Abstract

Software field widening of a Fourier-transform spectrometer is investigated with a large multielement focal plane array detector. Experimental results are presented that stem from previous work in instrument line-shape correction. Here, pixels with calibrated wavenumber scales are binned to emulate a large-area single-pixel detector. The field of view and the signal-to-noise ratio are accordingly increased. A monochromatic source is used to characterize signal-to-noise ratio gain, and limitations are discussed. This work is motivated by the emergence of affordable infrared integrating cameras, which enable Fourier-transform spectrometers to perform massively parallel spatial sampling.

© 2008 Optical Society of America

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References

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  1. R. J. Bell and R. N. Bracewell, Introductory Fourier Transform Spectroscopy (Academic, 1972).
  2. J. Genest and P. Tremblay, “Instrument line shape of Fourier-transform spectrometers: analytic solutions for nonuniformly illuminated off-axis detectors,” Appl. Opt. 38, 5438-5446(1999).
    [CrossRef]
  3. A. Kuze, H. Nakajima, J. Tanii, and Y. Sasano, “Conceptual design of solar occultation FTS for inclined-orbit satellite (SOFIS) on GCOM-A1,” Proc. SPIE 4131, 4541-4548 (2000).
  4. J.-P. Bouchard, P. Tremblay, R. Desbiens, and F. Bouffard, “Detailed line-shape measurements using a high resolution, high divergence Fourier transform spectrometer,” in Fourier Transform Spectroscopy, OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), Vol. 84, pp. 25-27.
  5. M. Chamberland, V. Farley, L. Belhumeur, F. Williams, J. Lawrence, P. Tremblay, and R. Desbiens, “The instrument lineshape, an imperative parameter for the absolute spectral calibration of an FTS,” Fourier Transform Spectroscopy, OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), Vol. 84, pp. 160-166.
  6. J. Connes, “Domaine d'utilisation de la méthode par transformée de Fourier,” J. Phys. Radium 19, 197-208 (1958).
    [CrossRef]
  7. E. Niple, A. Pires, and K. Poultney, “Exact modeling of line-shape and wavenumber variations for aff-axis detectors in Fourier-transform spectrometers (FTS) sensor systems,” Proc. SPIE 0364, 11-20 (1982).
  8. R. Desbiens, P. Tremblay, J. Genest, and J.-P. Bouchard, “Matrix form for the instrument line shape of Fourier-transform spectrometers yielding a fast integration algorithm to theoretical spectra,” Appl. Opt. 45, 546-557 (2006).
    [CrossRef]
  9. R. Desbiens, J. Genest, P. Tremblay, and J.-P. Bouchard, “Correction of instrument line shape in Fourier transform spectrometry using matrix inversion,” Appl. Opt. 45, 5270-5280(2006).
    [CrossRef]
  10. S. A. Roy, S. Potvin, and J. Genest, “Fast line shape correction procedure for imaging Fourier-transform spectrometers,” Appl. Opt. 46, 4674-4679 (2007).
    [CrossRef]
  11. S. A. Roy, “Data processing pipelines tailored for imaging Fourier-transform spectrometers,” Ph.D. dissertation (Université Laval, 2008).
  12. D. Lambert and P. Richards, “Martin-Puplett interferometer: an analysis,” Appl. Opt. 17, 1595-1602 (1978).
  13. J. Genest and P. Tremblay, “Modeling the instrument line shape of Fourier-transform spectrometers within the framework of partial coherence,” Appl. Opt. 44, 3912-3924 (2005).
    [CrossRef]
  14. R. Desbiens, J. Genest, and P. Tremblay, “Radiometry in line-shape modeling of Fourier-transform spectrometers,” Appl. Opt. 41, 1424-1432 (2002).
    [CrossRef]
  15. L. Mertz, Transformations in Optics (Wiley, 1965).

2007

2006

2005

2002

2000

A. Kuze, H. Nakajima, J. Tanii, and Y. Sasano, “Conceptual design of solar occultation FTS for inclined-orbit satellite (SOFIS) on GCOM-A1,” Proc. SPIE 4131, 4541-4548 (2000).

1999

1982

E. Niple, A. Pires, and K. Poultney, “Exact modeling of line-shape and wavenumber variations for aff-axis detectors in Fourier-transform spectrometers (FTS) sensor systems,” Proc. SPIE 0364, 11-20 (1982).

1978

1958

J. Connes, “Domaine d'utilisation de la méthode par transformée de Fourier,” J. Phys. Radium 19, 197-208 (1958).
[CrossRef]

Belhumeur, L.

