Abstract

We present several novel designs of static Fourier-transform spectrometers based on Wollaston prisms. By numerical modeling we show the increased field of view that can be obtained when an achromatic half-wave plate is included between the prisms or when prisms fabricated from positive and negative birefringent materials are combined. In addition, we model how a single Wollaston prism with an inclined optic axis produces a fringe plane localized behind its exit face, thus enabling the design of a static Fourier-transform spectrometer based on a single Wollaston prism.

© 1996 Optical Society of America

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References

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  1. J. Chamberlain, The Principles of Interferometric Spectroscopy (Wiley, Chichester, 1979), p. 16.
  2. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), p. 171.
  3. M. Hashimoto, S. Kawata, “Multichannel Fourier-transform infrared spectrometer,” Appl. Opt. 31, 6096–6101 (1992).
    [CrossRef] [PubMed]
  4. S. Takahashi, J. S. Ahn, S. Asaka, T. Kitagawa, “Multichannel Fourier-transform spectroscopy using 2-dimensional detection of the interferogram and its application to Raman-spectroscopy,” Appl. Spectros. 47, 863–868 (1993).
    [CrossRef]
  5. M. Franc¸on, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), p. 24–25.
  6. T. Okamoto, S. Kawata, S. Minami, “A photodiode array Fourier transform spectrometer based on a birefringent interferometer,” Appl. Spectros. 40, 691–695 (1986).
    [CrossRef]
  7. M. J. Padgett, A. R. Harvey, A. J. Duncan, W. Sibbett, “Single-pulse Fourier-transform spectrometer having no moving parts,” Appl. Opt. 33, 6035–6040 (1994).
    [CrossRef] [PubMed]
  8. M. J. Padgett, A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 2807–2811 (1995).
    [CrossRef]
  9. A. R. Harvey, M. Begbie, M. J. Padgett, “Stationary Fourier transform spectrometer for use as a teaching tool,” Am. J. Phys. 62, 1033–1036 (1994).
    [CrossRef]
  10. M. C. Simon, R. M. Echarri, “Ray tracing formulas for monoaxial optical components: vectorial formulation,” Appl. Opt. 25, 1935–1939 (1986).
    [CrossRef] [PubMed]
  11. Mathematica, Version 2.2 (Wolfram Research, Inc., Champaign, Ill., 1994).
  12. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), p. 149.
  13. M. Franc¸on, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), p. 28–33.
  14. J. M. Beckers, “Achromatic linear retarders,” Appl. Opt. 10, 973–975 (1971).
    [CrossRef] [PubMed]
  15. Halbo Optics, Essex CM3 5ZA, England, Model RPHLA15.
  16. B. A. Patterson, M. Antoni, J. Courtial, A. J. Duncan, W. Sibbett, M. J. Padgett, “An ultra-compact static Fourier-transform spectrometer based on a single birefringent component,” Opt. Commun. 130, 1–6 (1996).
    [CrossRef]

1996 (1)

B. A. Patterson, M. Antoni, J. Courtial, A. J. Duncan, W. Sibbett, M. J. Padgett, “An ultra-compact static Fourier-transform spectrometer based on a single birefringent component,” Opt. Commun. 130, 1–6 (1996).
[CrossRef]

1995 (1)

M. J. Padgett, A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 2807–2811 (1995).
[CrossRef]

1994 (2)

A. R. Harvey, M. Begbie, M. J. Padgett, “Stationary Fourier transform spectrometer for use as a teaching tool,” Am. J. Phys. 62, 1033–1036 (1994).
[CrossRef]

M. J. Padgett, A. R. Harvey, A. J. Duncan, W. Sibbett, “Single-pulse Fourier-transform spectrometer having no moving parts,” Appl. Opt. 33, 6035–6040 (1994).
[CrossRef] [PubMed]

1993 (1)

S. Takahashi, J. S. Ahn, S. Asaka, T. Kitagawa, “Multichannel Fourier-transform spectroscopy using 2-dimensional detection of the interferogram and its application to Raman-spectroscopy,” Appl. Spectros. 47, 863–868 (1993).
[CrossRef]

1992 (1)

1986 (2)

M. C. Simon, R. M. Echarri, “Ray tracing formulas for monoaxial optical components: vectorial formulation,” Appl. Opt. 25, 1935–1939 (1986).
[CrossRef] [PubMed]

T. Okamoto, S. Kawata, S. Minami, “A photodiode array Fourier transform spectrometer based on a birefringent interferometer,” Appl. Spectros. 40, 691–695 (1986).
[CrossRef]

1971 (1)

Ahn, J. S.

S. Takahashi, J. S. Ahn, S. Asaka, T. Kitagawa, “Multichannel Fourier-transform spectroscopy using 2-dimensional detection of the interferogram and its application to Raman-spectroscopy,” Appl. Spectros. 47, 863–868 (1993).
[CrossRef]

Antoni, M.

