Accumulated Optical Problems

15.1 Breaking the Camel's Back

What you have been shown thus far is how the individual aberrations and transmission variations can affect the image. More important, however, is the way minor problems add up. "The wobbly stack" of Fig. 3-1 shows how many errors accumulate as a collection of filters. Even if each filter is relatively unimportant, the total filtration could render the image fuzzy and indistinct.

The concept of modulation transfer outlined in Chapter 3 presented a single standard around which we could rally. By defining optical quality as the ability of the system to preserve contrast in an image, many disparate optical problems were compared on an equal footing.

As each optical problem was discussed, it was assumed that the single error was the only difficulty. Of course, this is nonsense. Like wolves, optical problems travel in packs. The expression "maximum tolerable" was used in earlier chapters to indicate the worst amount of a single error that can be endured. Unfortunately, any further loss of imaging quality, whether it was derived from that particular error or not, causes the MTF curve to sag even lower.

For an aperture troubled by acceptable amounts of several errors, let's calculate the ability to preserve contrast as each successive optical problem is piled on. This will show, as no individual aberration section could, the deterioration of optical quality as an accumulation of small weights. Eventually, the modulation transfer function collapses under the load. Ironically, we will see that the inadequacy of imaging performance in our example is not caused by any one error on the glass. Instead, poor imaging generally results from the summed effects of several errors, including poor telescope alignment and the unavoidable deterioration of atmospheric conditions.

The optical problems of Table 15-1 are sequentially added to a perfect aperture. The example pupil is not unusual and may even be considered better than normal. The total errors in the first column do not add up straightforwardly, so the root-mean-square deviation is shown as it accumulates in the last column. The amounts of cell pinching and misalignment seem excessive, but these errors do not compare well with the ^-wavelength Rayleigh criterion. Because they are more limited in area than correction mistakes, they have to have a higher total value to result in the same degradation. All of these errors are about equally bad, and none would significantly damage optical quality by itself.

Table 15-1 Aggregate errors in wavelengths




of each


RMS error

25% Obstruction








Cell pinching












Note that this aperture is not affected by a turned edge, zones, astigmatism, or surface roughness. In fact, it would bench test very nicely, with only l/5-wavelength undercorrection error. Warping is an important aberration here, so we might think of this aperture as one of the thin-mirror Newtonians common today. The value of misalignment is consistent. These fast instruments are difficult to keep collimated and many of them routinely are used in a state of poor alignment. A misalignment aberration of 0.3 wavelengths, when appearing alone, still reduces the contrast less than % wavelength of spherical aberration. The RMS deviation in the last column points out how some of the aberrations cancel others. For example, the misalignment appearing alone would affect the RMS deviation by a little less than 0.07 wavelengths.

The stacked MTF curves appear in Fig. 15-1. Only one curve for each asymmetrical aberration is shown, all for the same orientation of the target bars. Each optical error degrades the image slightly, some seeming to be stronger at some spatial frequencies than others. In fact, the particular mix appearing in this example appears to be complementary. The spherical aberration wipes out contrast at lower spatial frequencies (around 0.2 maximum) while the misalignment acts more strongly at medium spatial frequencies (0.5 maximum). The boxes represent an otherwise perfect aperture that has a defocusing aberration of 0.4 wavelengths. This single aberration follows the lower-limit envelope fairly well.

Surprisingly, this diagram represents the typical operating condition for a large astronomical telescope. The choice of aberration amounts in

Spherical Curve
Fig. 15-1. Filtering of a realistic aperture. The curves show the filtration as the aberrations are successively added.

the example has been especially generous to air turbulence. According to material presented earlier, the chosen amount of turbulence would rate a high 8 to low 9 on Pickering's "seeing" scale.

Star tests are shown in Fig. 15-2 as these optical problems added one-by-one. Each difficulty is not too much worse than the frame above, but the bottom row is considerably poorer than the first row.

Peter Ceravolo has made a well-calibrated set of 6-inch (150-mm) f/8 mirrors having peak-to-valley correction errors of 1, 1/2, 1/4, and 1/10 wavelength. When he set them up side-by-side and had observers rate them, he noticed that people had no trouble telling the 1 and V2-wavelength correction errors from the better pair, but had a hard time distinguishing the V4-wavelength mirror and the nearly perfect one (Ceravolo et al. 1992).

