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.

A whiff of success

Post-Obs scattered-light rem. Posted on Dec 19, 2012 14:07

We do have many problems to contend with – but now and then we are confirmed in what we set out to do: Here is an example of the scattered-light reduction of an observed image (2456034.114etc) where the EFM Method seems to be doing well compared to BBSO linear. We compare to a synthetic model image generated for the moment of observation (i.e. the libration and geometric factors are representative of the observing situation):

Top panel: slice across the Moon at row 296 so that Grimaldi near the edge is transected. The black curve is the synthetic model unconvolved – it is in units of W/m². The red curve is the scaled and offset profile along the same row of the EFM-cleaned image; and the blue curve is the BBSO-linear cleaned image identically scaled and offset.
Middle panel: detail of the above.
Bottom panel: difference between EFM and ideal and BBSO-linear and ideal, along row 296, expressed in percent of the ideal value.

The observed data were scaled since the units are different; they were offset because the EFM model did not have 0 value on the DS sky. The BBSO-linear, being ‘anchored in the DS sky’ did have a 0 value in the sky. The same scaling factor and offset was used on EFM and BBSO, for comparison, however – hence the little offset on the DS sky at right.

What do we see? Well, the EFM-cleaned (red) line follows the synthetic model quite nicely between column numbers 325 and 370 while the blue line (BBSO-cleaned) diverges all the time. Near the DS edge (columns 370-385) the synthetic model is higher than EFM.

What does it mean? The BBSO-linear method has better removed the flux on the sky – it is designed to do that, while the EFM is designed to minimize the residuals squared in a mask on the sky around the Moon. This implies that the BBSO-linear method, in the present case, would be better than EFM on the lunar disc near the DS sky. As we move further onto the DS disc the BBSO-linear method will fail more and more since the halo is not linear with distance from the edge – the method underestimates the amount of scattered light on the disc between the edge and the BS. We do see how the blue line diverges more and more; we do see the red line cling closer to the ‘true value’ (assuming the synthetic model is ‘true’) across the disc, before it too fails nearer the halo and the BS. The behavior nearer the edge may be a consequence of how we model the synthetic images – we have to use a reflectance model to make the synthetic images – and the angles of emergence and incidence corresponding to ‘near the edge’ is not one for which the reflectance model is inherently very good. The models we use are based on the simple ‘Hapke 63’ model. We speculate that the disparity between observations and synthetic models in the columns 370-385 is due to model inadequacy.

Anyone using a reflectance model as simple as the Hapke 63 model will encounter the above problem if they try to use pixels near the lunar disc edge – the natural thing to do, if the halo is removed using the linear method is to use edge or near-edge pixels.

Hence the problem of reflectance modeling and the inadequate linear method become coupled! Our EFM method seems to be a way around this obstacle – allowing use of disc areas further from the edge where simple reflectance modelling is adequate – hence we should be getting more reliable terrestrial albedo data. One day.

Are the PSF alfas correlated?

Post-Obs scattered-light rem. Posted on Dec 19, 2012 08:50

In the EFM-method we determine the alfa values for every image. Is there a link between the alfa value for one filter and the rest in an interval of time? It is our understanding that alfa is determined by the amount of scattering in the optics plus the atmosphere. We therefore expect that on ‘bad’ nights the alfa values will tend to move in the same direction. We investigate this here.

We find all alfa values in all EFM-treated images. We sort them into half-hour bins. We calculate all the alfa values in each bin and plot the results. Below is a pdf showing all the plots between some filters, at different ‘zoom-levels’. The image shows the last zoom-level, highlighting the dense ‘clump’ of points:

There seems to be a general agreement that the alfa values are correlated – bad nights (i.e. ‘broad PSFs’) occur in all filters at the same time. Since VE1 is just about identical to IRCUT the scatter seen above means that the fitting routine is unable to make a perfect match – or that observing conditions, during the half-hour bins used, changed.

Using 15 minute bins does not improve matters:
I therefore suspect that the fitting method does not find the best fit each time.