Abstract

This paper addresses detection and characterization of chemical vapor fugitive emissions in a non scattering atmosphere by processing of remotely-sensed long-wavelength infrared spectra. The analysis approach integrates a parameterized signal model based on the radiative transfer equation with a statistical model for the infrared background. The maximum likelihood model parameter values are defined as those that maximize a Bayesian posterior probability and are estimated using a Gauss–Newton algorithm. For algorithm performance evaluation we simulate observation of fugitive emissions by augmenting plume-free measured spectra with synthetic plume signatures. As plumes become optically thick, the Gauss–Newton algorithm yields significantly more accurate estimates of chemical vapor column density and significantly more favorable plume detection statistics than clutter-matched-filter-based and adaptive-subspace-detector-based plume characterization and detection.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. N. B. Gallagher, B. M. Wise, and D. M. Sheen, “Estimation of trace concentration-pathlength in plumes for remote sensing applications from hyperspectral images,” Anal. Chim. Acta 490, 139-152 (2003).
    [CrossRef]
  11. E. M. O'Donnell, D. W. Messinger, C. Salvaggio, and J. R. Schott, “Identification and detection of gaseous effluents from hyperspectral imagery using invariant algorithms,” Proc. SPIE 5425, 573-582 (2004).
    [CrossRef]
  12. D. Manolakis and F. M. D'Amico, “A taxonomy of algorithms for chemical vapor detection with hyperspectral imaging spectroscopy,” Proc. SPIE 5795, 125-133 (2005).
    [CrossRef]
  13. A. Vallières, A. Villemaire, M. Chamberland, L. Belhumeur, V. Farley, J. Giroux, and J.-F. Legault, “Algorithms for chemical detection, identification and quantification for thermal hyperspectral imagers,” Proc. SPIE 5995, 59950G-1 (2005).
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  20. D. M. Sheen, N. B. Gallagher, S. W. Sharpe, K. K. Anderson, and J. F. Shultz, “Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity,” Proc. SPIE 5093, 218-229 (2003).
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  21. R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis, 5th ed. (Prentice Hall, 2002), Chap. 9, pp. 477-532.
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  24. S. Kraut and L. L. Scharf, “The CFAR adaptive subspace detector is a scale invariant GLRT,” IEEE Trans. Signal Process. 47, 2538-2541 (1999).
    [CrossRef]
  25. S. Kraut, L. L. Scharf, and L. T. McWhorter, “Adaptive subspace detectors,” IEEE Trans. Signal Process. 49, 1-16 (2001).
    [CrossRef]
  26. W. J. Marinelli, C. M. Gittins, B. R. Cosofret, T. E. Ustun, and J. O. Jensen, “Development of the AIRIS-WAD multispectral sensor for airborne standoff chemical agent and toxic industrial chemical detection,” in Proceedings of the Meetings of the Mil. Sens. Symp. Specialty Groups on Passive Sensors; Camouflage, Concealment, and Deception; Detectors; and Materials, ADA444225 (DTIC, 2005).
  27. W. J. Marinelli, C. M. Gittins, A. H. Gelb, and B. D. Green, “Tunable Fabry-Perot etalon-based long-wavelength infrared imaging spectrometer,” Appl. Opt. 38, 2594-2604 (1999).
    [CrossRef]
  28. S. W. Sharpe, T. J. Johnson, R. L. Sams, P. M. Chu, G. C. Roderick, and P. A. Johnson, “Gas-phase databases for quantitative infrared spectrometry,” Appl. Spectrosc. 58, 1452-1461 (2004).
    [CrossRef]
  29. D. E. Tyler, “A distribution-free M-estimator of multivariate scatter,” Ann. Stat. 15, 234-251 (1987).
    [CrossRef]
  30. H. Cox and R. Pitre, “Robust DMR and multi-rate adaptive beamforming,” in Signals, Systems & Computers, 1997. Conference Record of the Thirty-First Asilomar Conference on, Vol. 1 (IEEE, 1997), pp. 920-924, http://dx.doi.org/10.1109/ACSSC.1997.680577
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    [CrossRef]

2005 (2)

D. Manolakis and F. M. D'Amico, “A taxonomy of algorithms for chemical vapor detection with hyperspectral imaging spectroscopy,” Proc. SPIE 5795, 125-133 (2005).
[CrossRef]

A. Vallières, A. Villemaire, M. Chamberland, L. Belhumeur, V. Farley, J. Giroux, and J.-F. Legault, “Algorithms for chemical detection, identification and quantification for thermal hyperspectral imagers,” Proc. SPIE 5995, 59950G-1 (2005).

