A logical approach to the analysis of your optical system will help in identification of astigmatism and determination of the cause. Once the problem is identified, curative measures may be undertaken.

The star test and the Ronchi grating are the preferred methods for evaluation of astigmatism. Can you find radial lines (pointing toward the center of the field) on either side of focus during the star test? Tangential lines on either side of focus? Is the out-of-focus star image circular? Does the Ronchi test show any hint of an "S" shaped curve as focus is varied?

Assuming you find astigmatism (most finders will show astigmatism if you can't find any in the main tube), the next step is to determine the root cause. If the out of focus star image assumes a triangular shape (as opposed to a dash or circle) the astigmatism is likely coming from poorly supported optics or from "pinched" elements. Is it from the objective? The diagonal? The secondary? The eyepiece? Your eye? Start with your eye and work successively on each optical element in turn.

With careful attention to a star, imaged as a dash on either side of focus, rotate your head. Does the axis of the dash change? If so, the astigmatism is in your eye. The fully dark adapted eye is much more sensitive to astigmatism than a contracted pupil during the day. Switch to a higher power eyepiece- astigmatism in the optical system will be more apparent at higher power. Try the other eye (they may differ), paying careful attention to the axis of the dash and the axis of your head relative to the field of view.

Next, check the eyepiece. Rotate the eyepiece and see if the axis changes. If it does not change the problem may still be with the eyepiece (remember this is a symmetric aberration, if residual). Try other eyepieces. Does it (the dashed image) vary? Most eyepieces will show some astigmatism with instruments of F/5 or faster. Remember astigmatism MAY be much less well seen in the center of the field of view, be it from the objective, the eyepiece, or the combination. The following exercise is difficult, but may be illustrative.

Astigmatism is most often concentric about the center of the optical axis- be it in the objective or eyepiece. Most often what we observe as astigmatism is the combined effect of astigmatism of the eyepiece and the telescope. There are two methods effective in "de-coupling" the effects of astigmatism in the eyepiece from astigmatism in the system.

In the Newtonian start with a well-collimated system, use the primary adjustment screws to bring a centrally located star to the edge of the field. Is the aberration unchanged? Switch to a high power eyepiece. With the image located in the center of the eyepiece (NOT, now, on the optical axis of the primary) the astigmatism from the eyepiece will be eliminated and what you are left with aberration from the system.

Separation of astigmatism in the eyepiece from astigmatism in the system can be accomplished by building a medium to high power eyepiece with the optics mounted in an eyepiece tube off-center, so that the field of view of the eyepiece is centered on the edge of the field of view of the telescope. This of course works on any system with equal ease. As the center of the eyepiece has essentially zero astigmatism what you now see is astigmatism from the system. The same eyepiece is useful for other off-axis aberrations as well. Such an eyepiece can be made from an existing eyepiece or a pair of 10mm FL achromats of 10-12mm diameter can be employed.

Watch for a while. Things will vary! Your telescope is NOT THE SAME FROM NIGHT TO NIGHT.

If the astigmatism is not coming from your eye, or the eyepiece, the next suspect is the secondary- particularly if it is a mirror. The secondary is likely the cause in the Newtonian, and rarely the cause in a catadioptric. Why should this be?

For a plane mirror, as in the secondary of a Newtonian or some star diagonals (those without a prism), a departure from perfection is likely a symmetric pit or hill around the center. If the incident ray is perpendicular this results in spherical aberration. HOWEVER this same departure from perfection when the incident ray is at 45 degrees, as with a secondary in the Newtonian, becomes significant astigmatism!

Astigmatism is easily introduced into the secondary by the mounting of the secondary. Does the holder grip the edge too tightly? Is there too much cotton backing behind the mirror? Take the secondary holder apart and re-assemble. Use a light touch- nothing should be tight. Use just enough support to keep things from falling apart. Astigmatism from the secondary in a catadioptric is not likely polished into the surface, as this would likely present itself as spherical aberration. However, stress from the holder, transferred to the secondary, will distort the mirror.

If you see astigmatism in a refractor, or a catadioptric, try using the instrument without a star diagonal, as this is a common source of astigmatism.

If you think the problem comes from the primary and is polished into the surface the aberration will still be seen on axis. Remove the primary from the cell and rotate the mirror by 120 degrees, rebuild and re-examine the stars. Has the axis changed? If so, the primary is at fault. If the images of an out of focus star are triangular in a Newtonian the primary is poorly supported and the mirror sags over a three-point suspension (common with thin plate glass mirrors) or is pinched by too tight mirror clips.

