Coma fits: update

[andrew.bennett@ns.sympatico.ca (Andrew Bennett)]

On Tue, 25 Jan 2000 21:55:16 GMT I wrote
>I have now got my fitting program to work
>on the CD7 data. It is very slow work: the
>progran choked on the 6th image of the first
>sequence and it may take days to get it
>going again so here are the results for
>the first 5.
Yes - it took days; lots of them. I have made a lot
of changes (see below) and I still don't know what I 
was doing wrong to get all those square roots of 
negative numbers, divisions by zero and floating point 
overflows but they have now gone away.
>
>My latest model has given up doughnuts (see
>previous posts) in favour of pancakes.
Herbert Johnson has helped me clarify this: he wrote
    Actually, a closer methphor would the the
  "towers of Hanoi" stack of disks. It is also a child's toy, a simple
   stack of disks of increasing size on a peg.
Thanks, Herbert. That's it exactly.

Here are my final results for CD7 V-images:

Image centre. The gaussian central core for the best focus, 
with about a third of the total flux, has gaussian spreading 
parameters:

Lens #1: No extra spacer 0.513 pixels; FWHM 1.21 pixels
         0.016" extra    0.579 pixels; FWHM 1.37 pixels
         0.032" extra    0.584 pixels; FWHM 1.38 pixels
Lens #2: No extra spacer 0.614 pixels; FWHM 1.45 pixels 

Corner Neff parameter (effective number of pixels over 
which the comatic image is spread) at the same focus
position that gives the best centre focus:

Lens #1: No extra spacer 54.6
         0.016" extra    62.3
         0.032" extra    32.3
Lens #2: No extra spacer 34.3

So the second lens with no extra spacer behaves very 
similarly to the first lens with the extra 0.032".
Whatever that means.

**************************
The current model.
Major changes since the last post include.

1) Doing the noise right. The original fits assumed
constant gaussian noise - which is fair enough for the
weakest resolvable sources but not right for the brighter
ones used in the fitting. Allowing for the fact that the
rms noise increases proportionally with the pixel value
gives a slightly different fit as well as increased error
estimates. The revised error estimates are a lot closer
to the estimates obtained from replicate images, suggesting
that I am beginning to get things right ... I underestimated
the increase before.

2) Using bicubic spline interpolation instead of
bicubic polynomial interpolation when shifting the PSF.
This reduces the roughness arising from discontinuous
derivatives at the grid points and gives smoother
convergence of the fit. It still doesn't eliminate spurious 
negative PSF values when interpolating narrow gaussians. 
These negative values were the source of some of my computing
problems (but not all!). I have "fixed" that problem
by simply lopping off the negative values.

3) I have replaced the assumed linear trail with a
3-point convolution. This makes absolutely no measurable
difference for most of the images. The best images have
around one pixel of trailing or even less. Some images
show larger trailing and in one case that I looked at
in detail a suggestion of uneven trailing or so I thought.
Neither 3-point nor 5-point convolution actually gave
any improvement (the total trail was about 4 pixels) but
I ended up with a working 3-point convolution program and
have not got around to turning it back to the linear trail
model. 3-point convolution computes faster than the 5-point
method I was using to implement the linear trail but adds
2 more fitted parameters for a total of 8.

Fitted parameters.
X1[1], X2[1], X1[2], X2[2] for the 3-point trail. The third 
  point is X1[3] = -(X1[1]+X1[2]), X2[3] = -(X2[1]+X2[2]).
Sigma   core gaussian spreading (centre)
SigFac  increase in spreading with radius
RScale  pancake radius factor for comatic halo
DScale  pancake displacement (from core)


Andrew Bennett, Avondale Vineyard, Nova Scotia, Canada.