M. Chamberland, V. Farley, L. Belhumeur, F. Williams, J. Lawrence, P. Tremblay, and R. Desbiens, “The instrument lineshape, an imperative parameter for the absolute spectral calibration of an FTS,” Fourier Transform Spectroscopy, OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), Vol. 84, pp. 160-166.

Bell, R. J.

R. J. Bell and R. N. Bracewell, Introductory Fourier Transform Spectroscopy (Academic, 1972).

Bouchard, J.-P.

R. Desbiens, P. Tremblay, J. Genest, and J.-P. Bouchard, “Matrix form for the instrument line shape of Fourier-transform spectrometers yielding a fast integration algorithm to theoretical spectra,” Appl. Opt. 45, 546-557 (2006).
[CrossRef]

R. Desbiens, J. Genest, P. Tremblay, and J.-P. Bouchard, “Correction of instrument line shape in Fourier transform spectrometry using matrix inversion,” Appl. Opt. 45, 5270-5280(2006).
[CrossRef]

J.-P. Bouchard, P. Tremblay, R. Desbiens, and F. Bouffard, “Detailed line-shape measurements using a high resolution, high divergence Fourier transform spectrometer,” in Fourier Transform Spectroscopy, OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), Vol. 84, pp. 25-27.

Bouffard, F.

J.-P. Bouchard, P. Tremblay, R. Desbiens, and F. Bouffard, “Detailed line-shape measurements using a high resolution, high divergence Fourier transform spectrometer,” in Fourier Transform Spectroscopy, OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), Vol. 84, pp. 25-27.

Bracewell, R. N.

R. J. Bell and R. N. Bracewell, Introductory Fourier Transform Spectroscopy (Academic, 1972).

Chamberland, M.

M. Chamberland, V. Farley, L. Belhumeur, F. Williams, J. Lawrence, P. Tremblay, and R. Desbiens, “The instrument lineshape, an imperative parameter for the absolute spectral calibration of an FTS,” Fourier Transform Spectroscopy, OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), Vol. 84, pp. 160-166.

Connes, J.

J. Connes, “Domaine d'utilisation de la méthode par transformée de Fourier,” J. Phys. Radium 19, 197-208 (1958).
[CrossRef]

Desbiens, R.

R. Desbiens, P. Tremblay, J. Genest, and J.-P. Bouchard, “Matrix form for the instrument line shape of Fourier-transform spectrometers yielding a fast integration algorithm to theoretical spectra,” Appl. Opt. 45, 546-557 (2006).
[CrossRef]

R. Desbiens, J. Genest, P. Tremblay, and J.-P. Bouchard, “Correction of instrument line shape in Fourier transform spectrometry using matrix inversion,” Appl. Opt. 45, 5270-5280(2006).
[CrossRef]

R. Desbiens, J. Genest, and P. Tremblay, “Radiometry in line-shape modeling of Fourier-transform spectrometers,” Appl. Opt. 41, 1424-1432 (2002).
[CrossRef]

M. Chamberland, V. Farley, L. Belhumeur, F. Williams, J. Lawrence, P. Tremblay, and R. Desbiens, “The instrument lineshape, an imperative parameter for the absolute spectral calibration of an FTS,” Fourier Transform Spectroscopy, OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), Vol. 84, pp. 160-166.

J.-P. Bouchard, P. Tremblay, R. Desbiens, and F. Bouffard, “Detailed line-shape measurements using a high resolution, high divergence Fourier transform spectrometer,” in Fourier Transform Spectroscopy, OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), Vol. 84, pp. 25-27.

Farley, V.

M. Chamberland, V. Farley, L. Belhumeur, F. Williams, J. Lawrence, P. Tremblay, and R. Desbiens, “The instrument lineshape, an imperative parameter for the absolute spectral calibration of an FTS,” Fourier Transform Spectroscopy, OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), Vol. 84, pp. 160-166.

Genest, J.

Kuze, A.

A. Kuze, H. Nakajima, J. Tanii, and Y. Sasano, “Conceptual design of solar occultation FTS for inclined-orbit satellite (SOFIS) on GCOM-A1,” Proc. SPIE 4131, 4541-4548 (2000).

Lambert, D.

Lawrence, J.

M. Chamberland, V. Farley, L. Belhumeur, F. Williams, J. Lawrence, P. Tremblay, and R. Desbiens, “The instrument lineshape, an imperative parameter for the absolute spectral calibration of an FTS,” Fourier Transform Spectroscopy, OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), Vol. 84, pp. 160-166.

