**NIS Calibration Report #7**

**Jim Bell and Andy Switala; 7/13/95**

__Issue:__

__Better wavelength calibration of Ge and InGaAs detectors__

__Methods:__

__(1) Use the May 13-15 OCF data for NIS placed on retro by Scott.
In particular, we examined the file NIEMH01.135, which are spectra acquired
by stepping the monochrometer through the Ge and InGaAs spectral ranges,
at low temperature (-17.1 C) and in vacuum.__

(2) Calculate averages and standard deviations of all 10 measurements in each block of data, and plot the results to verify data quality.

(3) Subtract an averaged dark spectrum from each average created in (2). Many darks were taken during the test, and our strategy was to subtract whichever dark measurement was taken just prior to each monochrometer measurement. Examples of the types of line profiles created in these tests can be found in NIS Calibration Report #6.

(4) Calculate the peak values of the lines seen in the spectra, and generate a plot of peak channel number versus input monochrometer wavelength. We used an automated peak-finding routine. For Ge, this routine locates the two largest detector responses (two because both second- and third-order light could fall in the same spectrum). These two points, and one neighboring point of the highest peak, are removed from the data set. The median and maximum absolute deviation of the remaining data are computed. If any previously removed point is greater than the maximum absolute deviation above the median, it is considered a real peak. We then used a simple harmonic mean formula to determine the actual channel of each peak. The procedure for the InGaAs detector is similar, except that only the largest response and one neighboring point are excluded from the data since that detector can never exhibit two peaks. Of two neighboring points, the one excluded is always the larger.

(5) Error analysis: To estimate the errors on the wavelength calibration, the spectral calibration was done twice, once using estimated error in peak position, and once using both this error and assuming a constant 1 nm uncertainty in the monochrometer. Since peak position is given by:

n_{p} = (n_{1}R_{1} + n_{2}R_{2}) /
(R_{1}+R_{2}),

where n_{x} is channel x and R_{x}
is the response of that channel, error propagation gives:

Enp^2 = (R2^2 * ER1^2 + R1^2 * ER2^2)^0.5 / (R1+R2)^2

for the error in peak position where ERx is the standard deviation of the response of channel x averaged over the ten measurements in a block of data. These errors are on the order of 0.01-0.001, tiny compared to the peak position. The fits taking only these errors into account are:

Ge: L = 795.44(0.03) + 21.77(0.00)n

InGaAs: L = 1316.60(0.11) + 43.20(0.00)n

where the number in parentheses is the uncertainty in a parameter of the fit. Due to the tiny errors in each point and the comparatively much larger scatter of points about the line, Chi^2 > 400000 for both fits.

Taking into account also a guess of monochrometer uncertainty of 1 nm,

Ge: L = 796.54(0.34) + 21.71(0.02)n, Chi**2 = 389.8

InGaAs: L = 1315.67(0.78) + 43.21(0.00)n, Chi**2 = 658.6

__Results:__

*Ge Detector:*

The wavelength calibration results for the Ge detector, along with the best-fit calibration equation, are shown in Figure 1 below. Along with input wavelengths at each monochrometer wavelength, extra lines were observed for Ge at one-half and one-third of the monochrometer wavelengths because the order-sorting filter was not used in these measurements.

Figure 1: Wavelength calibration for the NIS Ge detector, in vacuum and at T = -17.1 C.

*InGaAs Detector:*

The wavelength calibration results for the InGaAs detector, along with the best-fit calibration equation, are shown in Figure 2 below.

Figure 2: Wavelength calibration for the NIS InGaAs detector, in vacuum and at T = -17.1 C.

__Comparison with APL results:__

Our wavelength calibration results for Ge yield very good agreement with the wavelength calibration reported by Kieth Peacock in his NIS Calibration Report of 6/13/95 (APL Document S1I-95-064). There is a systematic disagreement in the InGaAs wavelength derivation that likely reflects a different fitting scheme (we eliminated several "noisy" points). Also, there is an obvious periodic signal remaining in the InGaAs measurments that we did not remove. Our best guess is that this periodicity is caused by time-variable changes in the dark current level as noted earlier by Jeff Warren. We did not remove this component because of lack of enough dark data to characterize the periodicity. It could be manually removed using an FFT or other similar technique, however.

Kieth's calculated best-fit line was for the beginning wavelength of each channel. Our best-fit line is calculated for the CENTER of each channel, and so the HWHM value of each detector must be subtracted in order to be compared with Kieth's (for Ge, we subtracted 11 nm, for InGaAs, we subtracted 22 nm):

Detector: Ge APL Science Team

Beginning of element 1 (nm): 807 807.39

End of element 32(nm): 1502 1501.78

Detector: InGaAs APL Science Team

Beginning of element 1 (nm): 1331 1337.32

End of element 32(nm): 2713 2719.90

__Wavelength calibration file:__

A Digital Data File of our current nominal wavelength calibration is also available.

__Summary:__

We have derived a nominal Ge and InGaAs wavelength calibration using the May OCF calibration data in vacuum and at low T. There are some small discrepancies between our derivation and APL's, but these can probably be resolved by a more detailed comparison of data reduction techniques. The errors on the wavelength calibration can be formally derived once the true erros on the monochrometer are known and factored in. Residual periodic signal in the InGaAs data are probably the result of time-depedent dark current drift. Every effort should be made during the July OCF run to characterize this drift over the short timescales of each of the monochrometer scan tests.

Additional caveats:

(a) No flatfielding has been done, so pixel-to-pixel variability, which will effect the apparent profile of the monochrometer lines, has not been removed.

(b) No consideration of the profile of the monochrometer line has been done.

Last Modified by Jim Bell on 7 November 1995.

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