Abstract

Complex domain calibration is an efficient method to correct the amplitude and phase of a spectrum obtained from a Fourier transform spectrometer. This method is, however, not directly applicable in the occurrence of a zero path difference (ZPD) shift between a scene interferogram and calibration blackbody interferograms. This situation is likely to happen for a system with thermal instabilities. It is found that a ZPD shift smaller than 1 sampling point can cause a large disagreement between the spectra evaluated from the two interferometer sweep directions. We have developed an algorithm for a complex calibration in the presence of ZPD shifts. The restricting aspect of the real-time capability is taken into account.

© 2010 Optical Society of America

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References

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  1. P. Fournier, T. Smithson, and D. St.-Germain, “AIRIS the Canadian hyperspectral imager: current status and future developments,” Int. J. Hi. Spe. Ele. Syst. 18, 545 (2008).
    [Crossref]
  2. A. Villemaire, S. Fortin, J. Giroux, T. Smithson, and R. Oermann, “An imaging Fourier transform spectrometer,” Proc. SPIE 2480, 387 (1995).
    [Crossref]
  3. S. Turbide, T. Smithson, D. St.-Germain, and P. Fournier, “Algorithms for the categorization and identification of IR military signatures,” Proc. SPIE 7457, 74570R (2009).
    [Crossref]
  4. H. E. Revercomb, H. Buijs, H. B. Howell, D. D. La Porte, W. L. Smith, and L. Sromovsky, “Radiometric calibration of IR Fourier transform spectrometers: solution to a problem with the high-resolution interferometer sounder,” Appl. Opt. 27, 3210(1988).
    [Crossref] [PubMed]
  5. A. Villemaire, M. Chamberland, J. Giroux, R. L. Lachance, and J. M. Thériault, “Radiometric calibration of FT-IR remote sensing instrument,” Proc. SPIE 3082, 83 (1997).
    [Crossref]
  6. R. J. Bell, Introductory Fourier Transform Spectroscopy(Academic, 1972).
  7. J. Singh, Semiconductor Optoelectronics-Physics and Technology (McGraw-Hill, 1995).
  8. J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optimiz. 9, 112–147 (1998).
    [Crossref]
  9. J. Schreiber, T. Blumenstock, and H. Fischer, “Effects of the self-emission of an IR Fourier-transform spectrometer on measured absorption spectra,” Appl. Opt. 35, 6203–6209(1996).
    [Crossref] [PubMed]
  10. P. Fournier, T. Smithson, D. St.-Germain, and P. Lahaie, “AIRIS real-time calibration trial,” Defence Research and Development Canada Valcartier TN 2009-172.

2009 (1)

S. Turbide, T. Smithson, D. St.-Germain, and P. Fournier, “Algorithms for the categorization and identification of IR military signatures,” Proc. SPIE 7457, 74570R (2009).
[Crossref]

2008 (1)

P. Fournier, T. Smithson, and D. St.-Germain, “AIRIS the Canadian hyperspectral imager: current status and future developments,” Int. J. Hi. Spe. Ele. Syst. 18, 545 (2008).
[Crossref]

1998 (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optimiz. 9, 112–147 (1998).
[Crossref]

1997 (1)

A. Villemaire, M. Chamberland, J. Giroux, R. L. Lachance, and J. M. Thériault, “Radiometric calibration of FT-IR remote sensing instrument,” Proc. SPIE 3082, 83 (1997).
[Crossref]

1996 (1)

1995 (1)

A. Villemaire, S. Fortin, J. Giroux, T. Smithson, and R. Oermann, “An imaging Fourier transform spectrometer,” Proc. SPIE 2480, 387 (1995).
[Crossref]

1988 (1)

Bell, R. J.

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

Blumenstock, T.

Buijs, H.

Chamberland, M.

A. Villemaire, M. Chamberland, J. Giroux, R. L. Lachance, and J. M. Thériault, “Radiometric calibration of FT-IR remote sensing instrument,” Proc. SPIE 3082, 83 (1997).
[Crossref]

Fischer, H.

Fortin, S.