In a refractor the elements in air spaced objectives may be rotated relative to each other, producing astigmatism. Spacing may be improper, or one element tilted. The elements may be off-center. Take the cell apart and look for the spacers (if air spaced). Do the lenses center well in the cell? Are the pencil or other marks, made by the craftsman, aligned? Refractors are subject to showing astigmatism from a number of sources. Also, coma in the Newtonian will hide astigmatism, while refractors, corrected for coma, may show a degree of astigmatism that goes undetected in the Newtonian.

Is the axis of the astigmatism related to the horizon? If the long axis of the out of focus star image is parallel to the horizon, or at right angles to it (on the other side of focus) the objective may be sagging under it's own weight. Rotate the

tube. Is the orientation still related to the horizon? If so, gravity is the culprit. Point the telescope toward the zenith. Is the aberration gone?

If the primary is a mirror take the mirror out of the cell and re-assemble. Go easy on the tightening of screws, etc. Re-assemble and retest. If the problem persists you may need to consider remounting the primary. Rarely is the problem polished into the surface! If it is, however, the mirror must be re-worked or replaced. If the mirror is glued down you have nothing to lose by breaking the seal and remounting optics!

Wow, this has been tough! Astigmatism is the most difficult aberration to come to grips with. Subsequent articles will deal with the remaining four Seidel aberrations and then with chromatic aberration. Aberrations are rarely seen in isolation, and astigmatism is closely associated with field curvature, so we will return to this topic in the future.

No telescope is free of aberration. Designers work hard to control those of greatest importance in any given application. We must work hard to keep aberration from creeping into our telescopes by careful attention to mounting the optics and maintaining collimation.

Explore astigmatism with ABERRATOR2.4. Residual astigmatism can be explored by use of ATMOS4, a very friendly telescope design program for Windows written by Massimo Riccardi and available on CD for $60. The spot diagrams and graphs presented here were generated by ATMOS4.

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I have no real goal in mind today, so here's some food for thought. A few years back I had made a list of 'things to tell beginners', every one of which was false. Many of those items raised questions. Here's some of those and some new ones, but this is all true stuff.

Over ten full moons would fit between Merak and Dubhe, the pointer stars of the Big Dipper. Also, the moon occasionally occults the Pleiades, but cannot possibly cover all the stars at once. The moon moves eastward with respect to the stars it's own width in one hour. That is, about 1/2 degree per hour. The full moon is over 10 times brighter, overall, than at first quarter.

The planet Jupiter, magnified about 30 to 60 times in your scope, will look as large as the moon to the naked eye. Saturn would require twice that, and Mars at the coming opposition about 100X. Really. The moon is about 1800 seconds of arc; Jupiter averages about 40; Saturn, and Mars this June, about 20. In a perfect scope on a good night, the moons of Jupiter will show disks in a 3" refractor. Cassini's division in Saturn's rings is easy in a 60mm refractor, and is in no way a test of optical quality. If not visible or difficult to see, either the seeing is dreadful or the scope is a hoser.

Don't believe everything you read about certain objects requiring a scope of large size. Roger Gordon has seen the companion to Sirius with a 3.5" Questar. Alan Daroff of the Willingboro club has seen the companion and also the moons of Mars with a 6" refractor from Philadelphia. Achmet has seen 14th mag stars with a 4.5" refractor, also a 12.8 mag planetary form Stella-Della's field. In Bob Jackson's home-made 10" f/6.7 reflector, several people have suspected spokes in Saturn's rings, also at the 2000 Stella-Della. Antoine, while one of the nicest people you've ever met, is after all, French, and cannot find the moon. (editor's note...no idea who added this)

Most everyone has seen the Trapezium in M42, as four stars in a lopsided quadrilateral. How many have tried to see the stars E and F? Achmet has seen E easily with the 4.5", and Scott Ewert of the Willingboro club can see F with the same scope.

From a good sky site, the North American Nebula is naked eye. As are the following objects. M35 in Gemini, M33 in Triangulum and one or two of the Auriga clusters are difficult. The Andromeda Nebula (M31), Lagoon (M8), Orion Nebula (M42), M22, M5, the Hercules cluster M13 and the Wild Duck (M11) in Scutum are medium to easy. Many clusters in Sagittarius and Scorpius are visible as hazy patches in the Milky Way. M3 should be visible on a really good night, but I've never tried. The Double Cluster (chi and h Persei), the Beehive and Coma Berenice resolved into stars are fairly easy. The Pleiades (M45) is an obvious sight. There are others waiting to be seen if one looks.