2004 (3)

2003 (3)

D. M. Sheen, N. B. Gallagher, S. W. Sharpe, K. K. Anderson, and J. F. Shultz, “Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity,” Proc. SPIE 5093, 218-229 (2003).
[CrossRef]

N. B. Gallagher, B. M. Wise, and D. M. Sheen, “Estimation of trace concentration-pathlength in plumes for remote sensing applications from hyperspectral images,” Anal. Chim. Acta 490, 139-152 (2003).
[CrossRef]

S. W. Seeman, J. Li, W. P. Menzel, and L. E. Gumley, “Operational retrieval of atmospheric temperature, moisture, and ozone from MODIS infrared radiances,” J. Appl. Meteorol. 42, 1072-1091 (2003).
[CrossRef]

2001 (3)

T. Steck and T. von Clarmann, “Constrained profile retrieval applied to the observation mode of the Michelson interferometer for passive atmospheric sounding,” Appl. Opt. 40, 3559-3571 (2001).
[CrossRef]

C. C. Funk, J. Theiler, D. A. Roberts, and C. C. Borel, “Clustering to improve matched filter detection of weak gas plumes in hyperspectral thermal imagery,” IEEE Trans. Geosci. Remote Sens. 39, 1410-1419 (2001).
[CrossRef]

S. Kraut, L. L. Scharf, and L. T. McWhorter, “Adaptive subspace detectors,” IEEE Trans. Signal Process. 49, 1-16 (2001).
[CrossRef]

2000 (1)

1999 (4)

X. L. Ma, T. J. Schmit, and W. L. Smith, “A nonlinear physical retrieval algorithm--its application to the GOES-8/9 Sounder,” J. Appl. Meteorol. 38, 501-513 (1999).
[CrossRef]

W. J. Marinelli, C. M. Gittins, A. H. Gelb, and B. D. Green, “Tunable Fabry-Perot etalon-based long-wavelength infrared imaging spectrometer,” Appl. Opt. 38, 2594-2604 (1999).
[CrossRef]

M. E. Tipping and C. M. Bishop, “Probabilistic principal components analysis,” J. R. Stat. Soc. B 61, Part 3, 611-622(1999).
[CrossRef]

S. Kraut and L. L. Scharf, “The CFAR adaptive subspace detector is a scale invariant GLRT,” IEEE Trans. Signal Process. 47, 2538-2541 (1999).
[CrossRef]

1996 (2)

1995 (1)

1992 (1)

S. A. Clough, M. J. Iacono, and J.-L. Moncet, “Line-by-line calculations of atmospheric fluxes and cooling rates: application for water vapor,” J. Geophys. Res. 97, 15761-15785 (1992).

1991 (1)

1989 (1)

J. R. Eyre, “Inversion of cloudy satellite sounding radiances by nonlinear optimal estimation. I: Theory and simulation for TOVS,” Q. J. R. Meteorol. Soc. 115, 1001-1026 (1989).
[CrossRef]

1987 (1)

D. E. Tyler, “A distribution-free M-estimator of multivariate scatter,” Ann. Stat. 15, 234-251 (1987).
[CrossRef]

1985 (1)

M. Wax and T. Kailath, “Detection of signals by information theoretic criteria,” IEEE Trans. Acoust. Speech Signal Process. 33, pp. 387-392 (1985).
[CrossRef]

1976 (1)

C. D. Rodgers, “Retrieval of atmospheric temperature and composition from remote measurements of thermal radiation,” Rev. Geophys. Space Phys. 14, 609-624 (1976).
[CrossRef]

Anderson, K. K.

D. M. Sheen, N. B. Gallagher, S. W. Sharpe, K. K. Anderson, and J. F. Shultz, “Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity,” Proc. SPIE 5093, 218-229 (2003).
[CrossRef]

Belhumeur, L.

A. Vallières, A. Villemaire, M. Chamberland, L. Belhumeur, V. Farley, J. Giroux, and J.-F. Legault, “Algorithms for chemical detection, identification and quantification for thermal hyperspectral imagers,” Proc. SPIE 5995, 59950G-1 (2005).

Bishop, C. M.

M. E. Tipping and C. M. Bishop, “Probabilistic principal components analysis,” J. R. Stat. Soc. B 61, Part 3, 611-622(1999).
[CrossRef]

Borel, C. C.

C. C. Funk, J. Theiler, D. A. Roberts, and C. C. Borel, “Clustering to improve matched filter detection of weak gas plumes in hyperspectral thermal imagery,” IEEE Trans. Geosci. Remote Sens. 39, 1410-1419 (2001).
[CrossRef]

Boyce, B.

Chamberland, M.

