Abstract

One of the major limitations to the use of infrared focal plane arrays (IRFPAs) in stationary Fourier transform spectrometers (FTSs) comes from the spatial inhomogeneities of the pixel responses, where the inhomogeneities of the cut-off wavenumbers of the pixels can prevail. The hypothesis commonly assumed for FTSs that all the pixels are equivalent is thus inaccurate and results in a degradation of the estimated spectrum, even far from the cut-off wavenumbers. However, if the individual spectral responses of the pixels are measured beforehand, this a priori information can be used in the inversion process to produce reliable spectra. Thus, spatial inhomogeneities are not an obstacle for the use of infrared stationary FTS. This result is illustrated in this paper by numerical simulations, based on a realistic description of an IRFPA.

© 2012 Optical Society of America

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  1. M. D. Nelson, J. F. Johnson, and T. S. Lomheim, “General noise processes in hybrid infrared focal plane arrays,” Opt. Eng. 30, 1682–1700 (1991).
    [CrossRef]
  2. A. F. Milton, F. R. Barone, and M. R. Kruer, “Influence of non-uniformity on infrared focal plane array performance,” Opt. Eng. 24, 855–862 (1985).
  3. M. Schulz and L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Infrared Phys. 36, 763–777 (1994).
  4. F. Gillard, S. Lefebvre, Y. Ferrec, L. Mugnier, S. Rommeluère, C. Benôt-Pasanau, N. Guérineau, and J. Taboury, “Inverse problem approach for stationary Fourier-transform spectrometers,” Opt. Lett. 36, 2444–2446 (2011).
    [CrossRef]
  5. Y. Ferrec, “Spectro-imagerie aéroportée par transformation de Fourier avec un interférométre statique à décalage latéral: réalisation et mise en oeuvre,” thesis manuscript (Université Paris-Sud XI (2008).
  6. N. Ayari-Matallah, “Imagerie hyperspectrale par transformée de Fourier: Limites de détection, caractérisation des images et nouveaux concepts d’imagerie,” thesis manuscript (Université Paris-Sud XI (2011).
  7. D. Bergstrom, I. Renhorn, T. Svensson, R. Persson, T. Hallberg, R. Lindell, and G. Boreman, “Noise properties of a corner-cube Michelson interferometer LWIR hyperspectral imager,” Proc. SPIE 7660, 76602F (2010).
    [CrossRef]
  8. D. Cabib, A. Gil, M. Lavi, R. A. Buckwald, and S. G. Lipson, “New 3‒5μ wavelength range hyperspectral imager for ground and airborne use based on a single element interferometer,” Proc. SPIE 6737, 673704 (2007).
    [CrossRef]
  9. S. Rommeluère, N. Guérineau, R. Haidar, J. Deschamps, E. De Borniol, A. Million, J. P. Chamonal, and G. Destefanis, “Infrared focal plane array with a built-in stationary Fourier-transform spectrometer: basic concepts,” Opt. Lett. 33, 1062–1064 (2008).
    [CrossRef]
  10. J. Ferrand, G. Custillon, S. Kochtcheev, S. Blaize, A. Morand, G. Leblond, P. Benech, P. Royer, P. Kern, and E. Le Coarer, “A SWIFTS operating in visible and near-infrared,” Proc. SPIE 7010, 701046 (2008).
    [CrossRef]
  11. S. Thétas, N. Guérineau, P. Cymbalista, H. Sauer, and J. Taboury, “Conception of a stationary Fourier transform infrared spectroradiometer for field measurements of radiance and emissivity,” in Fourier Transform Spectroscopy/Hyperspectral Imaging and Sounding of the Environment, OSA Technical Digest Series (CD) (Optical Society of America, 2005), paper FWC3.
  12. P. Hébert, E. Cansot, C. Pierangelo, C. Buil, F. Bernard, J. Loesel, T. Trémas, L. Perrin, E. Courau, C. Casteras, I. Maussang, and D. Simeoni, “Instrumental concept and preliminary performances of SIFTI: Static Infrared Fourier Transform Interferometer,” presented at International Conference on Space Optics, Toulouse, France, 14–17October2008.
  13. A. Dariel, P. Chorier, N. Reeb, B. Terrier, M. Vuillermet, and P. Tribolet, “Development of a long wave infrared detector for SGLI instrument,” Proc. SPIE 6744, 674413 (2007).
    [CrossRef]
  14. E. P. G. Smith, A. M. Gallagher, T. J. Kostrzewa, M. L. Brest, R. W. Graham, C. L. Kuzen, E. T. Hughes, T. F. McEwan, G. M. Venzor, E. A. Patten, and W. A. Radford, “Large format HgCdTe focal plane arrays for dual-band long-wavelength infrared detection,” Proc. SPIE 7298, 72981Y (2009).
    [CrossRef]
  15. E. De Borniol, G. Destefanis, A. Manissadjian, and P. Tribolet, “Characterization of high performances long wave and very long wave HgCdTe staring arrays,” Proc. SPIE 5978, 597819 (2005).
    [CrossRef]
  16. S. Rommeluère, R. Haidar, N. Gue, J. Deschamps, E. De Borniol, A. Million, J. P. Chamonal, and G. Destefanis, “Single-scan extraction of two-dimensional parameters of infrared focal plane arrays utilizing a Fourier-transform spectrometer,” Appl. Opt. 46, 1379–1384 (2007).
    [CrossRef]
  17. N. Guérineau, S. Rommeluère, E. Di Mambro, I. Ribet, and J. Primot, “New techniques of characterization,” C.R. Physique 4, 1175–1185 (2003).
    [CrossRef]
  18. Note that the spectrum was not apodized. The use of an apodization window would reduce the noise over the spectrum, if the latter is barely correlated. However, as is shown in Eq. (6), for a significant dispersion of the cut-off wavenumbers, the effects of the disparities are attenuated for high optical differences. This is also the case if the spectral cut-off is smoother than a Heaviside function (see Subsection 4.E). Then, the noise over the spectrum becomes correlated and apodization has only a limited impact on its level.
  19. C. L. Lawson and R. J. Hanson, Solving Least-Squares Problems (Prentice Hall, 1974).

