# 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.

## PSF with two parameters: Better?

Data reduction issues Posted on Jan 26, 2013 17:29

In this post: http://iloapp.thejll.com/blog/earthshine?Home&post=293 I proposed to fit more elaborate PSFs than we have been using.

I present here the results of fitting a 2-parameter PSF. The previous one was characterized by an exponent alfa, and had the form

PSF ~1/R^alfa.

The new one allows two exponents – one regulating the slope of the PSF up to a cutioff point in terms of radius, and the other parameter taking over outside that point. Thus we have 2 new parameters to fit – exponent and cutoff point.

Using such a PSF and evaluating success on the parts of the image designated by the mask – and using a mask consisting of sky on both sides of the Moon, but no polar areas – i.e. a ‘belt across the image’ – we arrive at images with slight changes in the estimated halo on the DS of the Moon and larger changes in the area on teh BS-sky.

This plot summarizes what was found:

The top panel shows absolute value of residuals (obs-EFM-model) in a slice across an image after the halo has been removed (along with most of the BS, as is always the case in the EFM method). The PSF used was the new tow-parameter PSF.
The middle panel shows the result when the usual one-parameter PSF has been used.
The last panel shows the difference between the two panels, expressed as a percentage of the first one. The illegible y-axis label for the bottom panel shows 10^-2 at the bottom, next label is at 10^0
.

Note that absolute values of residuals are plotted above.

We see the DS to the left, the almost-erased BS to the right and the sky on either sides.
Clearly, the BS sky has been removed much better in the first image – i.e. with the two-parameter PSF. On the DS we see changes in the range from 1 to a few percent on the sky-ward part, rising to tens of percent near the BS.

This implies that a signifcantly different amount of scattered light has been removed using the two PSFs – but which is the better result? Judging by the RMSE per pixel on the mask in the two cases there has been a significant improvement in going from one to two parameter PSFs. The RMSE per pixel in the one-parameter PSF case is about 5 [counts/pixel], while the RMSE per pixel is 0.23 [counts/pixel] in the two-parameter case. Most of this change has evidently taken place in the BS part of the sky.

We need to know if there has been an improvement on the part of the image that matters – the DS!

The best fitted parameters were quite alike – near alfa=1.7. The best-fit cutoff point was near 30 pixels.

## A Bold Proposal!

Exploring the PSF Posted on Jan 26, 2013 10:45

It seems that success for us will be linked to our ability to correctly remove scattered light from the BS. This hinges on our understanding of the scattering model – in essence, the PSF.

Currently we use a PSF that is empirical. The core is made up of values from a table generated from observations of bright stars and Jupiter. To that we link an extension, also empirical, that is based on what the far wings of the lunar halo looks like. This PSF is then ‘exponentiated’ during fitting to actual images in the EFM method.

We noted during several posts below that the values for the exponent varied little and only now and then seemed linked to the extinction. This could be an indication that most of the time (during good nights) we are limited by something fixed – such as the optics – rather than atmospheric conditions. On the other hand it could mean that the PSF is not very accurate in its basic from and that the fitting method gives up at some stage, leaving us with an exponent that is somewhat random, and therefore not linked to the atmospheric conditions.

We should also recall what happens during application of the EFM method: We have tested various forms of sky masks for this method – some that allowed fitting emphasis on both the DS and BS sky, and others that emphasized only one side. Common for the ones that focused on either just the DS sky or the BS sky was that the halo shape on the other side was not very good.

Might these things be indicating that a better PSF should be generated or a better way found to apply the fits?

I’d like to suggest the following: Perhaps the PSF has a form like

PSF ~1/R^alfa(R)

PSF ~1/R^const_alfa ?

I would like to try to use a piece-wise constant alfa so that the PSF is separated into radial zones, each of which has its own alfa, found by fitting.

## More on SKEs

Optical design Posted on Jan 26, 2013 10:06

In this post: http://iloapp.thejll.com/blog/earthshine?Home&post=289
the importance of the SKE for scattered light was discussed. The images shown, though, were not shown fairly – with intensities scaled to comparable levels. I therefore extracted a line across the BBSO image and a line across our image, at right angles to the SKEs, rescaled the intensities, aligned the plots and get this:
The black curve is from our image (whichis a sum of 10 well-exposed images). The red curve shows the cut across a single BBSO image.The BBSO image has only the DS peeking our behind the SKE, while our image has the BS in full view.

We see entirely comparable ‘halos’! The BBSO image ha a more pronounced sloping ‘tail’ onto the black side of the SKE than we do, and more noise. If that sloping tail is ‘halo’ we had a better system than the BBSO!

What does the above mean? It does NOT mean that we have less ‘halo problems’ than BBSO does – because the BBSO expose their DS so that the halo from the BS is not allowed to be formed. Yes there is a similar halo from the DS on their images as there is from the BS on our images – but the halo from our BS is very much stronger than their DS halo.

When the BS halo is small – i.e. near New Moon – we have minimal effect of the BS halo.