Figure 1: Ge_filter_plot
Date: 2/23/95
Here I describe the spectral responsivity of the NIS Ge detector, as determined by detector-level testing.
Please remember that this represents a first stab at this analysis. A better result must await Keith Peacock's measurements using an integrating sphere and NIST-traceable lamps, for reasons that are obvious below.
The radiance of the lamp was measured by placing calibrated photodiodes in the environment chamber, at approximately the same spot as the detector, and measuring power as nW when the photodiode is illuminated though each of the combination of filters. A Si photodiode covers the wavelength range of the CCD, and a Ge photodiode covers the wavelength range of the Ge detector.
I started this analysis with lamp measurements acquired within days of the detector testing, which I had put online in retro. I discovered that the Si and Ge photodiodes yielded an inconsistent spectral shape in one of the overlapping channels. By comparing the lamp measurements with others acquired at different times, I track down the inconsistency as a wrong setting used when that filter was measured with the Si photodiode. So I replaced the Si lamp measurements with another set that was consistent with duplicate runs. (I will replace both lamp files online with the versions used here.)
To get at the lamp spectrum without introducing uncertainties from the wavelength variation in transmissivity of the neutral density filter (as mentioned by Jim Bell), I recovered a radiance spectrum of the lamp using data with ND=0. The raw data in nW are divided by the area of the calibrated detector (1 cm² for Si, 0.234 cm² for Ge) and the area¹ of the wavelength filter as shown in Figure 1, to yield radiance as nW/cm²/ nm. The radiance spectra of the lamp in air, as determined using the Si and Ge photodiodes, are plotted in Figure 2, with the Si data on the left axis and the Ge data on the right axis. Note that the shapes of the spectra are closely similar, although the radiance calculated from the Ge photodiode is 42% higher. This can probably be attributed to placement of the Si photodiode not directly under the lamp. (The photodiode, as well as the detector being measured, should be situated directly under the lamp.)
¹ Note: Malin believes by "area of the wavelength filter" Scott actually means the "area under the curve" of the wavelength filter.
Note also the absorption-like feature at 1400 nanometers. This resembles an atmospheric water absorption, but it is uncommonly strong for the few dm or less pathlength from the lamp to the photodiode. Figure 3 shows two measurements of the lamp from the Ge photodiode, one in air and the other in vacuum, both at room temperature. Note that the measured radiance in vacuum is a few % higher, probably due to photodiode placement, but that the shapes of the spectra are the same. The ratio of the two spectra is nearly flat and indicates a precision on the order of 1.5%, consistent with Hugo's repetitions of measurements of the lamp with the same placement of the photodiode. Apparently the 1400-nm feature arises from one of the following: (a) inaccuracy in photodiode calibration, (b) repetitive measurement errors, or (c) properties of the lamp. I think that the magnitude of the feature make (a) and (b) unlikely. (c) could arise if the glass in the lamp contains an absorber such as carbonate.
From here on I'll proceed under the assumptions: (a) that the lamp spectrum measured from the Ge photodiode under vacuum is accurate and most comparable to the lamp under conditions of detector measurement (in vacuum); and (b) that the absolute value of radiance measured under this condition is closest to that directly under the lamp where the detector was measured. If (b) is incorrect it will affect calculation of the absolute sensitivity of the Ge detector but not the relative spectral responsivity.
The next 3 figures show the DN levels from 32 detectors, one wavelength at a time.
Figure 4 shows the raw data with only dark current subtracted. The abrupt increase in sensitivity beyond channel 22 is built into the detector for the day when it is mounted in NIS, to compensate for decreasing solar irradiance at longer wavelengths. The "hump" occurs because the central channels are located most directly beneath the light source, and the more distant channels are further from the source with incident radiation making a higher angle to the surface normal. I haven't made an attempt to correct this; the "hump" will disappear when measurements are taken of the integrating sphere. However, for estimating the absolute detector sensitivity later, I'll obviously make use only of the central channels where this variable is minimized.
