Abstract

We present a mathematical method used to determine the spectrum detected by a birefringence interference imaging spectrometer (BIIS). The reconstructed spectrum has good precision over a wide spectral range, 0.41.0μm. This method considers the light intensity as a function of wavelength and avoids the fatal error caused by birefringence effect in the conventional Fourier transform method. The experimental interferogram of the BIIS is processed in this new way, and the interference data and reconstructed spectrum are in good agreement, proving this method to be very exact and useful. Application of this method will greatly improve the instrument performance.

© 2010 Optical Society of America

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References

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  1. G. Zhan, K. Oka, T. Ishigaki, and N. Baba, Appl. Opt. 41, 734 (2002).
    [CrossRef] [PubMed]
  2. A. Harvey and D. F. Holmes, Opt. Express 12, 5368 (2004).
    [CrossRef] [PubMed]
  3. J. B. Rafert, R. G. Sellar, and J. H. Blatt, Appl. Opt. 34, 7228 (1995).
    [CrossRef] [PubMed]
  4. C. M. Zhang, B. Xiangli, and B. C. Zhao, Opt. Commun. 203, 21 (2002).
    [CrossRef]
  5. C. M. Zhang, B. Xiangli, and B. C. Zhao, Opt. Commun. 227, 221 (2003).
    [CrossRef]
  6. R. J. Bell, Introduction to Fourier Transform Spectroscopy (Academic, 1972).
  7. M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, in Handbook of Optics, 2nd ed. (McGraw-Hill, 1995), Volume II, pp. 1125.
  8. L. Wu, C. M. Zhang, and B. C. Zhao, Opt. Commun. 273, 67 (2007).
    [CrossRef]
  9. C. M. Zhang, X. G. Yan, and B. C. Zhao, Opt. Commun. 281, 2050 (2008).

2008 (1)

C. M. Zhang, X. G. Yan, and B. C. Zhao, Opt. Commun. 281, 2050 (2008).

2007 (1)

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

2004 (1)

2003 (1)

C. M. Zhang, B. Xiangli, and B. C. Zhao, Opt. Commun. 227, 221 (2003).
[CrossRef]

2002 (2)

C. M. Zhang, B. Xiangli, and B. C. Zhao, Opt. Commun. 203, 21 (2002).
[CrossRef]

G. Zhan, K. Oka, T. Ishigaki, and N. Baba, Appl. Opt. 41, 734 (2002).
[CrossRef] [PubMed]

1995 (1)

Baba, N.

Bass, M.

M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, in Handbook of Optics, 2nd ed. (McGraw-Hill, 1995), Volume II, pp. 1125.

Bell, R. J.

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

Blatt, J. H.

Harvey, A.

Holmes, D. F.

Ishigaki, T.

Oka, K.

Rafert, J. B.

Sellar, R. G.

Van Stryland, E. W.

M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, in Handbook of Optics, 2nd ed. (McGraw-Hill, 1995), Volume II, pp. 1125.

Williams, D. R.

M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, in Handbook of Optics, 2nd ed. (McGraw-Hill, 1995), Volume II, pp. 1125.

Wolfe, W. L.

M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, in Handbook of Optics, 2nd ed. (McGraw-Hill, 1995), Volume II, pp. 1125.

Wu, L.

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

Xiangli, B.

C. M. Zhang, B. Xiangli, and B. C. Zhao, Opt. Commun. 227, 221 (2003).
[CrossRef]

C. M. Zhang, B. Xiangli, and B. C. Zhao, Opt. Commun. 203, 21 (2002).
[CrossRef]

Yan, X. G.

C. M. Zhang, X. G. Yan, and B. C. Zhao, Opt. Commun. 281, 2050 (2008).

Zhan, G.

Zhang, C. M.

C. M. Zhang, X. G. Yan, and B. C. Zhao, Opt. Commun. 281, 2050 (2008).

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

C. M. Zhang, B. Xiangli, and B. C. Zhao, Opt. Commun. 227, 221 (2003).
[CrossRef]

C. M. Zhang, B. Xiangli, and B. C. Zhao, Opt. Commun. 203, 21 (2002).
[CrossRef]

Zhao, B. C.

C. M. Zhang, X. G. Yan, and B. C. Zhao, Opt. Commun. 281, 2050 (2008).

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

C. M. Zhang, B. Xiangli, and B. C. Zhao, Opt. Commun. 227, 221 (2003).
[CrossRef]

C. M. Zhang, B. Xiangli, and B. C. Zhao, Opt. Commun. 203, 21 (2002).
[CrossRef]

Appl. Opt. (2)

Opt. Commun. (4)

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

C. M. Zhang, X. G. Yan, and B. C. Zhao, Opt. Commun. 281, 2050 (2008).

C. M. Zhang, B. Xiangli, and B. C. Zhao, Opt. Commun. 203, 21 (2002).
[CrossRef]

C. M. Zhang, B. Xiangli, and B. C. Zhao, Opt. Commun. 227, 221 (2003).
[CrossRef]

Opt. Express (1)

Other (2)

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

M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, in Handbook of Optics, 2nd ed. (McGraw-Hill, 1995), Volume II, pp. 1125.

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Figures (6)

Fig. 1
Fig. 1

Optical diagram of the BIIS.

Fig. 2
Fig. 2

Maximal OPD distribution of BIIS at the wavelength range of 0.350 0.862 μ m .

Fig. 3
Fig. 3

Simulated interferogram obtained by BIIS.

Fig. 4
Fig. 4

Reconstructed spectrum, by BIT.

Fig. 5
Fig. 5

Target plot’s interferogram and image of white light, by BIIS.

Fig. 6
Fig. 6

Reconstructed spectrum of the polychromatic light.

Equations (8)

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B ( σ ) = + [ I ( δ ) 1 2 I ( 0 ) ] e i 2 π σ δ d δ ,
n o 2 1 = 0.8559 λ 2 λ 2 ( 0.0588 ) 2 + 0.8391 λ 2 λ 2 ( 0.141 ) 2 + 0.0009 λ 2 λ 2 ( 0.197 ) 2 + 0.6845 λ 2 λ 2 ( 7.005 ) 2 ,
n e 2 1 = 1.0856 λ 2 λ 2 ( 0.07897 ) 2 + 0.0988 λ 2 λ 2 ( 0.142 ) 2 + 0.317 λ 2 λ 2 ( 11.468 ) 2 .
Δ = t [ a 2 b 2 a 2 + b 2 ( cos ω + sin ω ) sin i + a 2 ( a 2 b 2 ) 2 ( a 2 + b 2 ) 3 2 ( cos 2 ω sin 2 ω ) sin 2 i + ] ,
n = 1 K I λ n = I .
[ I λ 1 0 I λ 1 1 . . . I λ 1 N ] + [ I λ 2 0 I λ 2 1 . . . I λ 2 N ] + [ I λ 3 0 I λ 3 1 . . . I λ 3 N ] + + [ I λ K 0 I λ K 1 . . . I λ K N ] = [ I 0 I 1 . . . I N ] ,
I λ n m = I λ n 0 ( 1 + cos Δ λ m ) 2 ( n = 0 , 1 , 2 , , K ; m = 0 , 1 , 2 , , N ) ,
[ 1 1 1 C 1 1 C 2 1 C K 1 C 1 2 C 2 2 C K 2 . . . C 1 N C 2 N C K N ] [ I λ 1 0 I λ 2 0 . . . I λ K 0 ] = [ I 0 I 1 . . . I N ] ,

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