Abstract

A method is described for the measurement of the noise-equivalent spectral radiance (NESR) of Fourier transform infrared (FTIR) spectroradiometers at all wave numbers of a selected range. The method requires minimal detailed knowledge of the sensor and no support equipment beyond a blackbody source. The NESRs of the FTIR spectroradiometer are determined at every wave-number increment in the 700–1300 cm-1 range, for six resolutions, with a conventional blackbody source and ensembles of differential spectra. The NESRs are well behaved and consistent with the expected dependence on resolution; however, they depend on source temperature at the highest (1 cm-1) and lowest (32 cm-1) resolutions, with little or no statistical dependence at intermediate resolutions. Residual source drift is shown to be the likely cause of the dependence at 1 cm-1; the dependence on the source at 32 cm-1 resolution is shown to be most probably due to photon noise. At intermediate resolutions the sensor noise is dominant.

© 2004 Optical Society of America

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References

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  1. 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]
  2. “XM21 remote sensing chemical agent alarm acceptance test report background measurement spectroradiometer,” Contract No. DAAK1179-C-0051,” Honeywell Inc. Tactical Support Operations, 13350 U.S. Highway 19, Clearwater, Fla. 33516 (24February1981).
  3. HSCAD (High Sensitivity Chemical Agent Detector) performance data sheet, Block Engineering, 164 Locke Drive, Marlborough, Massachusetts 01752-1178 (12Nov.1997).
  4. J. R. Pierce, An Introduction to Information Theory—Symbols, Signals and Noise, 2nd rev. ed. (Dover, New York, 1980), pp. 57–59.
  5. C. L. Wyatt, Radiometric Calibration (Academic, New York, 1978), p. 80.
  6. R. J. Combs, D. F. Flanigan, R. B. Knapp, “Responsivity of an infrared Fourier transform spectroradiometer,” presented at the 45th Pittsburg Conference on Analytical Chemistry and Applied Spectroscopy, Chicago, Ill., March 1994.
  7. R. J. Combs, “Thermal stability evaluation for passive FTIR spectrometry,” Field Anal. Chem. Technol. 3, 81–94 (1999).
    [CrossRef]
  8. R. J. Combs, “Noise assessment for passive FT-IR spectrometer measurements,” in Electro-Optical Technology for Remote Chemical Detection and Identification, M. Fallahi, E. A. Howden, eds., Proc. SPIE3383, 75–91 (1998).
    [CrossRef]
  9. D. F. Flanigan, T. G. Quinn, “Model for the prediction of sensitivity of passive Fourier transform infrared sensors,” in Electro-Optical Technology for Remote Chemical Detection and Identification, M. Fallahi, E. A. Howden, eds., Proc. SPIE2763, 103–116 (1996).
    [CrossRef]
  10. D. F. Flanigan, “Prediction of the limits of detection of hazardous vapors by passive infrared with the use of modtran,” Appl. Opt. 35, 6090–6098 (1996), Eq. (10).
    [CrossRef] [PubMed]
  11. S. Wolfram, The Mathematica Book, 3rd ed. (Wolfram Media, Champaign, Ill., and Cambridge U. Press, New York, 1996), pp. 859–863.
  12. R. A. Johnson, D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice-Hall, Englewood Cliffs, N.J., 2002), p. 298.
  13. S. L. Marple, Digital Spectral Analysis with Applications (Prentice Hall, Englewood Cliffs, N.J., 1987), p. 116.
  14. Mathematica 3.0 Standard Add-on Packages (Wolfram Media, Champaign, Ill. and Cambridge U. Press, New York, 1996), p. 424.
  15. P. R. Griffiths, J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, New York, 1986), p. 251.
  16. Ref. 10, Eq. (19).
  17. A. J. LaRocca, “Atmospheric absorption,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, eds., Prepared by Infrared Information Analysis Center, Environmental Research Institute of Michigan (ERIM) (U.S. Government Printing Office, Washington, D.C., 1989), Chap. 5, pp. 5–10, Eqs. (5)–(9).
  18. C. L. Wyatt, Radiometric System Design (McMillan, New York, 1987), p. 236.
  19. R. Beer, Remote Sensing by Fourier Transform Spectrometry (Wiley, New York, 1992), p. 55.
  20. K. Seyrafi, Electro-Optical Systems Analysis (Electro-Optical Research Co., Los Angeles, Calif., 1973), p. 115.
  21. P. W. Kruse, L. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology: Generation, Transmission, and Detection (Wiley, New York, 1963), pp. 357–361.
  22. A. C. Samuels, D. F. Flanigan, A. Ben-David, “Analysis of noise in passive Fourier transform infrared measurements of some representative backgrounds as a function of meteorological conditions,” in SPIE Annual Meeting 2003: Remote Sensing and Space Technology, CD-ROM Vol. CDS 101, Vol. 5159, Imaging Spectrometry IX (SPIE, Bellingham, Wash., 2003).