Based on the calculated example above, we can speculate on the reasons for this failure to discriminate a nearly perfect mirror from a barely acceptable one. Ceravolo's telescopes were probably less troubled by misalignment, pinched optics, or obstruction than by turbulence. Terence Dickinson rated seeing at 7 out of 10 in one such session. When we consult the turbulence material in Chapter 7, we can estimate that a "seeing" of 7 induces an aberration somewhere near 0.10 wavelengths RMS. Recall that :/4 wavelength of correction error is about 0.075 wavelengths RMS. The lack of a visible performance difference between the better mirrors could have occurred because the contrast degradation was dominated by the seeing. Not until the spherical aberration became big enough to compare to the turbulence-generated roughness was the difference easy to perceive.

Spherical Aberration Central Obstruction

The images of the aberrations in Fig. 15-1 are shown as each additional difficulty is added.

Figure 15-3 shows focused examples of these correction errors with the turbulence aberration added (assuming no other aberrations contribute). A 20% obstruction is reasonable for a 150-mm f/8 Newtonian.

Place this figure at some distance from your eyes and try to perceive the difference between 710-wavelength and 74-wavelength image frames. Keep in mind that the turbulence patterns continuously change. The modulation transfer curves appear in Fig. 15-4. Turbulence is sufficient to corrupt the excellent optics of the 710-wavelength mirror and it dominates the correction error of the 74-wavelength mirror. Only the lower quality mirrors are so poor that spherical aberration overpowers turbulence.

15.2 Fixing the Telescope

In the absence of hard information, people tend to concentrate on one of the telescope's suspected optical difficulties and blame it for everything. Mirror-making enthusiasts, for example, go to extraordinary lengths to figure ultra-precise optical surfaces. They know optical fabrication, so they see all error in terms of improperly shaped surfaces. People who assemble their telescopes from prefabricated parts deal exclusively with telescope design. Some zealously reduce the size of the secondary obstruction. Others attempt to reduce the spider obstruction or at least mask it by bending the vanes. A few become specialists in the arcane tricks of baffling or try to seal the tubes of their reflectors with optical windows. Many suspect their telescope isn't adequately collimated and focus their primary attention on alignment.

The lesson of Fig. 15-1 is that no optical problem is all-important nor can any problem be neglected entirely. Each difficulty deserves an appropriate response, with the important word being appropriate. Each suspected error deserves some attention, but no error must be emphasized to the exclusion of others. More to the point, no problem should be emphasized so much that its cure damages good operating characteristics of the telescope.

Also, we must think about the type of observing as well as the errors. Specialized observing situations exist where a little spider diffraction, mi-croripple, or a few flecks of dust make a difference. In other cases, they don't matter much at all. Deal only with real threats.

If you mask your mirror to reduce a turned edge, be sure also to carefully baffle the instrument as well. After all, the image doesn't care about the source of the spurious light. One of the most neglected steps is a careful baffling of the final focuser tube, either by a series of shallow rings or by threading. (One clever manufacturer achieves this baffling by fitting a coiled

Fig. 15-3. A model of Ceravolo's four mirrors if they are used in the presence of atmospheric turbulence errors amounting to 0.1 wavelength RMS. Obstruction was arbitrarily chosen to be 20%. The aberrations caused by surface errors alone are in the left column. The other columns contain examples of fractally-derived turbulent wavefronts added to the correction errors.

Fig. 15-3. A model of Ceravolo's four mirrors if they are used in the presence of atmospheric turbulence errors amounting to 0.1 wavelength RMS. Obstruction was arbitrarily chosen to be 20%. The aberrations caused by surface errors alone are in the left column. The other columns contain examples of fractally-derived turbulent wavefronts added to the correction errors.

Spatial Frequency Mirror Telescope

Fraction of maximum spatial frequency

Fig. 15-4. The MTF curves of spherical aberration coupled with turbulence-induced roughness of 0.1 wavelength RMS.

Fraction of maximum spatial frequency

Fig. 15-4. The MTF curves of spherical aberration coupled with turbulence-induced roughness of 0.1 wavelength RMS.

spring inside the tube.)

Pay attention to everything visible from the inside of the focuser. Can a bright star just out of the field of view contaminate the image with internal reflections? Is your Newtonian tube long enough to prevent distant street lights from adding glow to the image?

If each of the degradations appearing in Fig. 15-1 is cut in half, you can derive an enormously improved image. Certainly, alignment tops the list of offenders, but if the telescope is aligned, consider the job only partly finished. Secondary size is important, but some of the small sizes suggested in the literature (10% to 15% of the aperture) can be too demanding. By reducing the secondary obstruction to 20% or below, you have climbed well up on the curve of diminishing returns. The important thing is that you have addressed each problem in turn. If each MTF degradation is boosted slightly, the net gain can be appreciable.

