With a 1-degree occulter I took an image of the Sun. A slice across that image, through the darkest spot on the occulter gives this profile, plotting from darkest spot and outwards:
A log-log plot of the radial profile of the occulted Sun, on August 1 2014, using f22 and 1/500 s exposure, and a 1-degree occulter. Pixel scale is 0.04 deg/pixel, so 1 degree is at 25 pixels and the 200 pixels are at 8 degrees. The image is from the R-plane, G and B are not shown.
The occulter is the dark part at left stopping near pixel 20. The drop-off after pixel 200 is some roof or something like that, while the curve between pixels 20 and 200 are what the halo around the Sun looks like. The CCD is 12-bit so saturation starts near 4000, and non-linear response, perhaps, before that. However, we see clearly that the dropoff due to scatter in the optics is faster than dropoff of halo intensity. This implies that optical scatter plays a smaller role in defining the halo than does atmospheric scattering.
Note that this is with a multi-element SIGMA telelens – albeit on a rather hazy day. Of interest for our own little earthshine telescope is to repeat the above on some crystal-clear day (hopefully approximating conditions on Mauna Loa) and see if the optics drop-off is also faster than atmospherics then.
On Mauna Loa, of course, the effects of optics are what they are, independent of altitude while the atmosphere is MUCH clearer there – and there is less of it than in Frederiksberg.
In this post below we compared our canonical PSF (raised to various power) to the PSF shown in Figure 6 of the AvD paper.
We have since re-estimated /below) our PSF from radii near 0.1 arc minutes to 13 arcminutes using excellent data from multiple images of the star MARKAB. This PSF is empirical for one specific night and does not need the raising-to-a-power that the canonical one does. We plot it as is on the AvD figur, trying now to re-create the twopanels of that Figure:
Right panel shows our PSF as surface brightness in magnitudes per area.
I’d say our empirical PSF (green line) looks like it is realistically modelled by the canonical one raised to 1.8 and still beats the AvD PSF (the crosses).
We extended our PSF beyond 13 arcminutes by a third order power-law.
We have assumed a few things: AvD speak of normalized flux – we take this to imply that the PSF is divided by its VOLUME, not its area. We assume that calculating the surface brightness involves taking the total flux inside some distance from the peak and dividing it by the area.
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.
The author, Michael Hirsch has kindly been in touch with us and pointed out that the isoplanatic patch is small so using the OBD on instantaneous images from a typical stack, will yield speckle-like PSFs that are then smeared by the method. A smeared PSF will cause the concurrently deconvolved image to have too sharp edges! This is what we see.
We should instead either
a) use subimages the size of the isoplanatic patch and receive the PSF for that image and a deconvolved version of that image, or
b) generate a series of stack-average images and apply the OBD to that, receiving the time-average PSF and the deconvolved image.
Of course, we thought we were doing b), but should instead perform the time averaging before OBDing.
Doing a) would not solve our halo-problem as the isoplanatic patch is small and we are looking for info on 1×1 degree PSFs.
Testing to follow …
Note that night JD 2456076 is the one with most (15) 100-image stacks in all filters. You could get 30 in a row if you combined IRCUT and VE1 …
By careful analysis of the halo around stars, Jupiter and the Moon, we have arrived at an understanding that the PSF is related to a power-function 1/r^alfa, where alfa is some number below 3.
It is also possible to estimnate the PSF using deconvolution techniques. In particular, the ‘multiframe blind deconvolution’ method produces estimates of both the deconvolved image and the PSF, without any other input than the requirement that the output image and the PSF be positive everywhere.
Fredrik Boberg and I – well, Fredrik – has tested the software on images pulled from a 100-stack on (nonaligned, but almost aligned) images. The output comes in the form of estimates of the PSF and estimates of the deconvolved image. The deconvolved image has an unnaturally sharp limb – but more on that somewhere else – for now, let us see the PSF!
The estimated PSF is highly non-rotationally symmetric, but does have a central peak. The ‘skirt’ wavers up and down over many orders of magnitude. A radial plot of the PSF and a surface plut looks like this:
The red line shows the 1/r³ profile. The elliptical shape of the PSF causes the broad tunnel seen above – the divergence at radii from 30 pixels and out is the ‘wavering skirt’.