1999

R. J. Combs, “Thermal stability evaluation for passive FTIR spectrometry,” Field Anal. Chem. Technol. 3, 81–94 (1999).
[CrossRef]

1996

1988

Beer, R.

R. Beer, Remote Sensing by Fourier Transform Spectrometry (Wiley, New York, 1992), p. 55.

Ben-David, A.

A. C. Samuels, D. F. Flanigan, A. Ben-David, “Analysis of noise in passive Fourier transform infrared measurements of some representative backgrounds as a function of meteorological conditions,” in SPIE Annual Meeting 2003: Remote Sensing and Space Technology, CD-ROM Vol. CDS 101, Vol. 5159, Imaging Spectrometry IX (SPIE, Bellingham, Wash., 2003).

Buijs, H.

Combs, R. J.

R. J. Combs, “Thermal stability evaluation for passive FTIR spectrometry,” Field Anal. Chem. Technol. 3, 81–94 (1999).
[CrossRef]

R. J. Combs, “Noise assessment for passive FT-IR spectrometer measurements,” in Electro-Optical Technology for Remote Chemical Detection and Identification, M. Fallahi, E. A. Howden, eds., Proc. SPIE3383, 75–91 (1998).
[CrossRef]

R. J. Combs, D. F. Flanigan, R. B. Knapp, “Responsivity of an infrared Fourier transform spectroradiometer,” presented at the 45th Pittsburg Conference on Analytical Chemistry and Applied Spectroscopy, Chicago, Ill., March 1994.

de Haseth, J. A.

P. R. Griffiths, J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, New York, 1986), p. 251.

Flanigan, D. F.

D. F. Flanigan, “Prediction of the limits of detection of hazardous vapors by passive infrared with the use of modtran,” Appl. Opt. 35, 6090–6098 (1996), Eq. (10).
[CrossRef] [PubMed]

R. J. Combs, D. F. Flanigan, R. B. Knapp, “Responsivity of an infrared Fourier transform spectroradiometer,” presented at the 45th Pittsburg Conference on Analytical Chemistry and Applied Spectroscopy, Chicago, Ill., March 1994.

D. F. Flanigan, T. G. Quinn, “Model for the prediction of sensitivity of passive Fourier transform infrared sensors,” in Electro-Optical Technology for Remote Chemical Detection and Identification, M. Fallahi, E. A. Howden, eds., Proc. SPIE2763, 103–116 (1996).
[CrossRef]

A. C. Samuels, D. F. Flanigan, A. Ben-David, “Analysis of noise in passive Fourier transform infrared measurements of some representative backgrounds as a function of meteorological conditions,” in SPIE Annual Meeting 2003: Remote Sensing and Space Technology, CD-ROM Vol. CDS 101, Vol. 5159, Imaging Spectrometry IX (SPIE, Bellingham, Wash., 2003).

Griffiths, P. R.

P. R. Griffiths, J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, New York, 1986), p. 251.

Howell, H. B.

Johnson, R. A.

R. A. Johnson, D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice-Hall, Englewood Cliffs, N.J., 2002), p. 298.

Knapp, R. B.

R. J. Combs, D. F. Flanigan, R. B. Knapp, “Responsivity of an infrared Fourier transform spectroradiometer,” presented at the 45th Pittsburg Conference on Analytical Chemistry and Applied Spectroscopy, Chicago, Ill., March 1994.

Kruse, P. W.

P. W. Kruse, L. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology: Generation, Transmission, and Detection (Wiley, New York, 1963), pp. 357–361.

LaPorte, D. D.

LaRocca, A. J.

A. J. LaRocca, “Atmospheric absorption,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, eds., Prepared by Infrared Information Analysis Center, Environmental Research Institute of Michigan (ERIM) (U.S. Government Printing Office, Washington, D.C., 1989), Chap. 5, pp. 5–10, Eqs. (5)–(9).

Marple, S. L.

S. L. Marple, Digital Spectral Analysis with Applications (Prentice Hall, Englewood Cliffs, N.J., 1987), p. 116.

McGlauchlin, L. D.

P. W. Kruse, L. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology: Generation, Transmission, and Detection (Wiley, New York, 1963), pp. 357–361.

McQuistan, R. B.

