterpreted as
being caused by secondary obstruction. In part, less-than-ideal comparisons were
made, because, an ideal test is not easy to come by, and the confusion that can occur
when comparing telescopes of different aperture is part of what may have be dealt
with to "ferret out" the cause of any weakness in performance.

  In order to accurately compare one instrument's performance to another's, "A" to "B,"
you must compensate for, or get control of, each point of variation. The rule that applies:
"for telescopes of different apertures, and because light gathering power is a function of
surface area, illumination of the field can only be expected to be similar if the comparison
is drawn using, the same power per-inch of aperture." This levels the playing field and
makes most factors at the test site have the same effect on both scopes. Any apparent
difference in the background illumination should then be a function of design and quality,
and not of any mismatch, or of any external factor.

  There is another factor affecting background illumination, which comes into play,
and has to do with the exit pupil of the eye, not of the telescope. This will be more
fully covered in Part 8, Issue (4.), but for now, to compare field illumination (or
field darkness), observing at a net magnification of about 17x per inch, or greater
provides a useful boost to apparent field darkness, as power increases. (To simplify
testing: The same focal length eyepiece will provide the same power per inch in
telescopes of different diameter if the "f" numbers are the same. If the "f" numbers
are different, some calculations will have to be made to achieve the same size exit
pupil and perform a balanced test. Matching the exit pupil size will have a conducive
effect on the pattern of light sensitivity, i.e., the distribution of rods and cones in the
eye. (An easy way to remember: To compare performance of telescopes, regardless
of size, use the same power per inch in both, and that will make the test as fair and
as useful as it can be! When the power per inch is the same, the exit pupil is the
same, and 17x per inch, or greater, will provide the darkest field of view, and the
most perceptive test!)

  It follows that when choosing the range of magnification for a given telescope,
to achieve the darkest background (another rule of thumb), "use the highest
workable magnification, with the given conditions. But for the sharpest image
and the least trouble with atmospheric limits there is a more circumspect rule,
regardless of skyglow and background illumination (already mentioned, near
the end of Part 2): "Use the lowest magnification that will bring the image up
to a scale sufficient to reveal the desired detail." These rules of thumb tend to
become second nature with more experience. Keeping them in mind, will help
deal with variations in "seeing" from night to night, and with variations in
performance, from scope to scope.)

  A contrary point of view: Other hobbyists have said to me that even though
the sky may appear brighter in a larger telescope, in the city, especially at the
same magnification as in a smaller scope, the overall superiority in image
brightness makes most faint objects easier to see! So, when contending with
city lights and smog, the extra aperture isn't entirely wasted (as is often
suggested)--you need to know the whole story!
 

  "Contrast is relative!" If all other factors could be eliminated or accounted for,
the secondary mirror might still seem to be a potential cause of background
illumination. Under a dark sky, and assuming clean and well collimated optics,
there is an effect of the secondary mirror, mentioned earlier, that might give the
impression that the background is slightly brighter than it really is. The dispersion
of light caused by a larger secondary will leave relatively less energy in the central
spot, and stars will appear less intensely bright at their center. This means there will
be less difference between a star's brightness at its central peak, or "tip," and the
level of illumination of the surrounding sky, but not actually more background
illumination! (There is probably a more scientific name, but I call this effect "peak
flattening.") The background isn't brighter in absolute terms, but it may appear to
be so, especially when viewing faint stars and clusters of stars near the limiting
threshold for the aperture, and/or for the "seeing" conditions. (A small secondary,
or no secondary, won't induce less light scatter across the field than a large secondary,
but more energy will be concentrated in the point at the center of the Airy disc, with
higher rejection of turbulence, and relatively brighter (i.e., the slightest bit more
"peaked" at the center) stellar images.)

The list of culprits continues: A marginal aluminizing process can leave
thousands of microscopic pin holes in a finished mirror. Once the mirror is
in the tube assembly, the edges of these holes randomly scatter the resulting
errors (as stray light) across the surface, and across the visible field. (The secondary
magnification in Cassegrain telescopes, tends to amplify this and other types of
residual errors. Consequently, systems with little or no secondary magnification,
and of relatively long primary focal length, will have a lesser potential for spurious
illumination of the field.)

 However, mismatched the earlier comparison (8-inch S-C versus 6-inch
Newtonian) might seem, the effect of secondary magnification and residual
errors probably increases background illumination in a Schmidt-Cass. by less
than 10%. Much more important, the light scatter caused by contaminated
surfaces, is often greater than 10%. (Schmidt-Casses are especially vulnerable
to the effects of oily film, dust, stray light and misalignment. Eyepieces,
secondary mirrors, Barlows, filters and the exposed surface of the corrector
plate should be kept perfectly clean and shielded from stray light.)

  The lack of a tube extension, or "chimney," intended to keep stray light off
the objective lens, or in the case of a reflector, away from the focuser tube,
secondary mirror, and the wall of the telescope tube, behind and around the
secondary mirror, can reduce contrast and increase background illumination.
Schmidt-Cassegrains are usually so well baffled, the lack of shielding may
seem to have little or no negative effect at the eyepiece. However, stray light,
striking the surface of any objective or corrector plate, at an acute angle, tends
to move laterally across the glass and the visible field. (Any off-axis light rays
that enter the optical tube can illuminate the side wall, and may reach the primary
optical surface. Adding an extension to the optical tube, with an overall length
about 1.5 times the aperture should block some of the intruding light rays,
especially where skyglow, neighborhood lighting or daylight viewing are part
of the mix. Lining the upper end of the tube with black felt, or installing a light
trap, almost always darkens the field.)

  (Schmidt-Cassegrain--more)

  The downside with closed optical tubes as well as dew tubes and extension
tubes, is an increased sensitivity or tendency for tube currents. Thermal activity
in the optical tube (a.k.a. tube currents) sometime shows itself as a subtle loss
of detail on the moon and planets or as an unsteady or fluctuating image. It
may be difficult to identify an image quality problem as being an effect of tube
currents rather than of poor "seeing," but looking through a second telescope
may help clear up any doubts. With a tube or a space-frame design, providing
adequate clearance, side to side and in all directions around the mirror, will
usually allow the quickest stabilization and the least air being trapped in the
optical tube. Space-framed (i.e., trussed) optical tube assemblies can still trap,
or retain, convected air, and settling time is always important, but because
refractors are completely closed and usually in aluminum tubes, Newtonian
reflectors are more likely to be affected by tube currents. For high stability,
Fiberglass, aluminum, phenolic, graphite and polycarb, in that order (worst to
best), have the least thermal problems. (Closing the mirror end of a Newtonian
reflector off, and trapping the air in a sono-tube or other closed tube, may add
hours to stabilization time, or the mirror may seem to never stop changing shape.)

  Any loss of precision or any dirty surface increases the "noise threshold" at
that point, or "plane," in the system, and the residual errors and imperfections
of the optical surface are considered the limits of current technology. The effect
of optical defects and contamination in a design with high secondary magnification
and severe incident angles will be amplified. (Highly reflective coatings (i.e., 95
to 99%) might seem to increase the potential for poor contrast in locales where
skyglow is a problem, but high performance coatings and surfaces usually have
less dropout (i.e., "pin-holing") and scatter, thus keeping the light trained in the
image, not scattered in the surrounding field.

  Some special coatings improve contrast by limiting reflectivity and/or
transmission at the blue end of the spectrum--wavelengths shorter than 440nm.
Scatter is more of a problem below 500nm, especially in the city, but by
peaking sensitivity in the red to green range, skyglow and haze are less visible.
With these special coatings, objects like Saturn and Jupiter take on a slight, but
pleasing, yellow hue, and the backdrop around the planets becomes a shade darker.
By limiting the blue end of the spectrum it may be possible to improve contrast
by offsetting some of the unwanted light pollution encountered in urban areas;
however, this coating is not desirable for studying red objects, such as Mars, and
if it is used when "star-testing" a refractor, it will produce misleading results.
While "frequency selective" reflective coatings can be useful, in the city, under
darker skies, the benefit is less noteworthy! (It takes persistent detective work to
come up with a combination of eyepieces and secondary/diagonal flats which
will yield the darkest possible field and the best image, but the improved results
should make it worth the effort, if not the expense!)

  (It's a big deal: With a six-inch telescope, the ratio of the primary lens area to
the area of the field lens in a typical 12mm Plössl eyepiece is approximately
140:1. Therefore, a smudge or speck on the lens of an eyepiece would be 140
times more important than the same contamination on the objective or mirror.
Similarly, a 6-inch instrument with a 1-inch secondary or a typical 1-1/4"
Barlow would have a 35:1 ratio for related contamination. Dust and oily film
usually settle evenly on exposed surfaces, so this point might seem moot;
however, because eyepieces are prone to getting dirty they need to be cleaned
fairly often. The accumulated oily film may not be noticeable on casual
inspection, but any dulling of lens surfaces will add to background illumination
around bright objects. Since oils and particulates are evenly dispersed in the
air, even the less exposed field lens of an eyepiece is subject to this problem.)

  Notes: (1) During an average night, at most urban viewing sites, a telescope's
light gain, versus the glow of the night sky, may cancel each other out.
(2) The visible pattern of illumination ("glow") around bright objects is often
the result of a smudged eye lens, and eyepieces with greater eye relief, are less
in contact with eyelashes, and are in need of being cleaned less often. Also,
longer eye relief seems to make the annoying effects of glare and shimmer less
noticeable. Abbe-orthoscopic eyepieces are good for this. They have reasonable
eye relief, and need to be cleaned infrequently! However, when the "seeing" is
fine, the sharpness of the Abbe-ortho will not rival the best Plössls and 5-element
hybrids!

  (Return to the "Guide")   ("Shedding a Little Light")
 

Part 5
A Fourth Order Relationship
 (Before getting into this section, another ground rule: For side by side testing,
reflectors usually require more time to stabilize than refractors! So, when
comparing a reflector to a refractor, it may take a few hours for the mirror to
settle to its most stable and best figure. This means that a reflector proven,
on one occasion, to be comparable to a refractor or a reflector, with a low
expansion or specially designed mirror or mirror cell, may, on another
occasion (possibly a cooler evening), and regardless of the "seeing" conditions,
need significantly more time to reach its best figure, and its best level of
performance. It could thus compare more favorably, early in the evening, on
one occasion than on another. With reflectors, even moderate sized mirrors
(e.g., 6"), can take most of the evening to stabilize! (Ask about stabilization
times, in warm and cool weather, before purchasing a telescope!)

  With a large secondary obstruction, the smallest point of starlight "spreads"
(i.e., there is more energy in the diffraction rings), and turbulence is a more
critical factor. Any potentially desirable effect of obstruction is lost, and the
edges of planetary discs may seem fuzzy, during times of marginal "seeing."
The sky surrounding such bright objects as Jupiter may appear misty, or
"peppered," with thousands of fine points of light.

It has been noted that with increased turbulence, the image seen in a reflector
(an obstructed optic) suffers more than in the refractor or other unobstructed
or less obstructed system, and compound optics suffer more than prime-focus
optics! Part of the explanation for turbulence having a more severe effect on image
quality with an obstruction, or with anything that increases diffraction, goes back
to the principle reason for lost resolution and contrast--increased diffraction.
(Anything that adds diffraction mismatches the optic to the transmitting medium!)
It has to do with how much light is displaced into the diffraction rings, and the
resulting ratio of the peak energy cross-section (i.e., the percentage of energy in
the central peak) of the Airy disc, versus the atmospheric disruption, caused by
the movement of typical air cells, at a given point in time (i.e., mtf--the modulation
transfer function). (The smaller the resulting point of light (i.e., the less "peak
flattening"), and the less effect turbulence will have--the point (i.e., Airy disc) is a
function of the optic, not of the source.)***

  Let's try that again: Because of factors related to attention span, fatigue and
the "veil" produced by the secondary mirror, the image in a telescope is time
sensitive. Imagery is about time and diffraction...how long and how much,
where less is better. The central nervous system takes a snap shot, and we look
at it. If the ratio of air cells to primary size is a higher number, turbulence
will have a greater effect on the cumulative image. Of course, reflectors
are usually larger in diameter, and thus look at more air cells, and a bigger
piece of the sky in a period of time. Air cells move, and the image interrogated
by the eyepiece is cast on a rapidly moving, floating mosaic, where more air
cells are crammed into the same space and time. Or, maybe we could say
with no obstruction, the central image is the best replica of the light source,
and in the obstructed telescope, there is no central image, it is blocked out,
"veiled," and effectively, the obstructed area produces the worst replica. (The
center of the lens, is the most important, in terms of symmetry, providing the
most uniform (i.e., least affected by refraction) and concentric part of the
image. The larger the secondary, the less of the center will get through!)***

November 14, 2006--an addendum
  Previously, an explanation was misstated in this section. The term (adc) is not equivalent to mtf (as previously stated)...it is, in fact, the reciprocal of mtf, either of which will work for my purposes. In the course of writing this essay it became apparent there was a need for such a function. So, without knowing of the term modulation transfer function, I made up a statement to explain the effect. Because of the tendency of a medium (such as atmosphere or a telescope) to modulate a coherent signal passing through it, an equation, representing the effect of the, medium can be constructed: If you observe/measure a uniform/standard beam of light, transferred through a medium, it will usually be larger coming out of the medium than it was going in. So, if the medium is disruptive to such transmission, the input beam might be 1.0 microns across, and the output could be 1.2 microns (1.2/1.0 = an mtf  of 1.2, representing about 20% modulation. Ideal being no change, hence the quotient would be 1.0 (the ideal), where 1.0 divided by 1.0 = no effect.

 (1) Modulation transfer function: virgin transmission or "transfer," is represented by
the number 1.0. Anything less than perfect "seeing," is more than 1.0. More specifically,
the measured diametric value of a standard beam as it exits a given medium, versus
the dimension of the source is its mtf. If the "seeing" is poor, the final image at the
focal point will take on artifacts produced by distortions in the field, and the beam
exiting the medium will be modulated, becoming larger and more imperfect than the
source (i.e., standard reference image--an input).

 (2) A law of physics: Stars are so distant, they could not be seen if it were not
for the incredible intensity of the emanations produced by a "stellar furnace." Thus,
the point of light a star presents to a telescope has a dimension of zero. However,
because of the diffraction limitations, inherent to any optical instrument, the visible
disc takes on measurable dimensions (i.e., an optical artifact, an Airy disc, named for
its discoverer George Biddle Airy--1834), as the "f" number, expressed in microns.
Any point of light, and any variation in the structure of the image (i.e., a radius), as
described in an earlier section, entitled, "A 3-dimensional description of the image
plane," will take on the characteristics of diffraction. When the Airy disc is magnified
sufficiently to be resolved, a well made, minimally obstructed telescope will produce
a radiation pattern with 86% of the light concentrated in the central spot, with the
remainder of the energy displaced, or distributed, in outlying rings, the balance of
the energy being reduced by half, with each successive ring--ideally the remaining
14% forms rings exhibiting 7, 3.5, 1.75, .875, .4375%, and so on, moving outward
from the center.

   While most stars are so distant their true disc cannot be seen or measured, with
Earth-bound instruments, a telescopes's ability to separate two equal and adjacent
points of light can be expressed in arc-seconds by dividing 4.56 arc-seconds
(i.e., the Dawes limit: a constant) by the system's aperture in inches, to determine
resolving power, rp in arc seconds (") = 4.56/a. Dawes required very specific
circumstances to meet his standard. Lord Rayleigh came up with a less critical
limit: rp = 5.4/a. However, where the image/object under study is close enough
to Earth, such as a planet, or the Moon, and the intensity of the light striking and
reflecting off is sufficient to illuminate surface markings, recognition of details
smaller than either formula for the theoretical (rp) limit, for the aperture, is common,
especially when working with small and moderate sized telescopes.

