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Re: Coma, work to date

On Wed, 29 Dec 1999 18:38:35 -0500, Stupendous Man <richmond@a188-l009.rit.edu> wrote:
*>  Herb asks "how can one characterize coma in the Mark IV images?"
*>  The short answer: pick one of the following two methods:
*>     - measure the fraction of all light from a star which falls
*>          within an aperture of some fixed size, as a function
*>          of the star's distance from optical axis.  I did a very
*>          brief, inadequate version of this in TN 59

Enough to show there was an issue, and to put numbers to it as measured.
As those measurements correspond to methods about to be used, this work
was "adequate", Michael is being shy.
*>     - measure the length -- from the bright core to the most distant
*>          visible portion of the tail -- of the PSF, as a function
*>          of a star's distance from the optical axis.  Express this
*>          length in micrometers, noting that each pixel is 15 micrometers
*>          in size
*>In each case, express the distance from the optical axis in degrees.
*>Recall that each pixel is about 7.5 arcseconds in size.

*>  An optical expert could take either of the above measurements and
*>try to figure out how the optical design of the lenses was implemented

I imagine we need to measure not just the "tail" but the width of the
tail; and also where the core is relative to that oval-shaped comatic
image. But this the sort of thinking we need. I suspect there are already
methodologies to measure coma, I HOPE we don't have to reinvent them.

As to how the optical design should have been or how it should be...
frankly, HOW is irrelevant, just to cut to the chase. Measure the effect,
then compensate for it SUFFICIENTLY. That is the proposition. The lenses
are as they are. Let's save some time and chat and focus on a software
solution, not optical re-re-design. That was already done, as I think
Tom will point out. IF, if we see a lot of per-camera variation,
maybe THEN this would have to be revisited. I hope not. Meanwhile,
keep this in mind: any analytical solution based on the design parameters
of the lens system would be "a theory based on a theory". This does
not fill me with confidence, but you may disagree. Enuf said.

Michael includes some apparently previous discussion in his reply
which I guess I missed during my illness. Rather than respond point
for point, which would make for a long message, I'd like to save some
time and fuss by summarizing his statement and responding in general.

He essentially says that a pixel-by-pixel solution would involve
taking a lot of images and trying to come up with a function that
describes the distortion effects. He speculates that some kind of
analytical solution could also be based on an "expert" analysis of
the optical design. He suggests that a "correction factor" would be
hard to obtain as the images would all be different in one way or
another. Also, the solution would be inconsistent in results as each
lens system may be different. He also notes that results from the
center of the field will be better, simply because they will be
brighter and so have relatively less noise. And, he notes that with
fixed apertures, different aperture sizes will yield different results.
He hints (I think) that a solution may vary over time, the cameras
may need to be monitor and checked regularly.

I think his comments are useful, as they frame the KIND of problems
and issues. However, I find his comments provocative, because I think they
complicate a PRACTICAL solution with (my opinion) too much theoretical
methodology: the problem is not as complex as he suggests.

We simply do not need (I'll bet) a point-by-point solution and a lot
of analytical work. Once we measure the effects of pincusioning and
coma, we will be able to confirm it is, as Michael also suggests,
symmetric with radial angle and somewhat proportional (first or
second degree) with radius. That is halfway to a correction. Also,
we can with minimal regret eliminate the corners if a correction
algorithm is too complicated, or even some of the edges. AGAIN, we
need some *numbers* to see what we lose by this. (Comment: could
somebody PLEASE tell us how "star" does photometry - fixed aperture
is obvious, but what is its "psf" algorithm??)

With similar reasoning, we will see by measurement what the error
or loss is when testing the "correction" across several lenses and
cameras. As Michael suggests, imaging the same area of the sky
is a good idea, in any experiment the more "variables" you can
eliminate the better. Also, we can simply LOOK at the images,
y'know, and SEE if they are different. Nothing like a reality check
to keep us on track. (Astrometrica uses image average background as
black, 3 sigma above it as white, and in between as grey: this seems
to be a useful method for visual display, if you have a choice.)

As for the fixed aperture arguement: that is a decision to be made
as to whether a fixed aperture will serve our needs or not. Maybe
not. Look over the reports to date, see what YOU think.

I appreciate my friend Michael's analysis. But
here is the difference between theory and practice, between research &
design vs application and products. I DON'T CARE if a solution is
exact or complete: only if it is good to some KNOWN amount. We can
simply discard data in the corners, solve the problem for say 80%
of the radius, and still do good work. If a general solution will work
100% for one lens system, but only 98% for another, then call
out the error accordingly and live with it. All surveys throw out data,
throw out observations, discard some results. Mark III did this.
So will Mark IV, the question is how much, and in what way.

So let's see if we can nail down the effects of coma and pincushioning
in a numeric way, and see what that tells us. At this point, I only
have time to play cheerleader (and I suppose critic) but I see progress!

Herb Johnson

Herbert R. Johnson              http://pluto.njcc.com/~hjohnson
hjohnson@pluto.njcc.com         voice 609-771-1503, New Jersey USA
             amateur astronomer and astro-tour guide
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