Figure
4: Response_plot_1 - Raw Data minus Dark Current
Figure 5 shows the same data now divided by filter area for the given wavelength, but not corrected for lamp radiance.
Figure 5:
Response_plot_2 - Dark Current Corrected Divided by Filter
Area
Figure 6 shows the data once they have also been divided by lamp radiance at a given wavelength. The units are as DN's after removal of dark current, per nW/cm²/nm of incident radiance.
Figure 6:
Response_plot_3 - Dark Current Corrected Divided by
Filter Area and Lamp Radiance
For a given channel in Figure 6, the values for the 8 filters define a plot of the response function of the detector. Figure 7 shows the response functions for channels 1-11, and Figure 8 shows the response functions for channels 12-22. Figure 9 shows the response functions for the more sensitive channels 23-32, so the scale is different.
Figure 7:
Response_plot_4 - Response Functions for Channels
1-11
Figure 8:
Response_plot_4 - Response Functions for Channels
12-22
Figure 9:
Response_plot_5 - Response Functions for Channels
23-32
In all three plots there is very little difference in relative spectral response from channel to channel. Also, in general sensitivity increases systematically with wavelength, except at 1400 nm where there is a spike in sensitivity. Given the issues with the lamp spectrum at this wavelength, I wouldn't discount the possibility that an error has propagated itself to this point.
One last word about the scales of these plots. Recall that, with the excpetion of the 1400 nm filter, we can feel reasonably confident in the shapes of the spectral responses: sources of error include areas of the filters, DN, dark current subtraction, and the relative spectrum of the lamp. In each case the uncertainty is at the percent level, so (once again except for 1400 nm) the wavelength variation in relative detector sensitivity is on the order of a few percent. However, the absolute radiance of the lamp is uncertain at the 10's percent level, as is evident from the mismatch of the scales of the axis in Figure 1.
DN = detector sensitivity (DN/nW/cm² /nm) * detector spectral width (nm) * transmissivity of out-of-order blocking filter at given wavelength * dichroic efficiency at given wavelength * grating efficiency at given wavelength * collector area (cm² ) / area of detector element (cm² ) * reflectivity of mirrors at given wavelength * solid angle FOV in steradians * solar irradiance at 1 AU at a given wavelength (nW/cm² /nm) * distance from sun² (AU² ) * normal albedo of Eros at given wavelength * radiometric scaling factor
The detector sensitivity was derived from the above work, for detector elements in the central part of the array, taking into account the increased sensitivity of detectors that ultimately will measure wavelengths >1250 nm. The spectral width is nominally 22 nm, and the solid angle FOV I used corresponds to that of the narrow slit plate (0.38° X 0.76° ). Collector area is 5 cm² , and area of the detector element is 0.5 mm X 1.0 mm. The mirrors' reflectivity was assumed to be 0.9 at all wavelengths. Transmissivities and efficiencies were supplied by Keith Peacock. The spectrum of Eros used was the spectral model I've put on-line. For distance from the sun I've used 1.75 AU, the distance at time of the flyby and 0° phase angle observations. The radiometric scaling factor, assuming a backscattering material observed at 0° phase angle, reduces to 1/pi. Values of the wavelength dependent parameters are shown in Figure 10, and are keyed to the left axis. Predicted DN levels are also shown here, keyed to the right axis.
Figure 10:
DN_calculation_plot
DN levels occupy the approximate range 150-600, with peaks at 1000 and 1300-1400 nm.
Ideally, we want the highest DN levels that would not saturate if the same scene were observed under the brightest conditions. That would be at 1.1 AU, using the wide slit (0.76° X 0.76° ), while observing a bright feature (assuming that to be 1.3X as bright as average). Under such conditions, the peak DN is predicted to be ~3900 compared to saturation at 4095. In other words, the sensitivity of the detectors appears at this stage to nearly optimal! However, given the uncertainty in absolute DN values for different wavelengths, this calculation must be revisited when Keith gets calibration measurements using the integrating sphere and NIST-traceable lamp.