  The Rayleigh Criterion, mentioned in Part 1, paragraph 4: When a test is
conducted at the Airy disc, performance is actually being verified at a point
of "optical overload." (The term "diffraction limited" applies to performance,
at 50x per inch, or .5 mm ep (i.e., exit pupil), assuming, at least 1/4 wave
accuracy, at the wave front, for all errors, and is not usually considered a
severely critical indicator of performance. While standards and claims vary,
the "resolution limit" (point of optimal scale and sharpness) for a given
aperture, occurs at 32x per inch (i.e., .8mm exit pupil), the point at which
components of the diffraction image begin to resolve, and become individually
visible (as concentric circles of light), in the eyepiece (a point of diminishing
return--pdr). (The "diffraction limit" is a "terminal limit," discovered by
investigation and experimentation, and while resolution is limited by diffraction,
"seeing" fine detail still depends, in large part, on the accuracy and perfection
of each component, and it is unique to, and variable in, each instrument,
when summed together, with test and "seeing" conditions, at a given site,
on a given occasion. Resolution of fine detail is affected by the fit and finish
of each component, but it is ultimately bounded (i.e., terminated) by, and at
the same time, a "predecessor" of (i.e., foretelling of the event), the reaching
of a point of diminishing return (pdr), related to diffraction. Put another way,
resolution, as sharpness, begins to decline at the beginning (i.e., "onset") of
an event, a window (of sorts), as it opens ("unfolds"), and the "diffraction limit"
(50x per inch) is the point at which the window is fully open, but just barely.)***

  The rule: Any optic with added diffraction, will interface, with a given medium,
less efficiently, for its aperture, than would a more ideal system. For systems
applied at scales approaching 50x per inch (.5 mm exit pupil), if the "mtf"
declines or if system diffraction increases a divergent relationship develops.
Any improvement in either will produce a less fuzzy (i.e., crisper) image. "The
effects of the total diffraction of the optic are compounded by poor 'seeing!'"
That is, any related divergence in performance, optical tube assembly versus
"seeing," will be noticeable to any observer! (To find the size of the exit pupil,
in millimeters, for any telescope and eyepiece combination, divide the focal
length of the eyepiece, in millimeters, by the "f" number of the telescope.
Example: 12 mm eyepiece and an f/6 telescope 12/6 = 2.0 mm exit pupil.)

  While performance is limited by "seeing" conditions, the mind's opportunistic
ability to take a snapshot and frame it in consciousness, makes any momentary
instant of good "seeing" a window of opportunity. The effective resolving power
(rp'), determined as a reduced function, expressed in arc-seconds, for a given
aperture, is shown as rp' = 4.56/d/adc, where "a" is the aperture in inches and
"adc," as the reciprocal of "mtf," is always something less than 1.0. Expressed
for mtf, effective resolving power (rp') = 4.56x mtf/d, and the mtf is always more
than 1.0. The window of opportunity is a variable expressed as (v/n) or "v," the
number of "oscillators" in view, divided by "n," the charge/discharge cycle
(i.e., duty cycle) of the neuron, or .002 sec. (As a student of behavior, this is my
way of explaining and characterizing atmospheric diffraction, and the total
diffraction produced by an optic, given existing conditions, versus the limits of
the eye and nervous system. (As mentioned above, not being an expert or an
academic, this paragraph and the equations for "rp'" and "v/n" were originally
written not knowing there was such a thing as "modulation transfer function."
The correct term was added later, and corrections evolved from there.)

   (modulation transfer function--more)

  Theoretically, with unobstructed optics (figured to 1/4 wave or better), 86% of
the light from a point source will be in the central spot (14% goes to the rings).
At 35% of the diameter of the primary mirror, the diffraction caused by the
secondary is almost tripled, with more than 40% of the light displaced into the
rings. (The more point-like (i.e., "elevated") the diffraction pattern of the optic,
the less will be the interaction with air cells. Low diffraction systems are more
able to "see between the lines." Think of the "profile" of an Airy disc, produced
by an optic as though it were a needle of a record player--the sharper and finer
the needle, and the more elevated the central spot, the more easily penetrated
will be the intervening medium, and the more resolved will be the changes in
the structure of the image or object in view.)

  If a reflector and a refractor seem to be about equal in performance in poor
"seeing" conditions, the reflector will probably benefit more, and present its best
images, or come closer to those of the refractor, when the "seeing" conditions
improve! This also applies when one reflector is compared to another. That is,
when the "seeing" improves, where two reflecting telescopes are of the same
aperture, and comparable in quality, the reflector with the larger secondary
(and the most added diffraction), being the most hampered by turbulence
and poor "seeing," should benefit most. Of course, the scope with the smaller
secondary will still produce sharper images, especially above 32x per inch,
the point of diminishing return, and if the instruments being compared are
not of the same diameter and quality, test results will be difficult to evaluate.
(Contradictions: Good "seeing" tends to close the gap between reasonably
well made and very well made telescopes. That is, given the occurence of ideal
atmospheric conditions, there is so much more to see that minor defects and
differences seem to become relatively less important. Of course, that is largely
a judgement call. However, when "seeing" is only fair, good and very good
telescopes may each be limited to, for the sake of discussion, let's say, something
like 1/4 wave performance, or less, and logic says, as conditions improve the
finer telescope should come into its own, and leave the less ideal telescope behind.
Interestingly, both statements have a place! What happens is, as the "seeing"
conditions get better, the lesser telescope works better than expected. (It was
not the telescope, it was the "seeing" that caused most of the poor images, but
the limitations of the lesser telescope made the atmospheric problem more visible.)

  The results from comparing telescopes not identical in size can easily be
misinterpreted! Several things must be taken into consideration! There is a
need to understand diffraction, and any related spurious dispersion of light,
due to any and all obstructions in the light path, with regard to the optical
system's ability to converge energy into the smallest possible point, versus
any atmospheric condition, which might negatively affect (i.e., refract or
scatter) the frequencies making up the visible spectrum.

  This is about the performance of a lens or mirror system with increased
diffraction, from any cause, when confronted with increased scattering of light
in the atmosphere! If you got it right the first time (I did not) this section will
seem redundant: Seemingly simple questions cannot be answered by supposing
the problem is with whatever apparent predominant difference or weakness
characterizes the system or systems being evaluated. Attention must be paid
to wave theory as it applies to the properties and behavior of different light
frequencies, and as it applies to the properties of light transmitting media--
coherence, propagation, diffraction and refraction.

  If figure (i.e., shape) and surface smoothness are less than ideal, even
unobstructed optics, will displace more than the normal (i.e., theoretical)
amount of energy into the diffraction rings, and even when the "seeing" is poor,
the difference in performance between two refractors of different wavefront
accuracy will be apparent. Do not make a decision to acquire a telescope based
solely on its performance at times of good "seeing!" Before purchase, see how
well it works in moderate to poor conditions! (The numbers, indicating the
wavefront performance of the lens or mirror are lumped together to represent
both the spherical error and the surface smoothness. Spherical wavefront error
is a measure of how precisely the overall shape (i.e., figure) of the lens or mirror
brings light to the focal plane. The flatter and more perfect the wavefront, the
smaller the fractional error--1/8th, 1/16th or 1/20th wave. If a lens or mirror is
relatively smooth and finely polished, but the overall figure is not well corrected,
or vice versa, "the good will not offset the bad!")

  If air cells move faster, there will be more disruption of the image. It follows that
slower moving cells are less of a problem for larger apertures, and for any optic
with an obstruction. (Theoretically, optimum performance will be achieved if
the image is only made up of one cell, and a typical air cell is 3 to 5 inches
across. Therefore, with a telescope of 3 to 5 inches aperture, there is a potential
for a one-to-one relationship. (For any size telescope, the cells become more
"seamless" when the air moves more slowly. Each cell of air is like a lens, or
a window, within a mosaic of lenses, or windows, and the mosaic is always
moving and active. I have watched cells move along like leaves in a pond,
occasionally stopping, and then starting up again, like a "jam up" occurred
and then broke loose again, allowing the leaves to proceed down stream.)

  If the aperture of a telescope is 12 to 16 inches, there are between 9 and 16 cells
in view at any instant. Because amateur owned refractors are usually smaller
than the reflectors they are compared to, with fewer cells in the field of view, the
differences in the effect turbulence has on the image can be dramatic. (The size of
the reflector's secondary could be almost as large as an air cell, and it might be a
significant percentage of the aperture of a typical refractor. Because turbulence
is  more detrimental as aperture increases, the usually greater sized, reflector over
refractor, suffers most. The effect of turbulence is less confusing when instruments
of the same aperture are compared!)

  There are several traps to sidestep in if you are to gain control! "Local turbulence,"
(i.e., tube currents, etc.) in the optical path, is yet another factor putting the reflector
at a disadvantage. Thermal waves come and go in an open tube, and again, with the
normally larger aperture of the reflector vs a typical refractor the potential for reduced
performance is greater. All these things mount up and have to be dealt with, but the
advantages of aperture and the reward for precision and accuracy in the moderate to
intermediate sized reflector, even at speeds as low as f/5 or f/5.6,usually outweigh
the shortcomings.

  Since surface area has an exponential relationship to radius, the relative effect
of turbulence is also exponential! However, if the cells are slow moving, i.e., "flat,"
the "window" can be smooth to within .1 or .2 arc seconds. "Seeing" conditions that
fine are very rare anywhere, and in most parts of the world, .2 to .3 arc seconds is a
more likely (and still rare) limit. (A reasonably well made 6-inch telescope will
resolve, to .75 arc seconds, center to center, between two stars, each of magnitude 6.0.
However, in a well made telescope, and under ideal conditions, a planetary or lunar
marking, equal to less than half the theoretical resolving power can be made out
(as small as .35 arc seconds for a 6-inch telescope). (Where the secondary mirror
obstructs more than 20% of the aperture, or there errors in workmanship, fine detail
will be lost.)

  As aperture increases above 6 inches, the theoretical resolving power and the
resolution limits of the optic come closer to the nominal "seeing" limit of .2 or .3
arc seconds, and in most "parts," the three will come together at apertures between
12 inches and 16 inches. That suggests, all that can be seen, will eventually be
seen, regarding fine detail, in a telescope between 12 and 16 inches in diameter.
However, I have observed through 12, 13, 16, 20, 24 and 36 inch telescopes, and
the aperture is very definitely not wasted, but a very still, and very dark, observing
site will be needed to see all that is possible a fairly large telescope.

  "Resolving power is an almost unwavering function of diameter, given reasonable
optical quality, but resolution is derivative of surface area and purity, reduced by
harmonic variations, such as those induced by an obstruction in the field." With
the stability and transparency of the atmosphere, so important, large, ground based
instruments need to be on mountain tops and in parts of the world known for clear
and stable skies. (To overcome Earth's 5 mile layer of air pollution, the  92-inch
Hubble Space Telescope, was constructed and put into orbit, where, unfettered by
atmospheric effects, it is many times more effective than much larger ground based
instruments.)

  The maximum usable aperture is dependent on the "seeing" conditions, and the
conditions in many locations are seldom good enough for even a 6-inch telescope
to perform up to its potential for resolution. Of course, if light gain is the major issue,
and/or if the observer is more interested in deep-sky objects than in lunar/planetary
objects, the larger instrument will produce much brighter and more satisfying images.
This assumes that transport to a site with a reasonably dark sky, more conducive to
larger apertures, is a possibility. (Buying a larger telescope because of disappointment
with a smaller model, when the cause or causes of the problem is not fully understood,
may bring even greater disappointment!)

  The more troublesome, faster moving, air cells cannot be detected by just going
outside and looking for twinkling stars--a common test. The twinkle caused by
faster cells occurs at too high a frequency to be detected by the human nervous
system. (A lack of twinkling may indicate good "seeing," or it may indicate fast
moving cells and not-so-good "seeing!")

  In a prime focus telescope, everything is visible, there are no unseen, or largely
unseen, elements. The eye and motor centers are thus free to analyze the image
through a field made up of billions of minute atmospheric particles. (The principles
of capillarity and equalization cause evenly dispersed sphere-shaped droplets of
water and dust to form in the atmosphere. The resolution of the sky is limited by
the activity of these droplets. It follows that scattering of light is less a factor in
dry, still air.)

There is a varying physical relationship between turbulence and light of
different wavelengths. A lack of "transmission integrity" (i.e., coherence across
the visible spectrum) in the atmosphere was explained by Lord Rayleigh and
others, more than 100 years ago--1871. That is, there is a fourth order relationship
between frequency and lateral displacement (i.e., scatter). Given this rule, and
at low frequencies (i.e., the red end of the spectrum--7,200 Å), if the atmospheric
diffraction constant (i.e., similar to modulation transfer function) is assigned a
value of one (ideally) then, at the violet end (3,800 Å), the frequency doubles,
and scatter is 16 times greater. (Oscillation, as shear angle, becomes more
perpendicular to the light path as frequency increases, and wave length decreases.
Hence, the tendency to lose coherence at the violet (blue) end increases.) This is
a law of physics and wave mechanics, and as aperture and resolving power increase,
"glow" and image degradation become more apparent. (The Stefan-Boltzmann Law,
1879-1884/89 is stated as: radiation (scatter) in a cavity is proportional to the fourth
power of the absolute temperature, i.e., frequency--stated as T4.)

   (Return to the "Guide")   (modulation transfer function)

  Rayleigh's contribution was that the cavity is described as resonant, and the
effect depends on the number of standing waves at a given frequency, in that,
dW=CTL-4dL, where -4 is an exponent and "L" represents the Greek
letter lambda, the symbol for wavelength. All this led to Planck's radiation law
and the quantum hypothesis in 1900: dW=8pichL-5dL/ehc/kt-1', where -5,  hc
and kt are exponents, and again "L" represents the symbol for wavelength.
Einstein's photoelectric equation E =hv-ø and the Special Theory of Relativity
in 1905: E =MC2, added quantum radiation (i.e., light quanta and radiation at
the subatomic level) to the equations and to the stated effects.

  Paul Dirac, one year out of graduate school, and standing on Einstein's
shoulders, improved the standard model in 1928 by adding components
implied by the uncertainty principle: E = c(axpx+aypy+azpz)ßmc2. The
components of Dirac's equation shown in parenthesis bring reality to relativity.
That is, Dirac made the statement (MC2) take on real-time characteristics
(i.e., allowing for "uncertainty"). Rayleigh received the Nobel Prize in physics
in 1904. Einstein received the Nobel prize in 1923, and Dirac in 1933. (The
existence of the T4 relationship is why optical coatings, that roll off at 440nm,
improve visual contrast, while a smaller secondary obstruction, ideally none,
improves resolution by "elevating" the "central peak" of the Airy-disc, closer
to an ideal distribution (i.e., 86%) of the energy in the pattern.) (The 57 years
from 1871 through 1928 were an amazingly fruitful period in the history of science!)