A. Vallières, A. Villemaire, M. Chamberland, L. Belhumeur, V. Farley, J. Giroux, and J.-F. Legault, “Algorithms for chemical detection, identification and quantification for thermal hyperspectral imagers,” Proc. SPIE 5995, 59950G-1 (2005).

Chu, P. M.

Clough, S. A.

S. A. Clough, M. J. Iacono, and J.-L. Moncet, “Line-by-line calculations of atmospheric fluxes and cooling rates: application for water vapor,” J. Geophys. Res. 97, 15761-15785 (1992).

Cosofret, B. R.

W. J. Marinelli, C. M. Gittins, B. R. Cosofret, T. E. Ustun, and J. O. Jensen, “Development of the AIRIS-WAD multispectral sensor for airborne standoff chemical agent and toxic industrial chemical detection,” in Proceedings of the Meetings of the Mil. Sens. Symp. Specialty Groups on Passive Sensors; Camouflage, Concealment, and Deception; Detectors; and Materials, ADA444225 (DTIC, 2005).

Cox, H.

H. Cox and R. Pitre, “Robust DMR and multi-rate adaptive beamforming,” in Signals, Systems & Computers, 1997. Conference Record of the Thirty-First Asilomar Conference on, Vol. 1 (IEEE, 1997), pp. 920-924, http://dx.doi.org/10.1109/ACSSC.1997.680577

D'Amico, F. M.

D. Manolakis and F. M. D'Amico, “A taxonomy of algorithms for chemical vapor detection with hyperspectral imaging spectroscopy,” Proc. SPIE 5795, 125-133 (2005).
[CrossRef]

Eyre, J. R.

J. R. Eyre, “Inversion of cloudy satellite sounding radiances by nonlinear optimal estimation. I: Theory and simulation for TOVS,” Q. J. R. Meteorol. Soc. 115, 1001-1026 (1989).
[CrossRef]

Farley, V.

A. Vallières, A. Villemaire, M. Chamberland, L. Belhumeur, V. Farley, J. Giroux, and J.-F. Legault, “Algorithms for chemical detection, identification and quantification for thermal hyperspectral imagers,” Proc. SPIE 5995, 59950G-1 (2005).

Flanigan, D.

Funk, C. C.

C. C. Funk, J. Theiler, D. A. Roberts, and C. C. Borel, “Clustering to improve matched filter detection of weak gas plumes in hyperspectral thermal imagery,” IEEE Trans. Geosci. Remote Sens. 39, 1410-1419 (2001).
[CrossRef]

Gallagher, N. B.

N. B. Gallagher, B. M. Wise, and D. M. Sheen, “Estimation of trace concentration-pathlength in plumes for remote sensing applications from hyperspectral images,” Anal. Chim. Acta 490, 139-152 (2003).
[CrossRef]

D. M. Sheen, N. B. Gallagher, S. W. Sharpe, K. K. Anderson, and J. F. Shultz, “Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity,” Proc. SPIE 5093, 218-229 (2003).
[CrossRef]

Gelb, A. H.

Giroux, J.

A. Vallières, A. Villemaire, M. Chamberland, L. Belhumeur, V. Farley, J. Giroux, and J.-F. Legault, “Algorithms for chemical detection, identification and quantification for thermal hyperspectral imagers,” Proc. SPIE 5995, 59950G-1 (2005).

Gittins, C. M.

W. J. Marinelli, C. M. Gittins, A. H. Gelb, and B. D. Green, “Tunable Fabry-Perot etalon-based long-wavelength infrared imaging spectrometer,” Appl. Opt. 38, 2594-2604 (1999).
[CrossRef]

W. J. Marinelli, C. M. Gittins, B. R. Cosofret, T. E. Ustun, and J. O. Jensen, “Development of the AIRIS-WAD multispectral sensor for airborne standoff chemical agent and toxic industrial chemical detection,” in Proceedings of the Meetings of the Mil. Sens. Symp. Specialty Groups on Passive Sensors; Camouflage, Concealment, and Deception; Detectors; and Materials, ADA444225 (DTIC, 2005).

Goody, R. M.

R. M. Goody and Y. L. Yung, Atmospheric Radiation: Theoretical Basis (Oxford University, 1989), Chap. 2, pp. 46.

Green, B. D.

Gumley, L. E.

S. W. Seeman, J. Li, W. P. Menzel, and L. E. Gumley, “Operational retrieval of atmospheric temperature, moisture, and ozone from MODIS infrared radiances,” J. Appl. Meteorol. 42, 1072-1091 (2003).
[CrossRef]

X. L. Ma, Z. Wan, C. C. Moeller, W. P. Menzel, L. E. Gumley, and Y. Zhang, “Retrieval of geophysical parameters from moderate resolution imaging spectroradiometer thermal infrared data: evaluation of a two-step physical algorithm,” Appl. Opt. 39, 3537-3550 (2000).
[CrossRef]

Hall, J. L.

