Here's an initial look at the expected vs. observed photometry from the three Oct. 11 images for which Yorke got the payload (at a range of about 14 km from the telescope, with green LED source turned on) inside the SBIG camera field of view -- i.e. the last three images at:
http://altair1.dartmouth.edu/ALTAIR11/index.htm
(which are mirrored at http://projectaltair.org/page/sample_images#A11 )
The observed number of photo-electrons that I measure is correct within a factor of 2, a good sign ... but it is approximately a factor of 2 _greater_ than the expected value for the photometry in the first and last of the two images (1001 and 1003), and approximately a factor of 2 _less_ than the expected value for the photometry in the second (1002). This is just an initial look, but please respond if you have any comments on the analysis below.
As preface to this, Yorke obtained measurements of the flux from the 10 Optek OVS5MGBCR4 green LED source in the lab, and there is also the expected source flux from the info on the spec sheets (http://www.optekinc/com/datasheets/OVS5MABCR4.pdf) for those LEDs. Yorke measures an on-axis radiant intensity of 68.7 mW/sr, and the spec-sheet expectation for the on-axis radiant intensity (given the measured voltage and current) is about 48 mW/sr. I'll use Yorke's value.
I obtain that the payload-to-telescope ranges for the three images are 14.499, 13.976, and 13.670 km respectively, whereas Yorke gives 14.926, 14.332, and 13.975 km respectively, a difference of about 3%. I'll ignore that and use my values for the ranges.
The 3 images were taken when the payload was at an elevation of approximately 15 degrees above the horizon. If, to start off, we just make the zeroth-order assumption that the payload was oriented straight down, then we get that the beam was viewed 75 degrees off-axis, and thus that the relative intensity, when compared with on-axis from the LED source, was approximately 20% (per the relative intensity vs. angle plot from the spec sheets above). We can (presumably..) be more accurate than this by using the pitch, roll, and heading info from the telemetry Excel file, as well as the exact elevation and azimuth. When I do this, I get that the first image (1001) was 87.5 (!) degrees off-axis (as the roll angle was 22.4 degrees, the pitch was 0.3 degrees, and the heading was 108 degrees at that point), the second (1002) was 76.3 degrees off-axis, and the third (1003) was 75.1 degrees off-axis. Note that with an 87.5 degrees off-axis viewing angle, one shouldn't see anything at all (the relative intensity from the LED source goes to zero at 90 degrees, of course), so I discount that and just assume that it is around 75 degrees off-axis like the others, and thus that the relative intensity (vs. on-axis) is always around 20%. Note that that is a _very_ big source of uncertainty, however, since the relative intensity as a function of angle is changing about 2% per degree relative to the on-axis value -- i.e. 10% per degree of error relative to the 75-degrees-off-axis value -- when one is nominally at 75 degrees off axis. (So if one is really 78 or 72 degrees off-axis, then one's expectation for the photometry is about 30% off from reality.) Anyway, we'll just assume that the ~75 degrees off-axis, i.e. 20% relative intensity compared with on-axis, holds for all three measurements.
The aperture of the Meade LX200 telescope is 12", which is equivalent to 729.7 cm^2, and thus the telescope subtends solid angles of 3.471 x 10^-10 sr, 3.736 x 10^-10 sr, and 3.905 x 10^-10 sr at the ranges of the 3 images respectively. Given that the radiant intensity is (68.7 mW/sr) x (the 0.2 relative intensity factor), and that these 3 exposures were each 90 ms, we get that the primary mirror of the telescope should have been exposed to 4.292 x 10^-13 J, 4.620 x 10^-13 J, and 4.829 x 10^-13 J from the source in the 3 images respectively, assuming 100% atmospheric transmission. Since the light from the LED is centered around 520 nm, which is a 3.8201 x 10-19 J photon, we get that the telescope primary mirror should have received 1.124 x 10^6 photons, 1.209 x 10^6 photons, and 1.264 x 10^6 photons in the three images respectively, again assuming 100% atmospheric transmission.
Meade LX200 telescopes have "Meade Ultra-High Transmission Coating" (UHTC) surfaces on their primary and secondary mirrors, and the Meade claim for UHTC reflectance at 520 nm is 90.5%. We use an SBIG ST-402ME camera, which claims a QE for 520 nm light of 59%. Thus, for every photon incident on the primary mirror, we expect (90.5%)^2 x 59% = 0.4832 photo-electrons read out. Thus, again assuming 100% atmospheric transmission, we expect 5.431 x 10^5 photo-electrons, 5.841 x 10^5 photo-electrons, and 6.108 x 10^5 photo-electrons from the source on the 3 images respectively.
I use SAO ds9 to view and analyze the 3 FITS images. After subtracting background, I measure 9.207 x 10^5 photo-electrons, 3.368 x 10^5 photoelectrons, and 12.070 x 10^5 photo-electrons from (what is presumably) the source on the 3 FITS images. (Note that the images are each very blurry, so one cannot tell the payload source from stars via shape/PSF -- one just has to presume that the payload source is the brightest thing on the images which obviously isn't the 2 broken (and unmoving) pixels.)
So we're correct within a factor of 2, which is a good start (especially for absolute photometry -- we can certainly do relative photometry a lot better when we have images of the multicolour source), but currently we're still off by around that amount (and not always more or always less). An analysis of the stars that are also on the images could very likely give us some additional hints -- but that has yet to be done. Please do follow up with comments or questions if you have them.
thanks, justin