A. Villemaire, S. Fortin, J. Giroux, T. Smithson, and R. Oermann, “An imaging Fourier transform spectrometer,” Proc. SPIE 2480, 387 (1995).
[Crossref]

Fournier, P.

S. Turbide, T. Smithson, D. St.-Germain, and P. Fournier, “Algorithms for the categorization and identification of IR military signatures,” Proc. SPIE 7457, 74570R (2009).
[Crossref]

P. Fournier, T. Smithson, and D. St.-Germain, “AIRIS the Canadian hyperspectral imager: current status and future developments,” Int. J. Hi. Spe. Ele. Syst. 18, 545 (2008).
[Crossref]

P. Fournier, T. Smithson, D. St.-Germain, and P. Lahaie, “AIRIS real-time calibration trial,” Defence Research and Development Canada Valcartier TN 2009-172.

Giroux, J.

A. Villemaire, M. Chamberland, J. Giroux, R. L. Lachance, and J. M. Thériault, “Radiometric calibration of FT-IR remote sensing instrument,” Proc. SPIE 3082, 83 (1997).
[Crossref]

A. Villemaire, S. Fortin, J. Giroux, T. Smithson, and R. Oermann, “An imaging Fourier transform spectrometer,” Proc. SPIE 2480, 387 (1995).
[Crossref]

Howell, H. B.

La Porte, D. D.

Lachance, R. L.

A. Villemaire, M. Chamberland, J. Giroux, R. L. Lachance, and J. M. Thériault, “Radiometric calibration of FT-IR remote sensing instrument,” Proc. SPIE 3082, 83 (1997).
[Crossref]

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optimiz. 9, 112–147 (1998).
[Crossref]

Lahaie, P.

P. Fournier, T. Smithson, D. St.-Germain, and P. Lahaie, “AIRIS real-time calibration trial,” Defence Research and Development Canada Valcartier TN 2009-172.

Oermann, R.

A. Villemaire, S. Fortin, J. Giroux, T. Smithson, and R. Oermann, “An imaging Fourier transform spectrometer,” Proc. SPIE 2480, 387 (1995).
[Crossref]

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optimiz. 9, 112–147 (1998).
[Crossref]

Revercomb, H. E.

Schreiber, J.

Singh, J.

J. Singh, Semiconductor Optoelectronics-Physics and Technology (McGraw-Hill, 1995).

Smith, W. L.

Smithson, T.

S. Turbide, T. Smithson, D. St.-Germain, and P. Fournier, “Algorithms for the categorization and identification of IR military signatures,” Proc. SPIE 7457, 74570R (2009).
[Crossref]

P. Fournier, T. Smithson, and D. St.-Germain, “AIRIS the Canadian hyperspectral imager: current status and future developments,” Int. J. Hi. Spe. Ele. Syst. 18, 545 (2008).
[Crossref]

A. Villemaire, S. Fortin, J. Giroux, T. Smithson, and R. Oermann, “An imaging Fourier transform spectrometer,” Proc. SPIE 2480, 387 (1995).
[Crossref]

P. Fournier, T. Smithson, D. St.-Germain, and P. Lahaie, “AIRIS real-time calibration trial,” Defence Research and Development Canada Valcartier TN 2009-172.

Sromovsky, L.

St.-Germain, D.

S. Turbide, T. Smithson, D. St.-Germain, and P. Fournier, “Algorithms for the categorization and identification of IR military signatures,” Proc. SPIE 7457, 74570R (2009).
[Crossref]

P. Fournier, T. Smithson, and D. St.-Germain, “AIRIS the Canadian hyperspectral imager: current status and future developments,” Int. J. Hi. Spe. Ele. Syst. 18, 545 (2008).
[Crossref]

P. Fournier, T. Smithson, D. St.-Germain, and P. Lahaie, “AIRIS real-time calibration trial,” Defence Research and Development Canada Valcartier TN 2009-172.

Thériault, J. M.

A. Villemaire, M. Chamberland, J. Giroux, R. L. Lachance, and J. M. Thériault, “Radiometric calibration of FT-IR remote sensing instrument,” Proc. SPIE 3082, 83 (1997).
[Crossref]

Turbide, S.

