Abstract

A procedure to calibrate a Fourier transform spectrometer is presented. Blackbody sources of three different temperatures are used to eliminate errors in the calibration that result from the limited accuracy of the temperature measurement of the calibration sources. With three spectra of blackbodies it is possible to assume that the temperatures are unknown variables as are the parameters of the functions that describe the spectrometer. A nonlinear Gaussian balancing calculation is used to determine these unknown variables and to minimize the influence of noise. A comparison between the results obtained with this method and a conventional calibration procedure is presented.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. Tank, “Infrarottemperaturmessung mit selbsttätiger Berücksichtigung des Emissionsgrades,” Forschungsbericht Nr. DFVLR-FB-88-22 (DFVLR, Cologne, 1988).
  2. H. Driescher, M. Scheiding, B. Chares, M. Hartmann, “Eichstrahler grosser Apertur für den Spektralbereich des mittleren und fernen Infrarot,” Feingerätetechnik 6, 247–250 (1990).
  3. V. Tank, “A spectroscopic blackbody radiance calibration procedure with inherent source temperature calibration,” Infrared Phys. 29, 209–210 (1989).
    [CrossRef]
  4. B. J. Vastag, S. R. Hormann, “Calibration of a Michelson interferometer spectrometer,” in 1981 International Conference on Fourier Transform Infrared Spectroscopy, H. Sakai, ed., Proc. Soc. Photo-Opt. Instrum. Eng.289, 74–79 (1981).
    [CrossRef]
  5. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), Chap. 14.
  6. K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math 2, 164–168 (1944).
  7. H. E. Revercomb, H. Buijs, H. B. Howell, D. D. LaPorte, W. L. Smith, L. A. Sromovsky, “Radiometric calibration of IR Fourier transform spectrometers: solution to a problem with the High-Resolution Interferometer Sounder,” Appl. Opt. 27, 3210–3218 (1988).
    [CrossRef] [PubMed]

1990

H. Driescher, M. Scheiding, B. Chares, M. Hartmann, “Eichstrahler grosser Apertur für den Spektralbereich des mittleren und fernen Infrarot,” Feingerätetechnik 6, 247–250 (1990).

1989

V. Tank, “A spectroscopic blackbody radiance calibration procedure with inherent source temperature calibration,” Infrared Phys. 29, 209–210 (1989).
[CrossRef]

1988

1944

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math 2, 164–168 (1944).

Buijs, H.

Chares, B.

H. Driescher, M. Scheiding, B. Chares, M. Hartmann, “Eichstrahler grosser Apertur für den Spektralbereich des mittleren und fernen Infrarot,” Feingerätetechnik 6, 247–250 (1990).

Driescher, H.

H. Driescher, M. Scheiding, B. Chares, M. Hartmann, “Eichstrahler grosser Apertur für den Spektralbereich des mittleren und fernen Infrarot,” Feingerätetechnik 6, 247–250 (1990).

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), Chap. 14.

Hartmann, M.

H. Driescher, M. Scheiding, B. Chares, M. Hartmann, “Eichstrahler grosser Apertur für den Spektralbereich des mittleren und fernen Infrarot,” Feingerätetechnik 6, 247–250 (1990).

Hormann, S. R.

B. J. Vastag, S. R. Hormann, “Calibration of a Michelson interferometer spectrometer,” in 1981 International Conference on Fourier Transform Infrared Spectroscopy, H. Sakai, ed., Proc. Soc. Photo-Opt. Instrum. Eng.289, 74–79 (1981).
[CrossRef]

Howell, H. B.

LaPorte, D. D.

Levenberg, K.

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math 2, 164–168 (1944).

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), Chap. 14.

Revercomb, H. E.

Scheiding, M.

H. Driescher, M. Scheiding, B. Chares, M. Hartmann, “Eichstrahler grosser Apertur für den Spektralbereich des mittleren und fernen Infrarot,” Feingerätetechnik 6, 247–250 (1990).

Smith, W. L.

Sromovsky, L. A.

Tank, V.

