Abstract

A method was proposed to precisely reconstruct the spectrum from the interferogram taken by the Fourier transform imaging spectrometer (FTIS) based on the polarization beam splitters. Taken the FTISs based on the Savart polariscope and Wollaston prism as examples, the distorted spectrums were corrected via the proposed method effectively. The feasibility of the method was verified via simulation. The distorted spectrum, recovered from the interferogram taken by the polarization imaging spectrometer developed by us, was corrected.

© 2013 Optical Society of America

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References

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  1. A. R. Harvey and D. W. Fletcher-Holmes, Opt. Express 12, 5368 (2004).
    [CrossRef]
  2. S. P. Davis, M. C. Abrams, and J. W. Brault, Fourier Transform Spectrometry (Academic, 2001).
  3. J. Craven, M. W. Kudenov, M. G. Stapelbroek, and E. L. Dereniak, Appl. Opt. 50, 1170 (2011).
    [CrossRef]
  4. M. J. Padgett and A. R. Harvey, Rev. Sci. Instrum. 66, 2807 (1995).
    [CrossRef]
  5. G. Boer, T. Scharf, and R. Dändliker, Appl. Opt. 41, 1400 (2002).
    [CrossRef]
  6. J. W. Brault, Appl. Opt. 35, 2891 (1996).
    [CrossRef]
  7. G. Hirsehberg, Appl. Opt. 38, 136 (1999).
    [CrossRef]
  8. J. B. Rafert, R. G. Sellar, and J. H. Blatt, Appl. Opt. 34, 7228 (1995).
    [CrossRef]
  9. J. Courtial, B. A. Patterson, A. R. Harvey, W. Sibbett, and M. J. Padgett, Appl. Opt. 35, 6698 (1996).
    [CrossRef]
  10. G. Zhan, K. Oka, T. Ishigaki, and N. Baba, Appl. Opt. 41, 734 (2002).
    [CrossRef]
  11. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).
  12. S. Prunet, B. Journet, and G. Fortunato, Opt. Eng. 38, 983 (1999).
    [CrossRef]
  13. W. Ren, C. Zhang, T. Mu, and H. Dai, Opt. Lett. 37, 2580 (2012).
    [CrossRef]
  14. A. Barducci, D. Guzzi, C. Lastri, P. Marcoionni, V. Nardino, and I. Pippi, Opt. Express 18, 11622 (2010).
    [CrossRef]
  15. M. L. Salit, J. C. Travis, and M. R. Winchester, Appl. Opt. 35, 2960 (1996).
    [CrossRef]
  16. S. Prunet, B. Journet, and C. Durieu, in Proceedings of the 16th IEEE on Instrumentation and Measurement Technology (IEEE, 1999), pp. 1895–1900.
  17. M. L. Salit, C. J. Sansonetti, D. Veza, and J. C. Travis, J. Opt. Soc. Am. B 21, 1543 (2004).
    [CrossRef]
  18. T. A. Al-Saeed and D. A. Khalil, Appl. Opt. 48, 3979(2009).
    [CrossRef]
  19. M. Françon and S. Mallick, in Polarization Interferometers: Applications in Microscopy and Macroscopy (Wiley-Interscience, 1971), pp. 19–29.
  20. C. Zhang, X. Bin, and B. Zhao, Proc. SPIE 4087, 957(2000).
    [CrossRef]
  21. C. Zhang, W. Ren, T. Mu, L. Fu, and C. Jia, Opt. Express 21, 2592 (2013).
    [CrossRef]
  22. L. Wu and C. Zhang, Opt. Commun. 273, 67 (2007).
    [CrossRef]

2013 (1)

2012 (1)

2011 (1)

2010 (1)

2009 (1)

2007 (1)

L. Wu and C. Zhang, Opt. Commun. 273, 67 (2007).
[CrossRef]

2004 (2)

2002 (2)

2000 (1)

C. Zhang, X. Bin, and B. Zhao, Proc. SPIE 4087, 957(2000).
[CrossRef]

1999 (2)

S. Prunet, B. Journet, and G. Fortunato, Opt. Eng. 38, 983 (1999).
[CrossRef]

G. Hirsehberg, Appl. Opt. 38, 136 (1999).
[CrossRef]

1996 (3)

1995 (2)

M. J. Padgett and A. R. Harvey, Rev. Sci. Instrum. 66, 2807 (1995).
[CrossRef]

J. B. Rafert, R. G. Sellar, and J. H. Blatt, Appl. Opt. 34, 7228 (1995).
[CrossRef]

Abrams, M. C.

S. P. Davis, M. C. Abrams, and J. W. Brault, Fourier Transform Spectrometry (Academic, 2001).

Al-Saeed, T. A.

Baba, N.

Barducci, A.

Bell, R. J.

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

Bin, X.

C. Zhang, X. Bin, and B. Zhao, Proc. SPIE 4087, 957(2000).
[CrossRef]

Blatt, J. H.

Boer, G.

Brault, J. W.

J. W. Brault, Appl. Opt. 35, 2891 (1996).
[CrossRef]

S. P. Davis, M. C. Abrams, and J. W. Brault, Fourier Transform Spectrometry (Academic, 2001).

Courtial, J.

Craven, J.

Dai, H.

Dändliker, R.

Davis, S. P.

S. P. Davis, M. C. Abrams, and J. W. Brault, Fourier Transform Spectrometry (Academic, 2001).

Dereniak, E. L.