A solution to a lower MTF that may not be obvious to some readers— and to others may seem like cheating—is to obtain a larger telescope. Recall that the maximum spatial frequency (in units of cycles/angle) is D/X. Hence, if Fig. 15-1 depicts the response of a 400 mm (16 inch) reflector, we can see that it delivers contrast about as well as a perfect unobstructed aperture one-third to half its size. That means it's behaving about as well as the finest 6-inch unobstructed telescope.1 In fact, a 16-inch reflector

1 differences caused by the atmospheric turbulence scale, changes in eyepiece performance at lower focal ratios, and brighter images mean that performance won't be precisely duplicated.

possessing only those aberrations depicted in Fig. 15-1 would be judged an excellent telescope for its size. Therefore, if we are troubled by the performance of a small telescope, we can accept similar degradations in a larger aperture and still come out ahead (Zmek 1993). Using such a steamroller method to cure errors may not be subtle, but it's effective. Anything that results in a better image is legitimate.

Many issues having nothing to do with design or optical quality affect the performance of the telescope. For example, ask yourself if you have properly dealt with obvious things like obtaining a smoothly operating focuser before you ever consider obscure items like minimizing obstruction.

Some instruments are so shaky that one touch on the knob sends the image into wild gyrations. Such telescopes cannot be focused using common intuitive hand-eye coordination. Other telescopes are solid enough, but have focusers so tight and hard to turn that an observer is forced to wrestle with them. Some focusers are lubricated with a particularly heavy grease that stiffens in the cold.

No amount of optical perfection can improve a telescope that cannot be focused. No matter how much you have reduced the obstruction, carefully aligned the optics, or baffled the tube, the image of a poorly focused instrument is still substandard. Figure 15-1 demonstrates this principle in a backhanded manner. The little boxes were intended to show how simple defocusing mimics the aggregate curve, but the implied message is that defocusing alone is enough to destroy the image.

Telescopes are a mature technology. Severe modifications are probably mistakes. Yet a careful tweak here and there, as long as it's not excessive, can ensure that your telescope operates as well as it possibly can. It will probably even work better than you would have believed before you started.

15.3 Errors on the Glass

Errors polished into the glass are permanent. Things like spherical aberration, turned-down edge, or ground-in astigmatism cannot be adjusted out, nor can the user just wait, as in atmospheric or cooling effects. The telescope will never be able to perform adequately.

Glass errors demand sober thought. Say you have inexpensively obtained a fast, thin-mirror altazimuth reflector, a "light bucket" having low to medium magnifications as the primary purpose. You cannot possibly expect crisp Airy disks and clearly defined diffraction rings. Few would want to pay for the optician's time needed to obtain such perfection in a large instrument, and few living under typical skies could often make use of such perfection. An optician cannot give an optical surface a great deal of singular attention without charging an enormous amount of money for the service. The time required to figure mirrors to the diffraction limit increases explosively with aperture or low focal ratio. Large and fast mirrors have both in abundance. This large telescope will not give razor-sharp planetary views, but it should at least perform well on the objects it was meant to observe.

If you have obtained a general-purpose telescope of moderate focal ratio and moderate aperture, however, you have a right to expect reasonable performance whenever seeing allows it. Before complaining to a manufacturer, star test the telescope again under different conditions. Make absolutely certain that the telescope is aligned and that the error doesn't originate with the eyepiece. Determine which optical component produced the error. If at all possible, try to see a star test on a good instrument before you judge a telescope as bad. Either stop down the offending instrument with an off-axis mask or perform the star test on a small or slow telescope likelier to give a nearly perfect result. Don't fully trust spherical aberration estimates gathered under rapidly changing temperature conditions.

If, at the end of all these checks, you are still convinced that the telescope has unacceptable optics, contact the manufacturer. Don't waste time discussing your optical suspicions unless you are very sure. Telescope makers can draw on reserves of confusing jargon unavailable to you. Unless you are very knowledgeable, such terminology will soon have you gasping like a landed fish. In your complaint, merely indicate that the telescope is bad. Clearly and carefully explain that the instrument does not focus to a tight spot and say that you are not pleased with the product.

Becoming angry in your dealings with makers serves no purpose and may be contrary to your interests. Always follow phone calls with written correspondence. Few manufacturers knowingly offer poorly made telescopes. Most will work with you until you receive satisfaction.