P. W. Kruse, L. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology: Generation, Transmission, and Detection (Wiley, New York, 1963), pp. 357–361.

Pierce, J. R.

J. R. Pierce, An Introduction to Information Theory—Symbols, Signals and Noise, 2nd rev. ed. (Dover, New York, 1980), pp. 57–59.

Quinn, T. G.

D. F. Flanigan, T. G. Quinn, “Model for the prediction of sensitivity of passive Fourier transform infrared sensors,” in Electro-Optical Technology for Remote Chemical Detection and Identification, M. Fallahi, E. A. Howden, eds., Proc. SPIE2763, 103–116 (1996).
[CrossRef]

Revercomb, H. E.

Samuels, A. C.

A. C. Samuels, D. F. Flanigan, A. Ben-David, “Analysis of noise in passive Fourier transform infrared measurements of some representative backgrounds as a function of meteorological conditions,” in SPIE Annual Meeting 2003: Remote Sensing and Space Technology, CD-ROM Vol. CDS 101, Vol. 5159, Imaging Spectrometry IX (SPIE, Bellingham, Wash., 2003).

Seyrafi, K.

K. Seyrafi, Electro-Optical Systems Analysis (Electro-Optical Research Co., Los Angeles, Calif., 1973), p. 115.

Smith, W. L.

Sromovsky, L. A.

Wichern, D. W.

R. A. Johnson, D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice-Hall, Englewood Cliffs, N.J., 2002), p. 298.

Wolfram, S.

S. Wolfram, The Mathematica Book, 3rd ed. (Wolfram Media, Champaign, Ill., and Cambridge U. Press, New York, 1996), pp. 859–863.

Wyatt, C. L.

C. L. Wyatt, Radiometric System Design (McMillan, New York, 1987), p. 236.

C. L. Wyatt, Radiometric Calibration (Academic, New York, 1978), p. 80.

Appl. Opt.

Field Anal. Chem. Technol.

R. J. Combs, “Thermal stability evaluation for passive FTIR spectrometry,” Field Anal. Chem. Technol. 3, 81–94 (1999).
[CrossRef]

Other

R. J. Combs, “Noise assessment for passive FT-IR spectrometer measurements,” in Electro-Optical Technology for Remote Chemical Detection and Identification, M. Fallahi, E. A. Howden, eds., Proc. SPIE3383, 75–91 (1998).
[CrossRef]

D. F. Flanigan, T. G. Quinn, “Model for the prediction of sensitivity of passive Fourier transform infrared sensors,” in Electro-Optical Technology for Remote Chemical Detection and Identification, M. Fallahi, E. A. Howden, eds., Proc. SPIE2763, 103–116 (1996).
[CrossRef]

S. Wolfram, The Mathematica Book, 3rd ed. (Wolfram Media, Champaign, Ill., and Cambridge U. Press, New York, 1996), pp. 859–863.

R. A. Johnson, D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice-Hall, Englewood Cliffs, N.J., 2002), p. 298.

S. L. Marple, Digital Spectral Analysis with Applications (Prentice Hall, Englewood Cliffs, N.J., 1987), p. 116.

Mathematica 3.0 Standard Add-on Packages (Wolfram Media, Champaign, Ill. and Cambridge U. Press, New York, 1996), p. 424.

P. R. Griffiths, J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, New York, 1986), p. 251.

Ref. 10, Eq. (19).

A. J. LaRocca, “Atmospheric absorption,” in The Infrared Handbook, W. L. Wolfe, G. J. Zissis, eds., Prepared by Infrared Information Analysis Center, Environmental Research Institute of Michigan (ERIM) (U.S. Government Printing Office, Washington, D.C., 1989), Chap. 5, pp. 5–10, Eqs. (5)–(9).

C. L. Wyatt, Radiometric System Design (McMillan, New York, 1987), p. 236.

R. Beer, Remote Sensing by Fourier Transform Spectrometry (Wiley, New York, 1992), p. 55.

K. Seyrafi, Electro-Optical Systems Analysis (Electro-Optical Research Co., Los Angeles, Calif., 1973), p. 115.

P. W. Kruse, L. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology: Generation, Transmission, and Detection (Wiley, New York, 1963), pp. 357–361.

A. C. Samuels, D. F. Flanigan, A. Ben-David, “Analysis of noise in passive Fourier transform infrared measurements of some representative backgrounds as a function of meteorological conditions,” in SPIE Annual Meeting 2003: Remote Sensing and Space Technology, CD-ROM Vol. CDS 101, Vol. 5159, Imaging Spectrometry IX (SPIE, Bellingham, Wash., 2003).