V. Tank, “A spectroscopic blackbody radiance calibration procedure with inherent source temperature calibration,” Infrared Phys. 29, 209–210 (1989).
[CrossRef]

V. Tank, “Infrarottemperaturmessung mit selbsttätiger Berücksichtigung des Emissionsgrades,” Forschungsbericht Nr. DFVLR-FB-88-22 (DFVLR, Cologne, 1988).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), Chap. 14.

Vastag, B. J.

B. J. Vastag, S. R. Hormann, “Calibration of a Michelson interferometer spectrometer,” in 1981 International Conference on Fourier Transform Infrared Spectroscopy, H. Sakai, ed., Proc. Soc. Photo-Opt. Instrum. Eng.289, 74–79 (1981).
[CrossRef]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), Chap. 14.

Appl. Opt.

Feingerätetechnik

H. Driescher, M. Scheiding, B. Chares, M. Hartmann, “Eichstrahler grosser Apertur für den Spektralbereich des mittleren und fernen Infrarot,” Feingerätetechnik 6, 247–250 (1990).

Infrared Phys.

V. Tank, “A spectroscopic blackbody radiance calibration procedure with inherent source temperature calibration,” Infrared Phys. 29, 209–210 (1989).
[CrossRef]

Q. Appl. Math

K. Levenberg, “A method for the solution of certain non-linear problems in least squares,” Q. Appl. Math 2, 164–168 (1944).

Other

V. Tank, “Infrarottemperaturmessung mit selbsttätiger Berücksichtigung des Emissionsgrades,” Forschungsbericht Nr. DFVLR-FB-88-22 (DFVLR, Cologne, 1988).

B. J. Vastag, S. R. Hormann, “Calibration of a Michelson interferometer spectrometer,” in 1981 International Conference on Fourier Transform Infrared Spectroscopy, H. Sakai, ed., Proc. Soc. Photo-Opt. Instrum. Eng.289, 74–79 (1981).
[CrossRef]

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), Chap. 14.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Relative error [LBB(T + ΔT) − LBB(T)]/LBB(T) in black-body radiance caused by an error in temperature of ΔT = 1 K for (a) T = 273 K, (b) T = 373 K, (c) T = 573 K.

Fig. 2
Fig. 2

Sketch of the mathematical model S(σ) = R(σ) × [L(σ) + G(σ)].

Fig. 3
Fig. 3

Experimental setup. The radiation of each of the four blackbodies is reflected into the aperture of the spectrometer.

Fig. 4
Fig. 4

Four spectra of blackbodies with different temperatures: (a) S1, T1 = 446.4 K; (b) S2, T2 = 394.8 K; (c) S3, T3 = 351.7 K; (d) S, T = 381.8 K.

Fig. 5
Fig. 5

Spectral response R(σ) obtained from (a) balancing calculation; (b) S1 and S2 with measured temperatures; (c) S1 and S3 with measured temperatures; (d) S2 and S3 with measured temperatures; (e) S1 and S3 with corrected temperatures.

Fig. 6
Fig. 6

Instrument radiance G(σ) obtained from (a) balancing calculation; (b) S1 and S2 with measured temperatures; (c) S1 and S3 with measured temperatures; (d) S2 and S3 with measured temperatures; (e) S1 and S3 with corrected temperatures.

Fig. 7
Fig. 7

Relative differences (a) ν12/S12;(b) ν13/S13; (c) ν23/S23.

Fig. 8
Fig. 8

Calibrated spectrum of the fourth blackbody together with a fitted Planck curve.

Fig. 9
Fig. 9

Relative differences of the calibrated spectrum and the fitted Planck curve.

Fig. 10
Fig. 10

Brightness temperature of the fourth blackbody calculated from the spectrum obtained by (a) the balancing calculation; (b) S1 and S2 with the measured temperatures; (c) S1 and S3 with the measured temperatures; (d) S2 and S3 with the measured temperatures; (e) S1 and S2 with the corrected temperatures.

Equations (33)

Equations on this page are rendered with MathJax. Learn more.