2011 (1)

2010 (1)

D. Bergstrom, I. Renhorn, T. Svensson, R. Persson, T. Hallberg, R. Lindell, and G. Boreman, “Noise properties of a corner-cube Michelson interferometer LWIR hyperspectral imager,” Proc. SPIE 7660, 76602F (2010).
[CrossRef]

2009 (1)

E. P. G. Smith, A. M. Gallagher, T. J. Kostrzewa, M. L. Brest, R. W. Graham, C. L. Kuzen, E. T. Hughes, T. F. McEwan, G. M. Venzor, E. A. Patten, and W. A. Radford, “Large format HgCdTe focal plane arrays for dual-band long-wavelength infrared detection,” Proc. SPIE 7298, 72981Y (2009).
[CrossRef]

2008 (2)

J. Ferrand, G. Custillon, S. Kochtcheev, S. Blaize, A. Morand, G. Leblond, P. Benech, P. Royer, P. Kern, and E. Le Coarer, “A SWIFTS operating in visible and near-infrared,” Proc. SPIE 7010, 701046 (2008).
[CrossRef]

S. Rommeluère, N. Guérineau, R. Haidar, J. Deschamps, E. De Borniol, A. Million, J. P. Chamonal, and G. Destefanis, “Infrared focal plane array with a built-in stationary Fourier-transform spectrometer: basic concepts,” Opt. Lett. 33, 1062–1064 (2008).
[CrossRef]

2007 (3)

S. Rommeluère, R. Haidar, N. Gue, J. Deschamps, E. De Borniol, A. Million, J. P. Chamonal, and G. Destefanis, “Single-scan extraction of two-dimensional parameters of infrared focal plane arrays utilizing a Fourier-transform spectrometer,” Appl. Opt. 46, 1379–1384 (2007).
[CrossRef]

A. Dariel, P. Chorier, N. Reeb, B. Terrier, M. Vuillermet, and P. Tribolet, “Development of a long wave infrared detector for SGLI instrument,” Proc. SPIE 6744, 674413 (2007).
[CrossRef]

D. Cabib, A. Gil, M. Lavi, R. A. Buckwald, and S. G. Lipson, “New 3‒5μ wavelength range hyperspectral imager for ground and airborne use based on a single element interferometer,” Proc. SPIE 6737, 673704 (2007).
[CrossRef]

2005 (1)

E. De Borniol, G. Destefanis, A. Manissadjian, and P. Tribolet, “Characterization of high performances long wave and very long wave HgCdTe staring arrays,” Proc. SPIE 5978, 597819 (2005).
[CrossRef]

2003 (1)

N. Guérineau, S. Rommeluère, E. Di Mambro, I. Ribet, and J. Primot, “New techniques of characterization,” C.R. Physique 4, 1175–1185 (2003).
[CrossRef]

1994 (1)

M. Schulz and L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Infrared Phys. 36, 763–777 (1994).

1991 (1)

M. D. Nelson, J. F. Johnson, and T. S. Lomheim, “General noise processes in hybrid infrared focal plane arrays,” Opt. Eng. 30, 1682–1700 (1991).
[CrossRef]

1985 (1)

A. F. Milton, F. R. Barone, and M. R. Kruer, “Influence of non-uniformity on infrared focal plane array performance,” Opt. Eng. 24, 855–862 (1985).

Ayari-Matallah, N.

N. Ayari-Matallah, “Imagerie hyperspectrale par transformée de Fourier: Limites de détection, caractérisation des images et nouveaux concepts d’imagerie,” thesis manuscript (Université Paris-Sud XI (2011).

Barone, F. R.

A. F. Milton, F. R. Barone, and M. R. Kruer, “Influence of non-uniformity on infrared focal plane array performance,” Opt. Eng. 24, 855–862 (1985).

Benech, P.

J. Ferrand, G. Custillon, S. Kochtcheev, S. Blaize, A. Morand, G. Leblond, P. Benech, P. Royer, P. Kern, and E. Le Coarer, “A SWIFTS operating in visible and near-infrared,” Proc. SPIE 7010, 701046 (2008).
[CrossRef]

Benôt-Pasanau, C.

Bergstrom, D.

D. Bergstrom, I. Renhorn, T. Svensson, R. Persson, T. Hallberg, R. Lindell, and G. Boreman, “Noise properties of a corner-cube Michelson interferometer LWIR hyperspectral imager,” Proc. SPIE 7660, 76602F (2010).
[CrossRef]

Bernard, F.

P. Hébert, E. Cansot, C. Pierangelo, C. Buil, F. Bernard, J. Loesel, T. Trémas, L. Perrin, E. Courau, C. Casteras, I. Maussang, and D. Simeoni, “Instrumental concept and preliminary performances of SIFTI: Static Infrared Fourier Transform Interferometer,” presented at International Conference on Space Optics, Toulouse, France, 14–17October2008.

