Here are some results from a sensitivity-tst of one of our scattered-light-removal techniques. The technique is a forward convolution method but is not the EFM method, but shares elements from that method.
The EFM method consists of these steps:
0) An observed image is at hand.
1) From the observed image an idealized ‘source’ is constructed from all the bright pixels of the image.
2) A model observed image is calculated on the basis of trial values of alfa (the power-law exponent in the PSF) and the source image in 1 by FFT convolution
3) The model image is now shifted and scaled in intensity so that the halo matches the sky part on the DS and so that the brightest part on the BS disc matches.
4) the RMSE between the model image and the observed image is calculated on an area of the image that includes large parts of the sky around the Moon.
5) The trial image that has the smallest RMSE ‘wins’
6) That winning image is subtracted from the observed image. Since the model image did not contain any DS pixels (see step 1) the difference between the observed image and the model image should be the DS.
That was the EFM method. The method I test now is based on the above but omits step 3. In the EFM method step 3 was included in order to ensure flux conservation while making the model ‘fit the sky’ (this is reminiscent of the BBSO method where the sky if fitted ensuring that the model is anchored in the actual sky level thus making the residuals there 0).
We show two plots. Each plot has 3 panels – they are:
Panel 1: The Moon image being analysed.
Panel 2: A slice through the lunar disc with three graphs – the red one shows the known solution (the tests here are performed on synthetic images where a halo is applied with a convolution, using aflfa=1.8, to simulate effects of atmosphere and optics); the black one is the ‘observed’ image in step 0 above; the blue curve is from the image in step 2.
Panel 3: The black curve is the ideal image showing the structure on the DS, the thick green curve is the difference between the blue and the black curve in Panel 2 – i.e. it should be the model estimate of the DS.
Panel 4: This is the percentage difference between the two curves in panel 3.
The difference between the panels on the left and the right is that on the left a small value has been subtracted from the image in step 0 to simulate an uncertainty in bias subtraction; on the right no such value has been subtracted. The value subtracted on the left is 0.01.
A typical uncertainty in bias level may be a number of that magnitude – the consequence is an error in the estimate of the DS flux of 5-10 %.
Henriette’s estimates of how well we can subtract bias levels can be used here to introduce more realistic values of the error (0.01 may be too large, we hope).
The above shows the sensitivity in a scattered-light-removal technique to small errors in bias subtraction. This was NOT the EFM method which anchors itself in the DS sky, but a similar analysis is required for that method before we can present it in a paper.
Note how the slopes of the DS sky in the above plots do not match, despite the same alfa being used in the generation of the test image and the model image. Remember that in a lin-log plot like this a power law is not linear. Inspection of the blue curve in panels 2 above shows that it does indeed curve – the different slopes on the DS sky may be due to the proximity of the DS flux itself (which is also convolved and contributes to the DS sky halo) in the black curve. In other words: the halo on the DS sky in a real image may not be entirely due to the scattered BS, which we have assumed in the above.
This suggests that we should test methods based on convolving entire synthetic images of the Moon for the modelling part – make up the model of more than just the BS as in step 1. If we make up the models of BS+DS images we will have to enter the intensity of the DS, or directly, the terrestrial albedo, as a parameter in the grid search.
This is actually a feature of ‘Chris Method’ that we have seen in this blog.
This is our next step, but first we want to know if the above simpler method (just loop over values of alfa, not alfa and albedo) can be shown to work better if we do as we actually do in the EFM method – namely, we ‘force a fit’ on the DS sky. Since the preliminary trials of the EFM has shown up some not-understood problems of their own we are still working on the matter.