L BB ( σ , ɛ , T ) = ɛ c 1 σ 3 exp ( c 2 σ / T ) - 1 ,
S ( σ ) = R ( σ ) [ L ( σ ) + G ( σ ) ] ,
L ( σ ) = S ( σ ) R ( σ ) - G ( σ ) .
S 1 ( σ ) = R ( σ ) [ L BB ( σ , T 1 ) + G ( σ ) ] ,
S 2 ( σ ) = R ( σ ) [ L BB ( σ , T 2 ) + G ( σ ) ] ,
R ( σ ) = S 1 ( σ ) - S 2 ( σ ) L BB ( σ , T 1 ) - L BB ( σ , T 2 ) ,
G ( σ ) = S 1 ( σ ) R ( σ ) - L BB ( σ , T 1 ) .
S 3 ( σ ) = R ( σ ) [ L BB ( σ , T 3 ) + G ( σ ) ] .
S 12 ( σ ) = S 1 ( σ ) - S 2 ( σ ) = R ( σ ) [ L BB ( σ , T 1 ) - L BB ( σ , T 2 ) ] ,
S 13 ( σ ) = S 1 ( σ ) - S 3 ( σ ) = R ( σ ) [ L BB ( σ , T 1 ) - L BB ( σ , T 3 ) ] ,
S 23 ( σ ) = S 2 ( σ ) - S 3 ( σ ) = R ( σ ) [ L BB ( σ , T 2 ) - L BB ( σ , T 3 ) ] .
G ( σ ) = 1 3 [ S 1 ( σ ) + S 2 ( σ ) + S 3 ( σ ) R ( σ ) - L BB ( σ , T 1 ) - L BB ( σ , T 2 ) - L BB ( σ , T 3 ) ] .
ν 12 ( σ ) = S 12 ( σ ) - R ( σ ) [ L BB ( σ , T 1 ) - L BB ( σ , T 2 ) ] ,
ν 13 ( σ ) = S 13 ( σ ) - R ( σ ) [ L BB ( σ , T 1 ) - L BB ( σ , T 3 ) ] ,
ν 23 ( σ ) = S 23 ( σ ) - R ( σ ) [ L BB ( σ , T 2 ) - L BB ( σ , T 3 ) ] .
A [ R ( σ 1 ) , , R ( σ N ) , T 1 , T 2 , T 3 ] = i = 1 N ( ν 12 2 + ν 13 2 + ν 23 2 ) ! = min .
x = [ T 1 , T 2 , T 3 , R ( σ 1 ) , , R ( σ N ) ] T .
grad [ A ( x * ) ] = 0 T .
A ( x k + 1 ) < A ( x k ) .
x k + 1 = x k + α d x ,
d A ( x k + α d x ) d α = 0.
S 1 ( σ ) = R ( σ ) [ p L BB ( σ , T 1 ) + G ( σ ) ] ,
S 2 ( σ ) = R ( σ ) [ p L BB ( σ , T 2 ) + G ( σ ) ] ,
S 3 ( σ ) = R ( σ ) [ p L BB ( σ , T 3 ) + G ( σ ) ] .
S 12 ( σ ) = p R ( σ ) [ L BB ( σ , T 1 ) - L BB ( σ , T 2 ) ] ,
S 13 ( σ ) = p R ( σ ) [ l BB ( σ , T 1 ) - L BB ( σ , T 3 ) ] ,
S 23 ( σ ) = p R ( σ ) [ L BB ( σ , T 2 ) - L BB ( σ , T 3 ) ] .
R ( σ ) = p R ( σ ) .
G ( σ ) = G ( σ ) p .
L ( σ ) = S ( σ ) R ( σ ) - G ( σ ) = R ( σ ) [ L BB ( σ ) + G ( σ ) ] p R ( σ ) - G ( σ ) p = L BB ( σ ) p .
= 1 p .
p = 1 = 0.98
T brightness ( σ ) = c 2 σ ln [ c 1 σ 3 / L BB ( σ ) + 1 ] .

Metrics