Abstract

In a passive infrared remote sensing measurement, the spectral radiance difference caused by the presence of a pollutant cloud is proportional to the difference between the temperature of the cloud and the brightness temperature of the background (first-order approximation). In many cases, this difference is of the order of a few kelvins. Thus the measured signals are small, and the signal-to-noise ratio (SNR) is one of the most important quantities to be optimized in passive remote sensing. A model for the SNR resulting from passive remote sensing measurements with a Fourier-transform infrared spectrometer is presented. Analytical expressions for the SNR of a single Lorentzian line for the limiting cases of high and low spectral resolutions are derived. For constant measurement time the SNR increases with decreasing spectral resolution, i.e., low spectral resolutions yield the highest SNRs. For a single scan of the interferometer, a spectral resolution that maximizes the SNR exists. The calculated SNRs are in good agreement with the measured SNRs.

© 2004 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  21. The author is preparing a manuscript to be called “Remote sensing of airborne pollutants by passive FTIR spectrometry: method for the retrieval of the column density.”
  22. R. Harig, G. Matz, P. Rusch, “Scanning infrared remote sensing system for identification, visualization, and quantification of airborne pollutants,” in Instrumentation for Air Pollution and Global Atmospheric Monitoring, J. O. Jensen, R. L. Spellicy, eds., Proc. SPIE4574, 83–94 (2002).
    [CrossRef]
  23. J.-M. Thériault, “Modeling the responsivity and self-emission of a double-beam Fourier-transform infrared interferometer,” Appl. Opt. 38, 505–515 (1999).
    [CrossRef]
  24. R. Harig, G. Matz, “Toxic cloud imaging by infrared spectrometry: a scanning FTIR system for identification and visualization,” Field Anal. Chem. Technol. 5, 75–90 (2001).
    [CrossRef]
  25. S. P. Davis, M. C. Abrams, J. W. Brault, Fourier Transform Spectrometry (Academic, San Diego, Calif., 2001).

2001 (1)

R. Harig, G. Matz, “Toxic cloud imaging by infrared spectrometry: a scanning FTIR system for identification and visualization,” Field Anal. Chem. Technol. 5, 75–90 (2001).
[CrossRef]

2000 (1)

G. Bianchini, P. Raspollini, “Characterisation of instrumental line shape distortions due to path difference dependent phase errors in a Fourier transform spectrometer,” Infrared Phys. Technol. 41, 287–292 (2000).
[CrossRef]

1999 (3)

1998 (1)

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

1996 (1)

1995 (1)

1992 (2)

1989 (1)

1964 (1)

1961 (1)

J. Connes, “Recherches sur la spectroscopie par la transformation de Fourier,” Rev. Opt. Theor. Exp. 40, 41–79, 116–140, 171–190, 231–265 (1961).

1960 (1)

Abrams, M. C.

S. P. Davis, M. C. Abrams, J. W. Brault, Fourier Transform Spectrometry (Academic, San Diego, Calif., 2001).

Beer, R.

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

Berk, A.

A. Berk, L. S. Bernstein, D. C. Robertson, “MODTRAN: A Moderate Resolution Model for LOWTRAN 7,” AFGL-TR-89-0122 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1989).

Bernstein, L. S.

A. Berk, L. S. Bernstein, D. C. Robertson, “MODTRAN: A Moderate Resolution Model for LOWTRAN 7,” AFGL-TR-89-0122 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1989).

Bianchini, G.

G. Bianchini, P. Raspollini, “Characterisation of instrumental line shape distortions due to path difference dependent phase errors in a Fourier transform spectrometer,” Infrared Phys. Technol. 41, 287–292 (2000).
[CrossRef]

Blumenstock, T.

Brault, J. W.

S. P. Davis, M. C. Abrams, J. W. Brault, Fourier Transform Spectrometry (Academic, San Diego, Calif., 2001).

Brown, L.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Camy-Peyret, C.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Chance, K.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Clough, S. A.