S. Turbide, T. Smithson, D. St.-Germain, and P. Fournier, “Algorithms for the categorization and identification of IR military signatures,” Proc. SPIE 7457, 74570R (2009).
[Crossref]

Villemaire, A.

A. Villemaire, M. Chamberland, J. Giroux, R. L. Lachance, and J. M. Thériault, “Radiometric calibration of FT-IR remote sensing instrument,” Proc. SPIE 3082, 83 (1997).
[Crossref]

A. Villemaire, S. Fortin, J. Giroux, T. Smithson, and R. Oermann, “An imaging Fourier transform spectrometer,” Proc. SPIE 2480, 387 (1995).
[Crossref]

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optimiz. 9, 112–147 (1998).
[Crossref]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optimiz. 9, 112–147 (1998).
[Crossref]

Appl. Opt. (2)

Int. J. Hi. Spe. Ele. Syst. (1)

P. Fournier, T. Smithson, and D. St.-Germain, “AIRIS the Canadian hyperspectral imager: current status and future developments,” Int. J. Hi. Spe. Ele. Syst. 18, 545 (2008).
[Crossref]

Proc. SPIE (3)

A. Villemaire, S. Fortin, J. Giroux, T. Smithson, and R. Oermann, “An imaging Fourier transform spectrometer,” Proc. SPIE 2480, 387 (1995).
[Crossref]

S. Turbide, T. Smithson, D. St.-Germain, and P. Fournier, “Algorithms for the categorization and identification of IR military signatures,” Proc. SPIE 7457, 74570R (2009).
[Crossref]

A. Villemaire, M. Chamberland, J. Giroux, R. L. Lachance, and J. M. Thériault, “Radiometric calibration of FT-IR remote sensing instrument,” Proc. SPIE 3082, 83 (1997).
[Crossref]

SIAM J. Optimiz. (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optimiz. 9, 112–147 (1998).
[Crossref]

Other (3)

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

J. Singh, Semiconductor Optoelectronics-Physics and Technology (McGraw-Hill, 1995).

P. Fournier, T. Smithson, D. St.-Germain, and P. Lahaie, “AIRIS real-time calibration trial,” Defence Research and Development Canada Valcartier TN 2009-172.

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Figures (7)

Fig. 1
Fig. 1

Phases extracted from the combinations of three BBs’ complex spectra: (left panel) no ZPD shift correction and (right panel) ZPD shift corrections included.

Fig. 2
Fig. 2

Evaluated spectral error, in percentage, caused by a ZPD shift of Δ n = 0.5 (dashed curves) and Δ n = 0.8 (solid curves), with and without the ZPD shift correction algorithm. The temperature within the instrument, at the time of target measurement, has changed by 5 ° C (left panel) and + 10 ° C (right panel), relative to the time of calibration. The phase of the instrument self-emission is π / 3 .

Fig. 3
Fig. 3

Same as Fig. 2, but for an instrument self-emission phase of π / 4 .

Fig. 4
Fig. 4

Air-to-ground measurement of a lake with (right panel) and without (left panel) ZPD shift correction, for different frame numbers. The odd frame numbers correspond to forward single scans, while the even frame numbers correspond to reverse single scans. Data are from AIRIS observations.

Fig. 5
Fig. 5

Air-to-ground measurement of a propane burner with (right panel) and without (left panel) ZPD shift correction. Frame 1 corresponds to the forward single scan, and frame 2 corresponds to the reverse single scan. Data are from AIRIS observations.

Fig. 6
Fig. 6

Effect of the evaluated ZPD shift Δ n on a calibrated spectrum. Data are from AIRIS observations.

Fig. 7
Fig. 7

Time evolution of the evaluated ZPD shift Δ n , for two acquisitions. The figure displays only the forward sweep direction results. Data are from AIRIS observations.