  (Return to the "Guide") (a fourth order relationship--Part 5)
 

Part 6
Eyepieces, Barlow Lenses and Filters
   In the course of time, I decided to compare several eyepiece designs, on
and off 1.8, 2, 2.5 and 3x Televue Barlow lenses. A 6-inch f/9 Astro Physics
refractor was used to complete the test. There were some early revelations,
but with a few exceptions, and without regard for field size or eye relief,
repeated testing has shown nothing to be as important as good coatings,
clean optical surfaces and good "seeing" conditions. Two eyepieces did not
work well on the Barlow lens: A 25-year old, 9mm Abbe-orthoscopic and
a new, 7.5mm Ultrascopic. (Both appeared a bit dull when compared to an
8mm Brandon, using the same 2x Barlow lens.)

  A test was set up to determine where each eyepiece breaks down as the
Barlow's power and the "f" number of the light cone passing through the
field-stop increases. (Which Barlow is best and with which eyepieces--
that sort of thing.) I have heard it said that this or that eyepiece is designed
to work optimally at f/5, f/8, f/10 or f/15. (Designing for f/5 doesn't mean
everything can be done to accommodate a lower f/ number, and not
compromise or lose performance at higher "f" numbers.)

  I wanted to know why some eyepieces exhibit poor contrast--it isn't just about
coatings, and the "I see the glass problem"--it must be more complicated and
multifactorial. The number of lens elements, the field-stop size and position, the
coatings on air to glass surfaces, and painted edges, all play a role. (An error or
flaw, in any of these areas, could eliminate an eyepiece from further consideration,
and a Barlow lens can make an eyepiece work better or worse. I had questions
about eyepieces that worked fairly well on a Barlow lens, in one scope, but were
less successful when used similarly in another telescope. Before it was over, the
testing was done and redone several times!)

  Possibly, part of what I was seeing, as a difference between reflectors and
refractors, has to do with transmitting light through the central part of the
lens with the refractor, but I cannot qualify that except to say, the color error
in an APO makes eyepiece selection more critical than in a Newtonian.

  However, these findings are important in a Newtonian too, especially one that
is f/6 or greater, because they cover questions about Barlow-related scatter
and glow, which I think most amateurs do not give enough credit as a culprit
and a detractor. Finding the answers to questions by observing and testing is
time consuming and expensive. It could mean borrowing or buying several
sets of eyepieces.

  Contrast may suffer when increased field size is the be-all and end-all. Some
eyepieces are designed to yield the largest possible apparent angular field, and
if the field is well corrected, to the edge, we want to see every degree, but is that
always the best thing to do? Contrast is usually better when the field-stop is
smaller than (i.e. prevents light from reaching the edge of) the field lens--something
easily checked by direct inspection. An eyepiece, with a "tight" field-stop, one
smaller than the field lens, will be less likely to "excite" lens edges, and scatter
light across the visible field.

  What to look for: Cheaper and simpler designs are often tightly baffled because
of excessive curvature at the edge of the field, but such faults can be desirable
if part of the result is improved contrast!) Königs have fairly restrictive field stops,
partly because of a poorly corrected edge--a blessing in disguise, and part of why
they work as well as they do. However, the field-stop can be less important than
the number of elements and the transparency of the coatings. Some of my 20-50
year-old, 4 and 5-element eyepieces do well, even better, in some regards (e.g.,
contrast, relative background darkness and resolution), on and off the Barlow
than some modern wide-field designs.

  A Barlow lens can compensate for some off-axis aberrations in eyepieces,
but an Abbe-orthoscopic or Brandon, used by itself, is a good standard for
darkness and image quality, when observing stars, planets and the moon.
With variations in "seeing," and with the smudges, and the almost invisible
oily deposits that collect on the surface of exposed glass, every collection
should include a short focal length ortho, or Brandon eyepiece, as a standard!

  On or off the Barlow lens, above f/6 simpler (i.e., basic) eyepiece designs are
often very good performers, versus more complex, multi-element designs. Barlow
lenses produce clean images when used with simple eyepiece designs, but eyepiece
designs, in short focal lengths, off the Barlow lens, provide darker backgrounds than
the same design, in a longer focal length, on a Barlow lens (resulting in the same
net power). The effects will vary from telescope to telescope, and from design to
design, but the difference in performance, on and off the Barlow, when using a simple
eyepiece design, will usually be less noticeable than with a more complex design.
(With eyepieces, as with telescopes, simplicity has the advantage! The uniformity,
color correction and high light throughput of the simpler, (usually) narrower field
eyepiece, leave it with a noteworthy advantage, especially where image quality
is important.)

   observing with wide-field eyepieces in a 12-1/2-inch f/4.7 Dobson, I
noted a high degree of transparency, while my experience at f/9 and a 6-inch
aperture, with the same model of premium grade eyepieces, costing several
hundred dollars was that "I could see the glass." Why is it that lower "f"
numbers and larger apertures seem less troubled by multi-element, wide-field
eyepiece designs? (The phrase, "I can see the glass," means there are visible
reflections within the eyepiece, or the overall absorption of light and the number
of elements washes out the image.) Another eyepiece enthusiast, like myself,
theorized, with tongue in cheek, that the larger telescope gathers so much light
that the image just "blows through it!" The extra image brightness seemed
helpful, but we both knew instinctively there had to be more to it than that!
Later, I came up with the notion that certain wide-field eyepieces are designed
to work better at the severe angles presented by an f/4 light cone than at angles
characteristic of f/6, f/7, f/8 or higher. "Stranger than science," this appears to
be so, and there are several issues! With an eyepiece that accommodates the
multitude of f/4 and f/5 scopes, the cone of light may not be baffled tightly
enough to get the best possible contrast on "slower" scopes--f/7 and above.
Stray light from angles off-axis and spurious internal reflections, caused by
any light which does not penetrate the coatings (bouncing off) will be less
likely to be trapped if the "field stop" and any internal baffles are not optimally
"tight," when used on an f/7 or f/8 OTA.

   Another part of the answer is less obvious. With a telescope of f/4 or f/5,
the light cone angles in severely as it passes through the field lens, and there
is less likelihood of directly illuminating the edges of the separate elements,
even if the stop is relatively open to accommodate low "f" numbers. This
is arguable, and is of less significance if the edges are painted black, and
today, they usually are.

In the end, less-than-ideal coatings, and the contortions the light cone
goes through in some wide-field eyepieces, especially the super wide-field
designs, cause most of the lack-luster imagery. However, there are other
subjective and psychological problems that can add to the mystery of the "I
see the glass" problem. With a 70 or 80 degree field, the eye and the motor
centers are served a feast, when the sky is fairly dark, and the coatings are
of good quality. However, 70-plus degrees of field can have a downside,
especially if the "seeing" conditions are poor. In such conditions the eye
sees a big gray sky, behind the object in view. For some faint or nebulous
objects, a big gray sky may be all that can be seen. A smaller field of view
is less disappointing and works better when the level of skyglow is like it
is at many urban viewing sites. (On one occasion, I was complaining about
the reflections in a wide-field eyepiece and someone said, "yes, but when
the sky is dark they are incredible." Possibly, some of it is the negative effect
looking up at a gray sky has on the psyche and on the motor centers of the
visual cortex.)

  Most wide-field designs are aimed at the "fast" telescope market, where the
largest group of customers is. As a result, most modern designs are meant to
accommodate the severe cone angles of Dobsons and other fast scopes, but no
one is going to say "slower" lenses and mirrors (i.e., higher "f" numbers) may
be at a disadvantage. Unlike the 12-1/2-inch Dobson mentioned earlier, 3 to
6-inch scopes don't have enough light gain to "blow through it." (This problem
is even more relevant where aging eyes are a factor.)

  Another factor is what I call "backyard rejection." That is, some of us observe
primarily from a city location, and the skyglow there is worse than at a remote
 site. Anything that rejects light scatter, such as a diagonal mirror with a
"minus-440" coating, or a high-contrast eyepiece, can save the day...or the night.
Some eyepieces are designed for f/10 to f/15 scopes, and can be used with
same, with or without a Barlow, in poor "seeing" conditions, with surprising results.
(-440 means light at the blue end of the spectrum, 440 nm, where scattering is
most troublesome, is not as effectively reflected, or passed through, to the focal
plane, thus the background seems darker.)

  Not unlike the human eye, most eyepieces, and especially most four and five-
element eyepieces, work best toward the center of the field. Because of their
simple design, narrow field eyepieces are less modulated than 6, 7 and 8-element,
wide-field designs (i.e., the "sweet spot" at the center is more coherent and
converged). (Wide-field eyepieces are usually more divergent, i.e., undefined,
or modulated. The possible consequences: The lack of concentration at the center,
the looser baffling, and the number of optical surfaces tend to reduce throughput--
i.e., soften the image and lessen contrast.)

  Whatever their faults, wide-field eyepieces, especially those with fields greater
than 65 degrees, under dark sky conditions, seem to reveal fainter objects
than eyepieces with narrower fields of view (for some, maybe most, observers)!
This is probably because the somewhat claustrophobic effect of a visual field
of less than about 60 degrees tends to suppress the endocrine system, of some,
or most, observers, reducing the flow of adrenalin and dulling the excitatory
actions of the iris. The result is a smaller pupil opening and a subsequent loss
of sensitivity to light. To the contrary, the panoramic effect of a wide-field
eyepiece can be so exhilarating as to heighten adrenal response, stimulating
the iris and widening the pupil, thus increasing sensitivity to light. And this
happens in spite of the problems of multiple elements and too much glass.
Of course, the effect, in terms of any benefit, is just the opposite in the city,
where a wider field of view means more skyglow to cope with.

  Meditation and deep breathing can augment sensitivity to light! Taking a
few deep breaths when trying to see an object near the limiting threshold of a
given instrument may help see what cannot be readily seen. As we get older,
pupillary responses gradually weaken, and the more relaxing effect of an
eyepiece with a larger field and more eye relief may help make up for the losses.
For those over 50 or 60 years of age, there may be a 70 percent light loss
compared to performance in youth or early adulthood, and any benefit from
using a wide-field eyepiece can be lost or offset if the coatings and the sharpness
of the image are not exceptional.

  (Return to the "Guide") ("visual acuity")

  "Everyone else is talking field size, and we are talking headroom!" ("Headroom,
like resolution, goes to contrast.") The phrase "optimized for" may be used or
implied when one of the gurus writes or says that an eyepiece is designed to work
at f/4  or f/5. The mistake I made starting out on this project was in assuming
that, while the major marketing effort is aimed at owners of faster scopes, with
hard to accommodate light cones, slower scopes, with long dark chimney-like tubes
will inherently, and by design, take care of themselves... That is not entirely correct!
You need the right eyepiece, and what is selling like "hot cakes" may not be best,
if your telescope is not part of the targeted market, or if you are interested in lunar
and planetary observing.

  Information that might be part of articles and books may not be included because
the largest market is in eyepieces for "faster telescopes," and some books are edited
 to hit the biggest group of buyers in the most economical number of pages. (Having
said all that, some wide-field eyepieces intended for f/4 or f/5 have field-stops "tight"
enough to get a good result with an f/8 to f/15 telescope, but they will probably not
have a 70 or 80 degree field, and with 6-8 elements, they should probably not be used
with a Barlow lens.)

"When you ask which is best, you have to know what you need!" You have to
"dig" to find answers, and there may not be much help from popular magazines,
because articles are not usually written for the minority reader! Only one person
has ever said to me in the many calls and letters to designers, manufacturers,
writers on the subject and various knowledgeable amateurs, "in your situation
(6-inch f/9 apochromat) this eyepiece is best," and he said, Zeiss ED Abbe-
ortho was number one, and Pentax and Nikon ED Abbe-ortho were number two,
with Televue, Clavé, Takahashi and Vixen Lanthanum at number three position.
Actually, he said the monocentric was best, but at that time he had not redesigned
and begun manufacturing them yet. (More recent experience indicates that the
Televue Plössl, Ultima hybrid and Radians are among the sharpest eyepieces
presently available.)

  The field-stop may be less important than the coatings, but the shape of the lenses
and what is happening to the light cone may still be the most important factor,
with 7 and 8-element wide-field designs. Why else would a 4-element semi-wide-
field eyepiece do markedly better (.i.e., throughput, resolution, contrast) mounted
on a separate Barlow than wide-field designs, manufactured with a built-in
Barlow lens? Both concepts feature the same number of elements, but the 60
to 65 degree model isn't jerking the light out of shape at such extreme angles-
-in--out--in--out, girdle--bulge--girdle--bulge!

  Considering the fourth order (T4), 16:1, blue to red relationship! You could
say, the medium, the glass, will scatter the light more at the blue end of the
spectrum. A speculation: Most of the scattered rays, are toward the blue, and at
lower "f" numbers are reflected at low angles into the darkened wall of the
tube (possibly the way it was intended to work), but at higher "f" numbers,
the beam is more parallel to the tube wall, and more of the errant waves (i.e.,
stray reflections) remain in (i.e., follow) the light path, and are reaching the eye
lens and the eye as spurious illumination!

  The path the light follows is different at f/5 than at f/7! If you design for f/5
or less, higher "f" numbers (f/7 to f/9 or f/10) might not match up ideally!
(When looking through a super wide-field eyepiece on scopes that are f/4, f/5,
f/6, f/7 and up, will the effect of internal reflections and background illumination
tend to worsen as the "f" number increases?) Errors of any kind are additive,
and multi-element lenses have to correct for the lateness of the blue end of the
spectrum at every incident angle. It may be that, for observers who want the
best possible contrast, even with the latest coating technologies and rare-earth
glass, "simplest is still best."

  Conclusions: Some old designs are still the standard for contrast and imagery.
The task of retaining image quality and increasing field size presents a challenge
that has not been mastered as yet. The state of the art in wide-field design has
a way to go! With "f" numbers below f/6, the rule seems to be, "open up the
field stop, and design lens elements and coatings to deal with the consequences."
With "f" numbers above f/6, mechanical design plays a role in promoting
good contrast, and anything less than tight, even restrictive, baffling may show
up as some degree of spurious illumination where high contrast is a goal. For
some observers, it may be necessary to sacrifice some of the field size to get a
crisper and more pleasing image. There are eyepieces with a 60 degree field that
are relatively transparent and inexpensive. In a rapidly expanding market, with
incredible technology changes, in place, and coming, the mass production nature
of business, and the fear that the customer won't buy the product if he or she
realizes it isn't the best for his or her needs tends to determine the marketing
plan and how questions are answered. (That was my biggest problem when
I started this quest. The customer/hobbyist really has to study the subject and
ask well informed questions!)

The eyepieces listed below are designed for optimal performance in the
range of the "f" number indicated, and with regard to contrast and light
scatter, they have some degree of "headroom" (i.e., the ability to keep the field
dark, and images, clean and sharp as power increases--deriving from accuracy
at the wave front and from quality workmanship and components). An asterisk
(*) indicates a rating based, in part, on other reports. (Some eyepieces, with a
built-in Barlow lens, do not have much "headroom!" (To refresh on what is
meant by "headroom," and why it is important: "headroom" and visual acuity.)
"Headroom" problems are often caused by baffling and field-stop limitations
and/or by too many air-to-glass surfaces and inadequate coatings. Eyepieces,
with similar limitations, and no built-in Barlow lens, may display the same
kind of image quality problems when used on a seperate Barlow lens.