H. J. P. Smith, D. J. Dube, M. E. Gardner, S. A. Clough, F. X. Kneizys, L. S. Rothman, “FASCODE—Fast Atmospheric Signature Code (Spectral Transmittance and Radiance),” Tech. Rep. AFGL-TR-78-0081 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1978).

Combs, R. J.

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

Connes, J.

J. Connes, “Recherches sur la spectroscopie par la transformation de Fourier,” Rev. Opt. Theor. Exp. 40, 41–79, 116–140, 171–190, 231–265 (1961).

Conrath, B. J.

R. A. Hanel, B. J. Conrath, D. E. Jennings, R. E. Samuelson, Exploration of the Solar System by Infrared Remote Sensing (Cambridge U. Press, Cambridge, UK, 1992).

Dana, V.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Davis, S. P.

S. P. Davis, M. C. Abrams, J. W. Brault, Fourier Transform Spectrometry (Academic, San Diego, Calif., 2001).

de Haseth, J.

P. R. Griffiths, J. de Haseth, Fourier Transform Infrared Spectroscopy (Wiley, New York, 1986).

Dube, D. J.

H. J. P. Smith, D. J. Dube, M. E. Gardner, S. A. Clough, F. X. Kneizys, L. S. Rothman, “FASCODE—Fast Atmospheric Signature Code (Spectral Transmittance and Radiance),” Tech. Rep. AFGL-TR-78-0081 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1978).

Edwards, D.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Flanigan, D. F.

Flaud, J.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Gamache, R.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Gardner, M. E.

H. J. P. Smith, D. J. Dube, M. E. Gardner, S. A. Clough, F. X. Kneizys, L. S. Rothman, “FASCODE—Fast Atmospheric Signature Code (Spectral Transmittance and Radiance),” Tech. Rep. AFGL-TR-78-0081 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1978).

Goldman, A.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Griffiths, P. R.

P. R. Griffiths, “Fourier transform infrared spectrometry at low resolution: how low can you go?,” in Ninth International Conference on Fourier Transform Spectroscopy, J. E. Bertie, H. Wieser, eds., Proc. SPIE2089, 2–8 (1993).
[CrossRef]

P. R. Griffiths, J. de Haseth, Fourier Transform Infrared Spectroscopy (Wiley, New York, 1986).

Hanel, R. A.

R. A. Hanel, B. J. Conrath, D. E. Jennings, R. E. Samuelson, Exploration of the Solar System by Infrared Remote Sensing (Cambridge U. Press, Cambridge, UK, 1992).

Harig, R.

R. Harig, G. Matz, “Toxic cloud imaging by infrared spectrometry: a scanning FTIR system for identification and visualization,” Field Anal. Chem. Technol. 5, 75–90 (2001).
[CrossRef]

R. Harig, G. Matz, P. Rusch, “Scanning infrared remote sensing system for identification, visualization, and quantification of airborne pollutants,” in Instrumentation for Air Pollution and Global Atmospheric Monitoring, J. O. Jensen, R. L. Spellicy, eds., Proc. SPIE4574, 83–94 (2002).
[CrossRef]

Hase, F.

Jennings, D. E.

R. A. Hanel, B. J. Conrath, D. E. Jennings, R. E. Samuelson, Exploration of the Solar System by Infrared Remote Sensing (Cambridge U. Press, Cambridge, UK, 1992).

Jucks, K.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Kauppinen, J.

Kauppinnen, J.

J. Kauppinnen, J. Partanen, Fourier Transforms in Spectroscopy (Wiley-VCH, Berlin, 2001).
[CrossRef]

Kneizys, F. X.

H. J. P. Smith, D. J. Dube, M. E. Gardner, S. A. Clough, F. X. Kneizys, L. S. Rothman, “FASCODE—Fast Atmospheric Signature Code (Spectral Transmittance and Radiance),” Tech. Rep. AFGL-TR-78-0081 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1978).

Mandin, J.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Massie, S.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Matz, G.