15.4 Testing Other Telescopes

Once you become familiar with star testing, nothing prevents you from evaluating every instrument you come across. Such practice will help you to develop an eye for different aberrations. Sooner or later, an alert star tester will see every type of optical difficulty discussed in this book and some that are not discussed. You are encouraged in this effort to broaden your experience.

Keep the test results to yourself, though. Considerations of courtesy aside, such opinions could be wrong. You generally know nothing of the history of the instrument. You don't know if it is cool or warm. You have not had a chance to align it first, so you need to mentally subtract a significant alignment error from the pattern. Furthermore, one-shot tests are anecdotal and do not allow for follow-up testing. Remember, you were told to test your own telescope again and again. What makes you think you can evaluate someone else's from a glance in the eyepiece?

If you are asked for your opinion, give it along with a comment about the considerable uncertainties. Don't present the result as a pronouncement from heaven. Carefully explain how you developed the evaluation. If others don't know the star test, teach it to them. After all, I hope you realize by now that star testing is not that mysterious.

15.5 When Everything Goes Right

I don't want to leave you with a fatalistic interpretation of the star test. Once taught how to evaluate telescopes, people tend to be overly critical of their instruments. Nothing pleases them. It seems that the illusion of reality has been stripped away—and with it the wonder.

Here is an example of this loss of illusion: Years ago, a universal flaw in old motion pictures was pointed out to me. Just before the end of a reel, markers in the form of punched holes appear twice as an aid to projectionists. If punched in the negative, the holes are inverted to dark spots. Because most films are compressed horizontally, these marks appear as flattened ovals, one at about 10 seconds and another just before the reel changes. The second projector is always started at a point when the frame is dark or abruptly changes brightness.

I had never seen this tiny flaw before and I never fail to see it now. I almost wish I had never been told. This place where the bones of the technology poke through invariably jolts me from the film's comforting illusion and reminds me that I am just watching a movie.

Similarly, once optical phenomena are familiar, you will see them everywhere. Glasses wearers will be unable to walk in drizzle at night without noticing the interference bands in a refracted sparkle of light on the lenses. Looking upward into a clear blue sky, you will occasionally notice floaters in your eye surrounded by tiny diffraction rings. You'll see the ominous signature of chromatic aberration in every rainbow.

I hope that you will not become unnaturally sensitive to the flaws in your telescope. I know individuals who own telescopes having abominable optics, yet they continually conduct productive and frequent observing sessions. I have known other owners who complained about telescopes that were little removed from perfection. They hardly ever spent time under the stars but were always adjusting and modifying their light-starved instruments. It seems that the attitude of the telescope user is the final filter in the wobbly stack and often becomes the worst form of degradation. The star test enables more realistic images. It is not meant to turn a happy observer

15.5. When Everything Goes Right

into a sad one or to spoil the glorious illusion that a telescope produces.

Astronomical telescopes can weave delightful images, and I would serve readers badly if I were to leave them with a sense of disappointment to spoil the magic of starlight. I want to describe something I saw with my own eyes when everything went right—when much of the filtration dropped away and the optics were unimpeded.

It was one of those rare times when the temperature had been virtually constant all day. One evening, my observing group set up a 16-inch f/5.6 Newtonian telescope. It had a 3-inch thickness mirror that often had trouble cooling down, but that whole day it had been near ambient temperature. The evening was wonderfully steady. It was one of those infrequent nights when there seemed to be no upper limit to the useful magnification. We aligned the instrument and turned to Jupiter, then at about 45° elevation.

The shadow of a moon was crossing Jupiter's disk. It stood out crisp and distinct against the planet's brilliance. The gray disk of the moon itself was clearly visible as it transited the planet. So many whorls and crenelations were visible on the surface, that neither hours of sketching nor my limited artistry could have captured them. I wasn't looking through a telescope so much as I was being projected beyond one. I had passed through the eyepiece.

I have had similar experiences rarely but often enough to make it all worthwhile. Once I saw Cassini's division visible on the whole lit circle of Saturn's rings. The crepe ring was easily visible; it looked filmy against the darkness. Another time, at 350 power, I saw globular cluster M15 resolved clear across the core, each star visible as a tiny sparkle of light.

I wonder how many of the billions of human beings who have ever walked the earth have seen these things. I feel fortunate and humbled to have done so myself.

On these special nights, I did not see the telescope as a filter. I believed the image was real. And that is the point of all of this labor. We learn to judge the magnitude of optical errors to help the instrument fulfill its purpose. We do so for those brief moments when we can forget that we are looking through a telescope—when we can feel the quiet majesty of the sky.

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