  To make these determinations, Televue 1.8x, 2x, 2.5x and 3x Barlow lenses
were used. Test results are subjective, and sometimes only one sample (i.e.,
eyepiece) was available. As of 4-26-01, eyepiece testing stopped temporarily-
-problems in other areas postponed further testing until the fall of 2002.
(A numerical rating of 20 or 30 is poor "headroom," and is not recommend
for high contrast work. ("Headroom" is an indicator of how well an eyepiece
works at high power and on a Barlow lens.) 50 and above is good, and will
usually hold up well on a Barlow lens, or at high power--50x per inch and
above.)
 

Brand/Model	f/number  recommended	headroom	comments
Brandon	6-15	good---50+	pleasingly sharp, fair eye relief, 45 degree fov, probably best overall contrast, imagery and detail, pricey but unequaled--16 mm on Barlow best combination avoid 8mm.
Criterion (AR)  Symmetrical  (1974)	8-15	good---50+	slight color, but  darkest field
Clavé Plössl (1976)	6-10	fair----40+	need info on newer models
Galoc	12-30	good---50**	like ortho in the center, but needs Barlow at f/20+ to flatten field
König Type II	12-30	fair to good       30-50	fairly sharp and transparent, but shorter focal lengths have reflections on bright objects, with Barlow lens
Meade Ultrawide	5-6	fair----30	need more info
Nagler Type  I,II, Panoptic	4-6	fair----40	need more info
Omcon ortho	4-15	good---40**	best on double stars and in poor "seeing" but not on Barlow, 45° fov
Pentax XLC	8-10	fair----40	need more info
Radian	4-8	good---60	very crisp, but some color
Takahashi	6-10	good---60	need more info
Televue Plössl	4-8	good---50+	crisp, vignetting on Barlow above f/12, 42-45° fov
Celestron  Ultima (obsolete)	8-15  (10 by design)	good---60	51 degree fov crisp images, esp. good on Barlow lens
Ultrascopic    Antares	6-10	fair----40	7.5mm not good on a Barlow need more info
University  ortho (U.O.)	4-15	fair----40**	fine on double stars and planets, especially in poor seeing, best buy--benchmark
Vixen Plössl  (obsoleted, by Celestron/1990s)	8-10	fair----40**	sharpness similar to U.O. ortho, but 50° fov
Zeiss ED ortho	8 by design	good---60	crisp--need info

** The Galoc, Vixen and Abbe-orthos are pleasing to the eye, but "soft" on
critical resolution tests, done in fine "seeing" conditions. The Vixen is okay,
but not quite crisp and contrasty enough for planetary work.

(The goal here is the best possible planetary contrast and field darkness:
Most eyepiece lines have only one or two eyepieces, if any, that stand out as
excellent performers. The Televue Plössls are very sharp, but on a Barlow,
and/or when used above f/12 encounter some aperture vignetting, which may
be related to a "sharp but overbright," effect on planetary images, hence, the
Ultima's seeming superior imagery above f/8 (more noticeable on minimally
obstructed optics). (The Televue Plössl was designed to be ideal at f/4 or f/5,
the Ultima at f/10.) The 18 mm Ultima, though not alone, seems the most
desirable overall, on a Barlow lens (having to do with imagery and eye relief)!
(I find the Ultima ideal above f/20, however, the field is slightly curved at f/9.)
The 12 mm Brandon, on and off the Barlow, seems less affected by poor "seeing"
conditions than other eyepieces. Although I am very much up on the orthos
and the Ultimas, the Brandons are one of the best corrected eyepieces available,
with or without ED glass, and, in the right telescope, preferably medium-to-
long focus refractors, as Chester Brandon intended, come into their own.
The 24 mm König Type II, like the 32 mm, is impressive, but was not tested
on a Barlow lens. The 16 mm König Type II shows multiple reflections on
Jupiter with all Barlows tested, but not off the Barlow(?). None of the other
eyepieces tested had this problem. The orthos though clearly very effective,
when no Barlow is used, seem to fall behind the Televues and Ultimas when
a Barlow is in place. (Schmidt-Casses are critical of alignment and mounting
problems with Barlow lenses, and anything that adds reflections and back-focus.
The Ultima coatings seem to produce an ideally dark background even when
used with a Barlow lens. Cautions and notes: Indiscriminately mixing eyepieces
and Barlow lens, given a particular optical tube assembly, will produce varying
degrees of success and disappointment! The most recent testing was concluded
11-10-02.)

   (Schmidt-Cassegrain--more)

   (Return to the "Guide") (eyepiece test results)

   (Testing eyepieces at the telescope)

   (Return to "Eyepiece Testing: Abbe-ortho versus Televue Plössl")

  For fine tuning, color filters can be used to partially block the frequencies
(blue end) that produce the "gauzy," (i.e., "fuzzy" or "misty") effect (e.g.,
wratten #1A, #11, #21, 80A and #82A). Also, a broadband skyglow filter,
while most models make the image green, will exclude some of the most
offensive frequencies. Unfortunately, there is a consequence! At apertures
less than 8 inches, the typical skyglow filter will diminish the intensity of
most objects enough to be troublesome. "There is no substitute for good
"seeing,'" and this becomes more apparent as aperture increases!)

  Given the inevitable limits of technology and the laws of radiation, several
new statements and clarifications of previously mentioned "rules of thumb"
can be made: (1) Performance, related to and limited by technology (e.g.,
baffling, perfection of edges, field-stops, etc.), tends to shrink exponentially
with decreases in aperture (e. g., 12 mm fl is less critical than 6 because,
performance is, if all things are equal, a function of radius squared, thus
errors in precision will be 4 times more noticeable at 6 than at 12 mm).
This is an arguable point, given some of the wide-field eyepiece designs,
because they use lens elements of larger than normal aperture and focal
length, and a built-in Barlow lens (i.e., a sophisticated, multipurpose,
telenegative amplifier), to end up with the shorter focal lengths. However,
with the wide-field design, the need for precision and good baffling is more
critical, and built-in Barlows tend to compound problems (e.g., surface
reflections and color errors affecting transparence and contrast are often a
downside of the effort to achieve wider fields). (2) Performance tends to
decline with an increase in the angle of incidence. (3) Performance related
to sophisticated technology decreases with any decline in quality--does/can
the product meet the stated criteria? However, even if contamination,
workmanship and stated tolerances are relatively well controlled, as scrutiny
(i.e., power per-inch) increases, any flaw or contamination will be more likely
to impact image quality. (4) Atmospheric considerations play a major role in
contrast and definition, especially with regard to the inherent problems at the
violet/blue end of the spectrum!

  Conclusions: (1) When applied, the four statements (above) suggest that higher
 "f" numbers have an exponential advantage, regarding image quality, over lower
ones, and that minor variations in design, quality and in the rate of transmission
become more important, especially off-axis, as the cone of light becomes shorter
and more sloped. (2) Anything that "straightens out" the light cone and allows
the use of longer focal length eyepieces, with relatively fewer elements, tends to
overcome weaknesses in design, technology and quality.

 Given the best examples, simpler eyepiece designs are usually sharper and more
transparent than wide-field designs. While the edge of the field is usually not
as flat (save the orthoscopics), well baffled eyepieces with four or five elements
(i.e., Brandons, orthoscopics and hybrids) usually induce less reflection, and
provide the best contrast. While some of these and other simple eyepiece designs
may be challenged at speeds near or below f/5, they seem to be the most forgiving
of defects in the optics and in the observer's eye. (Weaknesses in eyepiece design,
such as poor contrast, may be more noticeable with compound telescopes--Schmidt
and Maksutov Cassegrains.)

  Note: For many observers, the advantages of the simpler eyepiece designs may
seem inconsequential, considering the effective field and panoramic views of modern
wide-field eyepieces! For planetary viewing, simplest is best, but for fast optics, and
for the more diffuse objects, the more sophisticated, wide-field eyepieces should
provide the best result. (No matter what the object in view, eyepiece coatings is the
finishing touch that makes the telescope a finished system!)

  (Return to the "Guide")  (eyepieces Barlow lenses and filters)
 

Part 7 ***
The Quest for a "Nailed" Image: Resonant Versus Non-Resonant Imagery
(Is Diffraction Ever a Good Thing?)
  Diffraction is a natural effect of aperture and obstruction, and it will work to
limit or impair the perfection of any optical system. However, diffraction caused
by an obstruction follows a more natural and forgivable pattern if the obstruction
is uniformly circular. With straight-vaned secondary supports, some of the
obstruction is not circular, and will not displace light evenly. However, diffraction
related to the secondary mirror and its holder (i.e., circular obstructions), is more
uniform, and can, if kept to a minimum, be acceptable, and it may even have a
useful side effect.

  A circular obstruction in the center of the light path produces a visible effect,
somewhat like a "resonant" condition. For some objects (e.g., Saturn's rings
and bright stars), this flaw may seem to reinforce the image. What looks like
enhancement is actually the "conversion" of fine detail into a broader, more
visible boundary between larger and more easily seen markings. In actuality,
there is less definition, but there appears to be more "dimensionality" (i.e., a
3 dimensional effect), and the image, bounded by this "reinforcement," seems
warmer and more bold (i.e., better "coupled" to the eye and nervous system).
An unobstructed optic is not like that--its performance is "cold," depending
entirely on purity and perfection of finish.

  (When diffraction is at a minimum, "edges" and details are crisp; hence, there
is little or no "resonant" effect! Diffraction, per se, is not resonance; however,
diffraction produces the visibly increased "dimensionality," and "cut off" of detail,
that in this section, will be referred to as "resonance." In some situations, it may
be possible to use this effect (i.e., a limitation) to achieve a more pleasing and
rewarding observing experience.)

"Resonance" and "reinforcement," are experienced in both vision and hearing.
They add "immediacy" (as "dimensionality") to the image. (Color and "transparence"
go to coherence and presence, and "immediacy" and presence improve "coupling.")

  Because most compound optical systems have relatively large secondary
obstructions, they are considered to be high diffraction designs, and as a result,
demonstrate significant "resonance." To work optimally, such systems must be
perfectly clean and precisely aligned. The high magnification factor of the secondary
in a compound system, in effect, "stacks the edges," and amplifies "resonance,"
but compound systems can, on occasions of good "seeing," stabilize quickly and
provide reasonably good results up to 40x per inch. (At magnifications greater
than 32x per inch, diffraction related to the size of the secondary, in compound
systems (e.g., 29% to 38% of aperture), works to degrade performance, more than
in a prime focus telescope, and atmospheric turbulence, versus the size of the
secondary, is a more noticeable problem!)

  As evidence of this "reinforcement" phenomenon, it has been noted that the
edges of planets are brighter in a compound telescope than in a minimally
obstructed Newtonian or a refractor. One noted planetary observer said that
the solidest edges on the rings of Saturn that he had seen were in a Schmidt-
Cassegrain. If the more resonant (i.e., softer) optic "converts" fine detail (i.e.,
reinforces edges and makes the overall image look more pronounced), and if
the sharper optic is subject to scattering of the finest detail, in the near field, such
scattered elements must, in the case of the latter, be visible (and interspersed)
in the structure of the image. (Having pointed out some of the weak points
in compound telescopes, it is only fair to add that Schmidt-Cassegrain and
Maksutov-Cassegrain telescopes are among the technologic marvels of the
20th century.)

  (A note: If using much more than 32x per inch is avoided, it will seem as though
there is no limit to power handling capability, but if pushing the limits to 40 or
50x per inch, becomes common practice, disappointment and less than dazzling
image quality is more likely. This applies to all designs!)

   (Schmidt-Cassegrain--more)

  Long focal length Newtonian reflectors, f/9 or greater, with the smallest
workable secondary, have just enough "resonance" and "reinforcement"
(i.e., added diffraction) to "enhance" the image, with little or no noticeable
degradation. Such instruments are often said to be equivalent to refractors and
unobstructed reflectors of the same aperture. Lower "f" numbers (f/6 to f/8).
with parabolized mirrors, and optimally small secondaries, also have a potential
for an "enhanced" result, but performance equal to a properly corrected
refractor or an unobstructed reflector of the same aperture will usually be
illusive. However, while the refractor is considered to have the advantage,
inch-for-inch, the need for precise convergence of all frequencies of the visible
spectrum, and the arguable potential advantage of "resonance," results in the
Newtonian reflector having a potential for a more "nailed" image, on some
nights, given sufficient cool down time. (More a problem for reflectors: Very
often, seemingly poor performance will actually be the effect of insufficient
time allowed for the temperature of the glass to reach that of the surrounding
air.)

(Notes: "Convergence" goes to fine edges, and "resonance" goes to elevated
edges! "Resonance" is a side effect of increased diffraction, a "softening" or
"aphrodizing" effect which can be likened to a filter or trap that removes negative
components of sight or sound. Example: In high fidelity sound systems, the
ideal is to form the best possible image, but only allow enough of what is on the
disk to reach the listeners ears to satisfy taste, and not pass on residual noise
and "trash" from the recording. When the playback equipment is "too good"
(i.e., too revealing), the opportunity for pleasing sound is limited to fewer sources
of recorded music (i.e., the best quality vinyl recording will standout when
compared to the best CD, and with regard to telescopes, if net performance is
as sharp and as accurate as possible, images will be dazzling, but there may seem
to be fewer nights of good "seeing." The reason being, the best, or sharpest,
telescope will tend to reveal increasingly more minor disruptions in the "seeing."
(When there is less resonance, and more accuracy, scrutiny increases and the
"seeing" is more severely tested!)

  (A debate develops: If turbulence is more of a problem for a larger reflector, how
can we say (generally and inclusively) "resonance" will cover up poor "seeing,"
and make a more reinforced and solider image? Either the secondary obstruction
is a detractor and counts to worsen image quality, or it reinforces the edge of the
image...which is it? With a moderate or small telescope, there is more working room,
versus the "seeing" conditions, and subtle effects can be experimented with, but with
a large telescope, the "seeing" conditions can overrule all other effects, making almost
any effort futile. However, there are ways to make "adjustments" in reasonably good
seeing, and both large and small telescopes can apply them, with some effect.)

  A well made refractor or minimally obstructed reflector will not, produce a
"resonant" image! The potential for purity and perfection with an unobstructed
or minimally obstructed optic promotes optimal performance and less interaction
with atmospheric turbulence. What I call "resonance" is a defect that "displaces"
fine detail, which would otherwise be visible in a superior instrument. With "resonance,"
there is a loss in resolution that reduces detail, and at the same time, tends to make
stellar and planetary images stand out from the background. This may, or may not,
sound good, but if the effect is kept to a minimum, it may, in some cases, look good!
(Added diffraction, seen as increased dimensionality, while causing a slight loss
of detail, reinforces (i.e, firms up), the image, and it can be seen as increased structure
in the outlying pattern of the "Airy disc.")

  It is logical to say, anything that adds diffraction is a negative force. However,
the effects of "resonance," "warmth" and "coupling," as demonstrated in audio
systems, can be experienced similarly as an advantage when the performance
of an obstructed optic is compared to that of an unobstructed optic. The natural
advantage of the unobstructed telescope may seem to be somewhat offset, except
in fine "seeing" conditions, or where the "net" diffraction of the obstructed
instrument is excessive or not well formed. As a rule, the sharper (higher quality
and/or minimally obstructed) telescope will begin to come into its own in moderate
to good "seeing," while larger, and more obstructed telescopes are seriously affected
by increased turbulence and poor "seeing." Therefore, the more obstructed telescope
is less versatile and needs fine "seeing" and fine workmanship to be at its best, and
to be competitive, in terms of sharpness, but in this section, we are not talking about
sharpness, we are talking about imagery (i.e., how it looks overall), and in ordinary
"seeing" conditions, slight reductions in sharpness can filter out some of the effects
of atmospheric turbulence--less is more!