Ach has no idea of how many objects are visible in binoculars. Has anyone in the club done a Messier binocular certificate? Perhaps they will advise me. I have seen many galaxies, some planetaries, and clusters everywhere through 10X50's. Larger binocs will show many more, especially if mounted.

There are reports of Jupiter's satellites being seen naked eye, usually be young children with no preconceived idea. Also, Venus as a crescent. Try also splitting Epsilon Lyrae, about 6 minutes apart. Pluto has been seen in a 4 1/4" reflector.

The optical quality of the eye has been likened to the lens of an old Bullseye lantern. Not only is it optically poor, but it also suffers serious chromatic aberration, yellowing of the lens, damage to the retina etc. etc. These are all filtered out by the brain.

Looking overhead while standing and bending the neck limits blood flow to the brain, and also causes tension. The estimated loss of sensitivity approaches one full magnitude. Look overhead by lying on a lounge chair or whatever. Tension, caffeine, nicotine, exhaustion and such limit sensitivity also.

Walter Scott Houston, of "Deep Sky Wonders" fame, claims dewing of optics is not noticeable on the optical surface until you have lost almost one full magnitude. Naturally, this will also cause loss of clarity. The moral is obvious; use dew heaters.

Contrary to popular belief, low power may not be best for viewing faint objects. Especially small galaxies and planetaries. Increasing the power not only will improve contrast but will enlarge the target, allowing the brain to interpret the faint glow as real and not to be dismissed as imaginary or below the threshold. Ach finds that sometimes prolonged observation makes the target easier, sometimes more difficult. I have no idea why. Perhaps it is drug abuse or 'imaginary vision' or the ever popular 'peripheral mirage'.

Deep breathing (don't hyperventilate) can add one or two magnitudes to your limit. Jogging your scope can increase the apparent sensitivity of the eye, which is very adept at picking up motion. A faint fuzzy may become visible with this technique. Peripheral vision can add up to two magnitudes in some people. This is due to the increased density of the rods away from the fovea, which are sensitive to low light, but are not color sensitive. The fovea is packed densely with cones, which are color receptors, but much less sensitive to light. This accounts for colorful daytime objects appearing as shades of gray at night, when almost all vision is by rods. It follows that objects away from the center of the field of view will look brighter than when centered.

When comparing objects of different colors or on different lines of sight, the Purkunjie effect takes over. This is characterized by several oddities. If two apparently equally bright stars are alternately observed in the center of the field, they will look unequal if one is centered and the other is at the edge. Likewise, if one is above the line. Staring at a bluish star will make it seem to become brighter compared to a red one. This is a fatigue effect also. To fully understand the effect, read the literature. Achmet only understands it a bit, and is confused by big words.

'Blinking planetaries' are an effect caused by the peripheral sensitivity of the eye. If one stares at the central star the nebulosity may disappear. If one looks a bit off center the star disappears amid the nebulosity.

The Orion Nebula and some planetaries look green to the observer, but appear reddish in photos. This is due to different sensitivity to color, the eye being most sensitive at low light levels in the region of 5300 Angstroms (530 nanometers for you metric oddballs). This is in the greenish yellow. At high light levels, the peak is about 5550 Angstroms. Much of the light in planetaries is emitted by the forbidden lines of oxygen in this region of the spectrum, only possible in near vacuum conditions not normally achievable on Earth, even in the laboratory.

The Airy limit of your scope, for separating double stars is about 4.5 arcseconds divided by the aperture in inches. Thus, Achmet's 4.5" will just split a double with a separation of 1 arcsecond, provided they are about equal and not too bright or dim. This limit has little to do with seeing fine lines, such as lunar rilles or planetary detail. Tests show a dark line about one tenth of this limit is readily visible against a light background. So a small high quality scope will show far more detail on planets than the theoretical limit.

There is no evidence of variance among normal eyes as far as resolution. To show as two objects, the light of a double star must fall on separate rods or cones. Apparently, nature has placed the spacing of the receptors at the resolving power of the eye lens. However, adequate power must be used for the eye to separate the double. The normal limit is 3 minutes of arc apparent separation, and 6 minutes of arc is easier, so a power exceeding 30 to the inch is necessary, while about 50 to the inch is better. Sources say the eye reaches its resolving limit at about 32 to the inch. Thus the clearest, sharpest images would be revealed at about 120 power in a 4", and about 375X in a 12.