Blaize, S.

J. Ferrand, G. Custillon, S. Kochtcheev, S. Blaize, A. Morand, G. Leblond, P. Benech, P. Royer, P. Kern, and E. Le Coarer, “A SWIFTS operating in visible and near-infrared,” Proc. SPIE 7010, 701046 (2008).
[CrossRef]

Boreman, G.

D. Bergstrom, I. Renhorn, T. Svensson, R. Persson, T. Hallberg, R. Lindell, and G. Boreman, “Noise properties of a corner-cube Michelson interferometer LWIR hyperspectral imager,” Proc. SPIE 7660, 76602F (2010).
[CrossRef]

Brest, M. L.

E. P. G. Smith, A. M. Gallagher, T. J. Kostrzewa, M. L. Brest, R. W. Graham, C. L. Kuzen, E. T. Hughes, T. F. McEwan, G. M. Venzor, E. A. Patten, and W. A. Radford, “Large format HgCdTe focal plane arrays for dual-band long-wavelength infrared detection,” Proc. SPIE 7298, 72981Y (2009).
[CrossRef]

Buckwald, R. A.

D. Cabib, A. Gil, M. Lavi, R. A. Buckwald, and S. G. Lipson, “New 3‒5μ wavelength range hyperspectral imager for ground and airborne use based on a single element interferometer,” Proc. SPIE 6737, 673704 (2007).
[CrossRef]

Buil, C.

P. Hébert, E. Cansot, C. Pierangelo, C. Buil, F. Bernard, J. Loesel, T. Trémas, L. Perrin, E. Courau, C. Casteras, I. Maussang, and D. Simeoni, “Instrumental concept and preliminary performances of SIFTI: Static Infrared Fourier Transform Interferometer,” presented at International Conference on Space Optics, Toulouse, France, 14–17October2008.

Cabib, D.

D. Cabib, A. Gil, M. Lavi, R. A. Buckwald, and S. G. Lipson, “New 3‒5μ wavelength range hyperspectral imager for ground and airborne use based on a single element interferometer,” Proc. SPIE 6737, 673704 (2007).
[CrossRef]

Caldwell, L.

M. Schulz and L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Infrared Phys. 36, 763–777 (1994).

Cansot, E.

P. Hébert, E. Cansot, C. Pierangelo, C. Buil, F. Bernard, J. Loesel, T. Trémas, L. Perrin, E. Courau, C. Casteras, I. Maussang, and D. Simeoni, “Instrumental concept and preliminary performances of SIFTI: Static Infrared Fourier Transform Interferometer,” presented at International Conference on Space Optics, Toulouse, France, 14–17October2008.

Casteras, C.

P. Hébert, E. Cansot, C. Pierangelo, C. Buil, F. Bernard, J. Loesel, T. Trémas, L. Perrin, E. Courau, C. Casteras, I. Maussang, and D. Simeoni, “Instrumental concept and preliminary performances of SIFTI: Static Infrared Fourier Transform Interferometer,” presented at International Conference on Space Optics, Toulouse, France, 14–17October2008.

Chamonal, J. P.

Chorier, P.

A. Dariel, P. Chorier, N. Reeb, B. Terrier, M. Vuillermet, and P. Tribolet, “Development of a long wave infrared detector for SGLI instrument,” Proc. SPIE 6744, 674413 (2007).
[CrossRef]

Courau, E.

P. Hébert, E. Cansot, C. Pierangelo, C. Buil, F. Bernard, J. Loesel, T. Trémas, L. Perrin, E. Courau, C. Casteras, I. Maussang, and D. Simeoni, “Instrumental concept and preliminary performances of SIFTI: Static Infrared Fourier Transform Interferometer,” presented at International Conference on Space Optics, Toulouse, France, 14–17October2008.

Custillon, G.

J. Ferrand, G. Custillon, S. Kochtcheev, S. Blaize, A. Morand, G. Leblond, P. Benech, P. Royer, P. Kern, and E. Le Coarer, “A SWIFTS operating in visible and near-infrared,” Proc. SPIE 7010, 701046 (2008).
[CrossRef]

Cymbalista, P.

S. Thétas, N. Guérineau, P. Cymbalista, H. Sauer, and J. Taboury, “Conception of a stationary Fourier transform infrared spectroradiometer for field measurements of radiance and emissivity,” in Fourier Transform Spectroscopy/Hyperspectral Imaging and Sounding of the Environment, OSA Technical Digest Series (CD) (Optical Society of America, 2005), paper FWC3.

Dariel, A.

A. Dariel, P. Chorier, N. Reeb, B. Terrier, M. Vuillermet, and P. Tribolet, “Development of a long wave infrared detector for SGLI instrument,” Proc. SPIE 6744, 674413 (2007).
[CrossRef]

De Borniol, E.

Deschamps, J.

Destefanis, G.

Di Mambro, E.

N. Guérineau, S. Rommeluère, E. Di Mambro, I. Ribet, and J. Primot, “New techniques of characterization,” C.R. Physique 4, 1175–1185 (2003).
[CrossRef]

Ferrand, J.

J. Ferrand, G. Custillon, S. Kochtcheev, S. Blaize, A. Morand, G. Leblond, P. Benech, P. Royer, P. Kern, and E. Le Coarer, “A SWIFTS operating in visible and near-infrared,” Proc. SPIE 7010, 701046 (2008).
[CrossRef]

Ferrec, Y.

