Posts Made By: Vladimir Sacek

Normally misaligned focuser will cause visible misalignment in the rest of optical train, so that it gets fixed. Assuming that focuser alone somehow gets out of alignement in a previously aligned scope, it will take center of the eyepiece field out of the center of mirror's image. That will bring off-axis coma into the center of eyepiece field. How much of coma, depends on the amount of tilt of the focuser(t, in degrees), image hight above the tube(h, in mm) and mirror's f# (F), and it's given as coma wavefront error (in units of 550nm wavelength) with w=th/1.5F^3. For sideways shift (s, in mm) the coma error in the field center is 38s/F^3 (independent of the image hight).

It's good to note that identical pick wavefront error of coma results in lower average wavefront deformation than that of spherical aberration. A 1/4 wave of coma causes 1/22.6 wave RMS, while 1/4 wave of spherical aberration causes 1/13.4 wave RMS wavefront error. The proportion between the two is constant: any given coma wavefront error compares in effect to 41% smaller error caused by spherical aberration.


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There is a detailed review at

http://www.cloudynights.com/reviews2/tal150k.htm

If you'd ask them to quote how much it would cost to make such mirror for you (expecting that you could adequately test it), the price would be much higher. And they'd probably let you know that it can't be done, if for no other reason, because this big chunk of (this thin) glass itself is not stable enough to support nothing close to this level of surface accuracy. But for the amatuer market, where such testing is very unlikely, they think can let figures like these fly. I don't see it as clever; rather the opposite.

Btw, the Strehl doesn't match the RMS (or the other way around). The 0.990 Strehl corresponds to 1/63 wave RMS, and the 1/128 wave RMS would result in 0.998 (tiny bit less) Strehl. Even if the Strehl is calculated for the 550nm wavelength (with the RMS being for 635nm), it is still 0.997 for the given RMS figure.

Ed, assuming these are spots for the best image plane, the blur (some coma, but astigmatism is clearly dominant) in the green light is about 30 microns 0.25 degree off axis. Tangential coma (full blur length) in an f/5 paraboloid would be about 41 microns, or nearly 40% larger. This far off-axis this configuration is inferior to the parabola, due to astigmatic blur being about 2.6 times smaller than tangential coma for nearly identical level of the RMS wavefront error. The astigmatic blur at 0.25 degrees off-axis is about 4.5 times larger than the Airy disc. For the diffraction limited level, it needs to be 0.6 times the Airy disc diameter, which sets diffraction limited field radius of the configuration at nearly 0.1 degree astigmatism-wise. This is about 50% wider than the parabola, whose diffraction limited field radius would be 0.064 degrees.

Farther off-axis it falls further behind the parabola, since both astigmatism and lateral color (originating from the sub-aperture corrector), increase with the square of off-axis distance.

If the corrector is a Jones-Bird variety, or at least have the same sign astigmatism, it might be considerably better than that for the visual use, since good part of astigmatism would be cancelled by the opposite astigmatism of the eyepiece, as long as you'd use ordinary (no-Nagler-type) eyepeices.

Practically chromatism-free, coma at the level of an f/8 parabola for the linear field (or nearly 0.5-degree diffraction-limited field). I'd say not bad.

No, the relationship between increase in the amount of light and the perceived brightness by the eye is approximately logaritmic. This means that doubling the amount of light results in ~30% increase in perceived brightness. This helps the eye to function more efficiently in handling enormous differences in absolute brightness that it encounters on everyday's basis.

The response could easily be expressed in decibels, which are also a logarithmic form. For any given increase in the amount of light, expressed in decibels, the perceived brightness by the eye would be 1+(dB/10) times higher.

I'd say that level is 1/4 wave to 1/5 wave of spherical aberration level, but talking about the entire telescope system, not any single element. Some time ago I was playing with low-contrast resolution limits determined by the MTF, the way it is outlined by Rutten and Venrooij. It is, of course, both approximation and generalization, but should give some basic insight in this matter.

If we express drop in limiting low-contrast resolution as aperture reduction, reduction at 1/8 wave of spherical aberration level is only ~2%. At 1/4 wave, it is ~11%, and at 1/2 wave s.a. it is as much as 57%. What these few figures illustrates clearly enough, is that drop in limiting low-contrast resolution is very slow up to ~1/8 wave s.a. level, noticeably faster between 1/8 wave and 1/4 wave, and then nearly plummets as the system error exceeds 1/4 wave level.

