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.

We have some excellent data from observing the star Markab, in Pegasus. We have 334 images at 4 seconds exposure, and each is bordered by dark frames of the same expsoure time – thus we can subtract bias and any dark current easily.

We did this, and aligned and coadded the many images. Then we inspect the PSF by cosnidering the intensity around teh star in concentric rings:

We see that the core of the PSF is about 2.5-3 orders of magnitude above the point where the wings start. We see the wings drop off and join the sky level. The red crosses are median bin values. The blue curve is a polynomial fit, the coefficient of which are given in the table.The polynomial is found for a fit to 1/radius against PSF for the wings, and a Voigt function for the core out to about 1 arc minute.

Some points: The curve is not the PSF – because there are remnants of sky brightness – about 0.88 counts [star scaled to 50000 counts at the peak]. The PSF would be well approximated by the above polynomial without offset (first coefficient). The part of the PSF from 1-3 arc minutes is roughly linear, as if a simple 1/r ^alfa power-law applies. This is not the case when we consider the above.

We might revisit the extended halo we see in lunar images with the above insight into the effect of a sky level.

This paper discusses the use of novel lens coatings in commercial grade lenses (Canon) and DSLR cameras to build a multi-lens, co-additive system. They discuss the PSF they have in their Figures 6 and 8 (8 is about ghosts).

We can compare the PSF we believe we have to theirs: Here we have used the same axis-scaling as Figure 6 of AvD. The three curves are our normalized PSF profiles for three settings of the ‘power’. These are 1.8, 1.6, and 1.4 – the largest at the bottom. Remember that the ‘canonical PSF’ we use already has a power slope of close to 1.7 so with the extra powers above we reach 3.06, 2.72 and 2.38, respectively. We know that the power of 3 is the limit for the wings of a diffraction profile, so use of values of ‘power’ near 1.8 implies we think we are diffraction limited – in the wings. Actual fits to observed images tends to give powers nearer to 1.7 or a total power-law exponent near 2.9. The points on the plot above are taken (by eye) from Fig 6 of AvD.

They seem to have not only a broader PSF than us, but the ‘wings’ appear to be linear in lin-log: that is, their wide halo is not a power law as we infer, but is rather an exponential.

On the face of it, our optics are ‘better’ than theirs, but hold on:

1) we do not actually measure all of our PSF – we infer that a power-law tail is in order; we only have actual profile measurements from point sources such as stars and Jupiter (almost a point source) inside several arc minutes. The rest of the wings are inferred from how the halo around the Moon looks at distance.

2) In their Figure 8 an image of Venus and a star is seen – and a ghost of Venus. The authors state that “the ghost contains only 0.025% of Venus’ light”. I think that number is so small that our requirements of 0.1% accuracies in photometry would be met. Note that ghost and the PSF are unrelated – the PSF wings describe light scattered while ghosts are reflections off optical element surfaces. The paper says that it looks like not all lens elements were coated with the novel coating.

What do we get from this?

I would like to investigate the PSF we have some more – this can be done with repeated images of a point light source in the lab: this would clarify the non-atmospheric part of the PSF. Despite current problems with FWs we may be able to pull this off with what we have.

I would like to understand where the (inevitable) ghosts are in our system – did Ahmed park them on the Moon itself? If they are same size as the Moon and well-centered they may not cause any damage since they merely replicate the image information (if same size and in focus).

It seems the AvD system has very weak ghosts but larger scattering than us (if we understood our PSF wings correctly) – if the weak ghosts are due to these new lens coatings then they are of interest to us in possible future designs of the system. If the scattering really is as high as it looks, compared to our (guesstimated PSF wings) then we have a better system than them, period. Mette commented that these coatings can cause scattering – wonder if the AvD people chose the coatings to lower ghost intensities or to get rid of scattered light? They do not say so directly, but do compare to large telescope PSFs (their Fig 6), and find less scattered light in their own system.

We need to understand how they measure their PSF into the wings.