Abstract

A design of a miniaturized stationary Fourier transform IR spectrometer has been developed that produces a two-dimensional interferogram. The latter is disturbed by effects like parasitic interferences or disparities in the cutoff wavelength of the pixels. Thus, a simple Fourier transform cannot be used to estimate the spectrum of the scene. However, as these defects are deterministic, they can be measured and taken into account by inversion methods. A regularization term can also be added. The first experimental results prove the efficiency of this processing methodology.

© 2011 Optical Society of America

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References

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  1. S. Rommeluère, N. Guérineau, R. Haidar, J. Deschamps, E. De Borniol, A. Million, J.-P. Chamonal, and G. Destefanis, Opt. Lett. 33, 1062 (2008).
    [CrossRef] [PubMed]
  2. F. Gillard, N. Guérineau, S. Rommeluère, J. Taboury, and P. Chavel, Proc. SPIE 7716, 77162E (2010).
    [CrossRef]
  3. S. Rommeluère, R. Haïdar, N. Guérineau, J. Deschamps, E. De Borniol, A. Million, J. P. Chamonal, and G. Destefanis, Appl. Opt. 46, 1379 (2007).
    [CrossRef] [PubMed]
  4. J. Idier, Bayesian Approach to Inverse Problems (Wiley ISTE, 2008).
    [CrossRef]
  5. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, IEEE J. Sel. Top. Signal Process. 1, 586 (2007).
    [CrossRef]
  6. E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photon. 1, 473 (2007).
    [CrossRef]
  7. P. G. Lucey, K. A. Horton, and T. Williams, Appl. Opt. 47, F107 (2008).
    [CrossRef] [PubMed]

2010 (1)

F. Gillard, N. Guérineau, S. Rommeluère, J. Taboury, and P. Chavel, Proc. SPIE 7716, 77162E (2010).
[CrossRef]

2008 (3)

2007 (3)

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, IEEE J. Sel. Top. Signal Process. 1, 586 (2007).
[CrossRef]

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photon. 1, 473 (2007).
[CrossRef]

S. Rommeluère, R. Haïdar, N. Guérineau, J. Deschamps, E. De Borniol, A. Million, J. P. Chamonal, and G. Destefanis, Appl. Opt. 46, 1379 (2007).
[CrossRef] [PubMed]

Benech, P.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photon. 1, 473 (2007).
[CrossRef]

Blaize, S.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photon. 1, 473 (2007).
[CrossRef]

Chamonal, J. P.

Chamonal, J.-P.

Chavel, P.

F. Gillard, N. Guérineau, S. Rommeluère, J. Taboury, and P. Chavel, Proc. SPIE 7716, 77162E (2010).
[CrossRef]

De Borniol, E.

Deschamps, J.

Destefanis, G.

Fedeli, J. M.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photon. 1, 473 (2007).
[CrossRef]

Figueiredo, M. A. T.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, IEEE J. Sel. Top. Signal Process. 1, 586 (2007).
[CrossRef]

Gillard, F.

F. Gillard, N. Guérineau, S. Rommeluère, J. Taboury, and P. Chavel, Proc. SPIE 7716, 77162E (2010).
[CrossRef]

Guérineau, N.

Haidar, R.

Haïdar, R.

Horton, K. A.

Idier, J.

J. Idier, Bayesian Approach to Inverse Problems (Wiley ISTE, 2008).
[CrossRef]

Kern, P.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photon. 1, 473 (2007).
[CrossRef]

le Coarer, E.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photon. 1, 473 (2007).
[CrossRef]

Leblond, G.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photon. 1, 473 (2007).
[CrossRef]

Lérondel, G.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photon. 1, 473 (2007).
[CrossRef]

Lucey, P. G.

Million, A.

Morand, A.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photon. 1, 473 (2007).
[CrossRef]

Nowak, R. D.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, IEEE J. Sel. Top. Signal Process. 1, 586 (2007).
[CrossRef]

Rommeluère, S.

Royer, P.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photon. 1, 473 (2007).
[CrossRef]

Stefanon, I.

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photon. 1, 473 (2007).
[CrossRef]

Taboury, J.

F. Gillard, N. Guérineau, S. Rommeluère, J. Taboury, and P. Chavel, Proc. SPIE 7716, 77162E (2010).
[CrossRef]

Williams, T.

Wright, S. J.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, IEEE J. Sel. Top. Signal Process. 1, 586 (2007).
[CrossRef]

Appl. Opt. (2)

IEEE J. Sel. Top. Signal Process. (1)

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, IEEE J. Sel. Top. Signal Process. 1, 586 (2007).
[CrossRef]

Nat. Photon. (1)

E. le Coarer, S. Blaize, P. Benech, I. Stefanon, A. Morand, G. Lérondel, G. Leblond, P. Kern, J. M. Fedeli, and P. Royer, Nat. Photon. 1, 473 (2007).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

F. Gillard, N. Guérineau, S. Rommeluère, J. Taboury, and P. Chavel, Proc. SPIE 7716, 77162E (2010).
[CrossRef]

Other (1)

J. Idier, Bayesian Approach to Inverse Problems (Wiley ISTE, 2008).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

(a) Hyperspectral cartography at 4 μm ; (b) hyperspectral cartography at 5.2 μm .

Fig. 2
Fig. 2

Experimental setup for the measurement of spectral filters.

Fig. 3
Fig. 3

Preprocessing of an interferogram [in (c) and (d), the dead pixels are indicated in red].

Fig. 4
Fig. 4

Filter A transmission estimations by the three methods: method (a), TSVD; method (b), regularized inversion; method (c), regularized inversion on a wavelet basis. Around 2400 cm 1 , CO 2 absorption is eliminated in the reference spectrum.

Fig. 5
Fig. 5

Filter B transmission estimations by the three methods: method (a), TSVD; method (b), regularized inversion; method (c), regularized inversion on a wavelet basis.

Equations (2)

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Y = M X + noise.
X ^ = arg min ( Y M X 2 2 + α R ( X ) ) .

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