F. Gillard, S. Lefebvre, Y. Ferrec, L. Mugnier, S. Rommeluère, C. Benôt-Pasanau, N. Guérineau, and J. Taboury, “Inverse problem approach for stationary Fourier-transform spectrometers,” Opt. Lett. 36, 2444–2446 (2011).
[CrossRef]

Y. Ferrec, “Spectro-imagerie aéroportée par transformation de Fourier avec un interférométre statique à décalage latéral: réalisation et mise en oeuvre,” thesis manuscript (Université Paris-Sud XI (2008).

Gallagher, A. M.

E. P. G. Smith, A. M. Gallagher, T. J. Kostrzewa, M. L. Brest, R. W. Graham, C. L. Kuzen, E. T. Hughes, T. F. McEwan, G. M. Venzor, E. A. Patten, and W. A. Radford, “Large format HgCdTe focal plane arrays for dual-band long-wavelength infrared detection,” Proc. SPIE 7298, 72981Y (2009).
[CrossRef]

Gil, A.

D. Cabib, A. Gil, M. Lavi, R. A. Buckwald, and S. G. Lipson, “New 3‒5μ wavelength range hyperspectral imager for ground and airborne use based on a single element interferometer,” Proc. SPIE 6737, 673704 (2007).
[CrossRef]

Gillard, F.

Graham, R. W.

E. P. G. Smith, A. M. Gallagher, T. J. Kostrzewa, M. L. Brest, R. W. Graham, C. L. Kuzen, E. T. Hughes, T. F. McEwan, G. M. Venzor, E. A. Patten, and W. A. Radford, “Large format HgCdTe focal plane arrays for dual-band long-wavelength infrared detection,” Proc. SPIE 7298, 72981Y (2009).
[CrossRef]

Gue, N.

Guérineau, N.

F. Gillard, S. Lefebvre, Y. Ferrec, L. Mugnier, S. Rommeluère, C. Benôt-Pasanau, N. Guérineau, and J. Taboury, “Inverse problem approach for stationary Fourier-transform spectrometers,” Opt. Lett. 36, 2444–2446 (2011).
[CrossRef]

S. Rommeluère, N. Guérineau, R. Haidar, J. Deschamps, E. De Borniol, A. Million, J. P. Chamonal, and G. Destefanis, “Infrared focal plane array with a built-in stationary Fourier-transform spectrometer: basic concepts,” Opt. Lett. 33, 1062–1064 (2008).
[CrossRef]

N. Guérineau, S. Rommeluère, E. Di Mambro, I. Ribet, and J. Primot, “New techniques of characterization,” C.R. Physique 4, 1175–1185 (2003).
[CrossRef]

S. Thétas, N. Guérineau, P. Cymbalista, H. Sauer, and J. Taboury, “Conception of a stationary Fourier transform infrared spectroradiometer for field measurements of radiance and emissivity,” in Fourier Transform Spectroscopy/Hyperspectral Imaging and Sounding of the Environment, OSA Technical Digest Series (CD) (Optical Society of America, 2005), paper FWC3.

Haidar, R.

Hallberg, T.

D. Bergstrom, I. Renhorn, T. Svensson, R. Persson, T. Hallberg, R. Lindell, and G. Boreman, “Noise properties of a corner-cube Michelson interferometer LWIR hyperspectral imager,” Proc. SPIE 7660, 76602F (2010).
[CrossRef]

Hanson, R. J.

C. L. Lawson and R. J. Hanson, Solving Least-Squares Problems (Prentice Hall, 1974).

Hébert, P.

P. Hébert, E. Cansot, C. Pierangelo, C. Buil, F. Bernard, J. Loesel, T. Trémas, L. Perrin, E. Courau, C. Casteras, I. Maussang, and D. Simeoni, “Instrumental concept and preliminary performances of SIFTI: Static Infrared Fourier Transform Interferometer,” presented at International Conference on Space Optics, Toulouse, France, 14–17October2008.

Hughes, E. T.

E. P. G. Smith, A. M. Gallagher, T. J. Kostrzewa, M. L. Brest, R. W. Graham, C. L. Kuzen, E. T. Hughes, T. F. McEwan, G. M. Venzor, E. A. Patten, and W. A. Radford, “Large format HgCdTe focal plane arrays for dual-band long-wavelength infrared detection,” Proc. SPIE 7298, 72981Y (2009).
[CrossRef]

Johnson, J. F.

M. D. Nelson, J. F. Johnson, and T. S. Lomheim, “General noise processes in hybrid infrared focal plane arrays,” Opt. Eng. 30, 1682–1700 (1991).
[CrossRef]

Kern, P.

J. Ferrand, G. Custillon, S. Kochtcheev, S. Blaize, A. Morand, G. Leblond, P. Benech, P. Royer, P. Kern, and E. Le Coarer, “A SWIFTS operating in visible and near-infrared,” Proc. SPIE 7010, 701046 (2008).
[CrossRef]

Kochtcheev, S.

J. Ferrand, G. Custillon, S. Kochtcheev, S. Blaize, A. Morand, G. Leblond, P. Benech, P. Royer, P. Kern, and E. Le Coarer, “A SWIFTS operating in visible and near-infrared,” Proc. SPIE 7010, 701046 (2008).
[CrossRef]

Kostrzewa, T. J.

E. P. G. Smith, A. M. Gallagher, T. J. Kostrzewa, M. L. Brest, R. W. Graham, C. L. Kuzen, E. T. Hughes, T. F. McEwan, G. M. Venzor, E. A. Patten, and W. A. Radford, “Large format HgCdTe focal plane arrays for dual-band long-wavelength infrared detection,” Proc. SPIE 7298, 72981Y (2009).
[CrossRef]

Kruer, M. R.

