We describe how we measured the OSELOTS absolute throughput in the OSELOTS paper draft (see: https://www.overleaf.com/project/5d0804b6f70d77533f15bbc6). We don't repeat that information here.
What we do describe here is an apparent inconsistency between the measured throughput and the data taken on sight.
Inconsistency between lab-measured throughput and observations on-site
The reduced night sky spectrum observed with OSELOTS at AuxTel look generally like the following plot of the data taken on 2022/06/29 (averaged over the whole night):
Note that the lines on the red end of the spectrum (longer wavelengths than about 930 nm) quickly trail off in height. Why is this a problem? Let's compare this night sky spectrum to that observed at La Palma, and reported on this (old) website:
https://www.ing.iac.es/astronomy/observing/conditions/skybr/skybr.html
(we chose this example because their spectral resolution is close to ours, making a by-eye comparison easier).
Note how well our measured spectrum conforms to this spectrum, up to about 950 nm. The O3 band at 8646 nm, for example, sits right between the thickets of OH lines centered at about 850 nm and 890 nm. This seems to indicate that the wavelength solution of the spectrum is not TOO far off - the bands are roughly where we expect them to be. Certainly, they cannot viably be shifted by more than ~ 10nm.
But the subsequent thicket of OH lines starting around 920 nm is much reduced in our spectrum, relative to the La Palma results. The lines are there, and are detected above the background, but are very weak, relative to the main spectrum.
This suggests that the throughput of OSELOTS has been mismeasured. Specifically, it suggests that we have OVERESTIMATED the instrument's throughput in the NIR (this may also be true in the 'blue' end of our spectrum, though there are fewer strong emission structures at that end of the the spectrum for us to make such claims with confidence).
Another possible explanation is that the wavelength solution (pixel to wavelength) for this data is incorrect. But the good (by-eye) correspondence of our spectrum that the La Palma reference spectrum makes that hypothesis seem unlikely.
So let's walk through the OSELOTS throughput measurement, and double check the calculation. Specifically, let's compare the measurements at 800 nm and 1000 nm.
Double Checking Throughput Calculation
The method we used to determine the OSELOTS throughput (described in https://www.overleaf.com/project/5d0804b6f70d77533f15bbc6) was to illuminate a sphere with a monochromator at various wavelengths. Here are the two processed (bias-subtracted and normalized to 1 s) fits images (shown as pngs) for the monochromator set to 800 nm and 1000 nm:
The flux level of 1000 nm image is ~0.08 ADU, and the flux level of the 800 nm image is ~1.2 ADU. Doing an annulus sum, we find roughly similar results: 92.3 ADU for 1000 nm image, 2399.0 ADU for 800 nm image. So about 26 times more counts in the 800 nm image.
Measuring the photocurrent from the PD_1M_int_sphere_Data.txt data file (attached below), the reference photodiode measures 0.38 pA at 1000 nm and 1.21 pA at 800 nm.
The QE of the calibrated photodiode (see Hamamatsu_Photodiode_S2281_Spectral_Power_Response.txt below) is 0.4702 A/W at 1000 nm and 0.4238 A/W at 800 nm.
So 0.38 pA / 0.4702 A/W = 0.81 pW of photons are incident on the PD at 1000 nm and 1.21 pA / 0.4238 A/W = 2.86 pW at 800 nm. Meaning there is 2.86 pW / 0.81 pW = 3.53 times more energy incident at 800 nm than at 1000 nm. Equivalently, there are (2.86 pW X 800 nm) / (0.81 pW X 1000 nm) = 2.82 times more photons incident at 800 nm than at 1000 nm.
So the photon to ADU conversion is 26 / 2.82 = 9.2 times more efficient at 800 nm than at 1000 nm. In other words, the instrument throughput is 9.2 times higher at 800 nm.
(note, we've skipped the various numerical factors that allow us to calculate absolute throughput; in this sanity check, we're only concerned about relative throughput).
So what spectrum values do these suggest for our actual analysis? Well, for the above spectrum, at 800.5 nm, the spectrum measured 140.30 ADU /s, and at 1000.3 nm, the spectrum measures 0.66 ADU/s (see column 4 of the StackedSkyImage_img49To283_specSteps.txt file below). So correcting for the 9.2 relative throughput, this suggests that the sky is about 140.3 / 0.66 / 9.2 = 23.1 times brighter at 800 nm than at 1000 nm. This is not what we expect from the Las Palmas observations above.