  To the observer's eye, "resonance" works like a filter, and it seems to work best
with telescopes in the range of 3 to 6 inches of aperture. It works at larger apertures
too, but the smaller instrument is less challenged, and its image, less compromised,
by ordinary and poor "seeing" conditions.

  The best "package"--eyepieces are affected by "resonance" too: A "less fettered"
(i.e., simpler) telescope and/or a combining of the most accurate components, will
provide excellent images when the "seeing" is good, and, using a "softer" eyepiece
(e.g., orthoscopic), one with more inherent diffraction, as a function of the design, in
less than ideal "seeing" conditions, will induce enough "resonance," to effectively
filter out some of the minute artifacts of scattered light that a sharper eyepiece
would normally, and dutifully, reveal to the eye. (An orthoscopic, or other "soft,"
eyepiece, works as a "quarter-wave optical trap," as opposed to an eighth wave
or sixteenth wave capable eyepiece.) Diffraction can be added, and fine detail lost
(i.e., filtered out), at any point in the system, and it might have a beneficial effect
in poor or ordinary "seeing" conditions, but it would be better to select any such
(sometimes desirable) effect, by judicious use of certain eyepiece designs, as
opposed to losing detail permanently, due to a mediocre objective lens or primary
mirror. ("Acquire a telescope with the least diffraction, 'up front,' then select the
right eyepiece (i.e., "soft" or "sharp") to get the most desirable result (i.e., pleasing:
clean or crisp) for the given conditions!") (The number of evenings, on which,
reasonably good and pleasing images are attainable should increase if there is a
plan to use "softer" eyepieces, when "seeing" is only fairly good.)

  If "the observer is part of the optic," with a vigorous and restful state of health, the
heightened acuity of the eye and motor centers will detect more detail, and be more
critical of the shortcomings of such effects as "resonance." However, if managed
properly, "resonance" can be a useful tool, especially with small and moderate sized
telescopes. There is nothing that can be done to improve poor "seeing," but the right
eyepiece, may compensate enough to produce a more pleasant image, and it may
seem to show more detail, because of less strain on the eye and less degradation and
clutter in and around the Airy disc!

  Several ways to "look" at it--for better or for worse--there are many things
going on: Even an obstruction of less than 15% will have an effect which
slightly reduces fine detail (and as has been said, in some ways, beneficially so),
and performance will still be slightly more affected by turbulence than would
be the case in an unobstructed system. Interestingly, because of the slight loss
in sharpness, due to the obstruction, the image may seem cleaner, but it will also
be less finely delineated at the predicted resolution limits of the system (admittedly,
a thing very few could see, or should be concerned about. (For most amateurs,
the benefit of minimal obstruction and the potential for precision in other areas,
versus the cost of, and number of, polished surfaces in a refracting telescope weighs
heavily  in favor of Sir Isaac Newton's design.)

  Notes: (1) When choosing eyepieces and telescopes, think about matching and
balancing everything as a total system, with "soft" and "sharp" components. Don't
think of the various components as stand-alone devices, and then try to buy an
accessory without regard for its appropriateness, with the type of telescope to be
used! (2) Every component should be the sharpest and best possible, except for an
alternate set, or partial set, of short focal length, "soft" eyepieces. (3) Restraint in
buying expensive equipment should be tempered by a resolve to learn how to choose
and use the basic tools beforehand. Otherwise, relatively useless or inappropriate
eyepieces and other accessories may accumulate and remain in the accessory case.
(4) Sharp eyepieces are not always more expensive, or of more quality, than "soft"
eyepieces, and "soft" eyepieces are not necessarily less expensive or of less quality
than sharp eyepieces. There are good (and expensive), "soft" eyepieces, and there
are good and inexpensive "sharp" eyepieces. (5) Observational astronomy is not
about having a telescope, it is about knowing how to use one!

   (Return to "Astronomy News..." in library index)

   (Return to list of "Topics" in article on eyepieces--eyepiece.html.)

   (More observing techniques and Mars--2001)

   (Return to the "Guide")   ("...nailed image," resonance)
 

Part 8 ***
The Proper Mind Set--What Every Observer Should Know!
Vision is a scanning process, with the combined effect of the cone cells,
making up the foveola (the most central, and the most discerning part of the
eye), brought together in a tiny, dot-like point, with a dimension of .4mm).
Diffraction is moderated by the "fixation limit" of the eye (i.e., actually of the
nervous system), and in terms of how the eye and the brain work together,
there is nothing smaller than .4mm (i.e, virtual zero =s .4mm). (There is an
appendix for terminology, e.g., "fixation limit," in the back of this document.)

  (The fixation limit, or fixation potential, of the eye and nervous system: The
capacity for following movement and analyzing fine details, has to do with the
speed and accuracy with which the eye scans, and depends on the resilience of
the motor centers, and their ability to track incoming stimuli. (In psychology,
fixation is a behavior.) Related: In its turn, and to expand the information base,
the "scanning limit" of the eye is more particularly a function of the charge/
discharge period of the neuron (.002 seconds), and is the "determination" with
which the motor centers, and the central nervous system position the eye (In
neurology the "scanning limit" relates to action potential, and in psychology,
it equates to tenacity, as a subset of curiosity.), and is not a function of the cross
section of a cone cell, as might seem likely.)

  Vision is only optimal when the exit pupil of the optic is larger than the cross
section of the foveola--.4mm! This is born out by the fact that repeated testing
has shown the smallest usable exit pupil, for a telescope, to be about .5mm, but
images are sharper and more pleasing at .8mm. When the exit pupil of the optic
is similar to, or smaller than, the foveola, the effect is something like playing a
phonograph record with a nail. When there is not enough exit pupil, and image
size, for the foveola to move and scan, in its genetically programmed way, the
ability to make out (i.e., "visualize" in the occipital lobe of the brain) fine detail
diminishes.

note 1
  (The scanning process as a behavior: "Virtual zero is all that we can see!"
In the brain, the output of each of the cone cells, in the central area, are summed
together as one (i.e., ergo we have "central fixation"--Bates 114, Bloom 78)!
The eye does not see, it senses! The "seeing" is done by the brain! With the
normal visual performance of the eye as the basis for comparison, diffraction
is dependent on the purity of the medium through which light passes. The ideal
telescope, as a part of the "medium," would be a narrow band, linear amplifier,
where both resolution and resolving power are equal to "one," and no effect of
the system detracts from the image at the wavefront.)

note 2
  (The effects of diffraction are moderated by the "fixation limit" of the eye and
nervous system. The "fixation limit" is determined by the resilience of the motor
centers, and their ability to track incoming stimuli. (I decided to call the speed
and accuracy at which the eye tracks its "fixation limit.") If the brain and the
eye are sharp, the artifacts of diffraction will be discriminated (i.e., seen clearly),
but if the eye is less sharp (e.g., fatigued), the detail in the "Airy disc" may seem
less distinct, or more difficult to make out.)

note 3
  (In physical terms, the foveola, surrounded by the fovea centralis, corresponds
to the Airy disc, and the peak at the center (i.e., follow the same paradigm).
When health declines, central fixation and focus declines, just as the amount
of energy in the central peak of the Airy disc is reduced (i.e., "peak flattening"),
when the size of the secondary obstruction increases.)

  Given good eyes, good equipment and good "seeing" conditions: When,
at high power, the effects of diffraction show up in the eyepiece as rings
or spikes that is an "optical artifact," and not the object itself. (From this
distance, we can only see points of light). Even the tiny dot in the center of
the  Airy disc is an artifact, but as power is gradually increased, the diffraction
rings are the first thing to be revealed. The Airy disc begins to resolve, or open
up (i.e, "bloom"), at a magnification of about 32x per inch, characterized by
a .8 mm exit pupil. Above that power, and with good "seeing" conditions,
diffraction is revealed as a well formed pattern, but in poor "seeing," the rings
break up and scatter in the near field, with minute fragments, in disarray,
appearing as "optical trash," or as skyglow, around bright objects (e.g., planets
and stars). (Exit pupil diameter, in millimeters, equals, eyepiece focal length,
in millimeters, divided by the telescope's "f" number, shown as ep = efl/f.
The "f" number equals focal length divided by diameter, or aperture, shown
as f = flmm/dmm.

A review
  The quality of the telescope, and the keen sightedness of the observer, not
withstanding, empirical evidence suggests that related to the resolution of the
Airy disc, there is a "sweet spot," or "point of optimal scale," and it appears
in every telescope at the same power per inch--32x. Beyond this "point," the
artifacts of diffraction become more visible, and the image begins to "dull off,"
rather than continue to sharpen. (The term "sweet spot" was used earlier, in a
different context, to characterize the sharpest point of focus at the center of the
field of an eyepiece.)

  (Human physiology: A coincidence in kind: "Everything works together!"
The limited ability of the eye to move in minute increments at exit pupils
smaller than .8 mm appears to be a factor, but diffraction is an undisputed fact
of physical science, while the human element is more problematic. Reference:
The sight of the observer is more rigorously tested as the "diffraction limit" is
approached. Of course, the sharp-eyed (i.e., more vigorously healthy) observer
can see more in the range of the diffraction limit than one who is "less sighted."
The human element may seem unrelated, but "the observer is always a part of
the optic," and the same physical rule (i.e., a paradigm) that disperses energy
around an optical, or virtual, point disciplines human evolution, and determines
the size of the foveola, a manifestation of the "point" around which human
existence is formed. This "point" will come back to the discussion from time
to time, and it will become more and more apparent that the forces determining
the size and nature of the foveola are involved in all things telescopic, living
and otherwise (re: "point source paradigm"--see appendix). "The eye, the mind's
eye and the "self" all gather around an imaginary point, to form an island of
immunity"--Bloom 78, 201, 244, 254)

Issues to address:
(1.) It has been noted that the crispness of telescopic images begins to fall off
above 32x per inch (i.e., .8mm exit pupil), no matter what telescope is in use!
The principle cause, diffraction, has been discussed, but there are other factors.

(2.) Eyepieces vary in quality, but the best and the sharpest will not provide
the "best" image every time. ("When the 'seeing' changes, all bets are off!")

(3.) Near-field illumination, around bright objects (unrelated to skyglow),
seems to increase when power increases. (By staying within the range of
powers between 32x per inch (.8mm ep) and 17x per inch ( 1.5mm ep),
resolution, contrast and image quality are at their best.)

(4.) Low power background illumination: The field of view seems to exhibit
disproportionately more skyglow and background illumination at magnifications
of less than 17x per inch (i.e., 1.5mm exit pupil diameter), than at higher powers.

(5.) What can be done to help the eye see everything that it should see?
 

  The retina of the eye is embedded with millions of rod cells and cone cells, and
a small (1.5 mm--1/16th inch) circular patch of cells in the center of the eye makes
scrutiny of fine details possible. This "patch" is known as the fovea centralis, and it
is made up entirely of cone cells, cells sensitive to changes in color and structure.
The central most part of the fovea centralis, the foveola, is a tiny point of densely
packed cells, smaller than a period at the end of a sentence, just .4 mm across (.4 mm
equals 1/64th of an inch). (The cone cells of the fovea centralis and the foveola are
laid out like a tiny bull's eye, with the rod cells located in the field beyond the 1.5mm
central area of the fovea centralis. Rod cells are "light sensors," and make it possible
to almost see in the dark. The sensations transmitted from rods and cones, via the
optic nerve, to the vision centers of the brain, in the scanning process, described
as "a behavior," a few paragraphs back, thus form an image. (It is as if, the eye never
fixes (i.e., settles) on anything (it doesn't, and it isn't supposed to); i.e., the foveola
is in constant motion, a "fixation aversion" effect, In trying to study/analyze a
miniscule (about .5mm) image/detail, the foveola, the oblique muscles and related
moto-neurons, as a tracking system, will quickly go into torpor, and be unable to
track, not unlike a disorientated or staggering gaze. This happens because the motor
centers cannot maintain such "uncertain" fixation for any measurable time. However,
on looking away, the nervous system "comes out of it" (i.e., rebounds and "brings"
itself out of it) in 200 to 300 milliseconds.)

(Bloom 139, "adaptation and fixation aversion")
  There are two complementary agents involved in adaptation and this component of the life
force (i.e., the 21 day rule): (1) One has to do with not concentrating too long on a single thing
(i.e., fixation aversion). No matter what the body is doing, even if it is the best possible thing, it
needs a change of pace and situation. When the pattern of activity changes, some of the brain
cells, which were previously active, take time out to rest, and others begin to work. (2) When a
stimulus is removed, resilience plays its hand in a most remarkable way--anabiosis: resuscitation--
coming to life. Once aroused by something beneficial, the nervous system will react to losing that
stimulus by trying to "fill the void." (The greatest gains are made when a nourishing stimulus is
withdrawn--the psyche tries to compensate (i.e., reach out) for the loss by pushing every system
to its limits, via the hypothalamus.)

  In the course of daily events, normal visual tasks, reading, watching TV or driving
a car, there isn't much of a challenge to the eye and the nervous system. The cones
work best when there is plenty of light, and the rod cells are well suited for peering
into the shadows, and for after the Sun goes down.

   Issue (1.) (crisp images--other factors): During ordinary, day to day activities,
the eye will not likely encounter the phenomena discussed here. However, for an
astronomer or anyone who wants to look through a telescope, it will be helpful
to know how the eye works, under extreme conditions. And "extreme" for the
eye, can be an image, and a test, easily within normal telescope magnification
ranges. In fact, there can be a dimensional conflict between the physiology of
the eye, and the exit pupil produced by a telescope.

  The function of the exit pupil of a telescope, versus the limitations of the eye
brings several factors into play. (Again, the exit pupil of an optical assembly
is a function of the focal length (mm) of the eyepiece divided by the "f" number
of the telescope--rp = fl/f.) The same limits always apply, and knowing how the
eye works may make it possible to see more when conditions are less than ideal.

All optical systems "roll off" (i.e., decline in image sharpness) at exit pupil
diameters less than .8mm, but the performance of simpler and less obstructed
"prime-focus" systems degrades more gradually than the more critically designed
compound systems. Any added diffraction, and any other error in the optic,
become more of a problem when the exit pupil of the system is reduced to less
than twice the .4mm diameter of the foveola. (The optimal scanning range, or
"tracking limit," of the eye, .8mm ep, and the point of diminishing return in any
optical system, such as a telescope, both happen to take place at an exit pupil
dimension, twice the size of the foveola!)

  We tend to think diffraction only has to do with, or is seen with, the Airy disc
and what a star image looks like, but it is a component of the image, including
every point in the field of view, produced by the optic. That is, it is a part of
any image through any lens or optical system. It is present when viewing the
Moon and planets, and even a tree, or a bird, or a lamp on a power pole, off
in the distance. (We can say that on some occasions, of less than ideal "seeing,"
the sharpest eyepiece does not seem to work as well as some lesser eyepiece!
One might (logically) think, the sharpest eyepiece would always "work" better,
but there are exceptions. Not only is the finest detail unseeable when the "seeing"
is poor, but the artifacts of diffraction tend to be scattered in the foreground. If
we could filter out the "trash," related to turbulence, and only see what is left
of the image, that would be the best we could hope for, and some of the "less
sharp" eyepieces seem to do that.)