Harrig, R.

Hayden, A.

Herr, K. C.

Iacono, M. J.

S. A. Clough, M. J. Iacono, and J.-L. Moncet, “Line-by-line calculations of atmospheric fluxes and cooling rates: application for water vapor,” J. Geophys. Res. 97, 15761-15785 (1992).

Jensen, J. O.

W. J. Marinelli, C. M. Gittins, B. R. Cosofret, T. E. Ustun, and J. O. Jensen, “Development of the AIRIS-WAD multispectral sensor for airborne standoff chemical agent and toxic industrial chemical detection,” in Proceedings of the Meetings of the Mil. Sens. Symp. Specialty Groups on Passive Sensors; Camouflage, Concealment, and Deception; Detectors; and Materials, ADA444225 (DTIC, 2005).

Johnson, P. A.

Johnson, R. A.

R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis, 5th ed. (Prentice Hall, 2002), Chap. 9, pp. 477-532.

Johnson, T. J.

Kailath, T.

M. Wax and T. Kailath, “Detection of signals by information theoretic criteria,” IEEE Trans. Acoust. Speech Signal Process. 33, pp. 387-392 (1985).
[CrossRef]

Kay, S.

S. Kay, Fundamentals of Statistical Signal Processing: Volume 1, Estimation Theory (Prentice-Hall, 1993), p. 40.

Kraut, S.

S. Kraut, L. L. Scharf, and L. T. McWhorter, “Adaptive subspace detectors,” IEEE Trans. Signal Process. 49, 1-16 (2001).
[CrossRef]

S. Kraut and L. L. Scharf, “The CFAR adaptive subspace detector is a scale invariant GLRT,” IEEE Trans. Signal Process. 47, 2538-2541 (1999).
[CrossRef]

Legault, J.-F.

A. Vallières, A. Villemaire, M. Chamberland, L. Belhumeur, V. Farley, J. Giroux, and J.-F. Legault, “Algorithms for chemical detection, identification and quantification for thermal hyperspectral imagers,” Proc. SPIE 5995, 59950G-1 (2005).

Li, J.

S. W. Seeman, J. Li, W. P. Menzel, and L. E. Gumley, “Operational retrieval of atmospheric temperature, moisture, and ozone from MODIS infrared radiances,” J. Appl. Meteorol. 42, 1072-1091 (2003).
[CrossRef]

Ma, X. L.

Manolakis, D.

D. Manolakis and F. M. D'Amico, “A taxonomy of algorithms for chemical vapor detection with hyperspectral imaging spectroscopy,” Proc. SPIE 5795, 125-133 (2005).
[CrossRef]

Marinelli, W. J.

W. J. Marinelli, C. M. Gittins, A. H. Gelb, and B. D. Green, “Tunable Fabry-Perot etalon-based long-wavelength infrared imaging spectrometer,” Appl. Opt. 38, 2594-2604 (1999).
[CrossRef]

W. J. Marinelli, C. M. Gittins, B. R. Cosofret, T. E. Ustun, and J. O. Jensen, “Development of the AIRIS-WAD multispectral sensor for airborne standoff chemical agent and toxic industrial chemical detection,” in Proceedings of the Meetings of the Mil. Sens. Symp. Specialty Groups on Passive Sensors; Camouflage, Concealment, and Deception; Detectors; and Materials, ADA444225 (DTIC, 2005).

McWhorter, L. T.

S. Kraut, L. L. Scharf, and L. T. McWhorter, “Adaptive subspace detectors,” IEEE Trans. Signal Process. 49, 1-16 (2001).
[CrossRef]

Menzel, W. P.

S. W. Seeman, J. Li, W. P. Menzel, and L. E. Gumley, “Operational retrieval of atmospheric temperature, moisture, and ozone from MODIS infrared radiances,” J. Appl. Meteorol. 42, 1072-1091 (2003).
[CrossRef]

X. L. Ma, Z. Wan, C. C. Moeller, W. P. Menzel, L. E. Gumley, and Y. Zhang, “Retrieval of geophysical parameters from moderate resolution imaging spectroradiometer thermal infrared data: evaluation of a two-step physical algorithm,” Appl. Opt. 39, 3537-3550 (2000).
[CrossRef]

Messinger, D. W.

