Re: coma and optics

[hjohnson@pluto.njcc.com (Herbert R Johnson)]

On Thu, 10 Feb 2000 12:10:23 -0600, Tom Droege <droege@wwa.com> wrote:
*>Andrew,
*>
*>OK, I can do both.  Take a large step run.  Measure it once.  And put in a
*>stop. All should give useful information.
*>
*>Tom Droege
*>
*>>On Tue, 08 Feb 2000 20:08:40 -0600, [Andrew] wrote:
*>>
*>>On further thought, the results can be just about
*>>squared with the assumption that the entire coma
*>>comes from the outer reaches of the lens and the
*>>bright core is light that goes down the middle with
*>>a higher effective f number/lower aperture. It's still 
*>>a bit tight; 2/3 of the light is in the core so there's 
*>>a lot of middle and not much by way of outer reaches!
*>>
*>>The thing to try next dark night might be that
*>>cardboard stop that you were talking about rather
*>>than wasting time with calipers! The 1/3 coma
*>>suggests only covering 1/3 of the aperture.
*>>
*>>Andrew Bennett, Avondale Vineyard, Nova Scotia, Canada.

I did not previously offer the comments below, because I assumed that
someone with more optical knowledge than I would make these comments
or offer a similar reference. But that has not happened, so I hope
my modest homework on optics is useful. But the idea of testing a stop
has been suggested repeatedly: it now seems useful to explain why it
could be effective or at least informative, and offer a reference that
is repeatedly cited in the textbooks.
  
I've looked at a few bookstores and university libraries on the subject
of coma and lens design. Most of the textbooks and references have
chapters on thin lens design, and most of them refer to the same information
and terminology and references, to work done around the turn of the
20th century and revised early in the 20th century. Many of them refer
to A. E. Conrady's "Applied Optics and Optical Design", originally published
by Oxford University Press in 1929, and republished by Dover Books
in 1957 and 1960. The Dover editions are very inexpensive, the books
may still be in print. I have seen these books in used book stores and
in new.

Coma is essentially a condition where concentric parts of the lens system
focus the image at varying distances from the image plane. So one
part of the image is in focus, the next (going radially from the center
of the image plane) is slightly out of focus, the next moreso, and so
on. This forms the conic shape of the comatic image. It also suggests
the relationship of the comatic image with radius, and the text describes
those geometric relationships (among many others).

As the book provides methods for design and is intended as a tutorial
as well as for analysis. As it uses pre-computer methods
it is somewhat challenging to read even by an engineer. But a modest reading
can provide some insights such as I have noted above.

A number of books referencing this material suggest that coma can be reduced
by providing a stop, or dark ring, at some point in the lens system. The
above analysis explains the value of such a stop: it simply blocks that
portion of the lens which contributes light at one end of the comatic-
conic image. Stops are not proof of bad optical design, they are simply
a way to control the passage of light in an optical system.

A well-designed lens system can use the stop anywhere. But for purposes of
testing, a stop at the front of the lens system is easiest to apply. Given
the above analysis, the obvious effects of a stop would be to reduce the
lenght of the comatic image from one end toward the other end. It would
also POTENTIALLY reduce the field of view, or more precisely reduce
the light from the outer edges of the field.

I say potentially because
1) the CCD is not likely seeing all the actual field anyway, 2) some
of that field may be in the corners only, which would be a modest
but acceptable loss and 3) the edges of the field may not be what is
called "100% illuminated" because of other limitations in the optical
path, some other lens element may be blocked already (this is not
unusual at all).

I again suggest an experiment
where dark rings are placed on the front lens and images made. The
outer diameter should be the diameter of the lens, the inner diameter
various sizes up to perhaps half the diameter of the lens. We can
then simply see what the impact of these stops are and argue the results.

I regret that I simply do not have time or expertise to offer further
information or
details about this subject, but it all comes down to doing the experiment.

Herb Johnson

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