With a .4mm sensor, and with the exit pupil of the optic getting smaller
and smaller, with every increase in magnification, the scanning the eye does to
circumscribe and analyze the target is put to a greater test. The eye must move
in very small increments, and whatever the challenge, it has to be dealt with by
the motor centers and the central nervous system. "Therefore, the most rested
and knowledgeable observer will get the best result." So, while fatigue related
to coping with diffraction works to wear down mental sharpness and motor
sensitivity, the time that has elapsed since the last rest period, compounded
by the day's stresses and frustrations, suggests that a good tactic might be to,
periodically, during observing sessions, take rest breaks, away from the eyepiece.

  (A demonstration of the eye's scanning behavior: Look at this combination of
characters from the previous paragraph: "eye, .8mm." If the monitor is set to 12
pt font, and if the eye is focused on the "decimal point" preceding the number "8,"
the eye will tend to "jitter," as if by some reflex, but if the point of vision is "fixed"
on the "comma," preceding the "decimal point," the eye will "settle" (i.e., behave
normally), being more able to "track" the larger target. This is because the "decimal
point" is only .4mm (1/64 of an inch) across, while the "comma" is closer to .8mm,
about 1/32 of an inch (i.e., the optimal scanning range of the eye--a tracking limit).
Fonts and character sets may vary from computer to computer, and browser to
browser, but the point is, the eye is not meant to fixate on an image for an extended
period, especially not a critically small image. The smaller the image, the more
difficult it is for the oblique muscles, which position the eye and the foveola, to get
"a fix" (i.e., "track"), and as the size (i.e., measured cross section) of the image
decreases toward .4mm, the positioning movements of the eye will become erratic
and inexact from the "overwork" of dealing with the mismatch.)

   Physics and evolution: It is interesting that the point of diminishing return ("pdr")
of all optical devices, and the "tracking limit" of the eye, both occur at an exit pupil
of .8mm. All of nature follows the same rules, and the evolution of the mind and body
will come up to nature's limits. Therefore, over thousands and millions of years, the
mechanisms of vision adapted to or sought the same scale of things that make up the
rest of nature. (That may not seem to be correct, because, for instance, an eagle can
see much more...so what is the correct explanation?) No matter what other creatures,
with less sophisticated nervous systems, have adapted to, the human eye has settled
on a foveolar dimension accommodative to and (necessarily) half the size of the exit
pupil at the "point of diminishing return" (the "pdr" determines "scrutiny"--.8mm
compels .4mm--diffraction compels adaptation). What I call the "point of diminishing
return," at .8mm ep, has been noted, but the same rule, a paradigm--"carved in stone,"
and for us, an evolutionary sign post, and a part of nature's way, applies to all things!)
Issue (2.) ("When the 'seeing' changes..."): "If the 'seeing' is ideal, all eyepieces will
fall into place. The best design and the highest quality workmanship will come out on
top, and the second best (sharpest) will fall in behind that, and so on." An experienced
observer might thus say, "that is all there is to it," but to deal effectively with the
"seeing" conditions (by using the right eyepiece for the conditions), the other 98%
of the time, some investigation and note taking may have to be done.

  "Even with ideal 'seeing,' sharper may not always be better!" Some eyepieces,
with thicker coatings, will give a nicer and more contrasty image on Jupiter or
the Moon than will other eyepieces with greater sharpness and higher light
throughput. Because of their overall performance, the Brandons, may show a
cleaner and more pleasing image at or near the diffraction limits of a given
telescope, especially, when viewing something like Jupiter or Saturn, and
especially when the telescope is a long focal length refractor (approximately
f/11 or greater). This is largely because the Brandons have, for lack of a better
term, a "planetary coating." But there is still more to it than that, and the orthos
have similar advantages in some "seeing" conditions.

   On some occasions, and in some telescopes, the best eyepiece may "come in
second." When the "seeing" is poor, you have to know your eyepieces to get the
best result. Surprisingly, an eyepiece considered not to be the best design may
come out on top when the "seeing" conditions worsen. There are scientific and
physiologic reasons for such puzzling results. The differences vary for each
different eyepiece and telescope design. (Reports by experienced observers
indicate that when "seeing conditions" change, some eyepieces will do a better
job than expected, and some will do more poorly. When such phenomena are
noted again and again, there must be something going on that is not being
understood or explained.)

  The observer needs to know more at a behavioral level (i.e., how everything
works together) to get the best possible result. Sometimes, it seems as though
you almost need to be an optician, an ophthalmologist and a master detective
to figure out what is going on, and what will improve the image. But, once we
understand more of what is going on, right before our eyes, it is an empowering
feeling to get out of the mode of shopping or searching for something bigger or
better, and into the mode of being in control, and knowing exactly what works
and why.

   Diffraction breaks down at least 14% of any stellar image into concentric rings
of energy, each subsequent ring (moving outward) carrying half as much energy
as the one inside of it. Dealing with image degradation related to increasing
magnification and diffraction, or not having the most appropriate eyepiece for
the "seeing" conditions, can be frustrating. It is easy to get off course, and not
realize that solving observing problems may come down to "less is more."
Instead of spending more money to "fix" the image, spend less! (Investing in
more and "better" eyepieces and accessories, without understanding how
to select the most appropriate eyepiece for the conditions, may not be cost
effective, or pleasing to the eye.)

  The strain on the eye when dealing with degraded images and scattered light
can add to the fatigue and frustration. Exhaustion and dehydration, at a general
level, affects the motor centers of the brain and the muscles of the eye. All this
compounds the disappointment and adds to the stress that makes staying
"sharp-eyed and rested" harder to do as the evening wears on. (32x per inch
is a "crossover point." That is, beyond this point (i.e., the point of optimal scale
and diminishing return), diffraction becomes enough of a factor that choosing
the right eyepiece, given the "seeing" conditions, may improve the image and
the experience.)

  If the "seeing" is less than good, the "softer" eyepiece may "firm up" the image,
by intensifying edges. If the "seeing" is poor, the "softer" eyepiece may have an
advantage in any range, but more so above 32x per inch. And conversely, the
sharper eyepiece will reveal unexpected detail in the magnification range above
32x per inch, when the "seeing" improves.)

   Some combinations of telescope and eyepiece will seem crisp at 35x per inch,
or more, on some occasions, but another night, a lesser eyepiece design (working
in the same magnification range) may seem to work better, revealing more detail,
and less "clutter" and "skyglow" on and around planets and stars. However, in actual
practice, when trying to find the ideal power, and say which eyepiece works better
on a give occasion, the point at which a "softer," but still high quality, eyepiece
shows its advantage most is in the range between 35x and 40x per inch!

  (The softness of the orthos, and other similarly "limited," high quality eyepieces,
is a function of design. If the shape of the lens induces a quarter-wave limitation at
the focal plane, that would add diffraction, and more energy would be seen in the
diffraction rings. Whatever the cause of the marginal resolution, a "softer" eyepiece
can, in some circumstances match the eye and the telescope to the atmosphere,
when conditions are less than ideal.)

  For many amateur astronomers, sharpness and detail is not everything? Some of
the most memorable views are of nebular and galactic objects. Interestingly, no
matter what the evenings schedule includes, paying attention to which eyepiece
is sharpest, and which will have an advantage, when the conditions change, is
empowering, and should add new dimension to any observer's skills.

  A useful project might be to make a list of eyepieces, ranking each as "sharp" or
"soft!" This suggests that the next night of fine "seeing" could be a new beginning.
However, you can generally say, without doing any testing, that orthos, Brandons
and some plossls will be a bit "soft," while some of the hybrids are crisp and sharp.
Once the set is divided into two groups, the choice is to select the eyepiece that most
closely matches up (i.e., "couples") with the atmospheric conditions, on a given
occasion.

In theory, and as a method, an observer could set up his or her equipment, and
start with an eyepiece they have found works reasonably well, on most occasions,
and then switch to something sharper and more critical: I have hybrids and orthos,
and a few "odd balls." I use the orthos first, and if the "seeing" allows, the hybrids are
standing by to "step up." The Galoc, Brandon, Vixen and others fit in the soft category,
and it is satisfying to know exactly what each will do. (This approach should allow
almost any observer, regardless of experience, to put their equipment to maximum use.
The testing methods used here help determine telescope and eyepiece performance.
Ordinary or poor quality shows up without any test, but these tests readily reveal
minute differences, in an "A to B" environment--(eyepiece testing). A desirable side
effect: The tests are instructive, and will make the observer more proficient with little
effort.)

  This is a good place to add a few comments about the desirability of the Abbe-
ortho and the Brandon as planetary and double star eyepieces. This is subjective,
but it goes to why eyepieces like the ortho and Brandon, with their desirable overall
design criteria seem to compliment the eye, and make less performance seem like
more. I came on these sections while reviewing my observing notes.

  From the log--11-15-00 ("Human physiology is a part of the mix): A possible
explanation for some eyepieces seeming to be "just right," that unexplainable
something that draws the eye and the mind to them even though they prove not to
be sharp as other designs: The human nervous system is affected by stress, and at
the same time, it can correct some types of errors (e.g., refractive--color shift). If
an eyepiece converges color less than ideally, the stress on the eye to accommodate
refraction errors is a source of fatigue, at an almost subliminal level, and the error
may not be noticed outwardly, because the nervous system adapts quickly. What
appears to be good correction, may be "fixed" ("accommodated") by the eye and
the brain. However, when an eyepiece is well corrected, the work the eye has to
do lessens, the stress level is lower, and any improvement in performance, may be hard
to quantify, but the image is easier and more pleasing to study. (A compound effect:
With less stress, the effect of easier viewing adds to the body's energy, and in "the
way of the body," any added sense of ease and satisfaction will heighten sensitivity
and increase stamina, allowing just that much more to be seen.)

(an aside...7-31-03)
  Anything that makes the task of trying to see what there is to see, less arduous,
allows the eye to work more effortlessly; hence, the brain will be less antagonized
by optical errors and spurious artifacts! The observer feels like the image looks better
because he or she is more at ease, and the eye, being under less stress, will see all
there is to see, without a wearing feeling that something is wrong. If there is less
fatigue after a viewing session, that is a good outcome. (The idea of coming up with
a test to identify the best eyepiece for the conditions, came from the need to reduce
the recurring disappointment related to poor images, and a mismatch between
potential performance and existing conditions. Successful observing is about
efficiency, and not overpowering the "seeing" conditions!)

  7-17-06: With eyepieces that offer more performance (a.k.a. sharpness and light
transmission) than the older, single-coating eyepieces, it seems the higher transmission
coatings are not as "easy on the eye," even at exit pupils, in the ideal range of .8mm.
The old-fashioned coatings of the ortho, Brandon, Galoc and other older designs tend
to present a more pleasing planetary image, while faint galactic dust lanes favor high
transmission eyepieces. (The exception: High transmission eyepieces are superior at
a dark site, but the single layer, magnesium-fluoride coated eyepieces come forward
again, to present a darker background and a nicer image, in the city, even on deep
sky objects.)

(back to the text...)
  Earlier, I pointed out that if the surface of the Moon is viewed at high power,
the brightest and sharpest points on the surface will exhibit a tiny "diffraction
ring." In fact, this "ring" shrinks and disappears when the exit pupil increases
to .8 mm or more. Question: If a diffraction ring is visible at high power, when
the "seeing" is good, where is it when lesser "seeing" conditions scatter light?
Answer: If an eyepiece tends to "filter out" optical trash, because it is less crisp
than another eyepiece, the image will be less resolved, but it may be cleaner and
more pleasing to look at. Otherwise, the "crisper" eyepiece will reveal the remnants
of the tiny rings around mountain peaks as "fuzz," commingled with actual surface
markings. (Overall, the "softer" eyepiece will behave similarly, but the image will,
at times, appear to be cleaner, if a bit exaggerated around the edges.)

  Small to medium sized telescopes, of high quality, have remarkable advantages
in sharpness and contrast:With smaller apertures, in the range of 4 to 6 inches, the
size of the optic is ideal, versus the size of a typical air cell--3 to 5 inches. (The
advantage goes to smaller apertures with finer surfaces, because of the size of the
typical air cell, and because of the almost constant activity (i.e., turbulence) of the
transmission medium (i.e., the atmosphere). Hence, with small telescopes, we want,
and can use, all the accuracy and sharpness (1/16 wave or better, if possible) that
the optician's craft can bring to the focal plane. Then, the observer can select an
eyepiece that will be best, on that occasion. But because of "seeing" limitations,
and when observing at large apertures, typically more than 12 or 14 inches, a more
ordinary wave front accuracy (1/4 wave) will usually be sufficient to show all that can
be seen on the Moon, Jupiter or Mars, from an earthbound observing site. (The most
revealing and successful planetary telescopes are smaller than 20 inches in aperture,
because the atmosphere will rarely ever pass an image clean enough to utilize the
resolving power and theoretical limits of a telescope of larger aperture. For planetary
observing, "bigger is often less," or at least, it works out that way.)

   (Back to Mars/News--2001)

   (Return to Eyepiece Testing)
 

  Issue (3.) (near-field illumination): At high power (i.e., greater than 32x per inch),
light scatter and the effects of quality problems are substantially magnified. Views
of bright objects, such as Saturn, Jupiter and the Moon are those most affected.
If the "seeing" is good, and if the equipment is of reasonable optical quality, light
scatter (e.g., illumination) in the near field, related to various factors (e.g., poor
coatings, surface contamination, large secondary obstruction), will tend to increase
exponentially, becoming noticeably more visible as power increases. (Any such
effect related to the size of the secondary mirror, and its obstruction, will only be
visible in the near field, and then, only when observing bright objects, but it will
be noticeable at powers below 32x per inch.

  There is the state of the art to consider: At some point, psychological,
physiological and technological problems reach the point of diminishing return.
If you consider that the eye of the craftsman and optician is limited by the same
phenomena, and while not being aware of all these things 120 years ago, science
and technology, as it was then, noted certain limits and moved to establish
performance criteria. Today, 1/16 wave is often considered near perfection, and 1/8
wave is fine, but 1/4 wave (i.e., the Rayleigh Criteria) has, for over 100 years, been
considered the standard for determining optical performance. If we think beyond
ordinary limits, and attempt to produce 1/32 wave surfaces, cleaner images in the
range of .5 mm exit pupil (50x per inch) should be possible. (Increased optical
accuracy won't change the "resolving power" or the point of diminishing return
for a given aperture, but resolution should come closer to the ideal.)

  Summary: If the "seeing" and the optics are good, points of light will resolve
as tiny, well formed concentric circles, around intense points of light. If there is
an optical defect, there will be increasingly more deformity of the image, as the
"seeing" worsens, or as magnification is increased. Because a "softer" eyepiece
will lose, or cutoff, some of the fine detail, it may provide a cleaner image, and
appear to work more favorably under poor conditions. When using more than
32x per inch, if the marriage of telescope and eyepiece is intentionally set up to
be "soft," the effect of slight to moderate atmospheric turbulence, should be less
noticeable, or more subdued, than with a sharper eyepiece!

  Issue (4.) Low power background illumination--LPBI Syndrome: As the exit
pupil of the telescope, or the iris of the eye, opens wider, the light sensitive area
(i.e., rods) surrounding the foveola and fovea centralis is stimulated. The "night
vision capability" of the eye works well under a dark sky, but mother nature did
not plan on the advent of skyglow. Of course, we want the eye to be as sensitive
to light as possible, but in locales where there is significant skyglow, something
may need to be done to facilitate seeing low luminosity objects, where low power
and wide-field views prove to be disappointing. Using a moderately higher power
eyepiece (yielding less light per unit area), will in effect, darken the field of view
and improve large scale contrast, with a noteworthy reduction in background
illumination.

