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I Camera Flatness
Michael has replied to my comments about the flatness of the lenses. This
has prompted a little work.
First, I want you all to recall how the lenses were designed. In
discussions with Elliot, we chose to optimize the lenses in a circle
tangent to the sides of the 2048x2048 square. That is, the corners were
left out of the optimization. We could have used a circle that included
the corners. That would have proved to be somewhat more demanding. We
chose to leave out the corners in hopes of a better over all result. I
believe that Elliot's program sought to optimize the RMS deviation from
flatness over the circle above. I also recall (mail is on a
dead computer) that we set 1% as the goal for the flatness. Below, I
attempt to look at the flatness in the same way as Elliot's optimization
To look at the flatness, I made a sky flat from 20 of the I images on Disk
17c. I made a dark from 3 images on 17c. I subtracted the dark from the
flat. I then examined the sky at various points on the image to get a
rough idea of the flatness.
The mean of the entire image, less a few pixels along the edges to avoid
putting the covered pixels in the computation was 3677.
I took the image and subtracted 3677 from each pixel. This left me with an
image with +/- deviations from the mean for each pixel. I then computed
statistics for the image. The result:
sigma = 30.4
30.4/3677 = 0.8 %
Note that this number includes readout and sky noise, albeit reduced by the
dark and flat fielding process. It also includes the corners.
It would thus appear that Elliot did what he set out to do. Further, I
think we were all in on this decision. So if this is not good enough we
are all to blame. ;^) I also note that it is much better than the camera
lens that I tested which was down by 50% at the circle edges, worse at the
corners. I believe ROTSE had similar results (somewhat less deviation)
with very expensive camera lenses.
I think things are really a little better than this since on TOM the
optical axis may not be perpindicular to the CCD. The images certainly
give this impression. I also think Andrew's work supports an out of square
axis. This will be corrected when I have a chance to change out the
mounting plates. Also, looking at the corners, they are not so bad. The
worst one had a mean of 3350 compared to 3677 or down by 8.9%
OK, I think this is a lot different way of looking at things than Michael's
approach. I think what is important is how it works for measuring real
stars. Michael's approach does this. The above tries to separate out the
BTW, the server was so slow today that I never succeeded in loading the
plots from TN-76. I assume Michael was referring to the plots with various
sized circles. I had to go on how I remembered them.
At 09:37 AM 3/29/01 -0500, you wrote:
> If you look at Tech Note 76, you can see examples of flatfields in
>both V and I taken with Tom's Mark IV last fall. The variation from
>center to edge is very roughly 10% in V-band, and very roughly
>20% in I-band. Tom has warned us that some of the V-band images
>included a tree branch, so my guess is these are worse than the
>performance of the optics alone.
> Michael Richmond