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S/N image

Error budgetPosted by Henriette Schwarz Dec 07, 2011 04:20PM
From night JD2455864 V-filter moon images I have selected images with similar count levels in the bright part of the Moon. This resulted in 23 images. These I have aligned and coadded (mean-half-median method) thus obtaining a coadded object image O, and a standard deviation image, delO. From these two images (and images with estimates of B, delB, F, delF) I constructed a S/N image calculated pixel by pixel. I found the DS to have S/N ~2-3 and the BS to have S/N ~30-40. The S/N image looks like this

While the DS S/N value might be realistic, the BS S/N value is much lower than expected. This is likely due to the fact that co-add mode necessarily is observed close to a rising or setting moon. On this particular night the Moon was setting, and the 23 selected images are obtained with a 30 minutes interval - in which time the Moon went from an altitude of 22 degrees to 17 degrees. The typical BS count level falls in this period from 27900 to 26400. A decrease of about 5.4%.
Next I tried scaling the images after alignment before coadding. I have scaled them using an 11x11 area in Mare Crisium as reference. This area had a mean in the unscaled coadded image of 10300, and I have scaled so that each image has the value 10500 in that area.
scale_factor = 10500.0/AVG(im[360:371,230:241])
This gave a DS S/N ~1.5 and BS S/N ~100+. The BS S/N seems pretty stable of the exact scaling factor, but the DS S/N increases dramatically (S/N ~12) if I use for instance 15000 instead of 10500. I simply don't think we can count on the S/N values calculated per pixel basis after scaling.

Conclusions and thoughts: If we scale the moon images to counter the setting/rising moon we seem to be able to achieve a S/N on the bright side similar to the poisson noise. It is much more troublesome to estimate the S/N on the dark side. The S/N on the dark side is very sensitive to the method of scaling and the scaling factor. But perhaps a S/N of 2-3 (as determined without scaling using only images selected to have at least somewhat similar bright side count levels) is a decent estimate.

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Posted by Henriette Schwarz Dec 08, 2011 12:51PM

@ Peter: Just rechecked! I am pretty sure I got it right.

@ Chris: In the ideal case we would be able to achieve S/N on the BS of sqrt(50000). However in practice the bright limb is overexposed whenever the count values in mare Crisium gets higher than about 11000, and the highlands have a count of 35000 - perhaps we can do slightly better in the B-filter, but that is yet to be confirmed. So if the noise was purely Poisson, we would expect perhaps a S/N of 100-200 on different parts of the BS - closer to 200 if all images are well-exposed. In reality we use subpixel shifts, and delO seems to be dominated by actual intensity changes due to the setting moon rather than noise. I try to remove the effect of the increasing extinction of the BS by scaling the images.
In the first scaling I tried (the one that gives DS 1.5 and BS 100+) I chose an 11x11 area in Mare Crisium and scaled each image so that this area had an average (10500) counts close to the average of this area in the coadded unscaled images. This must be considered to be a realistic count level.
Next I tested what would happen to the S/N if I instead scaled each image so that the chosen area had an average of 15000. This didn't do much to the BS S/N, but the DS S/N became an unrealistic 12. Using 27000 the DS S/N became 20+. This is due to the dominating part of the error equation (delO/O-B)**2. When I scale the image up, both O and delO are scaled, but O-B becomes much larger, and all of a sudden this part of the equation is not dominant any longer.
Another thing is that it makes sense to scale the DS along with the BS. The BS needs scaling due to extinction. But the earthshine changes in intensity may not be dominated by extinction. As the moon sets, different parts of the Earth contribute to the earthshine, and this might make a larger change than the extra airmass.

Posted by Chris Flynn Dec 08, 2011 09:16AM

Hi again,

I'm not sure I followed the paragraph beginning "This gave a DS S/N ~1.5 and BS S/N ~100+".... can you clarify the change from the figure of ~1.5 to ~12?

Posted by Chris Flynn Dec 08, 2011 09:12AM

Very interesting indeed. The DS S/N sounds right -- it's consistent with the typical flux of 10 photons in ~30 ms exposures when the BS is well exposed but not saturated. The BS side is certainly less than expected! That's slightly surprising. My feeling is that the image alignment procedure -- shifting -- might be part of the problem. If you are doing subpixel shifts, then that will introduce noise -- although it would have to be quite a lot. The S/N one would expect would be more like 50000/sqrt(50000), or much better than 100 to 1. Have you tried using the light off the BS limb to measure S/N? Shifting this light is much less sensitive to structure in the BS image, since it just falls off smoothly. I tried that with my S/N modeling, and got what seemed to be consistency with Poisson expectations -- see my blog post. However, I agree this is less direct -- we are really much more interested in the BS noise. A series of full moon images for a range of very short to 30ms exposure times would be useful in this regard.

Posted by Peter Thejll Dec 07, 2011 05:39PM

Me no understand - did you switch "DS" and "BS" a few times in the text?