The PSF does appear to generally be a 1/r³ power law, which is encouraging. It appears to be quite flat out to 2 or 3 pixels – which also generally matches what we have seen in the PSFs empirically generated from imags of stars.
Next: Test on a synthetic image convolved by a known PSF. pre-align the images in the stack – perhaps a slow drift causes the non-round psf. Repeat the above for several stack from different nights. Repeat the above for stacks taken through different filters – any indication that PSFs are different?
We have indications that the halo seen in B and V images are somewhat similar, but that VE2 images of the Moon have decidedly different halo profiles. Because the filters used in B, V and VE2 are fabricated (and function) differently we may have the situation that this causes the differences in halo profiles. B and V are ‘coloured glass’ filters while VE2 is a thin-film filter. In a DSLR detector the R,G and B filters are essentially bits of coloured semiconductor material. As a test we inspect the halo seen around the Moon in images taken with a DSLR camera. In such images the R,G and B channels are obtained at the same time at precisely the same observing conditions.
On the internet (http://bit.ly/13YZIOU) we have found a very detailed large-scale JPG (i.e. 8 bit only) 10-min exposure image of the sky near Orion containing the Moon. We submitted the image to nova.astrometry.net and received a solution back, including image scale. We took the resulting WCS-equipped image and extracted the profile of the lunar halo in R, G and B and plot these against radius from the estimated disk centre. We have subtracted a sky level for each colour, estimated by eye, and show the profile in the upper panel and repeat it in the lower panel with straight lines fitted:
The profiles are saturated out to about half a degree but after that they follow a remarkably similar shape in this log-log plot. Fitting power law functions (1/r^alfa), we may even see some sort of ‘straight line behaviour’ between radius 0.6 and just short of 2 degrees, with another linear trend taking over out until the sky-noise is reached at 4 degrees or so. The slopes are fitted-by-eye only but are -2.9 (near the canonical ‘can-never-be-steeper-than-3’) value, and -1.3.
Before assuming that ‘DSLR RGB imaging’ will solve all our filter problems, let us recall that the VE2 vs other profile differences we have found are subtle; that the above is based on an 8-bit image; that nothing is known about the image treatment performed by the author of that image, and that we do not have data similar to VE2 here – the R channel is not VE2 [ … but read more here link !]. Let us instead try to do something similar with 14-bit RAW images.
Note that the above image was obtained by tracking the sky. Apparently, tracking allowed a long exposure that gave us a wide halo to study. In our own DSLR-On-the-sky wide-field images we have failed to get results similar to the above – exposures were limited to several seconds to avoid overexposure and trailing. Our own MLO telescope images are restricted to the 1/2 degree reach from disc centre.
Note that the above essentially speaks very well for the sort of DSLR optics used – the amount of scattered light near sources must be low or we would not see so steep a PSF! Again, this may be easier to do with a wide-field lens such as used for the above image – trhings may be different with a tele-lens that allowed a closeup of the Moon. The ‘core’ of the PSF should be better investigated, if we can get some of our own images of e.g. Jupiter or bright stars – the above image is VERY wide-field and contains zillions of crowded stars, not likely to give us good point-source PSFs.
In this post we saw that the difference between B and V (magnitude) images could have the shape of a linear slope on the DS and plateau on the BS. We are trying to recreate that using synthetic models. It is surprisingly difficult!
Using V and V images we saw that differences typically had the shape of level offsets – not slopes. In the B-V images we saw linear slopes on the BS. I thought the linear slopes originated in different PSFs in two filters – different alfa-parameters, for instance.
Well, taking a synthetic image and convolving it twice with two slightly different PSFs and converting to magnitudes and subtracting gives this:
Upper panel shows the ideal image we are using – BS to the right and the rest is DS. Bottom panel shows the difference between the image convolved with alfa=1.73 and alfa=1.72*1.02. DS is columns left of 360 – there is no linear slope. There are plenty of features on the DS above, but none ‘slope away linearly from the BS’.
A straight line in a lin-log plot corresponds to an exponential term. The difference between two Gaussians of different width is probably another Gaussian. Are we learning that the real PSF has a Gaussian term in it that varies between filters? Since V-V images did not show this behaviour the Gaussian is not manifested by the inevitable slight image alignment problems. Our model PSF is an empirical core with power-law extensions – and the above experiments show that such PSFs do not yield linear-slope differences.
