Maybe I'm not following exactly, but it seems that you are trying to
correct for variations in responsivity across your CCD, and your
problem is that you are trying to do this correction using data that
is too noisy. Assuming the array responsivity is fixed (or at least
slowly varying), can you not just build up a high S/N data set by
staring at a known flat field source, and then use this data set to
produce your calibration (after dark correction), or at least fit a 2D
surface and use that? In other words, can't you make 1000 images
instead of 3, and have them all overlap exactly?
On Oct 23, 4:16 pm, Jonathan Joseph <j...@cornell.edu> wrote:
> HELP!
>
> I'm trying to reconstruct the flat-field information for a CCD from
> overlapping images of the same scene - with same exposure duration and
> same lighting conditions, but I'm failing miserably.
>
> I'm pretty sure I've got all the information I need. The CCD is
> 1024x1024, and I have 3 images that in are close to the following
> pattern (labeled 1,2,3 in lower left corners):
>
> (need fixed-width font like courier)
>
> +-----------+
> | |
> | |
> +--+--+-----+--+--+
> | | | | | |
> | |3 | | | |
> | +--+-----+--+ |
> | | | |
> |1 |2 | |
> +-----+-----+-----+
>
> The flat-field is horrendous - with a variation of more than a factor of
> two from brightest (middle left of image) to darkest (right edge).
>
> (For those not familiar with flat-fields, the flat field can be
> considered as the response function of the CCD/camera system. If you
> image a perfectly homogeneous source, the image you would get is the
> flat field - plus noise. If you know the flat-field, you can divide it
> out of the image to give you the correct brightness of each pixel in the
> scene.)
>
> So, for each place where two images above overlap, we know that the
> scene brigthness should be the same (within the noise) and we can
> calculate the ratio of the actual difference in the images.
>
> For example: img1[x1,y1] / img2[x2,y2] = R[x1,y1,x2,y2]
>
> Since the scene brightness for that pixel should be the same in both
> images, we can say that
>
> img1[x1,y1] img2[x2,y2]
> ----------- = -----------
> flat[x1,y1] flat[x2,y2]
>
> So, we know that
>
> flat[x1,y1]
> ----------- = R[x1,y1,x2,y2]
> flat[x2,y2]
>
> For these 3 overlapping images, I get ~ 1.4 million equations, each
> giving the ratio between 2 pixels in the flat field.
>
> Great!
>
> But I can't seem to solve for the best flat-field image that will
> minimize the residuals for this set of equations. This is clearly too
> large a set of parameters to pass to a minimization routine such as
> POWELL or mpfit, and the flat-field is so splotchy and irregular that I
> don't know how to model it with a 2-D function such that I could
> minimize the number of parameters and actually solve it with a
> minimization routine.
>
> I did write a routine that will step through the 1.4 million equations,
> and appropriately adjust the flat field for cases where the ratio is not
> already determined by the previous equations. For example if A/B = R1,
> B/C = R2, C/D = R3 (where A = flat[Ax,Yx], etc.) if we then get D/A =
> R4, that is a conflict, because that value of D/A is already determined
> by the previous equations. My function ignored about 400k equations,
> and the result, was a pretty much complete image that didn't look at all
> like the flat field but seemed to have a lot of structure that was
> related to the way the images overlapped.
>
> I think the problem with this method, is that it propagates and
> multiplies errors due to noise - which is why I think I need to minimize
> the residuals of all equations together rather than just throwing out
> some of the equations. Apart from the fact that it returned junk, the
> algorithm seemed OK. When I tried it with faked data with no noise, it
> worked perfectly. When I tried it with the same faked data with noise,
> I get the same junk.
>
> Any help on how to tackle this problem greatly appreciated.
>
> Thanks.
>
> -Jonathan Joseph
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