A. F. Milton, F. R. Barone, and M. R. Kruer, “Influence of non-uniformity on infrared focal plane array performance,” Opt. Eng. 24, 855–862 (1985).

Kuzen, C. L.

E. P. G. Smith, A. M. Gallagher, T. J. Kostrzewa, M. L. Brest, R. W. Graham, C. L. Kuzen, E. T. Hughes, T. F. McEwan, G. M. Venzor, E. A. Patten, and W. A. Radford, “Large format HgCdTe focal plane arrays for dual-band long-wavelength infrared detection,” Proc. SPIE 7298, 72981Y (2009).
[CrossRef]

Lavi, M.

D. Cabib, A. Gil, M. Lavi, R. A. Buckwald, and S. G. Lipson, “New 3‒5μ wavelength range hyperspectral imager for ground and airborne use based on a single element interferometer,” Proc. SPIE 6737, 673704 (2007).
[CrossRef]

Lawson, C. L.

C. L. Lawson and R. J. Hanson, Solving Least-Squares Problems (Prentice Hall, 1974).

Le Coarer, E.

J. Ferrand, G. Custillon, S. Kochtcheev, S. Blaize, A. Morand, G. Leblond, P. Benech, P. Royer, P. Kern, and E. Le Coarer, “A SWIFTS operating in visible and near-infrared,” Proc. SPIE 7010, 701046 (2008).
[CrossRef]

Leblond, G.

J. Ferrand, G. Custillon, S. Kochtcheev, S. Blaize, A. Morand, G. Leblond, P. Benech, P. Royer, P. Kern, and E. Le Coarer, “A SWIFTS operating in visible and near-infrared,” Proc. SPIE 7010, 701046 (2008).
[CrossRef]

Lefebvre, S.

Lindell, R.

D. Bergstrom, I. Renhorn, T. Svensson, R. Persson, T. Hallberg, R. Lindell, and G. Boreman, “Noise properties of a corner-cube Michelson interferometer LWIR hyperspectral imager,” Proc. SPIE 7660, 76602F (2010).
[CrossRef]

Lipson, S. G.

D. Cabib, A. Gil, M. Lavi, R. A. Buckwald, and S. G. Lipson, “New 3‒5μ wavelength range hyperspectral imager for ground and airborne use based on a single element interferometer,” Proc. SPIE 6737, 673704 (2007).
[CrossRef]

Loesel, J.

P. Hébert, E. Cansot, C. Pierangelo, C. Buil, F. Bernard, J. Loesel, T. Trémas, L. Perrin, E. Courau, C. Casteras, I. Maussang, and D. Simeoni, “Instrumental concept and preliminary performances of SIFTI: Static Infrared Fourier Transform Interferometer,” presented at International Conference on Space Optics, Toulouse, France, 14–17October2008.

Lomheim, T. S.

M. D. Nelson, J. F. Johnson, and T. S. Lomheim, “General noise processes in hybrid infrared focal plane arrays,” Opt. Eng. 30, 1682–1700 (1991).
[CrossRef]

Manissadjian, A.

E. De Borniol, G. Destefanis, A. Manissadjian, and P. Tribolet, “Characterization of high performances long wave and very long wave HgCdTe staring arrays,” Proc. SPIE 5978, 597819 (2005).
[CrossRef]

Maussang, I.

P. Hébert, E. Cansot, C. Pierangelo, C. Buil, F. Bernard, J. Loesel, T. Trémas, L. Perrin, E. Courau, C. Casteras, I. Maussang, and D. Simeoni, “Instrumental concept and preliminary performances of SIFTI: Static Infrared Fourier Transform Interferometer,” presented at International Conference on Space Optics, Toulouse, France, 14–17October2008.

McEwan, T. F.

E. P. G. Smith, A. M. Gallagher, T. J. Kostrzewa, M. L. Brest, R. W. Graham, C. L. Kuzen, E. T. Hughes, T. F. McEwan, G. M. Venzor, E. A. Patten, and W. A. Radford, “Large format HgCdTe focal plane arrays for dual-band long-wavelength infrared detection,” Proc. SPIE 7298, 72981Y (2009).
[CrossRef]

Million, A.

Milton, A. F.

A. F. Milton, F. R. Barone, and M. R. Kruer, “Influence of non-uniformity on infrared focal plane array performance,” Opt. Eng. 24, 855–862 (1985).

Morand, A.

J. Ferrand, G. Custillon, S. Kochtcheev, S. Blaize, A. Morand, G. Leblond, P. Benech, P. Royer, P. Kern, and E. Le Coarer, “A SWIFTS operating in visible and near-infrared,” Proc. SPIE 7010, 701046 (2008).
[CrossRef]

Mugnier, L.

Nelson, M. D.

M. D. Nelson, J. F. Johnson, and T. S. Lomheim, “General noise processes in hybrid infrared focal plane arrays,” Opt. Eng. 30, 1682–1700 (1991).
[CrossRef]

Patten, E. A.

E. P. G. Smith, A. M. Gallagher, T. J. Kostrzewa, M. L. Brest, R. W. Graham, C. L. Kuzen, E. T. Hughes, T. F. McEwan, G. M. Venzor, E. A. Patten, and W. A. Radford, “Large format HgCdTe focal plane arrays for dual-band long-wavelength infrared detection,” Proc. SPIE 7298, 72981Y (2009).
[CrossRef]

Perrin, L.