  It seems reasonable to assume that there would be a uniform but, exponential
darkening of the field as power increases (area decreases on the square of the radius).
However, as power increases, up to a certain power per inch, the rate of improvement
(i.e., darkening of the field), is more than expected. If you know how this comes about,
you may be able take advantage of it when observing deep sky objects, in the city.
(Background illumination, in urban areas, can be so distracting and annoying that
nothing much fainter than 8th or 9th magnitude can be seen, with most telescopes.)

  When viewing at high power, there is more going on than just dispersing light
over a larger area. With an increase in magnification, the size of telescope's exit
pupil decreases, exposing fewer rod cells, those light sensitive cells, located farther
from the center of the eye. As the exit pupil decreases (with increasing power) it
can become so small it will only illuminate the less light sensitive cone cells, in a
small area, at the center of the eye, and the background will appear to be darker.
This is another useful tool! An increase in magnification reduces background
illumination; however, because of the distribution and nature of the rod and
cone cells, the rate of change is accelerated, and more noticeable, in a narrow
range at the low end of the scale, exit pupil wise. (Under a dark sky, background
illumination is less of a problem, and working with a smaller exit pupil, when
there is no need, will limit the detection of faint objects. So, using higher power
to improve large scale contrast, works best in light polluted skies.)

  Knowing of the effect of the structure of the foveola in the phenomenon I call
LPBI Syndrome, is not important in terms of the way to deal with it! The solution
is the same, but this explains why the sky looks remarkably gray, worsening
more than exponentially, in the eyepiece of a telescope, at magnifications below
17x per inch of aperture (i.e., characteristic of an exit pupil equal to 1.5mm--1/16th
of an inch), but darkens more than exponentially as the exit pupil comes closer to
1.5mm. Of course, the downside of a smaller exit pupil (at a dark site) is that, along
with the darker background, nebulae and galaxies will lose illumination too. So, the
rule is, to use the best eyepiece, and the best magnification, for the conditions. (At
one end of the scale, something akin to averted vision, increases the amount of light
reaching the vision centers of the brain, and effectively brightens faint objects, when
the "seeing" allows, while a smaller exit pupil and higher power can make the field
of view seem darker and more pleasing to the eye, than expected.)

  (With an increase in the size of the exit pupil, and a reduction in power, the
beam of light striking the retina, begins to overlap the field beyond the fovea
centralis, into the domain of light sensitive rod cells. To the contrary, with more
magnification, the field will become disproportionately darker as the size of the
exit pupil is reduced to equal the area of highest cone cell concentration, the
fovea centralis.)

  If that isn't enough, there is a complexity of things happening as the exit pupil
shrinks, and as the light sensitive rod cells are more "out of the picture." With a
smaller exit pupil, increasingly fewer cells will be stimulated in the motor centers
of the brain, and with less incoming data, what the mind sees, becomes more
concentrated and darkens further. This means that while a field of view produced
by an exit pupil of 1.5mm will seem substantially darker than one at 2.0 or 2.5mm,
there are stages of change, and as far as the eye and the mind are concerned, the
darkest field will be had as the exit pupil shrinks to the range from .8 and .4mm,
and as the effective "f" number of the optic increases. Of course, at high power,
greater than 32x per inch, the effects of near-field illumination related to quality
and contamination problems are exposed, and become factors. So, we have come
full circle, and the original point was that the apparent darkness of the field increases
disproportionately (i.e., more than exponentially), as the exit pupil approaches 1.5mm,
and becomes more similar in dimension to the part of the eye least sensitive to light,
the fovea centralis. The conclusion is that contrast, resolution and field darkness are
each, and all, conjoining and ideal at a magnification of 32x per inch of aperture--
.8mm ep! (Once the exit pupil falls below 1.5mm, the rate of reduction in illumination
declines to exponential proportions--skyglow and background illumination, not a
function of the optics, declines on the square of the radius.)

  To put an end to these speculations, we can say the "skyglow sensitivity problem,"
related to the construction of the eye, improves dramatically and optimally, in the
range near, and below, an exit pupil diameter of 1.5 mm, and that various related
and unrelated effects make it easier to see faint deep sky objects as the scale and
the "f" number increase. However, stellar images will tend to become more vague
and less "pointed," as the Airy disc is made more visible, at exit pupils smaller than
.8mm. Because of this "fovea/exit pupil phenomenon," and the "power per inch rule,"
a galaxy or nebula may continue to benefit from increases in scale up to 50x per inch,
while a globular cluster, with individual points of light, may seem to lose brightness
and image quality above 32x per inch, because of "peak flattening." Further, the
Brandon, the ortho, or something similar, may provide the darkest background
(no Barlow lens please) for galaxies and nebulae, in the range above 32x per inch,
especially in the city. Reports of "dark field" performance on nebular and galactic
objects, with the ortho, in the range above 50x per inch, seem to support this notion.

  The problem with a significant amount of skyglow when working below 17x
per inch, is best exemplified when an observer tries to, from an in-town site,
view an object like M 11 (a dense and reasonably bright galactic cluster)--total
mag. 7) in a 6 or 8-inch telescope. At 60 and 80 power, respectively, this easily
resolved, open cluster is nothing more than a faint fuzz ball, but that is because
at such a low image scale, 10x per inch (2.5mm ep), many light sensitive rods
are being stimulated. If the power is then increased to 96x and 128x (16x per
inch--1.6mm ep), it is as if a light fog is suddenly cleared away, and the cluster
is easier to see--the background seems darker, and individual stars stand out.
(One might think, none of this matters in a dark sky, but no matter what the
conditions, deep sky objects will only be seen optimally, as regards image
quality, when the exit pupil is in the range of 1.5mm or less--to be explained
further in the next five paragraphs.)

  (A perspective: The 1.5mm barrier isn't as much about the exit pupil of the
telescope as it is about the exposed central area of the retina. A 1.5mm exit
pupil will only illuminate the part of the retina made up of cone cells. So, the
more noteworthy skyglow, seen when the exit pupil is greater than, 1.5mm
(the effect of 2mm is more noticeable than 1.7 or 1.8mm, and so on) is related,
in large part, to activation of the light sensing rods in the part of the retina
beyond the fovea centralis, not just to the eyepiece or the telescope.)

 ("Scrutiny" and "surveillance" "hinge" (i.e., come together) at 1.5mm.)
  Why is there still a benefit with small exit pupils, even in very dark skies?
There is another side of human behavior, and how the eye and the brain form
and study images. It isn't just that rods are light sensitive. As a system, they do
something subliminally that relates to "environmental surveillance." Skyglow or
not, exit pupils greater than 1.5mm, illuminate rods and distract the observer,
challenging his or her efforts to concentrate. We don't have the physiologic
ability to focus or concentrate on objects in the periphery of our vision while
looking directly in front (obviously), and unlike driving a car or walking around,
allowing illumination of such areas serves no purpose in the eyepiece of a
telescope. However, when the exit pupil exceeds 1.5mm, the brain is biologically
compelled to (i.e., is wired to) "step back," in terms of consciousness--a duality
of self takes place, as the brain "switches" to the "panorama," or "surveillance"
mode, the intent being to "take it all in." The scanning pattern changes, and it
becomes difficult to concentrate on fine detail or on a single point of light...
there is "too much to see!" (Unfortunately, in the city, what there is most of
is "skyglow." All that we see is the "gray haze," which has infiltrated our
consciousness. This is distracting to efforts to get back on track, and switching
the brain back to the "scanning mode" requires discipline and the knowledge
that optimal scrutiny, and the least possible unwanted "surveillance," takes
place when the exit pupil is in the range of 1.5mm or less.)

  It is as if the nature of the eye is dual purpose. We consciously see what we
look at, but at some unconscious level, we are looking at everything else too.
So, to study and keep our minds on detailed images we can't allow those
peripheral light sensitive rod cells to be stimulated, skyglow or not! The part of
the eye intended for "scrutiny" is just this one tiny area. So isolating on it, and not
illuminating the outer field results in a greater mental focus and less distraction.
It is somewhat like wearing a patch over one eye, and "what you don't see can't
hurt you!" Therefore, for the best contrast, and to study images at high power, it
is best not to stimulate the cells away from the center.

  Does this say that employing an exit pupil greater than 1.5mm, even though
though the sky might be dark and/or not many rods would be stimulated at
say 1.7 or 1.8mm that there can be no slipping or "fudging" on this? I believe it
does...1.5mm is the maximum workable exit pupil for studying detail, and that
is that! But if you are looking at a globular cluster, and need a little more field
of view, to take it all in, and there are so many stars that you really cannot begin
to look at each of them, then there must be room for compromise. That is, you can
look at individual stars, and study the core of the cluster at 1.5mm or less, or you
can "step back" just a little, so as not to take in too much more skyglow, and look
at more of the cluster, but not to exceed about 1.8 or  2.0mm ep. This would be
the tactic to apply in the city. That says, viewing high and low contrast objects in
populated areas is a considerably headier task than at a dark site, where the observer
can indulge the eye and the mind, in the majesty and panorama of wide field views!

  "The eye's sensitivity to light is related to the number of exposed light sensitive
rod cells as the iris expands." There is a puzzle with this: If the iris opens wide
because of dark adaptation, that might seem to introduce another source of
apparent background light, or sensitivity thereto, but as long as the exit pupil of
the telescope and the eyepiece does not exceed the cross section of the fovea
centralis, 1.5mm, the rod cells will not  be triggered. That says, the iris could
open to 3 or 4mm, depending on the age and health of the observer, and on
the amount of stray light around the observing site, and the eye would still
see a relatively dark background in the eyepiece. This is because, the exit pupil
of the optic, in this example, is too small to allow a wide enough cone of light
to stimulate the rod cells, located beyond the area of the fovea centralis--1.5mm,
when looking straight ahead, and not using averted vision. This also suggests
that the brain will not switch to the "surveillance mode," and dampen the ability
to concentrate, as long as the cone of light does not trigger a certain nominal
concentration of rod cells. (There must be a detector, of sorts, that allows for a few
rod cells to be triggered, and not reach a threshold that will do the "switching"
until the number of rod cells stimulated accumulates to several thousand.)

  Issue (5.): A few tips (a healthy observer): 1) Something to try: With eyes closed,
slowly and deliberately, take a few deep breathes. In this more relaxed state, try to
visualize the blackest black. 2) Using both eyes for observing, by switching back
and forth may help maintain an "edge." 3) Eating a balanced meal, and taking a
multi-vitamin supplement about two hours before a viewing session may provide
extra energy. Vitamin C and pantothenic acid (vitamin B5) stimulate the adrenal
glands, and help achieve the most precise actuation and control of the tiny muscles
of the eye. 4) Preparing to view very faint objects by taking a nap or resting in
the darkest room in the house while waiting for a meridian crossing at 2 or 3 a.m.
can  add .5 mm to the opening of the iris, noticeably increasing sensitivity to light.
4b) Conversely, when observing bright objects, leaving a few lights on in the area
will keep the iris and the pupil more constricted, and effectively darken the background
and reduce  the "glow" around bright objects. 5) Sunflower seeds are said to be good
for the eyes, dehydration is not! 6) Deep breathing and other relaxation techniques
help maintain a rested state of mind and body. If the vision centers are rested, and
yet frequently exercised (but not to the point of exhaustion), the precision needed
to see and scrutinize fine detail, at moderate and high image scales, will be as good
as is physically possible. ("Every change in position of the eye breaks down into
thousands of electrochemical impulses. Good health allows each movement to be
made effortlessly, and to the most minute gradation"(Bloom 76). The "fixation limit"
of the eye (i.e., the capacity for following fine detail) will be at its best, and work
"closer" to .4 or .5mm, in the more healthy and rested observer. Therefore, those
physically up to it, will be able to work "closer," and not feel as much fatigue, or
feel so much that .8mm is a real limit.)

(a defect of vision)
  For those with a defect of the eye, such as astigmatism, working with small exit
pupils, may offset the problem sufficiently to avoid the use of eyeglasses, when
looking through the telescope. However, with a larger exit pupil (e.g., 2.0mm and
more, considered a good range for star clusters, galaxies and nebulae), it is likely
that enough of the affected part of the lens of the eye will be in use to cause some
degree of distortion and strain.

  It may be possible to see without distortion (or eyeglasses) at an exit pupil of
about 1.5mm, the ideal range to limit the effects of skyglow, and still allow
reasonably low power and a fairly wide field of view. If the astigmatism is still
not sufficiently minimized to reduce fatigue and distortion, the exit pupil may
have to be reduced to less than 1.0mm, to observe comfortably. For some, and
for various reasons, even at an exit pupil less than 1.0mm, the use of eyeglasses
may be unavoidable. (Rarely are both eyes the same. One eye may do better,
or it may be satisfactory at 1.5 or 2.0mm ep.)

   An explanation--detail and contrast: As the body matures, and with the normal
development and sophistication of the neocerebellum, we learn to move our eyes
in finer increments, first progressing from grade school primers with 18 pt print
and finally, as we mature, to 8 and 10 pt print. To deal with the ".8mm tracking
limit," and work "closer" to the .5mm diffraction limit, the eye must, as best it can,
respond to detail as small as the foveola itself. Deprivation and speed reading
training can be helpful. At the eyepiece, a fast reader can see more at moderate
and high image scales than will a slower reader! This is because of the sophisticated
scanning processes learned and adopted by the motor centers, and because of the
articulations of the neocerebellum (i.e., the fine detail and dexterity center located
on the back of the brainstem) of the more skilled observer and the faster reader.
(Because there is so much to know about the physiology of the eye and central
nervous system, it occurred to me that a good subtitle for this section, Part 8, might
be The Perfect Observer.)

  (Return to the "Guide")   (a proper mind set)
 

Part 9
Finishing Touches
  With regard to the diffraction caused by the secondary support, fewer
and thinner vanes is not the whole answer! In optics, circular obstructions
produce rings of light, while straight lines (vanes), formed as radii, produce
straight lines, appearing as two opposing spikes or sprays of light bisecting
bright objects. If the material used is the same thickness, reducing the
number of support vanes from 4 to 3 will produce 1/3 less diffraction.
However, there will be 6 radial lines, appearing as 3 bisecting, or crossing,
spikes or sprays, around bright objects, instead of 4, appearing as 2.

  Three vanes will induce less total diffraction than four; however, human
consciousness is more comfortable with the symmetry of 4, rather than
6 elements. In psychology, this is about "closure" and balance. Fatigue
develops more quickly when, even at a subliminal level, the brain senses
discontinuity in the image, and even if the image under study is more
accurate than when viewed in a more "closed" pattern, such as one with
4 lines, radiating from a point at right angles to each other.

  Most desirable to the psyche, a circular secondary support will produce
a ring of light, with no visible spikes, or lines, radiating outward from
bright objects. However, circular secondary supports are often made of
thicker stock, and may obstruct more of the incoming light than three-
vane supports. (The distortion produced by a single (straight) vane is even
more disturbing to the central nervous system than that produced by three
or four vanes! And a semicircular vane, though low in diffraction produces
a less perfect and less pleasing image than one which is fully circular!)

  Contrary to all this, and while the nervous system is usually less relaxed
with an image produced by a three-vane spider, the knowledge that a
state of minimal diffraction has been achieved may be so satisfying as to
offset the psychological effects of the discontinuity. This would make the
three-vane spider the best choice over all. (The circular design requires
considerable mechanical skill to fabricate, install and align!)

