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Inconsistency between lab-measured throughput and observations on-site 

Summary of Problem

The brightness of the sky measured with OSELOTS falls off unphysically in the blue and red ends of the bandpass.  The issue seems to be a very small quantity of incident flux being detected by OSELOTS, relative to what our measured lab-measured throughput would suggest. 

Step by Step Demonstration

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): 

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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.  

Next Steps

I cannot tell where the issue lies.  The data going into the calculations appears correct, and appears to be used correctly in the analysis.  We should illuminate OSELOTS with a sources of known wavelengths (say at 1000 nm and at 800 nm) to see if the relative throughput appears more consistent with the lab-measured results or with the sky-measured results.  I suggest taking a range of LEDs in the OSELOTS bandpass (~600 - ~1100), illuminate the fiber tip with them, and take a series of OSELOTS exposures of these LEDs.  Then, abut the slit and optical fiber pair to a reference PD, and measure the current from each LED.  If the PD is right next to the slit, it should capture all the light shining into OSELOTS, and you should get a good measurement of the flux these LEDs are shining into the spectrograph. 

This measurement will not provide a measurement of the absolute throughput - that requires using a surface of uniform surface brightness to simulate the sky.  But that should tell us if the relative throughput of the instrument is accurately measured.  And if the throughput appears to have shifted since the lab calibration, we can try to use these on-site measurements of relative throughput to correct our lab measurement of absolute throughput.