In order to make realistic simulations of the signal and noise in SNAP images, I have been trying to figure out the rate at which photons from the sky and from stars will strike our detectors, and the rate at which electrons will be knocked free by dark current. My goal isn't to do a perfect job, but be within a factor of 20 or 30 percent of the true numbers. That will suffice for my testing purposes.
Since others may be interested in the same quantities, I list them here. If I've made an error, please let me know so that I can fix these pages.
I assume the following:
Sky background for SNAP
SNAP central width photons per
filter waveln (Ang) sq. arcsec
index (Ang) per sec
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0 4753 974 65
1 5513 1130 88
2 6396 1311 94
3 7419 1521 112
4 8606 1764 134
5 9983 2046 129
6 11580 2374 104
7 13433 2754 101
8 15582 3194 91
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How many photons does SNAP collect from a star which has magnitude zero in each passband? I calculated this at three wavelengths (roughly 5500, 8000, 12500 Angstroms, corresponding to V, I, J passbands), and then simply made a linear fit to number of photons per second versus filter index. It should be within a factor of 25 percent, I would estimate. The linear fit is:
photons per sq.cm. per sec = 1,225,000 - 122,600*(filter_index)
Here are the numbers for each passband.
Approximate magnitude zeropoint for SNAP
SNAP central width photons per
filter waveln (Ang) sec for star
index (Ang) of mag = 0
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0 4753 974 3.84e10
1 5513 1130 3.46e10
2 6396 1311 3.08e10
3 7419 1521 2.69e10
4 8606 1764 2.31e10
5 9983 2046 1.92e10
6 11580 2374 1.54e10
7 13433 2754 1.15e10
8 15582 3194 0.77e10
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What about the background due to the instruments? We can break this up into readout noise (fixed) and dark current (increases with time). I grabbed these numbers from Chris Bebek's presentation on the camera, dated 2/8/2002. I treat the properties of the chips as uniform within each of the two wavelength ranges. Chris Bebek provided a value for the dark current of the visible CCD chips, but it was so small that I've treated it as zero.
visible IR
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quantum efficiency 80% 70%
readnoise 4 e-/pix 5 e-/pix
dark current 0 e-/pix/sec 0.05 e-/pix/sec
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One needs some additional information to add up the number of photons or electrons which will contaminate the measurement of a single star. I assume that a reasonable aperture to use for measuring the light has a radius of about three times the FWHM.
visible IR
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pixel size (arcsec) 0.1 0.12
FWHM (arcsec) 0.14 0.14
radius of aperture 0.42 0.42
(arcsec)
number of pixels 55 38
in aperture
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Putting all this together, a quick first pass at the signal-to-noise ratio for stars of magnitude 20 with the standard 4x300-second exposure set turns out to be:
SNAP filter index signal S/N
(electrons)
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0 368,640 580
1 332,160 540
2 295,680 503
3 258,240 458
4 221,760 410
5 184,320 367
6 129,360 305
7 96,600 253
8 64,680 196
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