E. M. O'Donnell, D. W. Messinger, C. Salvaggio, and J. R. Schott, “Identification and detection of gaseous effluents from hyperspectral imagery using invariant algorithms,” Proc. SPIE 5425, 573-582 (2004).
[CrossRef]

Moeller, C. C.

Moncet, J.-L.

S. A. Clough, M. J. Iacono, and J.-L. Moncet, “Line-by-line calculations of atmospheric fluxes and cooling rates: application for water vapor,” J. Geophys. Res. 97, 15761-15785 (1992).

Niple, E.

O'Donnell, E. M.

E. M. O'Donnell, D. W. Messinger, C. Salvaggio, and J. R. Schott, “Identification and detection of gaseous effluents from hyperspectral imagery using invariant algorithms,” Proc. SPIE 5425, 573-582 (2004).
[CrossRef]

Pitre, R.

H. Cox and R. Pitre, “Robust DMR and multi-rate adaptive beamforming,” in Signals, Systems & Computers, 1997. Conference Record of the Thirty-First Asilomar Conference on, Vol. 1 (IEEE, 1997), pp. 920-924, http://dx.doi.org/10.1109/ACSSC.1997.680577

Polak, M. L.

Revercomb, H. E.

Roberts, D. A.

C. C. Funk, J. Theiler, D. A. Roberts, and C. C. Borel, “Clustering to improve matched filter detection of weak gas plumes in hyperspectral thermal imagery,” IEEE Trans. Geosci. Remote Sens. 39, 1410-1419 (2001).
[CrossRef]

Roderick, G. C.

Rodgers, C. D.

C. D. Rodgers, “Retrieval of atmospheric temperature and composition from remote measurements of thermal radiation,” Rev. Geophys. Space Phys. 14, 609-624 (1976).
[CrossRef]

C. D. Rodgers, Inverse Methods for Atmospheric Sounding: Theory and Practice (World Scientific, 2000), Chap. , pp. 30.

Salvaggio, C.

E. M. O'Donnell, D. W. Messinger, C. Salvaggio, and J. R. Schott, “Identification and detection of gaseous effluents from hyperspectral imagery using invariant algorithms,” Proc. SPIE 5425, 573-582 (2004).
[CrossRef]

Sams, R. L.

Scharf, L. L.

S. Kraut, L. L. Scharf, and L. T. McWhorter, “Adaptive subspace detectors,” IEEE Trans. Signal Process. 49, 1-16 (2001).
[CrossRef]

S. Kraut and L. L. Scharf, “The CFAR adaptive subspace detector is a scale invariant GLRT,” IEEE Trans. Signal Process. 47, 2538-2541 (1999).
[CrossRef]

Schmit, T. J.

X. L. Ma, T. J. Schmit, and W. L. Smith, “A nonlinear physical retrieval algorithm--its application to the GOES-8/9 Sounder,” J. Appl. Meteorol. 38, 501-513 (1999).
[CrossRef]

Schott, J. R.

E. M. O'Donnell, D. W. Messinger, C. Salvaggio, and J. R. Schott, “Identification and detection of gaseous effluents from hyperspectral imagery using invariant algorithms,” Proc. SPIE 5425, 573-582 (2004).
[CrossRef]

Seeman, S. W.

S. W. Seeman, J. Li, W. P. Menzel, and L. E. Gumley, “Operational retrieval of atmospheric temperature, moisture, and ozone from MODIS infrared radiances,” J. Appl. Meteorol. 42, 1072-1091 (2003).
[CrossRef]

Sharpe, S. W.

S. W. Sharpe, T. J. Johnson, R. L. Sams, P. M. Chu, G. C. Roderick, and P. A. Johnson, “Gas-phase databases for quantitative infrared spectrometry,” Appl. Spectrosc. 58, 1452-1461 (2004).
[CrossRef]

D. M. Sheen, N. B. Gallagher, S. W. Sharpe, K. K. Anderson, and J. F. Shultz, “Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity,” Proc. SPIE 5093, 218-229 (2003).
[CrossRef]

Sheen, D. M.

D. M. Sheen, N. B. Gallagher, S. W. Sharpe, K. K. Anderson, and J. F. Shultz, “Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity,” Proc. SPIE 5093, 218-229 (2003).
[CrossRef]

N. B. Gallagher, B. M. Wise, and D. M. Sheen, “Estimation of trace concentration-pathlength in plumes for remote sensing applications from hyperspectral images,” Anal. Chim. Acta 490, 139-152 (2003).
[CrossRef]

Shultz, J. F.

D. M. Sheen, N. B. Gallagher, S. W. Sharpe, K. K. Anderson, and J. F. Shultz, “Impact of background and atmospheric variability on infrared hyperspectral chemical detection sensitivity,” Proc. SPIE 5093, 218-229 (2003).
[CrossRef]

Smith, W. L.

