Earthshine blog

A required image analysis step is the determination of lunar disc centre and radius.

We currently use a hybrid method: First we fit circles to points on the BS rim (found as an image by using edge-detection image-analysis methods: SOBEL filters!) of the lunar disc image – this is done many times using different points and then the median is extracted for x0,y0 and radius. These values are then used as starting guesses for a more refined method that searches a range of possible values near the starting guesses and determines a ‘winner’ based on how well a synthetic circle matches the ‘rim image’ generated above.

We compare the statistics of the starting guesses and the final adopted values. In two separate runs on 88 different images we assemble these values:

Run 1:
x0 start guess: 311.82352 +/- 2.7447506
x0 final guess: 310.44694 +/- 2.3127377
y0 start guess: 248.49938 +/- 1.1339389
y0 final guess: 248.70556 +/- 1.0812740
radius start guess: 136.32425 +/- 0.98834739
radius final guess: 136.90833 +/- 0.44461002

Run 2:
x0 start guess: 311.78076 +/- 2.9802184
x0 final guess: 310.46767 +/- 2.3079720
y0 start guess: 248.51968 +/- 1.0747726
y0 final guess: 248.70327 +/- 1.1017349
radius start guess: 136.42162 +/- 1.2634192
radius final guess: 136.90870 +/- 0.40265642

x0 is found slightly more precisely with the final method (2.3 pixels vs 2.8).
y0 is found with similar precision in the two methods (about 1.1 pixels).
radius is found better with the final method (0.4 vs about 1 pixels).

We seem to be able to determine the centre of the lunar disc with image analysis techniques to the 1-2 pixel level, and radius to better than half a pixel.

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.