Abstract

We present designs of static Fourier transform spectrometers that are based on a Wollaston prism with a large field of view. Besides the usual advantages of static Fourier spectrometers (large resolving power, large wave-number range, high throughput), these designs also present the advantage of using relatively cheap liquid-crystal technology. The use of twisted liquid-crystal structures gives a large field of view, which in turn gives the ability to collect more light from a divergent light source. Measurements are compared with simulations. Different simulation principles are used. We found new configurations by using twisted structures that show a large field of view.

© 2002 Optical Society of America

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References

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  1. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972).
  2. J. Chamberlin, The Principle of Interferometric Spectroscopy (Wiley Interscience, Chichester, UK, 1979).
  3. O. Manzardo, P. Kipfer, H. P. Herzig, “Dispersive compact Fourier transform spectrometer for the visible,” presented at the Fourier Transform Spectroscopy: New Methods and Applications Conference, Santa Barbara, Calif., 22–24 June 1999.
  4. M. Françon, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971).
  5. 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]
  6. 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 birefrigent component,” Opt. Commun. 130, 1–6 (1996).
    [CrossRef]
  7. J. Courtial, B. A. Patterson, A. R. Harvey, W. Sibbett, M. J. Padgett, “Design of a static Fourier-transform spectrometer with increased field of view,” Appl. Opt. 35, 6698–6702 (1996).
    [CrossRef] [PubMed]
  8. T. Inoue, A. Hirai, K. Itoh, Y. Ichioka, “Compact spectral imaging system using liquid crystal for fast measurement,” Opt. Rev. 1, 129–131 (1994).
    [CrossRef]
  9. B. H. Billings, “Visual Fourier-transform spectroscopy with single crystal plate,” J. Opt. Soc. Am. 65, 817–824 (1975).
    [CrossRef] [PubMed]
  10. P. Yeh, C. Gu, Optics of Liquid Crystal Displays (Wiley Interscience, New York, 1999).
  11. M. Born, E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, New York, 1980).
  12. I. C. Khoo, S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1993).
    [CrossRef]
  13. Advanced Stray Light Analysis Program, B. R. Organization, Tucson, Ariz., 1999.
  14. LCD Master, Shintech, Yamaguchi, Japan (1997).
  15. F. Rinne, M. Berek, Anleitung zur allgemeinen und Polarisationsmikroskopie der Festkörper im Durchlicht (Schweizerbart’sche Verlagsbuchhandlung, Stuttgart, 1973).
  16. A. F. Hallimond, The Polarizing Microscope (Vickers Instruments, York, UK, 1970).
  17. A. R. Harvey, M. Begbie, M. J. Padjett, “Stationary Fourier transform spectrometer for use as teaching tool,” Am. J. Phys. 62, 1033–1036 (1994).
    [CrossRef]
  18. J. Courtial, B. A. Patterson, W. Hirst, A. R. Harvey, A. J. Duncan, W. Sibbett, M. J. Padgett, “Static Fourier-transform ultraviolet spectrometer for gas detection,” Appl. Opt. 36, 2813–2817 (1997).
    [CrossRef] [PubMed]
  19. F. J. Dunmore, L. M. Hanssen, “Miniature Fourier instrument for radiation thermometry,” presented at the Fourier Transform Spectroscopy: 11th International Conference, Athens, Ga., 10–15 August 1997.
  20. C. C. Montarou, T. K. Gaylord, “Analysis and design of modified Wollaston prisms,” Appl. Opt. 33, 6604–6613 (1999).
    [CrossRef]

1999 (1)

C. C. Montarou, T. K. Gaylord, “Analysis and design of modified Wollaston prisms,” Appl. Opt. 33, 6604–6613 (1999).
[CrossRef]

1997 (1)

1996 (2)

J. Courtial, B. A. Patterson, A. R. Harvey, W. Sibbett, M. J. Padgett, “Design of a static Fourier-transform spectrometer with increased field of view,” Appl. Opt. 35, 6698–6702 (1996).
[CrossRef] [PubMed]

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 birefrigent component,” Opt. Commun. 130, 1–6 (1996).
[CrossRef]

1994 (3)

T. Inoue, A. Hirai, K. Itoh, Y. Ichioka, “Compact spectral imaging system using liquid crystal for fast measurement,” Opt. Rev. 1, 129–131 (1994).
[CrossRef]

A. R. Harvey, M. Begbie, M. J. Padjett, “Stationary Fourier transform spectrometer for use as 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]

1975 (1)

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 birefrigent component,” Opt. Commun. 130, 1–6 (1996).
[CrossRef]

Begbie, M.

