Using synthetic images where the DS intensity is known, we have generated 'fake' observed images by convolving with a PSF and adding noise (Chris's syntheticmoon.f used; alpha=1.8). We then forward modelled these images using the EFM method (i.e. using the 'observed' image BS as the source and allowing that to scatter in model images until the model images matched the input image).
Subtracting the model images left us with the DS corrected (the BS goes away, per construction). We extracted DS intensities only (adding the BS is a separate chapter of complexities!). We extracted DS intensities from the corrected image, from the synthetic observed image, and from the known input ideal image. We plot these images as a fucntion of the day number during one month.
The black symbols show the DS intensity in a 15x15 patch at 2/3 of the radius for the synthetic observed images (i.e. the ones that suffer from realistic scattered light from the BS); the blue symbols show the known intensity from the ideal pre-scattering images; the red symbols are from the EFM-corrected images. The period of New Moon is excluded because our method fails there (there is not enough crescent to make a good model of the halo from). Near Full Moon is inaccessible since the DS is so small then and it becomes difficult to extract the DS intensity (nowhere to put the patch!).
Annotations in the upper panel show the choices of various settings of the analysis code.
Bottom panel shows the difference between true and corrected DS intensity expressed as percent of the true value. In the upper panel points inside the two sets of dotted lines have been selected for analysis in the lower panel - the mean absolute error is printed.
We should next apply the BBSO method to these images.
We see that this method also reaches the 1% error level but that the number of days during which this level is attainable is smaller than with the FME method.