Mertz, L.

L. Mertz, Transformations in Optics (Wiley, 1965).

Nakajima, H.

A. Kuze, H. Nakajima, J. Tanii, and Y. Sasano, “Conceptual design of solar occultation FTS for inclined-orbit satellite (SOFIS) on GCOM-A1,” Proc. SPIE 4131, 4541-4548 (2000).

Niple, E.

E. Niple, A. Pires, and K. Poultney, “Exact modeling of line-shape and wavenumber variations for aff-axis detectors in Fourier-transform spectrometers (FTS) sensor systems,” Proc. SPIE 0364, 11-20 (1982).

Pires, A.

E. Niple, A. Pires, and K. Poultney, “Exact modeling of line-shape and wavenumber variations for aff-axis detectors in Fourier-transform spectrometers (FTS) sensor systems,” Proc. SPIE 0364, 11-20 (1982).

Potvin, S.

Poultney, K.

E. Niple, A. Pires, and K. Poultney, “Exact modeling of line-shape and wavenumber variations for aff-axis detectors in Fourier-transform spectrometers (FTS) sensor systems,” Proc. SPIE 0364, 11-20 (1982).

Richards, P.

Roy, S. A.

S. A. Roy, S. Potvin, and J. Genest, “Fast line shape correction procedure for imaging Fourier-transform spectrometers,” Appl. Opt. 46, 4674-4679 (2007).
[CrossRef]

S. A. Roy, “Data processing pipelines tailored for imaging Fourier-transform spectrometers,” Ph.D. dissertation (Université Laval, 2008).

Sasano, Y.

A. Kuze, H. Nakajima, J. Tanii, and Y. Sasano, “Conceptual design of solar occultation FTS for inclined-orbit satellite (SOFIS) on GCOM-A1,” Proc. SPIE 4131, 4541-4548 (2000).

Tanii, J.

A. Kuze, H. Nakajima, J. Tanii, and Y. Sasano, “Conceptual design of solar occultation FTS for inclined-orbit satellite (SOFIS) on GCOM-A1,” Proc. SPIE 4131, 4541-4548 (2000).

Tremblay, P.

R. Desbiens, J. Genest, P. Tremblay, and J.-P. Bouchard, “Correction of instrument line shape in Fourier transform spectrometry using matrix inversion,” Appl. Opt. 45, 5270-5280(2006).
[CrossRef]

R. Desbiens, P. Tremblay, J. Genest, and J.-P. Bouchard, “Matrix form for the instrument line shape of Fourier-transform spectrometers yielding a fast integration algorithm to theoretical spectra,” Appl. Opt. 45, 546-557 (2006).
[CrossRef]

J. Genest and P. Tremblay, “Modeling the instrument line shape of Fourier-transform spectrometers within the framework of partial coherence,” Appl. Opt. 44, 3912-3924 (2005).
[CrossRef]

R. Desbiens, J. Genest, and P. Tremblay, “Radiometry in line-shape modeling of Fourier-transform spectrometers,” Appl. Opt. 41, 1424-1432 (2002).
[CrossRef]

J. Genest and P. Tremblay, “Instrument line shape of Fourier-transform spectrometers: analytic solutions for nonuniformly illuminated off-axis detectors,” Appl. Opt. 38, 5438-5446(1999).
[CrossRef]

J.-P. Bouchard, P. Tremblay, R. Desbiens, and F. Bouffard, “Detailed line-shape measurements using a high resolution, high divergence Fourier transform spectrometer,” in Fourier Transform Spectroscopy, OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), Vol. 84, pp. 25-27.

M. Chamberland, V. Farley, L. Belhumeur, F. Williams, J. Lawrence, P. Tremblay, and R. Desbiens, “The instrument lineshape, an imperative parameter for the absolute spectral calibration of an FTS,” Fourier Transform Spectroscopy, OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), Vol. 84, pp. 160-166.

Williams, F.

M. Chamberland, V. Farley, L. Belhumeur, F. Williams, J. Lawrence, P. Tremblay, and R. Desbiens, “The instrument lineshape, an imperative parameter for the absolute spectral calibration of an FTS,” Fourier Transform Spectroscopy, OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), Vol. 84, pp. 160-166.

Appl. Opt.

