[ATM] what causes coma?

[mpeck1 at ix.netcom.com (Michael Peck)]

At 16:17 11-02-04 -0600, Good, Donald wrote:

>      "Coma can be defined as the variation of magnification with aperture."
>(p. 67).
>
>Don>I don't agree.  Choose another parabolic mirror with double the
>aperture.  Does the coma at the center change?  No, it is still zero.  A
>statement about coma had better say something about angle.</Don

"Aperture," in this case, means "pupil coordinate," not diameter. The usage 
is a little non-standard but from context its clear enough what he meant.

>Combine with the next sentence to get the best two sentence description of
>coma I've seen:
>
>      "Thus, when a bundle of oblique rays is incident on a lens with coma,
>the rays passing through the edge portions of the lens may be imaged at a
>different height than those passing through the center portion."
>
>Notice there is no mention of spherical aberration here. There's a reason
>for that.



>The reason it was not mentioned might be that the author didn't think of it.
>

That wasn't the reason I had in mind. In pure coma (which you're not likely 
to see in a real optical system) every pair of rays originating from 
opposite sides and at the same distance from the pupil center focus in the 
Gaussian image plane, but displaced *laterally* from the Gaussian image 
point, the location of which is determined by the principal ray. That's why 
coma is a variation of magnification with pupil coordinates, as Smith says. 
Coma is literally orthogonal to spherical aberration.

Any semi-competent textbook on geometric optics will discuss coma (and 
other classical aberrations) illustrated with some mix of graphics and 
equations. There's no good way to reproduce the contents of a text in a 
mailing list post, where you're limited to ascii math and graphics. That's 
one reason why every ATM should have at least a basic dead tree optics 
library in his or her possession. A lot of optics gurus consider Smith to 
be the "bible" of optical engineering. I find that he covers some topics in 
more detail than I want to know, and leaves out others I think are 
important (like Zernike polynomials; and his coverage of physical optics is 
superficial). But it's probably safe to say that if Smith doesn't mention 
something it isn't because he didn't think of it.

Mike Peck


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