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what about chromatism?

Started by vlad, 02/09/2003 07:08PM
Posted 02/09/2003 07:08PM Opening Post
There is always a lot of discussion about the effect of c.obstruction (which, btw, almost always takes more of the blame than it deserves). For some reason, people are much more tolerant to bad effects of chromatism. One of the reason is probably that its characterisation doesn't go beyond "chromatism-free" (for f/D~5D", or slower), or "least acceptable" (for f/D~3D"), for ordinary achromats. This doesn't give much info to compare it with other aberrations, or c.obstruction, does it?

Well, it bugged me enough that, since I couldn't find no "official" source for comparing chromatism to other aberrations (mtf, encircled energy,etc.), I did it on my own. Just an approximation, but seems to be making sense. The results are as follows: taking the chromatism-free level of F=5D" as a unit (Fo), energy lost to the Airy disc (beyond the unavoidable 16%) is 44% at F=0.2Fo, 29% at F=0.3Fo, 18% at F=0.5Fo, 14% at F=0.6Fo and 6% at F=Fo.
For a 4" refractor (Fo=20), that would be for an f/4, f/6,
f/10, f/12 and f/20 systems, respectively.

The amounts of energy lost allows for a rough comparison with the effects of spherical aberration and c.obstruction.
An f/4 4" achro is at the, level of 1/2.3 waves of spherical aberration, or 57% c.obstruction. An f/6 is at the level of 1/3 wave of s.a. or ~43% c.obstruction. An f/10 slightly better than 1/4 wave of s.a. or ~33% c.obstruction. An f/12 is at about 1/4.5 wave of s.a. or
~30% c.obstruction. And an f/20 is at about 1/7 wave of s.a. or ~18% c.obstruction.

In regard to the often quoted rule that an obstructed system of aperture D and obstruction C is about as good for low-contrast planetary details as a (D-C) unobstructed system, it may be close to a real-life situation, but it is not c.obstruction to be blamed for all of it. The rule is deducted very approximately, from a "regular" MTF graph, which is for brightly illuminated objects with high inherent contrast. Obviously, not quite appropriate for the purpose. As others already pointed out on different occasions, Rutten and Venrooij give much more appropriate approximation, with a low contrast graph and minimum contrast required taken into account. According to it, resolving power of obstructed apertures is not nearly as much inferior. In a simple form, the effective aperture reduction factor due to the effect of c.obstruction would be closely enough expressed by c^2/(1-c), with c=c.obstruction/aperture (linearly). For obstructions Bellow ~35% it would be even slightly smaller, with the reduction factor going to zero at ~20% c.o.

The rest of real-life inferiority of obstructed apertures should go on the account of their generally greater sensitivity to optical quality, (mis)collimation, thermal instability, baffling, etc.
Posted 02/10/2003 08:32AM #1
I think your reasoning makes a lot of sense. I believe high quality MAK's are at least as good as achromats on planets. In fact, I doubt anyone in their right mind would trade a 3.5" Questar for a 90 mm achromatic refractor.

Maybe the alledged lack of contrast in reflectors is due to surface roughness and straylight rather than central obstruction. (I think reflectors are more sensitive to surface roughness, but I'm not 100% sure)

Erlend