J. Phys. Radium

J. Connes, “Domaine d'utilisation de la méthode par transformée de Fourier,” J. Phys. Radium 19, 197-208 (1958).
[CrossRef]

Proc. SPIE

E. Niple, A. Pires, and K. Poultney, “Exact modeling of line-shape and wavenumber variations for aff-axis detectors in Fourier-transform spectrometers (FTS) sensor systems,” Proc. SPIE 0364, 11-20 (1982).

A. Kuze, H. Nakajima, J. Tanii, and Y. Sasano, “Conceptual design of solar occultation FTS for inclined-orbit satellite (SOFIS) on GCOM-A1,” Proc. SPIE 4131, 4541-4548 (2000).

Other

J.-P. Bouchard, P. Tremblay, R. Desbiens, and F. Bouffard, “Detailed line-shape measurements using a high resolution, high divergence Fourier transform spectrometer,” in Fourier Transform Spectroscopy, OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), Vol. 84, pp. 25-27.

M. Chamberland, V. Farley, L. Belhumeur, F. Williams, J. Lawrence, P. Tremblay, and R. Desbiens, “The instrument lineshape, an imperative parameter for the absolute spectral calibration of an FTS,” Fourier Transform Spectroscopy, OSA Trends in Optics and Photonics Series (Optical Society of America, 2003), Vol. 84, pp. 160-166.

S. A. Roy, “Data processing pipelines tailored for imaging Fourier-transform spectrometers,” Ph.D. dissertation (Université Laval, 2008).

R. J. Bell and R. N. Bracewell, Introductory Fourier Transform Spectroscopy (Academic, 1972).

L. Mertz, Transformations in Optics (Wiley, 1965).

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Figures (11)

Fig. 1
Fig. 1

Experimental setup for a near-IR/mid-IR imaging Fourier-transform spectrometer.

Fig. 2
Fig. 2

Apparent wavenumber mapping over a 200 × 200 window, obtained from a 1533.8 nm DFB laser. This mapping is used for the wavenumber scale calibration of each pixel.

Fig. 3
Fig. 3

Absolute value of ILS obtained for a square window of 200 × 200 binned pixels before and after spectral calibration, showing that field widening preserves modulation and resolution.

Fig. 4
Fig. 4

Haidinger fringes as a function of OPD simulated over a window of 200 × 200 pixels. A shear contribution of 16 μm is added in the simulation, which is discussed in Subsection 7A.

Fig. 5
Fig. 5

SNR mapping over a 200 × 200 window of calibrated pixels, illustrating the SNR of individual pixels prior to binning.

Fig. 6
Fig. 6

SNR gain resulting from binning calibrated pixels. The spectrum of an emulated large-area detector is obtained by directly coadding interferograms of a square window of 200 × 200 pixels. Applying spectral calibration prior to binning produces a 4 dB gain in SNR.

Fig. 7
Fig. 7

Superimposed interferograms of 200 pixels near ZPD for a same column (uppermost figure) and for a same row (lowermost figure), illustrating the phase difference caused by vertical and horizontal shear, respectively, as demonstrated in Section 7A.

Fig. 8
Fig. 8

Phase offset slope for 200 pixels of a same row with corresponding linear fit, exposing the contribution of horizontal shear.

Fig. 9
Fig. 9

Phase offset slope for 200 pixels of a same column with corresponding linear fit, exposing the contribution of vertical shear.

Fig. 10
Fig. 10

SNR gains obtained from binning phase-corrected calibrated pixels. The SNR gain was assessed by progressively binning pixels row by row and column by column.

Fig. 11
Fig. 11

SNR gain resulting from binning phase-corrected calibrated pixels. The spectrum obtained from a single pixel is compared to the spectrum of 100 × 100 binned pixels, which provide an 8 dB gain in SNR.

Tables (1)

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Table 1 Instrument Parameters and Measurement Characteristics for the Dataset Used to Investigate Software Field Widening

Equations (10)

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I = I o ( 1 + cos Φ ) ,
Φ = 2 π σ ( X cos θ + s x sin θ cos ϕ + s y sin θ sin ϕ ) ,
d Φ d X = 2 π σ cos θ .
Δ Φ = 2 π σ ( s x sin θ cos ϕ + s y sin θ sin ϕ ) .
Δ Φ = 2 π σ s x sin θ .
θ = arctan ( 200 × 30 μm 15 cm ) ,
0.04 rad ,
d Δ Φ d θ = 2 π σ s x .
s x = 1 2 π σ d Δ Φ d θ .
X s x = s x sin θ ,

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