Perhaps we could study the real PSF by studying difference images in a thorough way? Student project!
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
instead of the present
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.
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.
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).
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%.
As the night was fairly clear, I put the telescope on the lamps on the Antenna (Alt/Az: 21*34’/256*25′).
As the several lamps on the Antenna seem distinct it is at least not an ‘extremely foggy night’. I took V-band exposures at about 1 second.
Then I extracted the profile from the 25 coadded images. Only the quadrant below and to the right of the lower of the two sources above was used:
To about 20 pixels we see the actual lamp (i.e. the glass enclosure and filament). From about 30 pixels to short of 100 pixels we see the halo dropoff. The red line is a 1/r^(2.8) PSF.
This is contrary to what Chris found using the Moon and the occulting balcony! Unless the halo we see above is built up in the few hundred feet between the lamp and the telescope it must be due to the optics in the telescope. We cannot rule out that there was some fog, but the size of the exponent (2.8) indicates a ‘clear night’, I think – or is that circular thinking?
Anyway – it is not impossible that both optics and ‘air’ scatter in the same way.
Wonder if we can detect any examples where there is one halo from the optics and another from the atmosphere?
As a follow up to the knife edge imaging of the moon with the Canon 35
mm camera, I took images of a laserpointer shining into the lens.
Laserpointer was set on with tape and shone into the camera lens from a
distance of about 5 meters. Camera was on a good tripod. The laser
pointer was aligned to be pointing into the lens by watching to see it
emerge from the back of the camera out the viewfinder and onto a wall
behind the camera. Eyes were kept well away from everything! Exposure times of a few hundredths to a few thousandths of a second gave good halos.
Laser was pretty well centered. There is a weak secondary image off to lower right. The main image is saturated in the core out to about 10 pixels radius.
The laser has a strong core surrounded by a quite uniform intensity “platform”, after which the light falls away like a power law.
The radial profile of the laser (blue) compared to the moon (green) is shown below.
The laser pointer’s profile falls off faster than the moon — but not very much faster.
If we assume that the laser is a good point source, then there is scattering in the lens/CCD combination in the camera which is seen as a power law at large R.
Slope of the lunar halo is about -2.0, whereas the slope of the laser pointer halo is about -2.6. Getting close to the diffraction limit of -3!
The lunar profile is then interpreted as a combination of both scattering in the camera and scattering in the atmosphere. Its slope is shallower — so atmospheric scattering totally dominates at large R (scale both powerlaw falloffs to the same flux at log(R)=2 or 100 pixels to see this — atmospheric scatter would then dominate internal lens scatter by about an order of magnitude out at R=1000). Not sure what’s happening close in, as the laser pointer has a strong uniform intensity “platform” of light around the core — easily seen by eye just by pointing it at a piece of paper. A point like source of light, like a street lamp seen at a large distance might be a way around this problem.
I also imaged the laser pointer projected onto a white wall — long exposure times of many seconds — and got the same result — similar core and platform and a halo with the same slope.
Peter sent Chris a file called “ROLO_765nm_Vega_psf.dat”
which contains the PSF of Vega measured by Tom Stone.
Here is the profile:
the horizontal scale is log of r in arsecs.
the inner part is something like a Gaussian, like King finds.
the halo outer part goes at r^-2.4, in the range 1.2 < log(r) < 2.0, so steeper than King but not as steep as our steepest profiles to date (these are r^-3).
The very outer parts are certainly affected by sky subtraction, as the light will be well below sky at log(r)>2, one could fix this probably by choosing the sky so that the halo continues at the same gradient, but this is of course arbitrary.
It seems that for a wide range of telescopes and instruments, the distant stellar light falls off as a power law — we see this in the ES telescope, a 35 mm camera, King’s profile, and a range of other instruments/telescopes summarised in a paper by Bernstein (ApJ, 666, 663, 2007).
The slope of the power law can change even on the same telescope/instrument! We see different powers on different nights. This is important!
We obtained images of the full moon from Sydney with the Canon 35 mm camera, reaching out to about 15 degrees from the moon — three times further out than the King profile reaches. We are curious about how far out it goes as a power law.