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

Bell, R. J.

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

Berek, M.

F. Rinne, M. Berek, Anleitung zur allgemeinen und Polarisationsmikroskopie der Festkörper im Durchlicht (Schweizerbart’sche Verlagsbuchhandlung, Stuttgart, 1973).

Billings, B. H.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, New York, 1980).

Chamberlin, J.

J. Chamberlin, The Principle of Interferometric Spectroscopy (Wiley Interscience, Chichester, UK, 1979).

Courtial, J.

Duncan, A. J.

Dunmore, F. J.

F. J. Dunmore, L. M. Hanssen, “Miniature Fourier instrument for radiation thermometry,” presented at the Fourier Transform Spectroscopy: 11th International Conference, Athens, Ga., 10–15 August 1997.

Françon, M.

M. Françon, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971).

Gaylord, T. K.

C. C. Montarou, T. K. Gaylord, “Analysis and design of modified Wollaston prisms,” Appl. Opt. 33, 6604–6613 (1999).
[CrossRef]

Gu, C.

P. Yeh, C. Gu, Optics of Liquid Crystal Displays (Wiley Interscience, New York, 1999).

Hallimond, A. F.

A. F. Hallimond, The Polarizing Microscope (Vickers Instruments, York, UK, 1970).

Hanssen, L. M.

F. J. Dunmore, L. M. Hanssen, “Miniature Fourier instrument for radiation thermometry,” presented at the Fourier Transform Spectroscopy: 11th International Conference, Athens, Ga., 10–15 August 1997.

Harvey, A. R.

Herzig, H. P.

O. Manzardo, P. Kipfer, H. P. Herzig, “Dispersive compact Fourier transform spectrometer for the visible,” presented at the Fourier Transform Spectroscopy: New Methods and Applications Conference, Santa Barbara, Calif., 22–24 June 1999.

Hirai, A.

T. Inoue, A. Hirai, K. Itoh, Y. Ichioka, “Compact spectral imaging system using liquid crystal for fast measurement,” Opt. Rev. 1, 129–131 (1994).
[CrossRef]

Hirst, W.

Ichioka, Y.

T. Inoue, A. Hirai, K. Itoh, Y. Ichioka, “Compact spectral imaging system using liquid crystal for fast measurement,” Opt. Rev. 1, 129–131 (1994).
[CrossRef]

Inoue, T.

T. Inoue, A. Hirai, K. Itoh, Y. Ichioka, “Compact spectral imaging system using liquid crystal for fast measurement,” Opt. Rev. 1, 129–131 (1994).
[CrossRef]

Itoh, K.

T. Inoue, A. Hirai, K. Itoh, Y. Ichioka, “Compact spectral imaging system using liquid crystal for fast measurement,” Opt. Rev. 1, 129–131 (1994).
[CrossRef]

Khoo, I. C.

I. C. Khoo, S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1993).
[CrossRef]

Kipfer, P.

O. Manzardo, P. Kipfer, H. P. Herzig, “Dispersive compact Fourier transform spectrometer for the visible,” presented at the Fourier Transform Spectroscopy: New Methods and Applications Conference, Santa Barbara, Calif., 22–24 June 1999.

Mallick, S.

M. Françon, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971).

Manzardo, O.

O. Manzardo, P. Kipfer, H. P. Herzig, “Dispersive compact Fourier transform spectrometer for the visible,” presented at the Fourier Transform Spectroscopy: New Methods and Applications Conference, Santa Barbara, Calif., 22–24 June 1999.

Montarou, C. C.

C. C. Montarou, T. K. Gaylord, “Analysis and design of modified Wollaston prisms,” Appl. Opt. 33, 6604–6613 (1999).
[CrossRef]

Padgett, M. J.

Padjett, M. J.

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

Patterson, B. A.

Rinne, F.

F. Rinne, M. Berek, Anleitung zur allgemeinen und Polarisationsmikroskopie der Festkörper im Durchlicht (Schweizerbart’sche Verlagsbuchhandlung, Stuttgart, 1973).

Sibbett, W.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, New York, 1980).

Wu, S. T.

I. C. Khoo, S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1993).
[CrossRef]

Yeh, P.

