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my first comment is that we need to be sure the analysis pipeline appends a date+time stamp to file name when the FITS files are made. I think the reduction scripts I wrote long ago do that, if not we need to make sure we do that.
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- Find and kill the stray light source. But we can't go back in time and do that, so instead just cut off y<500 from the frames, to make things cleaner
- compute the median of all columns and subtract that from each column, to get rid of the horizontal streaking
- Either smooth the image with a Gaussian kernel with sigma~3 pixels to account for residual Bayer pixel artifacts and fragmentation of the PSF
- run a source detection code with a fairly high threshold of significance, and then select out the bright sources that have centroids near where we expect them.
- compute mean of all 7 centroids, call that the 'average position' of all 7. That is the origin of the center-of-spots coordinate system.
- Compute the mean position of each spot in that new coordinate system. This accounts for boresight jitter.
- For each frame and for each spot , subtract that average from each of the 7 positions, which is differential motion of each spotoff that mean-spot-position. This is the instantaneous offset of each spot. It's a 2-d vector
- For each pair of spots (i,j) in each frame, compute the vector difference r_i-r_j of their instantaneous offset vectors. Compute the norm of that quantity. If spot motions are 100% correlated, this quantity would be zero.
- Plot this magnitude-of-offset-difference vs. separation.
- I'd also compute the mean intensity for all 7 spots, and take the ratio of each spot's intensity to that mean. This will let us look at scintillation as well as image motion.
- Put the results into some sensible data structure(s)
For reasons of time I'm going to skip steps 1,2,3 and run Source Extractor on the four frames, with a tweaked configuration file that requires high significance for detection.
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make a diagnostic plot of flux vs. x
Sure enough, there is a discrepantly low flux point. So if we pick the 7 brightest sources we ought to be able to avoid the ghosts. This command line does that:
cat CU2A6081.cat | grep -v "#" | sort -k 4 -n -r | head -7 > stripped81.cat
That prints the file to the grep command that strips out comment lines, pipe the output to sort tool using column 4 interpreted as numbers, in descending order piped to head command to keep brightest 7 sources.
do 'man grep', 'man sort', etc to learn about command line tools.
What should we expect for sensitivity? RMS width of PSF is around 4 pixels, and FWHM=2.35*RMS ~ 9.5 pixels. Fluxes are around 100K. Assume (guess!) around 1e per ADU so that corresponds to 100K electrons. Signal to Noise ratio is square root of that, or ~300
Sigma of centroid should be FWHM/SNR = 9/300 ~ 0.03 pixels. Cool.
I made trimmed source catalogs that retained the brightest 7 compact sources in each image.
We then need to do source association in (x,y) space. I cheated a bit and did this in 1 dimension, using ordering in y. This suggests we arrange the sources and their orientation on the detector to not have overlap in either x or y, to ease source association.
Computed mean position for each spot, then computed magnitude of difference of (postiion-mean) for each spot pair, and plotted that vs. separation. Looks interesting. The different frames have different amounts of turbulence:
Motion of center-of-spots: 
Magnitude of differential motion vs. separation between pairs, for all 4 images:
Looks like fitting differential motion vs. sqrt(separation) might work. Did those fits, here are the results:
Fit to
differential motion = a + b * sqrt(separation)
| frame | b | a |
|---|---|---|
| 42 | 0.1150 | 0.0579 |
| 50 | 0.1139 | -0.0306 |
| 58 | 0.0654 | -0.0189 |
| 81 | 0.0309 | 0.0345 |
Those are the lines on the plot above.
A few other comments.
1) the assumption of isotropy does not hold. Motion in y is more than motion in x:
2) If image motions are totally uncorrelated, we expect the RMS of their separation to be sqrt(2) times the RMS of a single spot. So asymptotic value should be around 5.5 pixels or so?
3) We need to span a wider separation in order to reach asymptotic value, where relative motion becomes independent of separation, or else have smaller amounts of turbulence, or both.
MATLAB code DIMSUM.m is here: DIMSUM.m