X. L. Ma, T. J. Schmit, and W. L. Smith, “A nonlinear physical retrieval algorithm--its application to the GOES-8/9 Sounder,” J. Appl. Meteorol. 38, 501-513 (1999).
[CrossRef]

W. L. Smith, H. M. Woolf, and H. E. Revercomb, “Linear simultaneous solution for temperature and absorbing constituent profiles from radiance spectra,” Appl. Opt. 30, 1117-1123(1991).
[CrossRef]

Steck, T.

Theiler, J.

C. C. Funk, J. Theiler, D. A. Roberts, and C. C. Borel, “Clustering to improve matched filter detection of weak gas plumes in hyperspectral thermal imagery,” IEEE Trans. Geosci. Remote Sens. 39, 1410-1419 (2001).
[CrossRef]

Tipping, M. E.

M. E. Tipping and C. M. Bishop, “Probabilistic principal components analysis,” J. R. Stat. Soc. B 61, Part 3, 611-622(1999).
[CrossRef]

Tyler, D. E.

D. E. Tyler, “A distribution-free M-estimator of multivariate scatter,” Ann. Stat. 15, 234-251 (1987).
[CrossRef]

Ustun, T. E.

W. J. Marinelli, C. M. Gittins, B. R. Cosofret, T. E. Ustun, and J. O. Jensen, “Development of the AIRIS-WAD multispectral sensor for airborne standoff chemical agent and toxic industrial chemical detection,” in Proceedings of the Meetings of the Mil. Sens. Symp. Specialty Groups on Passive Sensors; Camouflage, Concealment, and Deception; Detectors; and Materials, ADA444225 (DTIC, 2005).

Vallières, A.

A. Vallières, A. Villemaire, M. Chamberland, L. Belhumeur, V. Farley, J. Giroux, and J.-F. Legault, “Algorithms for chemical detection, identification and quantification for thermal hyperspectral imagers,” Proc. SPIE 5995, 59950G-1 (2005).

Villemaire, A.

A. Vallières, A. Villemaire, M. Chamberland, L. Belhumeur, V. Farley, J. Giroux, and J.-F. Legault, “Algorithms for chemical detection, identification and quantification for thermal hyperspectral imagers,” Proc. SPIE 5995, 59950G-1 (2005).

von Clarmann, T.

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Figures (19)

Fig. 1
Fig. 1

Stratified atmosphere model. Each layer defined to have uniform temperature ( T i ), pressure, and chemical composition; layer transmission is τ i . Chemical vapor plume of interest is Layer p.

Fig. 2
Fig. 2

Grayscale representation of AIRIS-WAD datacube. Lighter pixels indicate higher average radiance values; average radiance calculated over all 20 spectral bands acquired by the sensor. Representative “sky,” “horizon,” and “ground” regions are indicated by the white boxes and black box, respectively.

Fig. 3
Fig. 3

Radiance spectra corresponding to the “sky,” “horizon,” and “ground” regions in Fig. 2. Spectra shown are the average of all pixels in the identified region.

Fig. 4
Fig. 4

Calculated transmission spectra of 20, 197, and 591 ppmv m R-134a plumes. High resolution spectra have peak optical density of 0.1, 1.0, and 3.0 (base e), respectively. The thick lines indicate the spectra calculated using Beer’s law and the R-134a spectrum from the PNNL database. The thin dotted lines indicate the effective transmission which results from convolving the high resolution spectrum with a 0.08 μm FWHM Lorentzian lineshape function. The lower resolution spectra were used to augment AIRIS-WAD data.

Fig. 5
Fig. 5

Effective thermal contrast between the local air temperature and the effective radiometric temperature of the background. Calculated median Δ T eff for each row in scene depicted in Fig. 2.

Fig. 6
Fig. 6

Uncertainty in the estimated column density as a function of elevation angle. Plot shows median for row in scene depicted in Fig. 2; uncertainty calculated using Eq. (36).

Fig. 7
Fig. 7

Locations where synthetic R-134a plumes were added to AIRIS-WAD data. The effective thermal contrast in Region 1 is 2.6 ± 0.5 K and the effective contrast in Region 2 is 5.9 ± 0.6 K .

Fig. 8
Fig. 8

R-134a optical densities estimated in Region 1 of Fig. 7. Black circles indicate median OD estimated by the Gauss–Newton algorithm. Open circles indicate median OD estimated using the linear signal model given by Eq. (31). The error bars in correspond to ± 1 σ variation in estimated column density calculated using Eq. (45).

