# Earthshine blog

## "Earthshine blog"

A blog about a telescopic system at the Mauna Loa Observatory on Hawaii to determine terrestrial albedo by earthshine observations. Feasible thanks to sheer determination.

## JD2455949

Observing log Posted on Jan 22, 2012 17:21

Ran scripts to observe Saturn and Mars. Strange problems with script not writing to disc. Rebooted and all was OK.

T 4C outside, 6.7 inside. 10 m/s, 40% RH. Clear.

## Conservation of flux

Exploring the PSF Posted on Jan 22, 2012 13:37

During convolution of synthetic images with various PSFs we need to consider if flux is conserved. We calculate such images for a range of alfas and show here the difference in percent of the total flux of the image relative to the ideal image.

Percentage-change PSF-file
——————————
-1.6768524 % out1p4.fits
-0.060953825 % out1p6.fits
0.014277556 % out1p8.fits
0.027423956 % out1p9.fits
——————————

That is, in an image convolved by the broad PSF with alfa=1.4 1.67% of the flux is lost, while only 0.03% of the flux is changed when convolving with a PSF with alfa=1.9 (the narrowest possible).

The loss (and gain) in flux is not understood yet – but is perhaps related to clipping (in the case of the broad PSF) of halo when the images are padded 3×3 in order to perform the FFT, or roundoff (narrow PSF – many values are rounded below 1 to 0).

## Effect of a PSF on the lunar disc

Exploring the PSF Posted on Jan 22, 2012 13:17

To show the effect of progressively wider PSFs smearing the ideal image, we apply the standard PSF with alfa set to 1.4, 1.6, 1.8 and 1,9 (close to the limit), and plot a ‘slice’ across the discs:

Top panel: In red the counts of the ideal image across the lunar disc, along with slices of smeared images for alfa=1.4 (top), 1.6, 1.8, and 1.9 (lowest).
Bottom panel: The absolute-value percentage difference between the slices in the top panel and the ideal image slice.

In the first panel we see that indeed the halo is approximately linear on the DS part of the sky.

We see in the bottom panel that the DS (columns 150-390, approximately) is strongly affected by the smearing by the PSF for values of alfa we have seen on even ‘good nights’ – alfa~1.6. Occasionally we have seen alfa~1.8 and even there the DS is strongly affected at the extreme edge of the disc, away from the BS, by approximately 10%.

## Testing stability of Poisson-noise ‘addition’

Post-Obs scattered-light rem. Posted on Jan 22, 2012 11:11

In our tests of various scattered-light removal techniques we are using synthetic images to which various realistic things have been done – smearing by a PSF and ‘adding’ Poisson noise, etc.

Poisson noise should not be ‘added’ because this will increase the mean value of a region of an image. Instead, Poissonian noise should be drawn from the Poisson distribution with a mean at the value of the image pixel under consideration.

We have two codes to generate Poisson noise in images and we test these next. We take one synthetic (i.e. noise-free) image and define a region on it. In that region we calculaet the mean. We then generate Poisson-noisy images using our IDL code and a Fortran code. These are different in that the IDL code writes out floating-point images while the Fortran code writes out integer images.

In a loop over 1000 trials we generate noisy images from the original image and each tine calculate the mean in the predefined region. We set aside the percentage difference between the IDL code and the ideal image and the Fortran code and the ideal image.

Then we plot these percentage differences:

The two distributions are symmetric about 0 and practically identical. From this we conclude that both codes ‘add’ Poisson noise to the image correctly and that the writing-out of the integer resulting image in the case of the Fortran code does not cause any rundoff problems, even if the region inside of which we tested had a small mean value (about 3.9 pcounts). The regiion was 19×19 pixels large.

We do note that the spread, although similar, is quite large – SD is 4 and 6 counts respectively. This implies, unsurprisingly, that the number of boxes of size 19×19 that must be averaged over is in the hundreds if the standard error of the mean is to be at our science goal of 0.1%. We knew that – this is just a reminder …

Final note: the Fortran code uses a fixed seed to generate random numbers. A modification was needed to read in a random seed instead, from the command line. This is supplied when the code is called by the user.