B. A. Patterson, M. Antoni, J. Courtial, A. J. Duncan, W. Sibbett, M. J. Padgett, “An ultra-compact static Fourier-transform spectrometer based on a single birefringent component,” Opt. Commun. 130, 1–6 (1996).
[CrossRef]

Asaka, S.

S. Takahashi, J. S. Ahn, S. Asaka, T. Kitagawa, “Multichannel Fourier-transform spectroscopy using 2-dimensional detection of the interferogram and its application to Raman-spectroscopy,” Appl. Spectros. 47, 863–868 (1993).
[CrossRef]

Beckers, J. M.

Begbie, M.

A. R. Harvey, M. Begbie, M. J. Padgett, “Stationary Fourier transform spectrometer for use as a teaching tool,” Am. J. Phys. 62, 1033–1036 (1994).
[CrossRef]

Bell, R. J.

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), p. 149.

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), p. 171.

Chamberlain, J.

J. Chamberlain, The Principles of Interferometric Spectroscopy (Wiley, Chichester, 1979), p. 16.

Courtial, J.

B. A. Patterson, M. Antoni, J. Courtial, A. J. Duncan, W. Sibbett, M. J. Padgett, “An ultra-compact static Fourier-transform spectrometer based on a single birefringent component,” Opt. Commun. 130, 1–6 (1996).
[CrossRef]

Duncan, A. J.

B. A. Patterson, M. Antoni, J. Courtial, A. J. Duncan, W. Sibbett, M. J. Padgett, “An ultra-compact static Fourier-transform spectrometer based on a single birefringent component,” Opt. Commun. 130, 1–6 (1996).
[CrossRef]

M. J. Padgett, A. R. Harvey, A. J. Duncan, W. Sibbett, “Single-pulse Fourier-transform spectrometer having no moving parts,” Appl. Opt. 33, 6035–6040 (1994).
[CrossRef] [PubMed]

Echarri, R. M.

Franc¸on, M.

M. Franc¸on, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), p. 28–33.

M. Franc¸on, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), p. 24–25.

Harvey, A. R.

M. J. Padgett, A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 2807–2811 (1995).
[CrossRef]

A. R. Harvey, M. Begbie, M. J. Padgett, “Stationary Fourier transform spectrometer for use as a teaching tool,” Am. J. Phys. 62, 1033–1036 (1994).
[CrossRef]

M. J. Padgett, A. R. Harvey, A. J. Duncan, W. Sibbett, “Single-pulse Fourier-transform spectrometer having no moving parts,” Appl. Opt. 33, 6035–6040 (1994).
[CrossRef] [PubMed]

Hashimoto, M.

Kawata, S.

M. Hashimoto, S. Kawata, “Multichannel Fourier-transform infrared spectrometer,” Appl. Opt. 31, 6096–6101 (1992).
[CrossRef] [PubMed]

T. Okamoto, S. Kawata, S. Minami, “A photodiode array Fourier transform spectrometer based on a birefringent interferometer,” Appl. Spectros. 40, 691–695 (1986).
[CrossRef]

Kitagawa, T.

S. Takahashi, J. S. Ahn, S. Asaka, T. Kitagawa, “Multichannel Fourier-transform spectroscopy using 2-dimensional detection of the interferogram and its application to Raman-spectroscopy,” Appl. Spectros. 47, 863–868 (1993).
[CrossRef]

Mallick, S.

M. Franc¸on, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), p. 28–33.

M. Franc¸on, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), p. 24–25.

Minami, S.

T. Okamoto, S. Kawata, S. Minami, “A photodiode array Fourier transform spectrometer based on a birefringent interferometer,” Appl. Spectros. 40, 691–695 (1986).
[CrossRef]

Okamoto, T.

T. Okamoto, S. Kawata, S. Minami, “A photodiode array Fourier transform spectrometer based on a birefringent interferometer,” Appl. Spectros. 40, 691–695 (1986).
[CrossRef]

Padgett, M. J.

B. A. Patterson, M. Antoni, J. Courtial, A. J. Duncan, W. Sibbett, M. J. Padgett, “An ultra-compact static Fourier-transform spectrometer based on a single birefringent component,” Opt. Commun. 130, 1–6 (1996).
[CrossRef]

M. J. Padgett, A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 2807–2811 (1995).
[CrossRef]

A. R. Harvey, M. Begbie, M. J. Padgett, “Stationary Fourier transform spectrometer for use as a teaching tool,” Am. J. Phys. 62, 1033–1036 (1994).
[CrossRef]

M. J. Padgett, A. R. Harvey, A. J. Duncan, W. Sibbett, “Single-pulse Fourier-transform spectrometer having no moving parts,” Appl. Opt. 33, 6035–6040 (1994).
[CrossRef] [PubMed]

Patterson, B. A.

