The analysis quoted below was a comparison of the expected and observed photometry from the ALTAIR 11 flight two years ago (Oct. 11, 2013). The quoted analysis was performed a month later, and then posted to Hypernews that Nov. 26. In the analysis, an unexplained factor of (approximately) 2 discrepancy was found between the expected and the observed photometry in the three ALTAIR images obtained during that flight.
Over these past few days, in analyzing stellar data from the ALTAIR 15 flight (flown Oct. 24, 2015), I've noticed an important piece of information that I left out of the analysis below. In the FITS header for each one of the 3 relevant ALTAIR 11 images, there is the following datum:
EGAIN = +3.700000000000E-001 / ELECTRONS PER ADU
There is also a pedestal of:
PEDESTAL= -100 / ADD TO ADU FOR 0-BASE
I had been under the mistaken assumption, when performing the quoted analysis, that each ADU recorded by the SBIG camera corresponds to exactly 1 photoelectron, i.e. that the electronic gain factor was 1, and that there was no pedestal shift. Apparently, each ADU in fact corresponds to 0.370 photoelectrons in those three images, and the pedestal shift also needs to be properly accounted for.
Properly correcting for the pedestal shift appears to make little difference, as pedestal is present in both signal and background, and thus it had largely just been properly removed in the background subtraction. Without pedestal correction, but with background subtraction as usual, I measured:
9.207 x 10^5 ALTAIR ADUs in image 1001, 3.368 x 10^5 ALTAIR ADUs in image 1002, and 12.070 x 10^5 ALTAIR ADUs in image 1003.
When I ensure proper pedestal correction, I obtain:
9.268 x 10^5 ALTAIR ADUs in image 1001, 3.337 x 10^5 ALTAIR ADUs in image 1002, and 11.725 x 10^5 ALTAIR ADUs in image 1003.
-- a difference of order 1% -- not significant. (Note that I am also ignoring statistical uncertainty on the above values, since that is approximately 0.3%, and thus also not important.)
However, the electronic gain multiplicative correction factor is of course extremely large: the above numbers must be multiplied by 0.370 to obtain observed number of photoelectrons. Thus, we actually observed:
3.429 x 10^5 ALTAIR photoelectrons in image 1001, 1.235 x 10^5 ALTAIR photoelectrons in image 1002, and 4.338 x 10^5 ALTAIR photoelectrons in image 1003.
That can be compared with the expected number of photoelectrons from the analysis below:
5.431 x 10^5 ALTAIR photoelectrons expected in image 1001, 5.841 x 10^5 ALTAIR photoelectrons expected in image 1002, and 6.108 x 10^5 ALTAIR photoelectrons expected in image 1003.
Note that there is a very great deal of uncertainty on the expected number of ALTAIR photoelectrons on the second image, due to the fact that the yaw-pitch-roll data indicated that ALTAIR was at an essentially-invisible off-axis viewing angle of 87.5 degrees during that particular image, whereas the expectation above was calculated using an assumption of an off-axis angle of 75 degrees (as 87.5 degrees would have resulted in an expectation of essentially zero photoelectrons). Most likely, the true angle was somewhere between those two values, and thus, the expected number of photoelectrons should be a factor of 2 or 3 lower than the above estimation (and thus much closer to the observed value), for that second image. Because of that large uncertainty, let's just consider the first and last of the three images.
What was previously a factor of 2 "too many" photoelectrons observed is now a factor of about 40% too few. However ... if, instead of assuming that atmospheric transmission was 100%, and that there had been 100% transmission through the Schmidt corrector plate at the front of the Meade telescope (note that I had not been accounting for imperfect transmission through the Schmidt corrector plate in the below analysis, but rather only for the imperfect reflection at the mirrors), we instead assume 90% for each of those factors, this 40% discrepancy is then reduced down to a 20% one.
Thus, instead of having a factor of 2 discrepancy, it now appears to me that we have only about an approximately 20% difference between the observed and the expected photometry, in ALTAIR 11 images 1001 and 1003.
Also note that, between 2013 and now, Yorke's major improvement in the yaw-pitch-roll measurement (by moving the yaw-pitch-roll sensor away from the cutdown motor), and the improvements from Karun, Yorke, and students in understanding the output of the light source, the transmission through the telescope optics, and the sensitivity of the camera, should each ensure that this 20% will be reduced very greatly in future flight observations ... and thus that we'll very shortly begin to see ALTAIR as the ultimate precision photometry calibration tool that it is becoming.
cheers, thanks, justin
On Tue, 26 Nov 2013 17:54:25 GMT, Justin Albert wrote:
> Hi, > > 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 >