Abstract

A Wollaston prism is used in the design of a polarizing Fourier-transform spectrometer with no moving parts. The effective path difference between orthogonally polarized components varies across the aperture of the instrument, forming an interferogram in the spatial rather than temporal domain. The use of a charge-integrating linear detector array permits the entire interferogram to be sampled simultaneously so that a full spectrum is obtained for a single pulse of light.

© 1994 Optical Society of America

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References

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  1. G. W. Stroke, A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16, 272–274 (1965).
    [CrossRef]
  2. T. Okamoto, S. Kawata, S. Minami, “Fourier transform spectrometer with a self-scanning photodiode array,” Appl. Opt. 23, 269–273 (1984).
    [CrossRef] [PubMed]
  3. T. H. Barnes, “Photodiode array Fourier transform spectrometer with improved dynamic range,” Appl. Opt. 24, 3702–3706 (1985).
    [CrossRef] [PubMed]
  4. L. V. Egorova, I. E. Leshcheva, B. N. Popov, A.Yu. Strogonaova, “Static fast-response Fourier spectrometer having a linear CCD image-forming system,” Sov. J. Opt. Technol. 56, 220–221 (1989).
  5. M. Françon, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), Chap. 2, pp. 19–34.
  6. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), Chap. 5, p. 57.
  7. Wollaston Prism Model PW20, Halbo Optics, 83 Haltwhistle Rd., Western Industrial Area, South Woodham Ferrers, Chelmsford, England.
  8. G. W. C. Kaye, T. H. Laby, Tables of Physical and Chemical Constants, 15th ed. (Longmans, London, 1986).

1989 (1)

L. V. Egorova, I. E. Leshcheva, B. N. Popov, A.Yu. Strogonaova, “Static fast-response Fourier spectrometer having a linear CCD image-forming system,” Sov. J. Opt. Technol. 56, 220–221 (1989).

1985 (1)

1984 (1)

1965 (1)

G. W. Stroke, A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16, 272–274 (1965).
[CrossRef]

Barnes, T. H.

Bell, R. J.

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), Chap. 5, p. 57.

Egorova, L. V.

L. V. Egorova, I. E. Leshcheva, B. N. Popov, A.Yu. Strogonaova, “Static fast-response Fourier spectrometer having a linear CCD image-forming system,” Sov. J. Opt. Technol. 56, 220–221 (1989).

Françon, M.

M. Françon, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), Chap. 2, pp. 19–34.

Funkhouser, A. T.

G. W. Stroke, A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16, 272–274 (1965).
[CrossRef]

Kawata, S.

Kaye, G. W. C.

G. W. C. Kaye, T. H. Laby, Tables of Physical and Chemical Constants, 15th ed. (Longmans, London, 1986).

Laby, T. H.

G. W. C. Kaye, T. H. Laby, Tables of Physical and Chemical Constants, 15th ed. (Longmans, London, 1986).

Leshcheva, I. E.

L. V. Egorova, I. E. Leshcheva, B. N. Popov, A.Yu. Strogonaova, “Static fast-response Fourier spectrometer having a linear CCD image-forming system,” Sov. J. Opt. Technol. 56, 220–221 (1989).

Mallick, S.

M. Françon, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), Chap. 2, pp. 19–34.

Minami, S.

Okamoto, T.

Popov, B. N.

L. V. Egorova, I. E. Leshcheva, B. N. Popov, A.Yu. Strogonaova, “Static fast-response Fourier spectrometer having a linear CCD image-forming system,” Sov. J. Opt. Technol. 56, 220–221 (1989).

Strogonaova, A.Yu.

L. V. Egorova, I. E. Leshcheva, B. N. Popov, A.Yu. Strogonaova, “Static fast-response Fourier spectrometer having a linear CCD image-forming system,” Sov. J. Opt. Technol. 56, 220–221 (1989).

Stroke, G. W.

G. W. Stroke, A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16, 272–274 (1965).
[CrossRef]

Appl. Opt. (2)

Phys. Lett. (1)

G. W. Stroke, A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16, 272–274 (1965).
[CrossRef]

Sov. J. Opt. Technol. (1)

L. V. Egorova, I. E. Leshcheva, B. N. Popov, A.Yu. Strogonaova, “Static fast-response Fourier spectrometer having a linear CCD image-forming system,” Sov. J. Opt. Technol. 56, 220–221 (1989).

Other (4)

M. Françon, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), Chap. 2, pp. 19–34.

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), Chap. 5, p. 57.

Wollaston Prism Model PW20, Halbo Optics, 83 Haltwhistle Rd., Western Industrial Area, South Woodham Ferrers, Chelmsford, England.

G. W. C. Kaye, T. H. Laby, Tables of Physical and Chemical Constants, 15th ed. (Longmans, London, 1986).

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Figures (6)

Fig. 1
Fig. 1

Fourier-transform spectrometer based on a Wollaston prism.

Fig. 2
Fig. 2

Fast fourier transform of a 632.8-nm helium–neon interferogram.

Fig. 3
Fig. 3

Interferogram obtained from a metal halide white-light source.

Fig. 4
Fig. 4

Fourier transform of Fig. 3, showing the spectral properties of the light source.

Fig. 5
Fig. 5

Interferogram for a 10-nm-wide bandpass interference filter centered at 560 nm.

Fig. 6
Fig. 6

Fast Fourier transform of Fig. 5.

Equations (14)

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Δ = 2 d ( n e n o ) tan ϑ ,
α = 2 ( n e n o ) tan ϑ .
δ σ FWHM = 1.79 2 Δ L .
λ min = 2 L tot N ,
δ Δ = t n o 2 n e 2 n o 2 n e sin 2 i ,
ν d = 2 ( n e n o ) tan ϑ λ M .
E ( t ) = î A ( ω ) exp ( i ω t ) d ω + ĵ A ( ω ) exp ( i ω t ) d ω ,
Δ = p y p x = ( n e n o ) l ,
Δ = 2 d ( n e n o ) tan ϑ .
E ( t ) = 1 2 A ( ω ) exp [ i ω ( t p x / c ) ] d ω + 1 2 A ( ω ) exp [ i ω ( t p y / c ) ] d ω .
S = k 4 π E ( t ) E * ( t ) d t ,
S = k 8 π A ( ω ) A * ( ω ) { exp [ i ω ( t p x / c ) ] × exp [ i ω ( t p x / c ) ] + exp [ i ω ( t p y / c ) ] exp [ i ω ( t p y / c ) ] + exp [ i ω ( t p x / c ) ] exp [ i ω ( t p y / c ) ] + exp [ i ω ( t p y / c ) ] exp [ i ω ( t p x / c ) ] } d ω d ω d t .
S = k 2 | A ( ω ) | 2 { 1 + cos [ ω ( p y p x ) c ] } d ω = k 0 | A ( ω ) | 2 { 1 + cos [ ω ( p y p x ) c ] } d ω ,
S S 0 S 0 = 0 | A ( ω ) | 2 cos [ ω 2 d ( n e n o ) tan ϑ c ] d ω 0 | A ( ω ) | 2 d ω .

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