The plot shows the profile done for a range of exposure times, getting longer and longer, at the cost of overexposing the moon and halo around it, but better sampling the faint halo far away.
I have shown the raw data merging into the background sky in the bottom panels. Subtracting this sky gives the halo only profile in the middle panel for the range of exposures.
Top panel shows the overall profile by using only the valid (not overexposed) parts of each curve — by simply accounting for the different exposure times — nothing more has been done. They sit on a pretty well defined locus all the way from the edge of the moon out to the edge of the frame (~15 degrees out) and follow roughly r^-1.8. It’s probably flatter than this closer in. This is of course the scattered light, not the PSF per se, but very far from the moon — like > a few degrees — the moon is essentially a point source anyway (it’s only 30 pixels across on a chip 3900 pixels wide).
I learned something important! The profile is r^-1.8 when sky subtracted! We can follow it well beyond the point that the halo is much fainter than the sky. So King I think is talking about the sky subtracted profile as well. I have been wondering when the King profile would actually join the sky and become a DC component… of course it doesn’t, that’s the point. The DC component, i.e. Rayleigh scattering (?) is caused by the bright source as well, but is not considered part of the profile. I guess. So if we were trying to model the scattering over very large angles we’d have to consider both components. My guess is that for our ES telescope the field of view is so small that the scattered light is the halo only — the Rayleigh component is negligible. One starts to see it in the 35mm camera data at about 1000 pixels (1 pix is approx 1 minute in these data) so about 10 degrees to 15 degrees from the moon (lower panel shows a blue curve which essentially joins the bias level at large r, whereas the green and black curves are flattening out to a level which is bias + a fair bit of sky). In these data, the sky is about 5*2.5 = 7.5 magnitudes below the full moon surface brightness (seen in upper panel, with brightness of the moon at log(r)=0 and the (subtracted) sky having similar brightness as the halo at about log(r)=3 — beyond which one traces the halo below the sky).
We now have good radial profiles of Altair and Menkab. Altair was observed in very good conditions, and its profile is close to the expectation of r^-3 for the diffraction limit — in three of the 5 bands. In B and VE1 funny things are happening which we don’t yet understand. The Menkab profiles have halos like r^-1.5 — much broader. The plots below compare both stars:
We think that Menkab might have been taken on a not-quite-perfect night photometrically. We’re looking into this, so watch this space!
Notes on the photometry for ALTAIR on JD2455845 (about October 11, 2001) ————————————————————————
Altair was observed with the B,V,VE1,VE2, and IRCUT filters. Dark frames were obtained before and after. Images had the interpolated dark field subtracted (i.e. the average of the closet DF before and after was formed and subtracted).
The IDL routine BASPHOTE.pro was used with a 9/9/12 annulus aperture to find the counts in each stellar image. The exposure time was read from the FITS header and was the actually measure exp time, not the requested one.
Fluxes were calculated for each filter and the standard deviation of the fluxes expressed as a percentage of the mean flux.
Band SD —————— B 8.5% V 8.4% VE1 9.9% VE2 4.5% IRCUT 7.6%
Exposure times were in the range from 0.17s to 1.1 s for the various bands.
Some frame-dropout was noted – about 5 frames in 100 failed to open at all.
The variability in the flux is consistent with previous considerations – i.e. there is scintillation. The increase in variability with blueness may be because there is more scintillation in the blue or because exposure times are shorter in the blue, or both.
Peter took data on Menkab in 5 bands (October 7th, 2011) – B, V, VE1, VE2 and IRCUT. Surprisingly, the halo around the star follows r^-1.5 in all bands. Was the night a bit hazy? On a clear night we have been expecting r^-3.
The central PSF, within ~5 pixels, is very regular, as the stars are nicely round (Altair, with the best inner PSF to date, was a very boxy image — see posting on this below).
The VE2 image has a significantly broader transition region to the outer halo. Quite strange!
The 5 profiles are here :
The are compared to the profile we got for Altair in V band a few nights ago and our best guess profile in V from the modeling the scattered light from the moon.
The halo slope is about r^-1.5 in all 5 bands for Menkab. They also wiggle a bit, unlike when we get r^-3, which is straight as best we can tell. The “shutter bounce” effect is also much harder to see because, presumably, the flatter halo is washing it out. It’s visible but weak in the 2-d images.