P. Hébert, E. Cansot, C. Pierangelo, C. Buil, F. Bernard, J. Loesel, T. Trémas, L. Perrin, E. Courau, C. Casteras, I. Maussang, and D. Simeoni, “Instrumental concept and preliminary performances of SIFTI: Static Infrared Fourier Transform Interferometer,” presented at International Conference on Space Optics, Toulouse, France, 14–17October2008.

Persson, R.

D. Bergstrom, I. Renhorn, T. Svensson, R. Persson, T. Hallberg, R. Lindell, and G. Boreman, “Noise properties of a corner-cube Michelson interferometer LWIR hyperspectral imager,” Proc. SPIE 7660, 76602F (2010).
[CrossRef]

Pierangelo, C.

P. Hébert, E. Cansot, C. Pierangelo, C. Buil, F. Bernard, J. Loesel, T. Trémas, L. Perrin, E. Courau, C. Casteras, I. Maussang, and D. Simeoni, “Instrumental concept and preliminary performances of SIFTI: Static Infrared Fourier Transform Interferometer,” presented at International Conference on Space Optics, Toulouse, France, 14–17October2008.

Primot, J.

N. Guérineau, S. Rommeluère, E. Di Mambro, I. Ribet, and J. Primot, “New techniques of characterization,” C.R. Physique 4, 1175–1185 (2003).
[CrossRef]

Radford, W. A.

E. P. G. Smith, A. M. Gallagher, T. J. Kostrzewa, M. L. Brest, R. W. Graham, C. L. Kuzen, E. T. Hughes, T. F. McEwan, G. M. Venzor, E. A. Patten, and W. A. Radford, “Large format HgCdTe focal plane arrays for dual-band long-wavelength infrared detection,” Proc. SPIE 7298, 72981Y (2009).
[CrossRef]

Reeb, N.

A. Dariel, P. Chorier, N. Reeb, B. Terrier, M. Vuillermet, and P. Tribolet, “Development of a long wave infrared detector for SGLI instrument,” Proc. SPIE 6744, 674413 (2007).
[CrossRef]

Renhorn, I.

D. Bergstrom, I. Renhorn, T. Svensson, R. Persson, T. Hallberg, R. Lindell, and G. Boreman, “Noise properties of a corner-cube Michelson interferometer LWIR hyperspectral imager,” Proc. SPIE 7660, 76602F (2010).
[CrossRef]

Ribet, I.

N. Guérineau, S. Rommeluère, E. Di Mambro, I. Ribet, and J. Primot, “New techniques of characterization,” C.R. Physique 4, 1175–1185 (2003).
[CrossRef]

Rommeluère, S.

Royer, P.

J. Ferrand, G. Custillon, S. Kochtcheev, S. Blaize, A. Morand, G. Leblond, P. Benech, P. Royer, P. Kern, and E. Le Coarer, “A SWIFTS operating in visible and near-infrared,” Proc. SPIE 7010, 701046 (2008).
[CrossRef]

Sauer, H.

S. Thétas, N. Guérineau, P. Cymbalista, H. Sauer, and J. Taboury, “Conception of a stationary Fourier transform infrared spectroradiometer for field measurements of radiance and emissivity,” in Fourier Transform Spectroscopy/Hyperspectral Imaging and Sounding of the Environment, OSA Technical Digest Series (CD) (Optical Society of America, 2005), paper FWC3.

Schulz, M.

M. Schulz and L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Infrared Phys. 36, 763–777 (1994).

Simeoni, D.

P. Hébert, E. Cansot, C. Pierangelo, C. Buil, F. Bernard, J. Loesel, T. Trémas, L. Perrin, E. Courau, C. Casteras, I. Maussang, and D. Simeoni, “Instrumental concept and preliminary performances of SIFTI: Static Infrared Fourier Transform Interferometer,” presented at International Conference on Space Optics, Toulouse, France, 14–17October2008.

Smith, E. P. G.

E. P. G. Smith, A. M. Gallagher, T. J. Kostrzewa, M. L. Brest, R. W. Graham, C. L. Kuzen, E. T. Hughes, T. F. McEwan, G. M. Venzor, E. A. Patten, and W. A. Radford, “Large format HgCdTe focal plane arrays for dual-band long-wavelength infrared detection,” Proc. SPIE 7298, 72981Y (2009).
[CrossRef]

Svensson, T.

D. Bergstrom, I. Renhorn, T. Svensson, R. Persson, T. Hallberg, R. Lindell, and G. Boreman, “Noise properties of a corner-cube Michelson interferometer LWIR hyperspectral imager,” Proc. SPIE 7660, 76602F (2010).
[CrossRef]

Taboury, J.

F. Gillard, S. Lefebvre, Y. Ferrec, L. Mugnier, S. Rommeluère, C. Benôt-Pasanau, N. Guérineau, and J. Taboury, “Inverse problem approach for stationary Fourier-transform spectrometers,” Opt. Lett. 36, 2444–2446 (2011).
[CrossRef]

S. Thétas, N. Guérineau, P. Cymbalista, H. Sauer, and J. Taboury, “Conception of a stationary Fourier transform infrared spectroradiometer for field measurements of radiance and emissivity,” in Fourier Transform Spectroscopy/Hyperspectral Imaging and Sounding of the Environment, OSA Technical Digest Series (CD) (Optical Society of America, 2005), paper FWC3.

Terrier, B.