Contrast of resolved details is also lower, and more so than the drop in limiting resolution. Approximately, for the 1/8 wave level, contrast of resolved details is up to 7% lower, while for the 1/4 wave level it is up to 20% lower than in a perfect aperture.

For a Newtonian, 1/8 wave s.a. level is out of question, if for nothing else, due to the central obstruction: 20% c.o. alone puts it down to 1/6.5 wave level. A 15% c.o. alone would put it at 1/8.9 wave level; but should we ad as little as 1/10 wave of spherical aberration from the primary mirror, the system goes down to 1/6.8 wave level. Add a bit (or a bit more) of thermal errors, miscollimation, pinching, astigmatism, turned edge, zone, diagonal... - and it becomes clear that it is hard to keep the system error for larger, fast Newtonians above 1/4 wave, regardless of the quality of primary mirror. Of course, less than good primary would certainly make it impossible.

How good is good enough? The bad news is that for ~12" aperture and larger, the combined error of all other sources besides primary is likely to be ~1/4 wave, or larger. In other words, the error budget is already spent, and the primary has to add as little as possible to the final error.
Beyond 1/8 wave to 1/10 wave s.a. (or 1/27 wave to 1/33.5 wave RMS) wavefront level, the difference in error added by the primary becomes entirely negligible for an average amateur.

If you know the focal plane curvature, the simplest field flattener would be a single negative (plano-concave) lens just in front of the focal plane (it would have to be installed inside your widest field ep barrel, just in front of the field stop). If the focal plane curvature is R, the lens' radius of curvature is r=R(n-1)/n, with "n" being the refractive index.

Floyd, the thread in which I said that miscollimation doesn't effect coma
was for Newtonians. Flat reflecting surface (the diagonal) doesn't induce any aberrations; it can only cause decentering of the primary's image in the eyepiece. This results in the coma-free portion of the image being shifted away from the center of the view, which now contains comatic portion of primary's image (that is, if miscollimation image shift is sufficient to bring in noticeable coma). At the same time, the coma free-portion becomes a "subject" of eyepiece's off-axis astigmatism (to the extent determined by the eyepiece type), so that no part of the field has really good definition. This grows in significance with the increase in magnification. At low magnification, moderate miscollimation has little effect.

It's different story with SCTs. Miscolimation here *creates* coma (some astigmatism too, but insignificant in comparison), even if the system is aplantic (coma-free) when properly collimated. And it is rather efficient in it.
So, while with fast near-perfectly collimated Newtonians coma still hangs in at medium-to-low powers in the outer field, with SCTs you can go from no visible coma at all to a very visible coma caused by miscollimation. There's nothing contradicting in your experience.

Almost missed to mention - Rick, good article. But if you want to get a real chance to win, change the subject. Optical theory, even in pre-digested form, is never very popular meal on the menu
:S

Walter, there are only three types of wavefront errors that can result from
the diagonal. One is astigmatism, caused by a smoothly distributed error
across the diagonal. The next is wavefront roughness, caused by diagonal's surface roughness, and the last is turned edge.

Astigmatism is the one most feared, for no good reason. I did some calculations, which also fairly well agree with empirical testings I'm aware of, and it shows that astigmatism induced by any given smooth surface error on the diagonal, is about 70% as large on the wavefront. That means, diagonal with only 1/8 wave surface error of this kind would induce not more than 1/11 wave of astigmatism (which compares to 1/17 wave of spherical aberration contrast-wise). And that is assuming diagonal not wider than the converging light cone. Since the diagonal is most often somewhat larger, it induces even less of astigmatism with this type of surface error.

Surface roughness can be more of a problem, because every surface irregularity magnifies 2x on average in the wavefront. So 1/8 wave surface diagonal with this type of error would actually cause ~1/4 wave wavefront roughness error.

Finally, turned edge is more of a problem with minimized diagonals, which are only slightly larger than the converging cone. In such case, the effect is roughly similar to that of the primary's TE.

Astigmatism is not likely to be seen with the Ronchi test at all. Roughness and turned edge may be seen if they are significant, and if test has sufficient sensitivity (this especially applies to fast systems; a good Barlow lens is necessary to multiply the test sensitivity). If nothing can be seen, other than known pattern of the primary, that indicates that diagonal is not bad, but still doesn't guarantee it is a high-quality surface.