This is all a bit surprising and very potentially very important. We may be much more dependent on the atmospheric conditions on each night that we thought.
It would be very good to do aperture photometry of the star as a function of time in each band for each obtained image, to check if the night really was “photometric”.
We decided to look at the scattered halo light around the moon in a conventional 35 mm Canon camera, out of sheer curiosity.
The field of view of the Canon of about 10 degrees across, with images of 3888×2592 pixels. There is a pincushion effect toward the very edges but otherwise the halo is well traced. 12 images starting from an exposure time of 1/2500 seconds and increasing exposure time by factors of two at each step were taken. The images were taken from Chris’ back garden in Sydney on a very clear night in September 2011.
Upper plot: halo around the saturated moon (seen at left) for the five longest exposures. The uniform separation of the profiles by 0.3 (in the log) is just as expected for factors of two increase in the exposure times, so the system appears to be linear. Lower plot: log-log plot of the halo flux versus distance shows a very closely followed power law with slope ~ -1: this we call a “Toto” profile (= r^-1). The earthshine camera instead shows a “Mitzi” profile, r^-3, which is as expected for a diffraction limited telescope. A 35 mm camera has a great deal more scattered light!
We took a few hundred 0.4 second exposures of Altair, to measure the stellar PSF. Plot below shows Altair (green) versus our current best model (red) of the PSF based on fitting the moon. Note x axis is log(r/pixels).
The match is excellent, especially for the outer halo with its r^-3 powerlaw! Disagreement in the inner PSF (r<3 pixels, log(r)<0.5) is because Altair is very elliptical — so the radial PSF shown here has a lot of scatter. Note that this might be due to saturation/miscentering during the coadd – we’ll look at that.
Sep 29 — Peter and Chris observed Markab — noticed much broader halo around the stars than usual. Image below shows that this can even be seen in the sky camera.
Left: clear night from 2011-09-27, Jupiter in center of frame. Right: not photometric conditions 2011-09-29, Jupiter has a slight halo. Note that the bright “star” right above Jupiter is possibly an internal reflection (of Jupiter?) in the sky camera.
We will observe Jupiter through whatever this stuff so we can compare directly to previous determinations of the PSF.
The plot shows astigmatism of the psf across the image plane. A short single exposure of the open cluster M7 was used, exposure time = 60 seconds. Ellipticity is shown by the length of the lines in the lower plot — and the lines are aligned with the position angle of the sources. The upper plot shows that ellipticity rises pretty sharply towards the CCD edges — from about 0.05 in the center to about 0.4 at the edge. n.b. ellipticity is defined as e = 1 – b/a, where a is the semimajor axis and b the semiminor axis. Ellipticity at the center of the field is about 0.05 – not 0.0. These results are for the ellipticity of the inner core of the PSF (it’s measured out to 3 pixels radius). Whether the power-law halo of the PSF is non-round on any scales is still under study.
Chris made this plot from two observing sessions of Jupiter. The first involved approx. 100 imags while the second (green) involved approx 1700 images.
Comments from Chris: The plot shows the psf around Jupiter. About
200 x 0.1 second exposures were averaged (black dots) and about 1700 a
few weeks later (green dots). T
Black dots: the psf can be traced out to log(r) ~ 1.5, Green dots: the
psf is very similar to the first one and can be traced out to about
log(r) ~ 1.8.
Note well: the background level of the sky has been adjusted be a small
amount — by not more than the uncertainty in the sky itself — to allow
the points at large to fall off with the same power law out to 100
The power law fall off of the PSF is ~ r^-3 in the outer regions.
Signs of the non-axisymmetric psf are seen as extra dots above the main
sequence of dots. This is mainly caused by shutter bounce, leaving a smear of photons to the right in the psf.
The clusters of points at particular radii and sticking up are the Galilean
The black line shows our current (Sept 29, 2011) best estimate of the psf from forward scattering of ideal lunar images and fitting them to lunar observations. It’s very close to the Jupiter PSF at large radii. This is the reason we think the
psf is falling as a power law all the way to the edge of the frame.
The departure of the inner part of the PSF around Jupiter from the black line is caused by the finite size of Jupiter — about 6 pixels across.
The inner part of the PSF is still not measured anyway. We are working on this!