R. Harig, G. Matz, “Toxic cloud imaging by infrared spectrometry: a scanning FTIR system for identification and visualization,” Field Anal. Chem. Technol. 5, 75–90 (2001).
[CrossRef]

R. Harig, G. Matz, P. Rusch, “Scanning infrared remote sensing system for identification, visualization, and quantification of airborne pollutants,” in Instrumentation for Air Pollution and Global Atmospheric Monitoring, J. O. Jensen, R. L. Spellicy, eds., Proc. SPIE4574, 83–94 (2002).
[CrossRef]

McCann, A.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Murty, M. V. R. K.

Nemtchinov, V.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Partanen, J.

J. Kauppinnen, J. Partanen, Fourier Transforms in Spectroscopy (Wiley-VCH, Berlin, 2001).
[CrossRef]

Paton-Walsh, C.

Perrin, A.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Raspollini, P.

G. Bianchini, P. Raspollini, “Characterisation of instrumental line shape distortions due to path difference dependent phase errors in a Fourier transform spectrometer,” Infrared Phys. Technol. 41, 287–292 (2000).
[CrossRef]

Rinsland, C.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Robertson, D. C.

A. Berk, L. S. Bernstein, D. C. Robertson, “MODTRAN: A Moderate Resolution Model for LOWTRAN 7,” AFGL-TR-89-0122 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1989).

Rothman, L.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Rothman, L. S.

H. J. P. Smith, D. J. Dube, M. E. Gardner, S. A. Clough, F. X. Kneizys, L. S. Rothman, “FASCODE—Fast Atmospheric Signature Code (Spectral Transmittance and Radiance),” Tech. Rep. AFGL-TR-78-0081 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1978).

Rusch, P.

R. Harig, G. Matz, P. Rusch, “Scanning infrared remote sensing system for identification, visualization, and quantification of airborne pollutants,” in Instrumentation for Air Pollution and Global Atmospheric Monitoring, J. O. Jensen, R. L. Spellicy, eds., Proc. SPIE4574, 83–94 (2002).
[CrossRef]

Saarinen, P.

Samuelson, R. E.

R. A. Hanel, B. J. Conrath, D. E. Jennings, R. E. Samuelson, Exploration of the Solar System by Infrared Remote Sensing (Cambridge U. Press, Cambridge, UK, 1992).

Schroeder, J.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Smith, H. J. P.

H. J. P. Smith, D. J. Dube, M. E. Gardner, S. A. Clough, F. X. Kneizys, L. S. Rothman, “FASCODE—Fast Atmospheric Signature Code (Spectral Transmittance and Radiance),” Tech. Rep. AFGL-TR-78-0081 (U.S. Air Force Geophysics Laboratory, Hanscom Air Force Base, Mass., 1978).

Steel, W. H.

Thériault, J.-M.

Varanasi, P.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Wattson, R.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Windpassinger, R.

R. Windpassinger, “Quantitative analysis of flue gas FTIR-spectra employing a new mathematical method to determine the instrumental line shape,” in Spectroscopic Atmospheric Environmental Monitoring Techniques, K. Schäfer, ed., Proc. SPIE3493, 64–70 (1998).
[CrossRef]

Wyatt, C. L.

Yoshino, K.

L. Rothman, C. Rinsland, A. Goldman, S. Massie, D. Edwards, J. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Mandin, J. Schroeder, A. McCann, R. Gamache, R. Wattson, K. Yoshino, K. Chance, K. Jucks, L. Brown, V. Nemtchinov, P. Varanasi, “The HITRAN Molecular Spectroscopic Database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer 60, 665–710 (1998).
[CrossRef]

Appl. Opt. (7)

Field Anal. Chem. Technol. (2)

R. Harig, G. Matz, “Toxic cloud imaging by infrared spectrometry: a scanning FTIR system for identification and visualization,” Field Anal. Chem. Technol. 5, 75–90 (2001).
[CrossRef]

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

Infrared Phys. Technol. (1)

G. Bianchini, P. Raspollini, “Characterisation of instrumental line shape distortions due to path difference dependent phase errors in a Fourier transform spectrometer,” Infrared Phys. Technol. 41, 287–292 (2000).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Quant. Spectrosc. Radiat. Transfer (1)

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The author is preparing a manuscript to be called “Remote sensing of airborne pollutants by passive FTIR spectrometry: method for the retrieval of the column density.”

