Jim Bell, Andy Switala; 11/28/95
NIS Spectral Crosstalk, Report #2
This is the second report concerning the issue of leakage of first-order InGaAs signal onto the second-order Ge detector, an effect known as spectral crosstalk. This crosstalk is an inherent "feature" of NIS, as opposed to a malfunction or design flaw of some kind. Thus, the team will need to develop a correction algorithm to apply to all of the NIS data in order to correct for this effect. A more preliminary discussion of this issue can be found in NIS Calibration Report #9. This report describes the problem with using the July OCF test data to characterize the NIS spectral crosstalk, and presents details on the ad hoc technique that we developed for getting around this problem.
Because this is a complex problem that we need to understand fully in order to properly correct our data, I think it is worthwhile to review the cause of the problem. The following synopsis has been paraphrased from various emails sent back and forth between NIS lead engineer Jeff Warren and members of the MSI/NIS team:
The specific case shown in NIS Calibration Report #9 has light input at 1700 nm to the NIS. A filter on the output of the OCF monochromator has the function of insuring that the monochromator is not outputting second order light at 850 nm. We thus have only 1700 nm light being input to the NIS (with some bandwidth). This is a critical point, that we are only dealing physically with 1700 nm light. This 1700 nm light enters the NIS and is diffracted at the grating, into the first order mostly, but also into 2nd, 3rd, 4th, etc. Only the first order is in a direction that it can reach either detector; the higher orders will be past the ends of the detector arrays. The first order 1700 nm light is incident on the dichroic beamsplitter, where most of it is passed thru (about 86%) and on to the InGaAs detector, but a little (about 8%) is reflected to the Ge detector. The dichroic beamsplitter is the source of the crosstalk. It's simply impossible, at present, to build a beamsplitter with near zero reflectance over the required bands. The light incident on the Ge detector will be located on a channel which is used for detecting 1700/2=850nm light, but it's still 1700 nm light.
A schematic representation of the crosstalk problem can be seen in Figure 1.
Figure 1: NIS Spectral Crosstalk Schematic
We thus see that about 1/11 of the light at 1700 nm ends up on the Ge detector in the 850nm channel. We now want to compare the DN we get in the simultaneously illuminated InGaAs and Ge channels. We need to consider the different spectral responsivity and the different electronic gain of the two channels. It hard to say what the responsivity of the Ge detector should be at the temps and wavelengths in question, because this wavelength is at the edge of cutoff, the cutoff changes with temp, and the vendors spec's are probably a little uncertain in this region. The Ge detectors may be about 1/3 as responsive. The Ge detector has 200 MegOhm feedback resistors in the lower channels, and InGaAs has 100 MegOhm. For Ge gain of 1, we expect the DN in Ge to be about 2/33 (= 1/11 x 2 x 1/3) the DN in InGaAs. We would normally run this test with a gain of 10, so we would expect the DN in Ge to be about 20/33 or about 60% of the DN in InGaAs. In NIS Calibration Report #9, the total DN for Ge (in two detectors) seems to be about 700, vs about 1600 for InGaAs. The data in the report don't exactly match the estimate, but the estimate is somewhat crude since the Ge responsivity at the edge of cutoff is not well known.
To understand the magnitude of correction to be made at the asteroid, we need to know the fractional crosstalk (about 60% of InGaAs DN gets to Ge DN at 1700 nm, for example) and also the predicted DN values. For the wavelength shown, the Ge DN is predicted to be about 10 times the InGaAs DN This implies that 6% of the DN on the Ge detector at the asteroid will be due to spectral crosstalk (for 850 nm on Ge and looking at 1700 nm crosstalk). The InGaAs data must have sufficient SNR that when we correct the 6% crosstalk in Ge we don't degrade the Ge SNR appreciably.
The primary reason that the crosstalk is diminishing with increasing wavelength is that the response of the Ge detector is cutting off at about 1800 nm, and so the effect is negligible longward of 1800/2 = 900 nm.
It is important to remember that the 1600 to 1800 nm spectral crosstalk is present in all data that include 1600-1800 nm input light. Specifically, it is present in the sphere data to be used for radiometric calibration. We need to keep this in mind in presenting radiometric calibration, and specify what we have corrected for and how. Note that this is a relatively larger effect for sphere data than asteroid data since the strength of 1600 nm light compared to 800 nm light is three and a half times greater for the gold sphere than sunlight (we have cooler sources than the sun).
We want to be able to express the amount of light, in DNs, falling on a Ge channel n' as a proportion of the light, also in DNs, falling on the InGaAs channel n at twice the Ge channel's wavelength. That is, we want to be able to say DN(n')/DN(n) = k, where k is a function only of n'.
The data taken using the monochrometer do not immediately allow us to find k because the monochrometer beam is not wide enough spectrally to cover an entire channel. Suppose the monochrometer beam has central wavelength w0 and a spectral width of 2D, and that the beam falls entirely inside the range of one channel. The DN we see on an InGaAs channel is
where L0 is the radiance of the monochrometer, T is the transmittivity of the dichroic beamsplitter, and r(w) is the radiometric sensitivity of the channel n as a function of wavelength. Similarly, the DN seen on the Ge channel n' is
where R is the reflectivity of the beamsplitter and r'(w) is the sensitivity of channel n'.
The problem is that each of these integrals is implicity a function of the central wavelength of the monochrometer (w0), and thus k, the quotient of the two integrals, is also a function of w0, not a constant as we would like.
