We have looked at the error in measuring the flux in a patch on the earthshine side if the position of the patch is uncertain by a few pixels.
A circular patch (aperture) was chosen, as shown by the green circle below:
The aperture is 31 pixels in radius, and is in a not particularly uniform luminosity area of the lunar disc.
The amount of scattered light into this area is rather small (~<10% of the flux) and has been ignored.
The flux in this aperture was computed for the correct registration (no offset in x or y) and for offsets of 1 and 2 pixels in both x and y (i.e. a rectangular grid of -2 to 2 pixels offset in x and the same in y).
Simply summing the flux in this aperture yields a 1.5% error in the flux, if the registration error is up to 2 pixels. The error reduces to 1.0%, if the registration error is just 1 pixel.
We tried rolling off the edge of the aperture with a cosine function (i.e. from 1.0 to 0.0) — it starts 6 pixels inside the edge of the aperture. We weight the flux in each pixel by this function. Pixels inside this rolloff zone are weighted with 1.0.
The improvement is rather small. For this “soft tophat” aperture, registration errors of order 2 pixels lead to a flux error of ~1.4%. This is to be compared to the error of 1.5% for the hard edged aperture. If we can achieve registration errors of 1 pixel, the soft edged aperture yields a flux error of 0.8%, compared to 1.0% for a hard edged aperture.
Next we tried a much more uniformly illuminated region of the moon:
The results are much better. In this region, a registration error of up to 2 pixels yields flux errors in the patch of order 0.2% (31 pixel hard edge aperture) and 0.15% (31 pixel soft edge aperture). This is very acceptable!
Conclusions:
Using a soft edged aperture helps ameliorate registration errors, but not as much as we had thought.
Selection of uniformly illuminated patches helps much more! Doing both is a good thing.