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Figures (8)

Fig. 1
Fig. 1

Illustration of the measurement setup of passive infrared remote sensing of airborne pollutants.

Fig. 2
Fig. 2

Instrument line shape calculated with Eqs. (6) and (8) (Δσ = 2 cm-1, σ′ = 1000 cm-1, no apodization).

Fig. 3
Fig. 3

Absolute value of the signal of a single absorption line as a function of the spectral resolution parameter (crosses) (Δσ in units of the full width of the line) and the approximation for low spectral resolution calculated with Eq. (16) (dashed line).

Fig. 4
Fig. 4

SNR of a single absorption line for measurement of a single scan as a function of spectral resolution (crosses) (in units of the width of the line), approximation for high spectral resolution [Eq. (18)] (dashed line), and approximation for low spectral resolution [Eq. (19)] (dashed-dotted line).

Fig. 5
Fig. 5

SNR of a single absorption line for constant measurement time (1 s) as a function of spectral resolution (crosses), approximation for high spectral resolution [Eq. (20)] (dashed line), and approximation for low spectral resolution [Eq. (21)] (dashed-dotted line).

Fig. 6
Fig. 6

Spectra of ammonia with different spectral resolutions calculated by Fourier transformation of the appropriate number of samples of the same interferogram (solid curve), simulated spectra (dashed curve), and the difference (dashed-dotted curve, offset subtracted). All simulated spectra were calculated with the same parameters (cl NH3 ≈ 600 ppm m, ΔT ≈ 12 K).

Fig. 7
Fig. 7

Measured and calculated [Eq. (12): f(Δσ) = const × Δσ-1/2] NESR for a single scan as a function of spectral resolution Δσ (error bars indicate the standard deviation, ten measurements).

Fig. 8
Fig. 8

Measured and calculated SNRs for a single scan as a function of spectral resolution Δσ (cl NH3 ≈ 600 ppm m, ΔT ≈ 12 K, σ i ≈ 931 cm-1; error bars indicate the standard deviation).

Equations (21)

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LS=1-τatBat+τat1-τcBc+τcLb
LS=Bat+τatτcLb-Bat.
ΔL=1-τatτcΔLcb,
Scσ=- SσAσ-σ, σdσ.
Aσ, σ=A0σ=2D sinc2πDσ,
Aσ, σ=A0σ*Ainhσ, σ,
Scσ=Sσ*Aσ, σ.
Ainhσ, σ=0for σ<-p1p2+p3σ+p12for -p1σ-p4p5rectσ+p42p4for σ>-p4.
ΔLMσ=ΔLσ*Aσ, σ.
SNRσi=|ΔLMσi|NESR.
NESR=ADΘξΔσEtD*.
NESR1Scan=2ADfS1/2ΘξD*σLΔσ1/2.
τσ=exp-βσcl.
βσcl=-lnτminγ2γ2+σ-σ02.
ΔLσ=1-τcσΔLcb-lnτminγ2γ2+σ-σ02 ΔLcb.
ΔLMσ0=- ΔLσA0σ0-σdσ- ΔLσA00dσ-2π lnτminγΔLcbΔσ.
ΔLMσ0=- ΔLσA0σ0-σdσ- ΔLσ0A0σ0-σdσ=ΔLσ0.
SNR1Scanσ0=|ΔLσ0|NESR1Scan=|ΔLσ0|ΘξD*σLΔσ1/22ADfS1/2.
SNR1Scanσ0=-2π lnτminγ|ΔLcb|Δσ NESR1Scan=-π lnτminγ|ΔLcb|ΘξD*2σL1/2ΔσADfS1/2.
SNRtσ0=|ΔLσ0|NESR=|ΔLσ0|ΘξD*Δσt2AD.
SNRtσ0=-2π lnτminγ|ΔLcb|Δσ NESR=-π lnτminγ|ΔLcb|ΘξD*tAD.

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