Visible light leakage model and associated noise

[wtbarnes]

We need a model for the visible light leakage. This has both a steady component as well as a shot noise component.

From @jacobdparker: "We could take the signal estimate from Tom over a uniform disk, and convolve it with an appropriately sized airy disk, and overlay it on the zero order image."

[wtbarnes]

The shot noise should be $\approx\sqrt{\mathrm{steady}\quad\mathrm{component}}$

[wtbarnes]

ref_solar_irradiance_whi-2008_ver2.txt

[wtbarnes]

The following is extracted from email correspondence between Tom, Amir, and others. I've preserved it here to make it more visible:

Tom:

The number of solar photons through 44 micron diameter aperture is 8.5E12 photons/sec. To get it in units of photons/sec/pixel, then you can reduce that number by solar image size (in pixels) on the detector. Of course, the actual out-of-band calculation is to convolve the solar spectrum with the filter transmission as a function of wavelength. The WHI reference solar spectrum is attached (Woods et al., 2009 paper). We normally fly with one foil filter with the aperture and one foil filter in front of detector for reduction of visible light by about a factor of 1E-12 (1E-6 per foil filter). Example is zeroth order diode of EVE ESP and for solar EUV imagers like SDO AIA. For grating spectrograph (e.g. EVE MEGS), one can fly just one foil filter because grating will reduce out-of-band by > 1E-5 for first (and higher) orders. Because CubIXSS is observing so close to the zeroth order, I think you need two foil filters (definitely required for zeroth order). The two foil filters also allow for some pinhole degradation in the foils (assuming a pinhole in one foil doesn’t align with pinhole in other foil).

Amir:

Thanks, much appreciated for this! We'll work through this to refine the filter calcs. In our case, the solar disk takes up about 1e5 pixels, so without any filter or grating we'd have 8.5e7 photons/sec/pix if the photons are (roughly) uniformly distributed on the disk. The grating will cut out everything but 0th order, and I imagine that's about 50% effective (the open area of the grating), so ~4e7 photons/sec/pix. With a 100 nm Al filter alone, we have visible/UV attenuation of about 1e6, so that would be about 40 photons/sec/pix (give or take a factor of two, I guess), which would correspond to 40 electrons/sec/pix. The pedestal itself can be subtracted if it's relatively consistent, but the shot noise is obviously not subtractable. But that being said, on the solar disk the worst case 1st order photon would be 2 nm or shorter (the longer wavelengths all diffract to larger angles and won't overlap the 0th order solar disk). A single 2 nm photon deposits 170 electrons, so even just one photon in a pixel is already 4x the pedestal and much more above the shot noise. So unless I'm messing up the calculation somewhere, it would seem that we're borderline OK with a 1e6 attenuation for this particular application, because the visible background is only a few tens of photons (or electrons) per second per pixel while each X-ray photon is already well above the background. Did I do something wrong in the calc? (Assuming I did not -- we would probably still want to go with something like 125 nm Al for margin. But if we go much thicker we'll cut the X-ray transmission pretty drastically.)

Tom:

I agree with your estimate. To help the case, the QE of visible light photons in Si is about 50%, so actual signal would then be 20 electrons/sec/pix. The higher background does hurt energy resolution though. The shot noise needs to be considered separately for the photon event and for the visible background. The X-ray 2nm shot noise is estimated as sqrt(170) or 13, so wavelength resolution at 2 nm is at best 0.15 nm (but I ignored Fano noise) if background visible signal is 0.0. With the 20 electrons/sec/pix background, then the extra shot noise of the visible background is sqrt(20) or 4.5 and so wavelength resolution degrades to 0.21 nm. HOWEVER, you do not necessarily have to resolve energy for each photon event but instead can rely on photon position location for determining the photon energy. IF you are trying to use both photon event intensity and photon position on detector to determine photon’s energy (wavelength), then I suggest you consider higher read-out rate of the CIS115 and do on-board processing to provide photon event data (energy, position, time). The LASP CSIE camera is capable for such processing on-board (e.g. for SunCET it will process 9 images on-board to make one merged image every 30 seconds).

Amir:

The calculation below suggests 20-40 e-/sec/pix based on concentrating the entire solar visible flux (8e12 photons, 1e6 filter attenuation, 0.5 grating attenuation) into the solar disk area of 1e5 pixels. But, in our extended discussion last week, I realized the diffraction from the pinhole would be quite significant ... in fact, the central spot size for visible light through a 44 µm pinhole may actually cover the entire detector. That is both good and bad -- it means there is more signal than expected in the off-Sun regions, but it also means the signal is spread over vastly more pixels and therefore much lower per pixel. Someone should, of course, check these calculations. The visible leakage through the filtergram pinholes should be pretty small or zero, especially for the Be filters. So I think it's basically just the spectroscopy pinhole we need to worry about.