Abstract

For mercury–cadmium–telluride detectors, frequently used in Fourier transform IR spectroscopy, the recorded signal is a nonlinear function of the light intensity. This behavior depends on a series resistor in the electronic circuit and thus the illumination of the detector. This nonlinearity must be accounted for to avoid spectroscopic errors. The results of theoretically calculating the effect permit a correction that can be applied, with corresponding lower accuracy, even after a phase correction. Also the use of the amplification stages does influence the phase of the signal electronically. For an accurate nonlinearity correction, compensation of the amplification of the analog signal is advisable.

© 1997 Optical Society of America

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References

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  1. D. B. Chase, “Nonlinear detector response in FT-IR,” Appl. Spectrosc. 38, 491–494 (1984).
    [CrossRef]
  2. F. Bartoli, R. Allen, L. Esterowitz, M. Kruer, “Auger-limited carrier lifetimes in HgCdTe at high excess carrier concentrations,” J. Appl. Phys. 45, 2150–2154 (1974).
    [CrossRef]
  3. R. O. Carter, N. E. Lindsay, D. Beduhn, “A solution to baseline uncertainty due to MCT detector nonlinearity in FT-IR,” Appl. Spectrosc. 44, 1147–1151 (1990).
    [CrossRef]
  4. M. C. Abrams, G. C. Toon, R. A. Schindler, “Practical example of the correction of Fourier-transform spectra for detector nonlinearity,” Appl. Opt. 33, 6307–6314 (1994).
    [CrossRef] [PubMed]
  5. Model D313/6 21296, EG&G Optoelectronics Judson, Montgomeryville, Pa. (1992).
  6. A. Keens, A. Simon, “Correction of non-linearities in detectors in Fourier transform spectroscopy,” U.S. patent4,927,269 (22May1990).
  7. R. Curbelo, “Techniques for correcting non-linearity in a photodetector using predefined calibration information,” U.S. patent5,262,635 (16November1993).
  8. Applications Manual for Operational Amplifiers (Philbrick/Nexus Research, Dedham, Mass., 1968).

1994 (1)

1990 (1)

1984 (1)

1974 (1)

F. Bartoli, R. Allen, L. Esterowitz, M. Kruer, “Auger-limited carrier lifetimes in HgCdTe at high excess carrier concentrations,” J. Appl. Phys. 45, 2150–2154 (1974).
[CrossRef]

Abrams, M. C.

Allen, R.

F. Bartoli, R. Allen, L. Esterowitz, M. Kruer, “Auger-limited carrier lifetimes in HgCdTe at high excess carrier concentrations,” J. Appl. Phys. 45, 2150–2154 (1974).
[CrossRef]

Bartoli, F.

F. Bartoli, R. Allen, L. Esterowitz, M. Kruer, “Auger-limited carrier lifetimes in HgCdTe at high excess carrier concentrations,” J. Appl. Phys. 45, 2150–2154 (1974).
[CrossRef]

Beduhn, D.

Carter, R. O.

Chase, D. B.

Curbelo, R.

R. Curbelo, “Techniques for correcting non-linearity in a photodetector using predefined calibration information,” U.S. patent5,262,635 (16November1993).

Esterowitz, L.

F. Bartoli, R. Allen, L. Esterowitz, M. Kruer, “Auger-limited carrier lifetimes in HgCdTe at high excess carrier concentrations,” J. Appl. Phys. 45, 2150–2154 (1974).
[CrossRef]

Keens, A.

A. Keens, A. Simon, “Correction of non-linearities in detectors in Fourier transform spectroscopy,” U.S. patent4,927,269 (22May1990).

Kruer, M.

F. Bartoli, R. Allen, L. Esterowitz, M. Kruer, “Auger-limited carrier lifetimes in HgCdTe at high excess carrier concentrations,” J. Appl. Phys. 45, 2150–2154 (1974).
[CrossRef]

Lindsay, N. E.

Schindler, R. A.

Simon, A.

