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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.