Equations (16)

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S ^ ( σ ) = n = 1 N / 2 N / 2 I ^ [ n ] e i 2 π σ n Δ x ,
I ^ [ n ] = I [ n ] cos ( π ( n 1 / 2 ) N 1 ) .
S ^ σ H 1 = R σ ( ϵ σ H 1 B σ H 1 + ( 1 ϵ σ H 1 ) B σ R + O σ ) e i ϕ σ ; S ^ σ H 2 = R σ ( ϵ σ H 2 B σ H 2 + ( 1 ϵ σ H 2 ) B σ R ) + O σ ) e i ϕ σ e i ψ σ b ; S ^ σ a = R σ ( ϵ σ a B σ a + ( 1 ϵ σ a ) B σ R + O σ ) e i ϕ σ e i ψ σ a .
S ^ σ H 1 = R σ ( ϵ σ H 1 B σ H 1 + ( 1 ϵ σ H 1 ) B σ a + O σ ) e i ϕ σ ; S ^ σ H 2 = R σ ( ϵ σ H 2 B σ H 2 + ( 1 ϵ σ H 2 ) B σ a + O σ ) e i ϕ σ e i ψ σ b ; S ^ σ a = R σ ( B σ a + O σ ) e i ϕ σ e i ψ σ a .
ϕ σ ϕ ¯ σ = - i log ( S ^ σ H 1 | S ^ σ H 1 | ) .
d a , b = 2 π Δ n a , b λ He Ne ,
χ a 2 = σ = σ 1 σ 2 ( ϕ ¯ σ + i log ( S ^ σ H 1 - S ^ σ a e - i d a σ | S ^ σ H 1 - S ^ σ a e - i d a σ | ) ) 2 .
χ b 2 = σ = σ 1 σ 2 ( ϕ ¯ σ + i log ( S ^ σ H 1 - S ^ σ H 2 e - i d b σ | S ^ σ H 1 - S ^ σ H 2 e - i d b σ | ) ) 2 .
χ c 2 = σ = σ 1 σ 2 ( i log ( S ^ σ H 1 S ^ σ a e i d a σ | S ^ σ H 1 S ^ σ a e i d a σ | ) i log ( S ^ σ H 2 e i d b σ S ^ σ a e i d a σ | S ^ σ H 2 e i d b σ S ^ σ a e i d a σ | ) ) 2 + σ = σ 1 σ 2 ( i log ( S ^ σ H 1 S ^ σ a e i d a σ | S ^ σ H 1 S ^ σ a e i d a σ | ) i log ( S ^ σ H 1 S ^ σ H 2 e i d b σ | S ^ σ H 1 S ^ σ H 2 e i d b σ | ) ) 2 + σ = σ 1 σ 2 ( i log ( S ^ σ H 2 e i d b σ S ^ σ a e i d a σ | S ^ σ H 2 e i d b σ S ^ σ a e i d a σ | ) i log ( S ^ σ H 1 S ^ σ H 2 e i d b σ | S ^ σ H 1 S ^ σ H 2 e i d b σ | ) ) 2 .
R σ = | S ^ σ H 1 S ^ σ a e i d a σ ϵ σ H 1 ( B σ H 1 B σ a ) | ; e i ϕ σ = S ^ σ H 1 S ^ σ a e i d a σ | S ^ σ H 1 S ^ σ a e i d a σ | ; O σ = S ^ σ a R σ e i ( ϕ σ + d a σ ) B σ a .
T B = 1.438786 σ [ log ( 3.741832 × 10 12 σ 3 π B + 1 ) ] 1 273.15 ,
S ^ σ = R σ ( S σ + O σ ) e i ϕ σ ,
χ 2 = σ = σ 1 σ 2 ( ϕ σ + i log ( ( | S ^ σ H 1 | | S ^ σ | ) | | S ^ σ H 1 | | S ^ σ | | ( S ^ σ H 1 S ^ σ e i d σ ) | S ^ σ H 1 S ^ σ e i d σ | ) ) ,
S σ = Re ( S ^ σ R σ e i ( ϕ σ + d σ ) O σ ) = Re ( S σ e i ( ψ σ d σ ) + ( O σ e i ( ψ σ d σ ) O σ ) ) .
S σ BG = Re ( S σ BG e i ( ψ σ d σ ) + ( O σ e i ( ψ σ d σ ) O σ ) ) .
S σ S σ BG = ( S σ S σ BG ) cos ( ψ σ d σ ) .

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