P. Yeh, C. Gu, Optics of Liquid Crystal Displays (Wiley Interscience, New York, 1999).

Am. J. Phys. (1)

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

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

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 birefrigent component,” Opt. Commun. 130, 1–6 (1996).
[CrossRef]

Opt. Rev. (1)

T. Inoue, A. Hirai, K. Itoh, Y. Ichioka, “Compact spectral imaging system using liquid crystal for fast measurement,” Opt. Rev. 1, 129–131 (1994).
[CrossRef]

Other (12)

P. Yeh, C. Gu, Optics of Liquid Crystal Displays (Wiley Interscience, New York, 1999).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, New York, 1980).

I. C. Khoo, S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, Singapore, 1993).
[CrossRef]

Advanced Stray Light Analysis Program, B. R. Organization, Tucson, Ariz., 1999.

LCD Master, Shintech, Yamaguchi, Japan (1997).

F. Rinne, M. Berek, Anleitung zur allgemeinen und Polarisationsmikroskopie der Festkörper im Durchlicht (Schweizerbart’sche Verlagsbuchhandlung, Stuttgart, 1973).

A. F. Hallimond, The Polarizing Microscope (Vickers Instruments, York, UK, 1970).

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

J. Chamberlin, The Principle of Interferometric Spectroscopy (Wiley Interscience, Chichester, UK, 1979).

O. Manzardo, P. Kipfer, H. P. Herzig, “Dispersive compact Fourier transform spectrometer for the visible,” presented at the Fourier Transform Spectroscopy: New Methods and Applications Conference, Santa Barbara, Calif., 22–24 June 1999.

M. Françon, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971).

F. J. Dunmore, L. M. Hanssen, “Miniature Fourier instrument for radiation thermometry,” presented at the Fourier Transform Spectroscopy: 11th International Conference, Athens, Ga., 10–15 August 1997.

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Figures (11)

Fig. 1
Fig. 1

Principle of a fast Fourier transform (FFT) spectrometer based on a Wollaston prism.

Fig. 2
Fig. 2

Central fringe of the interference pattern gives the acceptance angle (or field of view).

Fig. 3
Fig. 3

Schematic representation of the slice model used to simulate twisted nematic wedge cells in the ASAP program. The 90° twisted optical axis (represented by the arrows) is divided in slices with discrete rotation angles.

Fig. 4
Fig. 4

(a) Schematic of the design with a standard Wollaston prism consisting of two wedges with orthogonal optical axes. The field of view is simulated by (b) ASAP and (c) LCD Master. (d) Conoscopic observation. The circle has a radius of 35°.

Fig. 5
Fig. 5

(a) Schematic of the design with two LC wedges twisted in the same sense. The field of view is simulated by (b) ASAP and (c) LCD Master. (d) Conoscopic observation. The circle has a radius of 35°.

Fig. 6
Fig. 6

Schematic view of the evolution of the two polarization components (TE and TM) of an arbitrary path going through two wedges with equal twist sense.

Fig. 7
Fig. 7

(a) Schematic of the design with two LC wedges of opposite twist sense. The field of view is simulated by (b) ASAP and (c) LCD Master. (d) Conoscopic observation. The circle has a radius of 35°.

Fig. 8
Fig. 8

(a) Schematic of the design with two wedges with parallel optical axes and a twisted nematic cell in between. The field of view is simulated by (b) ASAP and (c) LCD Master. (d) Conoscopic observation. The circle has a radius of 35°.

Fig. 9
Fig. 9

Conoscopic observation of the field of view at different OPDs for the design with twisted structures (Fig. 5): (a) zero OPD; (b) 2/3 of the maximum OPD.

Fig. 10
Fig. 10

Graph representing the OPD dependence of the field of view for the configuration with equal twist sense (Fig. 5): circles represent the measured values and the curve represents the calculated values.

Fig. 11
Fig. 11

Graph representing the OPD dependence of the field of view for the three-cell configuration (Fig. 8). The circles represent the measured values and the curve represents the calculated values.

Equations (6)

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δ = 2π/λ2yne-notan θ,
I=I0cos2 χ - sin 2ϕ sin 2ϕ - χsin2δ/2,
I=I01 - sin2δ/2=I0cos2δ/2.
I=I0cos2Δχ - sinπ/2 + 2Δχsin2δ/2.
Δλ = λ2/ΔL = λ2/2TΔn,
i2=λTno2nene2-no2,

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