A. Dariel, P. Chorier, N. Reeb, B. Terrier, M. Vuillermet, and P. Tribolet, “Development of a long wave infrared detector for SGLI instrument,” Proc. SPIE 6744, 674413 (2007).
[CrossRef]

Thétas, S.

S. Thétas, N. Guérineau, P. Cymbalista, H. Sauer, and J. Taboury, “Conception of a stationary Fourier transform infrared spectroradiometer for field measurements of radiance and emissivity,” in Fourier Transform Spectroscopy/Hyperspectral Imaging and Sounding of the Environment, OSA Technical Digest Series (CD) (Optical Society of America, 2005), paper FWC3.

Trémas, T.

P. Hébert, E. Cansot, C. Pierangelo, C. Buil, F. Bernard, J. Loesel, T. Trémas, L. Perrin, E. Courau, C. Casteras, I. Maussang, and D. Simeoni, “Instrumental concept and preliminary performances of SIFTI: Static Infrared Fourier Transform Interferometer,” presented at International Conference on Space Optics, Toulouse, France, 14–17October2008.

Tribolet, P.

A. Dariel, P. Chorier, N. Reeb, B. Terrier, M. Vuillermet, and P. Tribolet, “Development of a long wave infrared detector for SGLI instrument,” Proc. SPIE 6744, 674413 (2007).
[CrossRef]

E. De Borniol, G. Destefanis, A. Manissadjian, and P. Tribolet, “Characterization of high performances long wave and very long wave HgCdTe staring arrays,” Proc. SPIE 5978, 597819 (2005).
[CrossRef]

Venzor, G. M.

E. P. G. Smith, A. M. Gallagher, T. J. Kostrzewa, M. L. Brest, R. W. Graham, C. L. Kuzen, E. T. Hughes, T. F. McEwan, G. M. Venzor, E. A. Patten, and W. A. Radford, “Large format HgCdTe focal plane arrays for dual-band long-wavelength infrared detection,” Proc. SPIE 7298, 72981Y (2009).
[CrossRef]

Vuillermet, M.

A. Dariel, P. Chorier, N. Reeb, B. Terrier, M. Vuillermet, and P. Tribolet, “Development of a long wave infrared detector for SGLI instrument,” Proc. SPIE 6744, 674413 (2007).
[CrossRef]

Appl. Opt. (1)

C.R. Physique (1)

N. Guérineau, S. Rommeluère, E. Di Mambro, I. Ribet, and J. Primot, “New techniques of characterization,” C.R. Physique 4, 1175–1185 (2003).
[CrossRef]

Infrared Phys. (1)

M. Schulz and L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Infrared Phys. 36, 763–777 (1994).

Opt. Eng. (2)

M. D. Nelson, J. F. Johnson, and T. S. Lomheim, “General noise processes in hybrid infrared focal plane arrays,” Opt. Eng. 30, 1682–1700 (1991).
[CrossRef]

A. F. Milton, F. R. Barone, and M. R. Kruer, “Influence of non-uniformity on infrared focal plane array performance,” Opt. Eng. 24, 855–862 (1985).

Opt. Lett. (2)

Proc. SPIE (6)

J. Ferrand, G. Custillon, S. Kochtcheev, S. Blaize, A. Morand, G. Leblond, P. Benech, P. Royer, P. Kern, and E. Le Coarer, “A SWIFTS operating in visible and near-infrared,” Proc. SPIE 7010, 701046 (2008).
[CrossRef]

D. Bergstrom, I. Renhorn, T. Svensson, R. Persson, T. Hallberg, R. Lindell, and G. Boreman, “Noise properties of a corner-cube Michelson interferometer LWIR hyperspectral imager,” Proc. SPIE 7660, 76602F (2010).
[CrossRef]

D. Cabib, A. Gil, M. Lavi, R. A. Buckwald, and S. G. Lipson, “New 3‒5μ wavelength range hyperspectral imager for ground and airborne use based on a single element interferometer,” Proc. SPIE 6737, 673704 (2007).
[CrossRef]

A. Dariel, P. Chorier, N. Reeb, B. Terrier, M. Vuillermet, and P. Tribolet, “Development of a long wave infrared detector for SGLI instrument,” Proc. SPIE 6744, 674413 (2007).
[CrossRef]

E. P. G. Smith, A. M. Gallagher, T. J. Kostrzewa, M. L. Brest, R. W. Graham, C. L. Kuzen, E. T. Hughes, T. F. McEwan, G. M. Venzor, E. A. Patten, and W. A. Radford, “Large format HgCdTe focal plane arrays for dual-band long-wavelength infrared detection,” Proc. SPIE 7298, 72981Y (2009).
[CrossRef]

E. De Borniol, G. Destefanis, A. Manissadjian, and P. Tribolet, “Characterization of high performances long wave and very long wave HgCdTe staring arrays,” Proc. SPIE 5978, 597819 (2005).
[CrossRef]

Other (6)

Y. Ferrec, “Spectro-imagerie aéroportée par transformation de Fourier avec un interférométre statique à décalage latéral: réalisation et mise en oeuvre,” thesis manuscript (Université Paris-Sud XI (2008).

N. Ayari-Matallah, “Imagerie hyperspectrale par transformée de Fourier: Limites de détection, caractérisation des images et nouveaux concepts d’imagerie,” thesis manuscript (Université Paris-Sud XI (2011).