A. Keens, A. Simon, “Correction of non-linearities in detectors in Fourier transform spectroscopy,” U.S. patent4,927,269 (22May1990).

Toon, G. C.

Appl. Opt. (1)

Appl. Spectrosc. (2)

J. Appl. Phys. (1)

F. Bartoli, R. Allen, L. Esterowitz, M. Kruer, “Auger-limited carrier lifetimes in HgCdTe at high excess carrier concentrations,” J. Appl. Phys. 45, 2150–2154 (1974).
[CrossRef]

Other (4)

Model D313/6 21296, EG&G Optoelectronics Judson, Montgomeryville, Pa. (1992).

A. Keens, A. Simon, “Correction of non-linearities in detectors in Fourier transform spectroscopy,” U.S. patent4,927,269 (22May1990).

R. Curbelo, “Techniques for correcting non-linearity in a photodetector using predefined calibration information,” U.S. patent5,262,635 (16November1993).

Applications Manual for Operational Amplifiers (Philbrick/Nexus Research, Dedham, Mass., 1968).

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Figures (15)

Fig. 1
Fig. 1

Detector wiring.

Fig. 2
Fig. 2

Small beam striking a large detector element and substitute circuit.

Fig. 3
Fig. 3

Displacement of the single-channel baseline below the detector cutoff versus the applied nonlinearity correction factor.

Fig. 4
Fig. 4

Comparison of interferograms reconstructed from single-channel spectra (--) with the original interferogram (—): (a) reconstructed symmetrically (no phase) and (b) reconstructed asymmetrically (constant phase angle, -π/2).

Fig. 5
Fig. 5

Consequences of nonlinearity correction (water sample): (a) corrected (—) and uncorrected (--) single-channel spectrum and (b) absorption resulting when corrected and uncorrected single channels (--) are compared and when corrections made to the original interferogram and subsequent corrections made to the reconstructed interferogram are compared.

Fig. 6
Fig. 6

Occurrence of signal for the uncorrected single-channel spectrum (---) compared with results after correction procedures: method described here (—) and OPUS method (--).

Fig. 7
Fig. 7

Voltage response for the described circuit with the given resistors (—) as well as linear and quadratic approximation.

Fig. 8
Fig. 8

Dependence of the amount of nonlinearity (described by the factor NLβ) on the size of the aperture (diameter, millimeters).

Fig. 9
Fig. 9

Illuminated fraction of the detector area versus the size of the aperture (diameter, millimeters) as determined by the geometry and as recalculated from the experimental nonlinearity coefficients.

Fig. 10
Fig. 10

Standard operational amplifier circuit.

Fig. 11
Fig. 11

(a) Logarithmic and (b) linear plot of amplification versus frequency.

Fig. 12
Fig. 12

Electronic phase for different velocities (a) calculated and (b) experimentally observed.

Fig. 13
Fig. 13

Single-channel spectra (without sample) at different velocities: slow (—) and fast (--).

Fig. 14
Fig. 14

Ratio of single-channel spectra recorded with different mirror velocities: (a) theoretically calculated and (b) experimental results.

Fig. 15
Fig. 15

Effect of a preceding correction for electronic influences: (a) uncorrected (—) and corrected (--) single-channel spectrum and (b) single-channel spectra obtained after the nonlinearity correction with (--) and without (—) prior amplification correction.

Equations (10)

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0=Il+If-Id=Il+UfRf+-UdRm.
Uf=UdRm-IlRf.
Rm=Rs+RsΦRp+Rp1+ΦRp.
Uf=--Ud-UdΦRp+IlRs+IlRsΦRp+IlRpRfRs+RsΦRp+Rp
Uf=-1100Φ1-2α+α2-45Φα+45Φα2-1.
Φ=-Um45α-45α2Um-1100+2200α-1100α2.
Φ=Um1-Umf,
f=9220αα-1.
11100-2200α+1100α2Um-9α220α-1Um2.
UoutUin=-iωCdRd1+iωRiCd1+iωRdCi.

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