If the monochrometer beam covered the whole of a channel, the limits of integration would be the spectral boundaries of the channel; the integrals would no longer be a function of w0. Using the data available, it should be possible to simulate such a "fat" monochrometer beam by adding DNs resulting from several non-overlapping beams that together cover one channel. Since, during the test, w0 was incremented in 20 nm steps while the monochrometer profile width (2D) was less than 20 nm, we have to plot the data we have as DN(n') or DN(n) versus w0, and interpolate the DNs of the points which span an entire channel, as shown in Figure 2.
In Fig. 2, the points are actual DNs from the data used to derive the crosstalk leakage factor (from the low temp test), the long dashed lines represent the spectral extent of Ge channel 2, and the dotted lines indicate how many narrow monochrometer beams are necessary to cover it. The solid line is part of the cubic spline used to interpolate DNs at the central points of these beams. Note that not all the points used to determine the shape of this spline have been plotted. In order to derive k we performed this same analysis on each of the first 10 Ge channels and on the 10 InGaAs channels corresponding to twice the wavelength of the first 10 Ge channels.
Our preliminary derived crosstalk factors are shown in Figure 3a. These factors are for a Ge gain of 10. The maximum crosstalk at gain 10 occurs in channels 1 and 2, and is about 0.65. The crosstalk falls off smoothly in channels 3 and beyond. The values of k for Ge gain 1 are simply 10 times less than those plotted in Fig. 3a.
For comparison, Figure 3b shows what the crosstalk coefficients would look like if we simply divided the Ge DN at a wavelength lambda by the InGaAs DN at a wavelength 2*lambda. The crosstalk coefficients are plotted as a function of input InGaAs wavelength. Because each wavelength measurement is detectable by several channels (the spectral widths of adjacent channels overlap), we have multiple measurements of the crosstalk at each wavelength. Fig. 3b shows there to be a considerable spread in the derived crosstalk coefficients at each wavelength. We believe that this is a manifestation of the problem: the derived crosstalk coefficients depend on where the input monochrometer beam falls on the spectral transmission curve of each channel (Fig. 2). In Fig. 3b the error-weighted average of the crosstalk coefficients is shown as a dashed line. It is qualitatively similar to the curve in Fig. 3a, but there appear to be substantial enough differences to call this simple channel-by-channel division technique into question.
The magnitude of the crosstalk correction in our Eros data can be estimated by assuming a certain DN level in InGaAs from 1600 to 1800 nm and in Ge from 800 to 900 nm. To estimate the expected typical DN levels at Eros, we used the techniques outlined in Jeff Warren's "Signal Calculations for Ge detectors" and "SNR calculations for InGaAs detector" spreadsheet handouts. These theoretical estimates need to be updated using actual Ge and InGaAs data from the OCF tests in July.
If we use the spreadsheet DN estimates as typical, then we can expect each InGaAs spectrum to have about 240 DN's around 1600 nm, meaning that 240*0.65 = 156 DN will be the crosstalk signal in Ge channel 1 at gain 10. The expected signal in Ge channel 1 at gain 10 in the absence of crosstalk is about 1500 DN, and so the magnitude of the correction that needs to be applied is 156/1500 = 10.4%. At Ge gain 1 the leakage factor in channel 1 is 6.5%, meaning that 240*0.065 = 15.6 DN will be the crosstalk signal in Ge channel 1 at gain 1. The expected signal in Ge channel 1 at gain 1 in the absence of crosstalk is about 150 DN, and so again the magnitude of the correction that needs to be applied is 15.6/150 = 10.4%. These values will of course be lower if we have overestimated the InGaAs signal; however, the InGaAs signals are highest in the 1600 to 1800 nm region, and the DN estimates assume the narrow slit is used and the solar flux values correspond to the initial encounter (1.75 AU), so the spreadsheet estimates may be realistic after all. The magnitude of the correction will be about the same for Ge channel number 2 (Fig. 3). By the time we get to Ge channel number 3, the crosstalk has dropped by a factor of 2.6, and thus the magnitude of the correction for typical DN values is about 4%. By Ge channel 4, the correction has fallen to about a 2.4% effect, and it is at 1.2% at Ge channel 5.
We have performed this crosstalk derviation on data obtained at three different temperatures to search for evidence of temperature variability associated with the expected rapid change in Ge sensitivity as a function of temperature near its cutoff wavelength. Figure 4 shows the results. There is a small, possibly-systematic temperature-dependent component to the crosstalk coefficients over the range of temperatures tested in the OCF, with the crosstalk coefficient decreasing with decreasing temperature. At present the details of this temperature dependence is not firmly established because of remaining uncertainties in the temperature calibrations of the Ge and InGaAs temperature sensors. Thus it is not obvious that any temperature-dependent correction to the crosstalk coefficients should be applied. Further analysis of this effect must await a detailed understanding of the detectors' temperature calibration, which was performed during the recent thermal vacuum testing at GSFC.
This analysis indicates that the OCF data obtained in July are not optimal for characterizing the NIS crosstalk because the light source used to obtain the test data did not fill each channel spectrally, and thus slight changes in the variation of spectral transmission of each channel introduce errors in the derivation of the crosstalk. We have outlined an ad hoc method of artifically "filling" each channel in order to derive the crosstalk, but this technique needs to be verified via analysis of data obtained during TV testing when the NIS channels can be spectrally filled by another light source.
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Last Modified by Jim Bell on 29 November 1995.