B. A. Patterson, M. Antoni, J. Courtial, A. J. Duncan, W. Sibbett, M. J. Padgett, “An ultra-compact static Fourier-transform spectrometer based on a single birefringent component,” Opt. Commun. 130, 1–6 (1996).
[CrossRef]

Sibbett, W.

B. A. Patterson, M. Antoni, J. Courtial, A. J. Duncan, W. Sibbett, M. J. Padgett, “An ultra-compact static Fourier-transform spectrometer based on a single birefringent component,” Opt. Commun. 130, 1–6 (1996).
[CrossRef]

M. J. Padgett, A. R. Harvey, A. J. Duncan, W. Sibbett, “Single-pulse Fourier-transform spectrometer having no moving parts,” Appl. Opt. 33, 6035–6040 (1994).
[CrossRef] [PubMed]

Simon, M. C.

Takahashi, S.

S. Takahashi, J. S. Ahn, S. Asaka, T. Kitagawa, “Multichannel Fourier-transform spectroscopy using 2-dimensional detection of the interferogram and its application to Raman-spectroscopy,” Appl. Spectros. 47, 863–868 (1993).
[CrossRef]

Am. J. Phys. (1)

A. R. Harvey, M. Begbie, M. J. Padgett, “Stationary Fourier transform spectrometer for use as a teaching tool,” Am. J. Phys. 62, 1033–1036 (1994).
[CrossRef]

Appl. Opt. (4)

Appl. Spectros. (2)

S. Takahashi, J. S. Ahn, S. Asaka, T. Kitagawa, “Multichannel Fourier-transform spectroscopy using 2-dimensional detection of the interferogram and its application to Raman-spectroscopy,” Appl. Spectros. 47, 863–868 (1993).
[CrossRef]

T. Okamoto, S. Kawata, S. Minami, “A photodiode array Fourier transform spectrometer based on a birefringent interferometer,” Appl. Spectros. 40, 691–695 (1986).
[CrossRef]

Opt. Commun. (1)

B. A. Patterson, M. Antoni, J. Courtial, A. J. Duncan, W. Sibbett, M. J. Padgett, “An ultra-compact static Fourier-transform spectrometer based on a single birefringent component,” Opt. Commun. 130, 1–6 (1996).
[CrossRef]

Rev. Sci. Instrum. (1)

M. J. Padgett, A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 2807–2811 (1995).
[CrossRef]

Other (7)

J. Chamberlain, The Principles of Interferometric Spectroscopy (Wiley, Chichester, 1979), p. 16.

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), p. 171.

M. Franc¸on, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), p. 24–25.

Mathematica, Version 2.2 (Wolfram Research, Inc., Champaign, Ill., 1994).

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), p. 149.

M. Franc¸on, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), p. 28–33.

Halbo Optics, Essex CM3 5ZA, England, Model RPHLA15.

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Figures (8)

Fig. 1
Fig. 1

Schematic layout of a static FT spectrometer based on a pair of Wollaston prisms.

Fig. 2
Fig. 2

Experimental arrangement for the observation of the interferogram corresponding to the field of view for a pair of Wollaston prisms.

Fig. 3
Fig. 3

Calculated field-of-view interferogram for the nonoptimized double Wollaston prism spectrometer described in Section 4. (a) P on axis in fringe plane, (b) P on axis 2.0 mm behind fringe plane.

Fig. 4
Fig. 4

Observed field-of-view interferogram for the double Wollaston prism spectrometer described in Section 4: (a) pinhole in fringe plane ±0.1 mm, (b) pinhole 2.0 ± 0.1 mm behind fringe plane.

Fig. 5
Fig. 5

Schematic layout of a wide-angle FT spectrometer based on two Wollaston prisms and an achromatic half-wave plate.

Fig. 6
Fig. 6

Calculated field-of-view interferogram for different detector positions P in the fringe plane of the wide-angle spectrometer based on two Wollaston prisms and a half-wave plate: (a) P on axis corresponding to ΔP(0°, 0°) = 0, (b) P 3 mm off axis corresponding to ΔP(0°, 0°) = 45 μm.

Fig. 7
Fig. 7

Calculated field-of-view interferogram for different detector positions P in the fringe plane of the wide-angle spectrometer based on two Wollaston prisms fabricated from crystals with different signs of birefringence: (a) P on axis corresponding to ΔP(0°, 0°) = 0, (b) P 3 mm off axis corresponding to ΔP(0°, 0°) = 45 μm.

Fig. 8
Fig. 8

Calculated field-of-view interferogram for the spectrometer based on a single Wollaston prism with inclined optic axis.

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α 2 + β 2 λ t ( n o 2 n e n e 2 n o 2 ) .
t W t c = | ( n e 2 n o 2 n o 2 n e ) c ( n e 2 n o 2 n o 2 n e ) W | .

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