  A fine mirror or lens (1/8 to 1/16 wave smooth) will be less affected by
skyglow, and reveal the darkest background, but the benefits show up in
other areas as well. With less diffraction, light will converge into a smaller
and brighter point. A faint star that might not be seen in most telescopes
of a stated size may thus be more easily detected. (Higher surface accuracy,
though expensive and painstaking to achieve, lends itself to superior light gain
when up against poor "seeing" and city lights! Of course, the effect less than
ideal! In this regard, a loosely mounted assembly or a poorly fitting adapter
somewhere in the system can cause periodically poor image quality and
endlessly plague what could be a fine telescope!)

Beyond the critical need to have a smooth primary surface, the effect of
any lack of smoothness on the surface of the secondary mirror of a reflector
or refractor will erode the image to about the same degree in both cases.
With the Newtonian system, the secondary is permanent, and the secondary
of a Schmidt-Cassegrain is even more sophisticated and demanding of
perfection, while, with the refractor, going to in-line viewing, to get an
optimal result, though often inconvenient, is always an option.

   (Schmidt-Cassegrain--more)

  Bright objects tend to light up the sky around them! Whatever atmospheric
glow is present is a corrupting influence the optic must deal with, and it
can vary widely, even in the space of a few minutes. There are detrimental
effects related to the state of the art, focal length, field-stop aperture, and
the design of the eyepiece. Further, the 45 degree reflection angle and the
surface imperfections of a diagonal mirror tend to scatter light in the near-
field, especially when viewing bright objects, and especially when mirrored
surfaces are not "squeaky" clean.

  Barlow lenses can scatter light, and taken together, the eyepiece, secondary
and Barlow can compound each other's problems. Worst case: If a Barlow
lens is used with some short focal length eyepieces (shorter than about 12 to
13mm and depending on the manufacturer) internal reflections and related
background illumination (using a reflector or a refractor), may increase more
than expected. That is: some short focus eyepieces seem to produce a less
pleasing and clean image when used with a Barlow lens, but the problem is
not noted off the Barlow. (A Barlow lens with a higher magnification factor,
possibly 3x to 5x, will bring a longer focal length eyepiece up to the same
magnification as a shorter focal length eyepiece, when used with a typical 2
or 2.5x Barlow lens.)

  When using a refractor, and for optical components prone to such problems,
light scatter will be less noticeable while viewing in-line or without a Barlow
lens! Very often, it is the compounding of effects that brings it out. Saturn is
the best subject for checking background illumination, and doing the test
under a dark and steady sky will make any conclusions more valid!

  With conventional and compound reflectors, it may be difficult to identify
the separate components of the illumination surrounding a bright object,
especially on something as bright as Jupiter or the Moon. Example: Due to
the obscuring effect of the sprays of light produced by the spider vanes of a
Newtonian reflector, it may be difficult to tell if a given eyepiece is affected.
In many cases, proper cleaning of all related surfaces will eliminate most
of the problem. (The disadvantages related to light scatter and decreasing
working area, within the barrel of the eyepiece, and with craftsmanship
problems, may be reduced by using a high quality Barlow lens, kept very
clean, with moderate focal length eyepieces, in the 12 to 25mm range.
Contamination of eyepiece lens surfaces is exponentially more noticeable
when a Barlow lens is used. The Barlow lens is a "dust and film multiplier.")

  The advantages may outweigh the disadvantages: When an eyepiece is
used with a Barlow lens there are more optical surfaces for the light to
pass through, but the manufacturing and design problems, typical of some
short focal length eyepieces, especially those with a built-in Barlow, often
make longer focal lengths and simpler designs the best choice when high
power and convenience are desired.

  Any contamination or defect will be more detrimental at high power, and
with conventional short focal length eyepieces, the observer's eyelashes are
more likely to come in contact with, and smudge, the surface of the eye lens.
These are the "rules of residual action." That is, with each step of "increased
scrutiny," the requirement for spotless perfection and craftsmanship increases
exponentially. Thus there will be more likelihood of seeing the effects of
manufacturing defects, design limitations, polishing errors and contamination.

  For this discussion, and, because most of us will ultimately opt for
convenience, it is assumed that a refractor will employ a diagonal mirror or
prism, preferably a mirror, especially in the faster apochromats. Further, the
secondary chosen for either type of instrument must be of the highest quality
available, at a minimum, better than 1/10 wave P-V. The comparisons
mentioned here are made with that in mind! It can be just as difficult to
find a fine secondary mirror as it is to find a fine primary mirror, or lens!

  There are other problems with diagonal mirrors. Most Barlows add some
color (i.e., chroma), but it will hardly be detectable with a reflecting telescope.
However, with a refractor, any error in the Barlow aggravates the spectral
errors of the objective, and if light strikes the diagonal mirror at angles typical
of lenses faster than f/10 or f/12, color shift and light scatter could be more of a
problem.

  Tips: If a Barlow lens is to be used with a refractor, especially a short-focus
APO, the image will be sharper if the Barlow is placed in front of the
diagonal, and the 1-1/4 inch models will probably be more accurate than
the 2-inch models. With the Barlow in front, the light rays arriving at the
secondary mirror are more parallel (less light is scattered with a less acute
angle of incidence), and because that much more of the amplifying is done
before the light strikes the secondary there will be less magnification of
the surface errors of the diagonal mirror. (In spite of the advantages, if the
desired image scale is attainable without using a Barlow lens, there will be
fewer optical surfaces to scatter light and obscure the view!)

  Larger Barlows are probably more likely to add errors because the light
cone has to negotiate its way through more glass. "For the very sharpest
image, any reflecting or refracting component should be as small and as
far from the primary lens or mirror as possible, but not too close to the
focal plane, (the point of focus)!: Getting too close to the focal plane is
more likely to be a problem with refractors and compound reflectors than
with Newtonians and Maksutov-Newtonians. If the focal plane is near
the surface of the diagonal mirror, dust specks, scratches and polishing
errors will be closer to focus, and might be visible in the eyepiece.

  (There is a rule of thumb that says a 1/8 wave primary mirror will
provide about 1/4 wave performance at the eyepiece. This reduction by
half is usually said to be caused by the residual errors on the surface of
the secondary and by the effects of diffraction related to the obstruction
in the light path. However, this rule is only an approximation, and
refinements such as those mentioned here will limit the losses, but both
mirrors should be equal to, or better than, 1/8 wave, P-V, at the wavefront
to get the sum of the limits closer to 1/8 wave overall. (In any optical
system, the sum of the two surfaces will always be something less ideal
than the worst of the two, but not necessarily just half the accuracy of
the primary!)

  Exacting performance is available in both refracting and reflecting
telescopes! In most textbooks, 1/4 wave accuracy is considered the
minimum criteria for acceptable performance. However, even at an
accuracy greater than 1/8 wave, errors in the image can be detected
by an experienced observer. If seeing fine planetary and lunar detail
is important, it follows that a telescope said to provide "diffraction
limited" performance, while of reasonably high quality (1/4 wave),
may not yield the hoped for result, even under the very best observing
conditions.

  For an amateur to determine whether a telescope is "diffraction limited,"
or not, is an area complicated by a number of variables. If a telescope
does not seem to reveal the finest detail for its aperture, it should not be
hastily assumed the mirror or lens is at fault. Any one of the problems
mentioned (i.e., primary collimation, secondary alignment, dirty surfaces,
vignetting, partial obstruction by some mismounted part or baffle, poor
quality eyepiece and loose parts) can cause significant distortions, or
might only add minor errors to the image. The latter category of defect
(a lack of structural soundness), can have varying symptoms. That is,
many telescopes do not work up to their potential, and it is not necessarily
because of a flaw in the mirror or lens. (Because of the complexity and
number of components, even telescopes considered to be the finest are
rarely as good as 1/8 wave P-V for all aberrations, at the eyepiece. When
an instrument is said to be "diffraction limited," consider asking for more
information!)

  Having said that, short-tube, prime-focus and compound systems may be
more likely to be less accurate than 1/8 wave for all aberrations (or it may be
much more difficult to keep them collimated and operating at their best), but
they are meant for special tasks, and may provide remarkable performance
in a more compact and portable design. Further, with apertures greater than
about 10 or 12 inches, it becomes much more costly to achieve high wavefront
accuracies. And even in moderate sized instruments, the effects of fair or
middling "seeing" (the way it is much of the time) can offset the advantage of
a fine mirror or lens when compared to one that is accurate to just 1/4 wave.

  (It's all in the point of view! You may find that with good "seeing," the increase
in transparency and atmospheric steadiness "raises all optics" (i.e., the difference
between good and very good becomes less noticeable--fine "seeing" makes added
diffraction and other weaknesses less troublesome). When trying to track down the
cause of poor or unsatisfactory performance, an evening of very good "seeing"
can provide answers that have evaded discovery for many months. Even marginal
coatings and eyepieces with many elements may produce fine images and become
minor issues when the sky "opens up." The "flip-side" is, when the atmosphere
returns to its usual state of turmoil, the more complex and less ideally coated
lenses do, as has been suggested in other sections, seem to suffer more. If in doubt
as to the quality of a lens or mirror, "it only has to work well once to be a good
optic." (Ultimately, the quality of the "seeing" conditions is more important than
subtle differences between telescopes.)

  Measurements for smoothness, taken "peak-to-valley" (P-V) are the most
exacting and revealing measure of performance. With this method, the
smoothness at every measured point on the surface is compared to every other
measured point, while RMS (root mean square) measurements are averaged
and more localized, RMS is generally 5 times less specific as an expression of
quality than is "peak-to-valley." A 1/16 wave P-V lens or mirror may also be
described as 1/80th wave RMS. If a lens, a mirror or a complete optical system
system is said to be 1/30 wave (RMS), it will probably be 1/5th or 1/6 wave
peak-to-valley.

  For the highest confidence, all measurements should be taken and expressed
at the wavefront, and several thousand points should be tested. (Some
advertised specifications are for accuracy at the mirror's surface. Dividing
measurements taken at the mirror's surface by "2" yields peak-to-valley
accuracy. In this example, errors claimed to be 1/16 wave at the mirror's
surface would actually produce a wavefront that is 1/8 wave P-V.)

Usually, the manufacturer's specifications tell the story, but star-test results
that seem to vary from the textbook illustrations, for an ideal out-of focus
diffraction pattern, by what seems too much to be acceptable, may have
very little effect on the in focus image. For example: It is possible to get very
good performance from refractors, Maksutovs, Schmidt-Cassegrains, and
Newtonians that have slightly turned edges, 25% secondaries and slight
under or overcorrection. The visible result with some aberration may be
indistinguishable from that yielded by a lens or mirror possessing a near
perfect wavefront, assuming the same specifications and treatment. If there
is a noteworthy defect in the image, the cause is probably somewhere else.

       *   *   *    (end text)
 

  (Return to the "Guide")    (Schmidt-Cass. "Finishing Touches")
 
 
 
 
 

Addendum

  Optical testing  (Lunar and planetary observing tips--testing for sharpness
   and accuracy: "terminator test," "scintillation test" and "snap technique")

           _______________________________________________
 
 

Appendix

Terminology

central fixation--is about the "self" and what it feels like to have a point of view.

"Diffraction limit"--a terminal limit: an optical event beginning at a .8 mm exit pupil, and ending at a .5 mm exit pupil. (If the only thing affecting performance is diffraction...there are essentially no visible signs of optical defect.)

fixation aversion--is about essence and the fragile nature of existence.

  (The "fixation limit," or "fixation potential," of the eye and nervous system: the capacity for following movement and analyzing fine details, has to do with the speed and accuracy with which the eye scans, and depends on the resilience of the motor centers, and their ability to track incoming stimuli. (In psychology, fixation is a behavior.)

point source paradigm--where virtual zero =s .4 mm, 86% of the energy is in the central peak, diffraction is the way of all things, and the universe is formed in "time domain compartments," as "multiple singularities" (re: A Collision of Two Infinities-- Bloom -- this site)

Resolution and resolving power--resolution is about detail and what you see, resolving power is about diffraction and angular displacement...it is about what you don't see.

"Resolution limit"--("point of optimal scale and sharpness"--characterized as a pdr) for a given aperture, occurs at 32x per inch (i.e., .8 mm exit pupil), and appears in conjunction with the tracking limit of the eye.

The "scanning limit" of the eye is a function of the charge/discharge period of the neuron (.002 seconds), and is the "determination" with which the motor centers and the neo-cerebellum position the eye (In neurology the "scanning limit" relates to action potential, and in psychology, it equates to tenacity, as a subset of curiosity.)

"tracking limit," or "optimal scanning range" of the eye--.8 mm exit pupil, which also happens to be (i.e., coincides with) the point of diminishing return (i.e., an effect of diffraction), in any optical system, such as a telescope. Both "events" happen to be twice the size of the foveola--.4 mm x 2!) (physics)

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History:

 This is a continuing work, and periodically, updates and new information
will be added. This is the latest nine part version. "The Perfect Telescope"
was formerly titled "Is Diffraction Ever a Good Thing?" The original series
was released during 1997 in The Meridian, the newsletter of the SFAAA,
and the original versions of what are now Parts 1, 2, 4, 7 and 9 were published
in Amateur Astronomy magazine, issues 16, 18, 20 and 21 in 1997, 1998
and 1999.

(This project was possible because of information provided by professional
opticians and knowledgeable amateurs. Special thanks to Paul Schofield for
contributing to the effort.)
 

   (Last entry: 11-07-06)
 

Good seeing,
Gary M. Bloom
 
 

Source material and recommended reading: W. H. Bates. The Cure of
Imperfect Sight by Treatment Without Glasses.New York: Central
Fixation Publishing Co., and Burr Printing House, 1920. Gary Bloom.
As Well as Nature Intended,copyright 1999/2006, formerly Decompression
Therapy: A Weapon Against Chronic Illness,copyright 1997, pp 69-108,
253-254. Gary Bloom. Under Southern Skies: 1950 through 2000,
copyright 2001. David Bruning. "Test Your Scope's Optics." Astronomy.
Waukesha, WI: Kalmbach Publishing Co. July 1994. pp 56-59. Charles
F. Capen Jr. "Filter Techniques for Planetary and Lunar Observations."
Encyclopedia Britannica. 1976. Micropedia. "Rayleigh scattering."
VIII: 439. Encyclopedia Britannica. 1976. Macropedia."Quantum
theory of radiation/Radiation laws." 6:653. Alan M. MacRobert.
"Secrets of Deep Sky Observing." Backyard Astronomy and Sky and
Telescope.Belmont, MA.: Sky Publishing Corp. Alan M. MacRobert.
"Star-Test Your Telescope" (An article based on H. R. Suiter's book,
Star Testing Astronomical Telescopes). Sky and Telescope.March 1995.
pp 42-47. Al Nagler. "Choosing Your Telescopes Magnification"
Sky and Telescope. May 1991. Mark D. Russell. with Roger W. Sinnott.
"Telescopic Performance on the Planets." Sky and Telescope.March
1995. pp 90-93. H. R. Suiter. "Diagonal: Fad and Fashion." Amateur
Astronomy.Publisher: Tom Clark, 5450 NW 52 Ct. Chiefland, FL. #17,
spring 1998. John Vogt. "Meade's 7-inch Maksutov-Cassegrains."
Sky and Telescope Nov. 1996. pp 48-51.
 

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