“XM21 remote sensing chemical agent alarm acceptance test report background measurement spectroradiometer,” Contract No. DAAK1179-C-0051,” Honeywell Inc. Tactical Support Operations, 13350 U.S. Highway 19, Clearwater, Fla. 33516 (24February1981).

HSCAD (High Sensitivity Chemical Agent Detector) performance data sheet, Block Engineering, 164 Locke Drive, Marlborough, Massachusetts 01752-1178 (12Nov.1997).

J. R. Pierce, An Introduction to Information Theory—Symbols, Signals and Noise, 2nd rev. ed. (Dover, New York, 1980), pp. 57–59.

C. L. Wyatt, Radiometric Calibration (Academic, New York, 1978), p. 80.

R. J. Combs, D. F. Flanigan, R. B. Knapp, “Responsivity of an infrared Fourier transform spectroradiometer,” presented at the 45th Pittsburg Conference on Analytical Chemistry and Applied Spectroscopy, Chicago, Ill., March 1994.

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Figures (14)

Fig. 1
Fig. 1

Mean p values as a function resolution and temperature for 15Oct02 data.

Fig. 2
Fig. 2

The coefficients of determination from 700 to 1300 cm-1 for the fit of the signal data to Eq. (3) for 15Oct02 data. These graphs are sparsely plotted for clarity; i.e., only every Nth wave-number bin is plotted, although the computations were done at every bin. The value of N ranges from 32 for 1-cm-1 resolution to 1 for 32-cm-1 resolution.

Fig. 3
Fig. 3

Responsivity for the 15Oct02 data.

Fig. 4
Fig. 4

(a) NESR, (b) NEDT, from 15Oct02 data for 0 °C.

Fig. 5
Fig. 5

Mean NESR as a function of source temperature and resolution for the 15Oct02 data.

Fig. 6
Fig. 6

Intercept, a NESR, for 15Oct02 data at all resolutions.

Fig. 7
Fig. 7

Mean intercept, āNESR as a function of resolution.

Fig. 8
Fig. 8

Mean slope for NESR on source radiance as a function of resolution.

Fig. 9
Fig. 9

Change (mean across all wave numbers) in brightness temperature as a function of scan number for the full signal (relative to the mean) and the difference signal (diff) for the 1-cm-1 resolution data at 80 °C. Every fifth mean brightness temperature is plotted for clarity.

Fig. 10
Fig. 10

Difference between the standard deviations of the two curves in Fig. 9 for all resolutions and all temperatures.

Fig. 11
Fig. 11

Absolute value of the mean REDT.

Fig. 12
Fig. 12

Coefficient of determination for the fit of 15Oct02 data to Eq. (13).

Fig. 13
Fig. 13

Comparison of the predicted photon noise from the measurements and the theoretical model.

Fig. 14
Fig. 14

SDSR spectra for woods background on 24 October 2002.

Tables (3)

Tables Icon

Table 1 Scan Time and Total Measurement Time for 500 Scans

Tables Icon

Table 2 Mean NESR as a Function of Source Temperature and Resolution for the 15Oct02 Test

Tables Icon

Table 3 Mean Values of r2, Standard Deviation of r2, aNESR, and b

Equations (20)

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

Si=si,1,, si,k,, si,n
S¯Tb=S1++Si++Sm/m.
sk=kLk+Ek,
LkTb=hc2ν˜k3exphcν˜k/kBTb-1,
Xi=Si-Si-1=xi,1,, xi,k,, xi,n,
NESR=AD/tsD*τsΔν˜,
NESR1 sec=NESRts.
αν˜=α0γ2γ2+ν˜-ν˜02.
0.138889, 0.222222, 0.277778, 0.222222,0.138889,
NESRkTb=σkkts21/2*αν˜,
Tb=c2ν˜klnc1ν˜k3Lk+1.
NEDTk=c1c2ν˜k4NESRkLk21+c1ν˜k3/Lkln1+c1ν˜k3/Lk2,
NESRk=aNESRk+bLkT,
TkD=Tki-T¯ki,
Tkd=Tki-Tki+1,
RESRkTb=x¯kkts21/2 * αν˜,
REDTk=c1c2ν˜k4RESRkLk21+c1ν˜k3/Lkln1+c1ν˜k3/Lk2.
Np=N¯exphcν˜/kBTexphcν˜/kBT-11/2,
NESRp=hc2ν˜3Δν˜exphcν˜/kBT-11hcν˜1/22hcν˜=2h2c3ν˜4Δν˜exphcν˜/kBT-11/2.
SDSRk=σkkts1/2.

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