Fig. 9
Fig. 9

R-134a optical densities estimated in Region 2 of Fig. 7. Black circles indicate median OD estimated by the Gauss–Newton algorithm. Open circles indicate median OD estimated using the linear signal model given by Eq. (31). The error bars in correspond to ± 1 σ variation in estimated column density calculated using Eq. (45).

Fig. 10
Fig. 10

Effective R-134a absorption cross sections for OD = 0.0 , OD = 1.0 , and OD = 3.0 . The OD = 0.0 spectrum is used for estimation of plume OD with the Gauss–Newton algorithm and linear estimator.

Fig. 11
Fig. 11

ROC curves for OD = 0.1 R-134a plumes added to Regions 1 and 2: solid squares = Gauss–Newton solver applied to Region 2; crossed open squares = ACE applied to Region 2; solid circles = Gauss–Newton solver applied to Region 1; crossed open circles = ACE applied to Region 1.

Fig. 12
Fig. 12

ROC curves for OD = 0.3 R-134a plumes added to Regions 1 and 2: solid squares = Gauss–Newton solver applied to Region 2; crossed open squares = ACE applied to Region 2; solid circles = Gauss–Newton solver applied to Region 1; crossed open circles = ACE applied to Region 1.

Fig. 13
Fig. 13

ROC curves for OD = 1.0 R-134a plumes added to Regions 1 and 2: solid squares = Gauss–Newton solver applied to Region 2; crossed open squares = ACE applied to Region 2; solid circles = Gauss–Newton solver applied to Region 1; crossed open circles = ACE applied to Region 1.

Fig. 14
Fig. 14

ROC curves for OD = 2.0 R-134a plumes added to Regions 1 and 2: solid squares = Gauss–Newton solver applied to Region 2; crossed open squares = ACE applied to Region 2; solid circles = Gauss–Newton solver applied to Region 1; crossed open circles = ACE applied to Region 1.

Fig. 15
Fig. 15

Representative spectra from Region 1 and best fits to data using linear and nonlinear models: crossed open squares = original spectrum; solid squares = original spectrum augmented with OD = 3.0 R-134a plume.

Fig. 16
Fig. 16

Rms fit residuals for Region 1: diamonds = fit to original data; crossed open squares = fit to data augmented with OD = 3.0 R-134a plume using nonlinear estimator; solid squares = fit to data augmented with OD = 3.0 R-134a plume using linear model.

Fig. 17
Fig. 17

Number of iterations required for Gauss–Newton algorithm to converge, convergence threshold = 0.01: black bars = plume-free pixels, white bars = Region 2 with no plume added, right-diagonal hashed thin-line bars = Region 2 with OD = 1.0 plume added, left-diagonal hashed bar = Region 2 with OD = 2.0 plume added, right-diagonal hashed thick-line bar = Region 2 with OD = 3.0 plume added.

Fig. 18
Fig. 18

Fraction of spectra passing F test, Eq. (A11), as function of number of basis functions used to model data. Pass criterion is F value for 5 % of the spectra exceed the F value for 95% significance. Data corresponds to upper middle quadrant of scene in Fig. 2.

Fig. 19
Fig. 19

RMS residuals between model and data as function of m for m = 4 7 . Six basis vectors were deemed to be statistically significant using the F-test criterion.

Equations (57)

