Earthshine blog

I have been testing two simple ways of estimating the earthshine-to-moonshine
ratio, DS/BS, in ISS images of the Moon. The first is the direct photometric
ratio: take robust median intensities on the dark side and the bright side of
the lunar disk, after excluding a strip around the terminator. The second uses
the same disk masks, but applies the measurement to Laplacian-filtered images
instead of to the original intensities.

The motivation for trying the Laplacian version is practical rather than
physical. The ISS images include scattered light, gradients, uneven sky
background, and occasional poor fits to the lunar disk. A Laplacian image
emphasises local structure and edges, so it gives an independent diagnostic of
whether the dark-side and bright-side regions are behaving consistently.

The per-channel panels show that the two measurements are strongly related, but
not identical. That is useful: if the Laplacian ratio were merely duplicating
the intensity ratio, it would add little information. Instead it behaves like a
related structural proxy. Points far from the one-to-one line are therefore
interesting candidates for inspection, because they may mark images where the
ordinary DS/BS estimate is influenced by gradients, scattered light, or mask
placement.

The bottom row is a check on internal consistency. The two green Bayer channels
should be closely related because they sample nearly the same spectral band.
The annotations give the log-space coefficient of determination and the
standard deviation of log10(G2/G1), in dex. Tight agreement in these panels is
a good sign that the measurement is repeatable within the camera data; large
departures flag cases that should not be trusted blindly.

The B-G comparison is deliberately severe: it combines three channels in each
method, so any channel mismatch, background error, or residual scattered-light
effect can move a point. In the current cut, 6283 images contribute to the
comparison. The log-ratio colour estimates have only a weak direct-to-Laplacian
correlation, with R² about 0.03 and a Laplacian-minus-direct scatter of about
0.22 mag. That argues against treating the Laplacian measurement as a direct
colour substitute. It is better interpreted as a separate quality-control
diagnostic.

The next step is to use these diagnostics as rejectors rather than as new
physics. A robust ISS earthshine pipeline should prefer methods that almost
never return a convincing but wrong fit. The Laplacian ratio and the G1/G2
agreement are useful because they can reject suspect images without using the
known answer.

For the future: one likely source of scatter in the
Laplacian-image comparisons is that different ISS images have different
effective PSFs. The Laplacian operator is deliberately sensitive to sharp
structure, so it will respond differently to the same lunar edge if one image is
slightly sharper than another. Following the idea used by Langford et al. for
PSF homogenisation, we should estimate a PSF width for each image directly from
the lunar disk edge, identify the worst-resolution image, and convolve the
sharper images to that common resolution before recomputing the Laplacian
ratios. That should make the structural DS/BS diagnostic more comparable from
image to image. This is not being done in the present run because processing
the full ISS set takes roughly a day each time.

Index words: Laplacian images; DS/BS; ISS Moon images; Bayer G1/G2;
B-G colour; PSF homogenisation; disk-edge PSF; Langford et al.; scattered
light; earthshine data reduction.