Durieu, C.

S. Prunet, B. Journet, and C. Durieu, in Proceedings of the 16th IEEE on Instrumentation and Measurement Technology (IEEE, 1999), pp. 1895–1900.

Fletcher-Holmes, D. W.

Fortunato, G.

S. Prunet, B. Journet, and G. Fortunato, Opt. Eng. 38, 983 (1999).
[CrossRef]

Françon, M.

M. Françon and S. Mallick, in Polarization Interferometers: Applications in Microscopy and Macroscopy (Wiley-Interscience, 1971), pp. 19–29.

Fu, L.

Guzzi, D.

Harvey, A. R.

Hirsehberg, G.

Ishigaki, T.

Jia, C.

Journet, B.

S. Prunet, B. Journet, and G. Fortunato, Opt. Eng. 38, 983 (1999).
[CrossRef]

S. Prunet, B. Journet, and C. Durieu, in Proceedings of the 16th IEEE on Instrumentation and Measurement Technology (IEEE, 1999), pp. 1895–1900.

Khalil, D. A.

Kudenov, M. W.

Lastri, C.

Mallick, S.

M. Françon and S. Mallick, in Polarization Interferometers: Applications in Microscopy and Macroscopy (Wiley-Interscience, 1971), pp. 19–29.

Marcoionni, P.

Mu, T.

Nardino, V.

Oka, K.

Padgett, M. J.

Patterson, B. A.

Pippi, I.

Prunet, S.

S. Prunet, B. Journet, and G. Fortunato, Opt. Eng. 38, 983 (1999).
[CrossRef]

S. Prunet, B. Journet, and C. Durieu, in Proceedings of the 16th IEEE on Instrumentation and Measurement Technology (IEEE, 1999), pp. 1895–1900.

Rafert, J. B.

Ren, W.

Salit, M. L.

Sansonetti, C. J.

Scharf, T.

Sellar, R. G.

Sibbett, W.

Stapelbroek, M. G.

Travis, J. C.

Veza, D.

Winchester, M. R.

Wu, L.

L. Wu and C. Zhang, Opt. Commun. 273, 67 (2007).
[CrossRef]

Zhan, G.

Zhang, C.

Zhao, B.

C. Zhang, X. Bin, and B. Zhao, Proc. SPIE 4087, 957(2000).
[CrossRef]

Appl. Opt. (9)

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

L. Wu and C. Zhang, Opt. Commun. 273, 67 (2007).
[CrossRef]

Opt. Eng. (1)

S. Prunet, B. Journet, and G. Fortunato, Opt. Eng. 38, 983 (1999).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Proc. SPIE (1)

C. Zhang, X. Bin, and B. Zhao, Proc. SPIE 4087, 957(2000).
[CrossRef]

Rev. Sci. Instrum. (1)

M. J. Padgett and A. R. Harvey, Rev. Sci. Instrum. 66, 2807 (1995).
[CrossRef]

Other (4)

S. P. Davis, M. C. Abrams, and J. W. Brault, Fourier Transform Spectrometry (Academic, 2001).

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

S. Prunet, B. Journet, and C. Durieu, in Proceedings of the 16th IEEE on Instrumentation and Measurement Technology (IEEE, 1999), pp. 1895–1900.

M. Françon and S. Mallick, in Polarization Interferometers: Applications in Microscopy and Macroscopy (Wiley-Interscience, 1971), pp. 19–29.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of the FTIS based on SP.

Fig. 2.
Fig. 2.

Simulated interferogram.

Fig. 3.
Fig. 3.

(a) κ(σ) and (b) the original (the black solid curve) and distorted (the red dashed curve) wavenumbers.

Fig. 4.
Fig. 4.

Corrected result of the FTIS based on SP. The black solid, red and blue curves, respectively, are the original, distorted, and corrected spectrums.

Fig. 5.
Fig. 5.

Interferogram taken by the PIIS.

Fig. 6.
Fig. 6.

Corrected result of PIIS.

Fig. 7.
Fig. 7.

Corrected result of the FTIS based on WP.

Equations (14)

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IR(Δ)=120+B(σ)[1+cos(2πσΔ)]dσ,
I(Δ)=14+B(σ)exp(j2πσΔ)dσ.
Δ(σ)=κ(σ)L,
I(L)=14+B(σ)exp(j2πσκ(σ)L)dσ.
BD(u)=4+I(L)exp(j2πuL)dL=4+14+B(σ)exp(j2πσκ(σ)L)dσexp(j2πuL)dL=+B(σ)dσδ[σκ(σ)u].
BD(u)=+B[g(τ)]g(τ)δ(τu)dτ=B[g(u)]g(u),
g(u)=dσdu=dσκ(σ)dσ+σκ(σ)dσ=1κ(σ)+σκ(σ).
B(σ)=BD(u)/g(u)=[κ(σ)+σκ(σ)]BD(u),σ=u/κ(σ).
ΔSavart(x,σ)=2no2(σ)ne2(σ)no2(σ)+ne2(σ)xft,
ΔWollaston(x,σ)=2x[no(σ)ne(σ)]tanθ,
κSavart(σ)=no2(σmax)+ne2(σmax)no2(σmax)ne2(σmax)no2(σ)ne2(σ)no2(σ)+ne2(σ),
κWollaston(σ)=no(σ)ne(σ)no(σmax)ne(σmax).
Δ(σi)=κ(σi)L,i=1,,N,
ui=κ(σi)σi.

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