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R i ( λ ) = R i 1 ( λ ) · τ i ( λ ) + L i ( λ ) · [ 1 τ i ( λ ) ] ,
R s = ( 1 τ a ) · L a + τ a · τ p · R b + ( 1 τ p ) · L p ,
τ p = exp [ ρ · κ ] ,
R s ( 0 ) = ( 1 τ a ) · L a + τ a · R b ,
R s R s ( 0 ) = ( 1 τ p ) · [ ( L a R s ( 0 ) ) + τ a · ( L p L a ) ] .
x ( λ s ) = R s ( λ ) · g ( λ ; λ s ) · d λ ,
x p ( λ s ) x 0 ( λ s ) = [ 1 τ p ( λ ) ] · [ L ( λ ) a R s ( 0 ) ( λ ) ] · g ( λ , λ s ) · d λ ,
x p x 0 = [ 1 τ e ] · [ L a x 0 ] ,
τ e = exp ( α · ρ 0 · κ ¯ ) .
κ ¯ ( λ s ) = κ ( λ ) · g ( λ , λ s ) · d λ .
x ˜ = x + e ,
x = μ + B β ,
β N ( 0 , I m ) ,
p ( θ | x ˜ ) = p ( x ˜ | θ ) p ( θ ) p ( x ˜ ) ,
f ( θ ) = τ e x 0 + [ 1 τ e ] L a ,
ln p ( x ˜ | θ ) = 1 2 [ x ˜ f ( θ ) ] T D 1 [ x ˜ f ( θ ) ] + c x | θ ,
ln p ( θ ) = 1 2 [ θ c θ a ] T S θ [ θ c θ a ] + c θ ,
C = [ x ˜ f ( θ ) ] T D 1 [ x ˜ f ( θ ) ] + [ θ c θ a ] T S θ [ θ c θ a ] .
[ θ c θ a ] T S θ [ θ c θ a ] = β T β .
C = r T r ,
θ i + 1 = θ i ( J i T J i ) 1 J i T r i ,
r = [ D 1 / 2 [ x ˜ f ( θ ) ] ; β ] .
J = [ r β ; r α ] ,
r β = [ D 1 / 2 · diag { τ e } · B I m ] ,
r α = [ D 1 / 2 · diag { τ e s } · δ 0 0 m ] ,
x p = x 0 + α s ( L a x 0 ) .
x p = x 0 + α s ,
s = s [ d L a d T ] T a Δ T 0 ,
α = α · Δ T eff Δ T 0 .
g ( θ ) = α s + B β + μ .
[ α ^ β ^ ] = [ s T D 1 s s T D 1 B B T D 1 s Λ m ] 1 [ ( x ˜ μ ) T D 1 s ( x ˜ μ ) T D 1 B ] .
α ^ = s T Σ ^ 1 ( x ˜ μ ) s T Σ ^ 1 s ,
[ σ ( θ ^ i ) ] 2 [ I 1 ( θ ^ ) ] i i
[ I ( θ ^ ) ] i j = E { 2 ln p ( θ | x ˜ ) θ i θ j } [ J T J ] i j .
[ σ ( α ^ ) ] 2 = [ ( J T J ) 1 ] i i .
[ σ ( α ^ L ) ] 2 = [ α α ] 2 [ σ ( α ^ ) ] 2 + [ α ( Δ T ) ] 2 [ σ ( Δ T ) ] 2 = ( Δ T 0 Δ T ) 2 ( [ σ ( α ^ ) ] 2 + ( α ^ ) 2 [ σ ( Δ T ) Δ T ] 2 ) ,
[ σ ( α ^ ) ] 2 [ s T D 1 s ] 1 .
[ σ ( α ^ L ) ] 2 = ( Δ T 0 Δ T eff ) 2 [ s T D 1 s ] 1 .
Δ T eff = Δ T 0 · ( s ) T [ s ( L a x 0 ) ] ( s ) T ( s ) ,
F ( x ˜ ) = ( k 1 ) · [ C ( x ˜ , θ ^ 0 ) C ( x ˜ , θ ^ ) 1 ] ,
C ( x ˜ ; θ 0 ) = [ x ˜ B β ^ 0 ] T D 1 [ x ˜ B β ^ 0 ] + β ^ 0 T β ^ 0 ,
D ACE ( x ˜ ) = ( s T Σ ^ 1 [ x ˜ μ ] ) 2 ( s T Σ ^ 1 s ) ( [ x ˜ μ ] T Σ ^ 1 [ x ˜ μ ] ) .
x p = [ 1 τ ¯ p ] L a + τ ¯ p x ^ 0 + e ^ ,
τ ¯ p ( λ s ) = exp [ ρ · κ ( λ ) ] · g ( λ , λ s ) · d λ .
σ ^ α ^ = median { | α ^ i median { α ^ i } | } 0.6745 .
0 1 C i + 1 C i ε .
x = μ + B β ,
x ˜ = x + e ,
D 1 / 2 Σ D 1 / 2 = U Λ U T ,
Σ ^ = D 1 / 2 [ U m ( Λ m ε I m ) U m T + ε I m ] D 1 / 2 ,
ε = 1 k m i = m + 1 k λ i .
B = D 1 / 2 U m ( Λ m ε I m ) 1 / 2 .
β N ( 0 , I m ) ,
C = ( x ˜ B β ) T ( ε D ) 1 ( x ˜ B β ) + β T β ,
β ^ = Λ m 1 ( Λ m ε I m ) 1 / 2 U m T D ^ 1 / 2 ( x ˜ μ ) .
x ^ = [ D 1 / 2 U m ( I m ε Λ m 1 ) U m T D 1 / 2 ] ( x ˜ μ ) + μ .
F ( x ; m ) = ( k m 1 ) [ ( x x ^ m 1 ) T D ^ 1 ( x x ^ m 1 ) ( x x ^ m ) T D ^ 1 ( x x ^ m ) 1 ] ,

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