Ordinary light sensitivity can vary from one person to the next enormously. Poor clarity of normal vision does not necessarily mean you will see less through the scope, as the narrow cone of light at higher powers will limit the negative effects of defects in the eyes lens. You may find that a person who sees fainter stars naked eye cannot see telescopically what the other with poorer naked eye vision is capable of achieving.

Airborne heat waves average somewhere around 4" to 10" apart. Small scopes will show a target moving physically in the field with little blurring, while scopes larger than the wave size will be blurred. This is why a small scope will show a clearer image more often than a large one. With equal optical quality and good seeing it is absolutely impossible for a small scope to outperform, on contrast and detail, a large one all the time. Achmet has heard often that a small scope, say a 6" refractor, will show more detail on the planets than a larger reflector. If the reflector has a minimal secondary and is otherwise in good shape, the laws of physics take over. Statements to the contrary are camel doo doo. Achmet becomes perturbed when argued with on this one.

The sky is never totally dark on a clear night. The air itself has some glow, as does the upper air from the solar particles and electrons trapped in he magnetic field. The unresolved glow of countless stars and galaxies also light up the sky. The interplanetary dust (cause of the Gegenschein and Zodiacal light) surrounding the sun is always present.

The moon can cause the same phenomena as the sun in air and water droplets, but much subdued. Take a look some hazy night when the moon is near full. There can be a 22-degree halo, arcs and a circumzenithal ring, along with rainbows, moondogs and spectral glows at cloud edges.

I'm rambling again. More later. Go out and observe. To quote the hockey legend Wayne Gretzky, "I have never scored a goal on a shot I didn't take". Achmet has never seen a faint fuzzy from indoors.

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COMA: A comet like distortion of the image of a star resulting when an oblique bundle of light enters an optical system.

APLANATIC: An optical system corrected simultaneously for spherical aberration and coma.

Illustration 1 shows a widely separated double (1.92 arcseconds) as seen in a 6 in Newtonian. On the right the same pair is shown with one-wavelength of coma. One wave sound excessive? Well, maybe a little to make a point, HOWEVER at about 75% of the way toward the edge of the field of view of a 6" F/6 this is exactly what happens in a perfect objective!

Coma, as with astigmatism, increases toward the edge of the field and is absent in the center. However, it increases directly with the distance, while astigmatism increases with the square of the distance. Never the less, coma dominates in the Newtonian. When it comes to the F/value however, a change here results in an increase by the inverse of the f/number squared. Consequently, short focus Newtonians suffer greatly from this aberration. Only at about F/8 is most of the field acceptable. Illustration 2 shows the relative amounts of coma at f/4.5 and f/8. Of course, much of the outer portions of coma are not seen in dim stars, but keep in mind this same light is lost from the central disc. Coma makes measurement of stellar positions particularly problematic.

Illustration 3 shows some characteristics of pure coma.

Interestingly, coma can be corrected in the Newtonian by use of an aperture stop located at the center of curvature (the so-called lensless Schmidt- any astrophotographers interested in trying this design?). In some designs the use of a properly placed stop may make the system APLANATIC, but NOT so the Newtonian. The lensless Schmidt suffers from spherical aberration.

Most eyepieces are well corrected for coma, and some can be designed to correct for coma in the objective. Supplemental lenses help reduce coma (coma correctors) enough for photographic application. At low power they often provide acceptable views in fast systems. The best we can hope to do in the Newtonian is keep coma in it's proper place- at the edge of the field of view!

Keeping coma out of the way as much as possible means careful collimation. Most of us like to think in terms of 1/4 wave optics (this discussion ignores other shortcomings). On a ten-inch f/4.5 instrument this amounts to only a few times the diameter of Jupiter at opposition! Illustration 4 shows the diameter of the 1/4 wave limit for f/4.5 (central SMALL circle) as well as f/6 and f/8 limits! Can you keep your scope this well aligned?

Illustration 3) One-quarter wave limits to scale. The central circle (not labeled) is for F/4.5. Can you keep your optics this well aligned? Of course, F/4.5 is generally not used for planetary work (but how about some of these guys with CCD's and fast systems!). While evident coma will NOT be seen extending this close to the center (the tail of the coma is dim), coma still represents loss of light (limiting magnitude), loss of contrast (and resolution), and prohibits astrometry. Keep in mind that at any given F/Value ALL paraboloids suffer with the SAME amount of coma. Use of 2-inch eyepieces shows more coma.

Illustration 4) Basic parameters of pure coma.

Illustration 5) Coma results when light strikes a parabolic mirror at an angle and is ABSENT in the center of the field of view. Spherical aberration results when the mirror is left as a sphere but is present over the ENTIRE field.