Abstract

The dispersion effect of birefringent material results in spectrally varying Nyquist frequency for the Fourier transform spectrometer based on birefringent prism. Correct spectral information cannot be retrieved from the observed interferogram if the dispersion effect is not appropriately compensated. Some methods, such as nonuniform fast Fourier transforms and compensation method, were proposed to reconstruct the spectrum. In this Letter, an alternative constrained spectrum reconstruction method is suggested for the stationary polarization interference imaging spectrometer (SPIIS) based on the Savart polariscope. In the theoretical model of the interferogram, the noise and the total measurement error are included, and the spectrum reconstruction is performed by using the constrained optimal linear inverse methods. From numerical simulation, it is found that the proposed method is much more effective and robust than the nonconstrained spectrum reconstruction method proposed by Jian, and provides a useful spectrum reconstruction approach for the SPIIS.

© 2012 Optical Society of America

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References

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  1. C. Zhang, B. Xiangli, and B. Zhao, Proc. SPIE 4087, 957 (2000).
    [CrossRef]
  2. M. Francon and S. Mallick, in Polarization Interferometer (Wiley, 1971), pp. 20–23.
  3. J. Craven, M. W. Kudenov, M. G. Stapelbroek, and E. L. Dereniak, Appl. Opt. 50, 1170 (2011).
    [CrossRef]
  4. Q. H. Liu and N. Nguyen, IEEE Microw. Guide Wave Lett. 8, 18 (1998).
    [CrossRef]
  5. X. Jian, C. Zhang, L. Zhang, and B. Zhao, Opt. Express 18, 5674 (2010).
    [CrossRef]
  6. C. Zhang and X. Jian, Opt. Lett. 35, 366 (2010).
    [CrossRef]
  7. R. J. Bell, in Introductory Fourier Transform Spectroscopy (Academic, 1972), pp. 143–145.
  8. L. Wu and C. Zhang, Opt. Commun. 273, 67 (2007).
    [CrossRef]
  9. C. D. Rodgers, in Inverse Methods for Atmospheric Sounding: Theory and Practice (World Scientific, 2000), pp. 65–74.
  10. F. van der Meer, Int. J. Appl. Earth Obs. Geoinform. 8, 3 (2006).
    [CrossRef]

2011 (1)

2010 (2)

2007 (1)

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

2006 (1)

F. van der Meer, Int. J. Appl. Earth Obs. Geoinform. 8, 3 (2006).
[CrossRef]

2000 (1)

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

1998 (1)

Q. H. Liu and N. Nguyen, IEEE Microw. Guide Wave Lett. 8, 18 (1998).
[CrossRef]

Bell, R. J.

R. J. Bell, in Introductory Fourier Transform Spectroscopy (Academic, 1972), pp. 143–145.

Craven, J.

Dereniak, E. L.

Francon, M.

M. Francon and S. Mallick, in Polarization Interferometer (Wiley, 1971), pp. 20–23.

Jian, X.

Kudenov, M. W.

Liu, Q. H.

Q. H. Liu and N. Nguyen, IEEE Microw. Guide Wave Lett. 8, 18 (1998).
[CrossRef]

Mallick, S.

M. Francon and S. Mallick, in Polarization Interferometer (Wiley, 1971), pp. 20–23.

Nguyen, N.

Q. H. Liu and N. Nguyen, IEEE Microw. Guide Wave Lett. 8, 18 (1998).
[CrossRef]

Rodgers, C. D.

C. D. Rodgers, in Inverse Methods for Atmospheric Sounding: Theory and Practice (World Scientific, 2000), pp. 65–74.

Stapelbroek, M. G.

van der Meer, F.

F. van der Meer, Int. J. Appl. Earth Obs. Geoinform. 8, 3 (2006).
[CrossRef]

Wu, L.

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

Xiangli, B.

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

Zhang, C.

X. Jian, C. Zhang, L. Zhang, and B. Zhao, Opt. Express 18, 5674 (2010).
[CrossRef]

C. Zhang and X. Jian, Opt. Lett. 35, 366 (2010).
[CrossRef]

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

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

Zhang, L.

Zhao, B.

X. Jian, C. Zhang, L. Zhang, and B. Zhao, Opt. Express 18, 5674 (2010).
[CrossRef]

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

Appl. Opt. (1)

IEEE Microw. Guide Wave Lett. (1)

Q. H. Liu and N. Nguyen, IEEE Microw. Guide Wave Lett. 8, 18 (1998).
[CrossRef]

Int. J. Appl. Earth Obs. Geoinform. (1)

F. van der Meer, Int. J. Appl. Earth Obs. Geoinform. 8, 3 (2006).
[CrossRef]

Opt. Commun. (1)

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

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (1)

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

Other (3)

M. Francon and S. Mallick, in Polarization Interferometer (Wiley, 1971), pp. 20–23.

C. D. Rodgers, in Inverse Methods for Atmospheric Sounding: Theory and Practice (World Scientific, 2000), pp. 65–74.

R. J. Bell, in Introductory Fourier Transform Spectroscopy (Academic, 1972), pp. 143–145.

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Figures (3)

Fig. 1.
Fig. 1.

The schematic diagram of SPIIS.

Fig. 2.
Fig. 2.

Spectral angles between the reconstructed and original spectral profiles: The ranges of SNR of the noisy interferogram used in CSRM and NSRM, respectively, are from 60 to 160 dB and from 160 to 300 dB.

Fig. 3.
Fig. 3.

The original and reconstructed spectrum profiles.

Equations (10)

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P(Δj)=i=1NB0(σi)[1+cos(2πσiΔj)]+εj,
Δ(λ)t[aλ2bλ2aλ2+bλ2(cosω+sinω)sini+aλ2bλ2(aλ2+bλ2)3/2aλ22(cos2ωsin2ω)sin2i],
P=KB+ε,
ki,j=1+cos(2πσiΔj).
B^=B0+GP,
E{(B^iBi)2}=E{(B0iBi+giTP)2},
G=SaKT(KSaKT+Sε)1B^=Ba+G(PKBa).
B^(m+1)=Ba(m)+SaKT(m)(K(m)SaKT(m)+Sε)1(PKBa(m)).
SA(Sm,Sn)=cos1(Sm,SnSmSn),
Rm,n=i=1N(Sm,iS¯m)(Sn,iS¯n)i=1N(Sm,iS¯m)2i=1N(Sn,iS¯n)2,

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