(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 vi