S. Thétas, N. Guérineau, P. Cymbalista, H. Sauer, and J. Taboury, “Conception of a stationary Fourier transform infrared spectroradiometer for field measurements of radiance and emissivity,” in Fourier Transform Spectroscopy/Hyperspectral Imaging and Sounding of the Environment, OSA Technical Digest Series (CD) (Optical Society of America, 2005), paper FWC3.

P. Hébert, E. Cansot, C. Pierangelo, C. Buil, F. Bernard, J. Loesel, T. Trémas, L. Perrin, E. Courau, C. Casteras, I. Maussang, and D. Simeoni, “Instrumental concept and preliminary performances of SIFTI: Static Infrared Fourier Transform Interferometer,” presented at International Conference on Space Optics, Toulouse, France, 14–17October2008.

Note that the spectrum was not apodized. The use of an apodization window would reduce the noise over the spectrum, if the latter is barely correlated. However, as is shown in Eq. (6), for a significant dispersion of the cut-off wavenumbers, the effects of the disparities are attenuated for high optical differences. This is also the case if the spectral cut-off is smoother than a Heaviside function (see Subsection 4.E). Then, the noise over the spectrum becomes correlated and apodization has only a limited impact on its level.

C. L. Lawson and R. J. Hanson, Solving Least-Squares Problems (Prentice Hall, 1974).

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Figures (12)

Fig. 1.
Fig. 1.

From classical dynamic FTS to stationary FTS.

Fig. 2.
Fig. 2.

Figure extracted from [13]. Spectral responses of an MCT detector operating in the LWIR spectral range.

Fig. 3.
Fig. 3.

Cartography of the low cut-off wavenumbers of an IRFPA.

Fig. 4.
Fig. 4.

Illustration of the low- and high-frequency effects of the cut-off wavenumbers over a spectrum restored by Fourier transform.

Fig. 5.
Fig. 5.

Spectral responses of three pixels denoted A, B, and C. Each pixel corresponds to a given optical path difference δA, δB, and δC.

Fig. 6.
Fig. 6.

Comparison between the simulated variance and the variance approximated by Eq. (10). The dotted line indicates a constant variance equal to 104.

Fig. 7.
Fig. 7.

Comparison of the peak of noise over the spectrum restored by Fourier transform around σcm. Dashed line: Ri(σ) is a Heaviside function. Solid line: Ri(σ) with σ=60cm1.

Fig. 8.
Fig. 8.

Illustration of the effects of the cut-off wavenumbers over a spectrum restored by TSVD—Truncation for λl1.

Fig. 9.
Fig. 9.

SVD singular values of MSVD for one realization of Fig. 8.

Fig. 10.
Fig. 10.

Comparison between Binput(σ) and the mean spectra restored by Fourier transform (Fig. 4) and TSVD (Fig. 8).

Fig. 11.
Fig. 11.

Reliability over temporal noise of both TSVD and Fourier transform methods for a given SNR of the interferogram.

Fig. 12.
Fig. 12.

Spectral lines at σ=σ0 obtained by both TSVD and Fourier transform methods in the presence of a cut-off wavenumbers disparity whose properties are the one of Table 1.

Tables (1)

Tables Icon

Table 1. Values of the Parameters for the Simulation of the Interferogramsa

Equations (25)

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Mintij=Ri(σj)[1+cos(2πσjδi)2].
Int(δ)=MintBinput(σ).
MTFij=1+cos(2πipδjpσ)2,
wherepσ=1(2n1)pδ.
B(σ)=MTF1·Int(δ).
Wi=σciσcmB01+cos(2πδiσ)2dσ
=B02(σciσcm)B02πδiA1cos(2πδiσci+σcm2)A2sin(2πδiσciσcm2)A3.
Wi=B02ΔσciB02Δσcicos(2πδiσcm),
Δσci=σciσcm.
E[Vk2]=22πnLB02pδ2std2[sinc(σkσcmpσ)+e2π2L2pδ2(σkσcm)2].
Wi=B02ΔσciB02πδicos(πδi(σci+σcm))sin(πδiΔσci)sinc(δiσ),
MSVD=UΣVtwhereΣ=diag(λ1,λ2,,λn),
B(σ)=MSVD1Int(δ)whereMSVD1=V1ΣUt.
SNR=Int(δi)stdn,
Vk=8pδi=0n1[Wi·cos(2πδiσk)]
=2B0pδi=0n1Δσci·cos(2πδi(σkσcm))+2B0pδi=0n1Δσci·cos(2πδi(σk+σcm)).
E[Vk2]=4B02pδ2i=0n1j=0n1E[ΔσciΔσcj]cos(2πδiσk¯)cos(2πδjσk¯),
E[ΔσciΔσcj]=std2·ρ(ij),
E[Vk2]=2B02pδ2std2i=0n1j=0n1ρ(ij)cos(2π(i+j)pδσk¯)B+2B02pδ2std2i=0n1j=0n1ρ(ij)cos(2π(ij)pδσk¯)C.
B=u=n+1n1ρ(u)v=0n1|u|cos(2πpδσk¯(|u|+v))=u=n+1n1ρ(u)cos(πpδσk¯(n+|u|1))sin(πpδσk¯(n|u|))sin(πpδσk¯).
B=nsinc(2npδσk¯)u=n+1n1ρ(u).
ρ(u)=exp(12u2L2).
BnL2π.sinc(σk¯/pσ).
C=u=n+1n1ρ(u)(n|u|)cos(2πpδσk¯u)nL2πe2π2L2pδ2σk¯2.
E[Vk2]22πnLB02pδ2std2[sinc(σk¯/pσ)+e2π2L2pδ2σk¯2].

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