Abstract

We devised a novel type of multichannel Fourier transform spectrometer (MCFTS) that incorporates a Wollaston prism, polarizing interferometer combined with two Savart plates and a phase-retarding plate. This original MCFTS produces a number of lines of folded interferograms recorded with a two-dimensional imaging detector such as a CCD detector. In the present type of MCFTS, the total incident light is available except for a small amount of reflection loss. It is possible to enhance the signal-to-noise ratio. The enhancement of the resolving power is also expected by the connection of the interferograms with a newly developed method.

© 1995 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), p. 63.
  2. 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]
  3. K. Yoshiwara, “Holographic spectra using a triangle path interferometer,” Jpn. J. Appl. Phys. 6, 116 (1967).
    [CrossRef]
  4. T. Okamoto, S. Kawata, S. Minami, “Fourier transform spectrometer with a self-scanning photodiode array,” Appl. Opt. 23, 269–273 (1984).
    [CrossRef] [PubMed]
  5. T. H. Barnes, “Photodiode array Fourier transform spectrometer with improved dynamic range,” Appl. Opt. 24, 3702–3706 (1985).
    [CrossRef] [PubMed]
  6. T. Okamoto, S. Kawata, S. Minami, “A photodiode array Fourier transform spectrometer based on a birefringent interferometer,” Appl. Spectrosc. 40, 691–695 (1986).
    [CrossRef]
  7. N. Ebizuka, M. Wakaki, “Trial manufacture of MCFTS with Wollaston prism and analysis of the optical system without collimating lens,” J. Spectrosc. Soc. Jpn. 42, 17–25 (1993).
    [CrossRef]
  8. M. Hashimoto, S. Kawata, “Multichannel Fourier-transform infrared spectrometer,” Appl. Opt. 31, 6096–6101 (1992).
    [CrossRef] [PubMed]
  9. N. Ebizuka, Y. Kobayashi, S. Sato, M. Wakaki, “Development and practical application of the novel type of two dimensional multi-channel Fourier transform spectrometer,” submitted to J. Spectrosc. Soc. Jpn.
  10. T. Okamoto, S. Kawata, S. Minami, “Optical method for resolution enhancement in photodiode array Fourier transform spectroscopy,” Appl. Opt. 24, 4221–4225 (1985).
    [CrossRef] [PubMed]
  11. T. H. Barnes, T. Eiju, K. Matsuda, “Heterodyned photodiode array Fourier transform spectrometer,” Appl. Opt. 25, 1864–1866 (1986).
    [CrossRef] [PubMed]
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), Chap. 14, p. 665.
  13. P. R. Griffiths, J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, New York, 1986), p. 93.
  14. K. Kudoh, Kiso Bussei Zuhyo [Charts and tables of chemistry and physics constants] (Kyoritu Shuppan, Tokyo, 1972), p. 526.
  15. A. M. Prokhorov, Y. S. Kuz’minov, Physics and Chemistry of Crystalline Lithium Niobate (Hilger, New York, 1990), p. 196.
  16. D. Tody, “The IRAF data reduction and analysis system,” in Instrumentation in Astronomy VI, D. L. Crawford, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 627, 773 (1986).
  17. M. L. Forman, W. H. Steel, G. A. Vanasse, “Correction of asymmetric interferograms obtained in Fourier spectroscopy,” J. Opt. Soc. Am. 56, 59–63 (1966).
    [CrossRef]

1993

N. Ebizuka, M. Wakaki, “Trial manufacture of MCFTS with Wollaston prism and analysis of the optical system without collimating lens,” J. Spectrosc. Soc. Jpn. 42, 17–25 (1993).
[CrossRef]

1992

1986

1985

1984

1967

K. Yoshiwara, “Holographic spectra using a triangle path interferometer,” Jpn. J. Appl. Phys. 6, 116 (1967).
[CrossRef]

1966

1965

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), p. 63.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), Chap. 14, p. 665.

de Haseth, J. A.

P. R. Griffiths, J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, New York, 1986), p. 93.

Ebizuka, N.

N. Ebizuka, M. Wakaki, “Trial manufacture of MCFTS with Wollaston prism and analysis of the optical system without collimating lens,” J. Spectrosc. Soc. Jpn. 42, 17–25 (1993).
[CrossRef]

N. Ebizuka, Y. Kobayashi, S. Sato, M. Wakaki, “Development and practical application of the novel type of two dimensional multi-channel Fourier transform spectrometer,” submitted to J. Spectrosc. Soc. Jpn.

Eiju, T.

Forman, M. L.

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]

Griffiths, P. R.

P. R. Griffiths, J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, New York, 1986), p. 93.

Hashimoto, M.

Kawata, S.

Kobayashi, Y.

N. Ebizuka, Y. Kobayashi, S. Sato, M. Wakaki, “Development and practical application of the novel type of two dimensional multi-channel Fourier transform spectrometer,” submitted to J. Spectrosc. Soc. Jpn.

Kudoh, K.

K. Kudoh, Kiso Bussei Zuhyo [Charts and tables of chemistry and physics constants] (Kyoritu Shuppan, Tokyo, 1972), p. 526.

Kuz’minov, Y. S.

A. M. Prokhorov, Y. S. Kuz’minov, Physics and Chemistry of Crystalline Lithium Niobate (Hilger, New York, 1990), p. 196.

Matsuda, K.

Minami, S.

Okamoto, T.

Prokhorov, A. M.

A. M. Prokhorov, Y. S. Kuz’minov, Physics and Chemistry of Crystalline Lithium Niobate (Hilger, New York, 1990), p. 196.

Sato, S.

N. Ebizuka, Y. Kobayashi, S. Sato, M. Wakaki, “Development and practical application of the novel type of two dimensional multi-channel Fourier transform spectrometer,” submitted to J. Spectrosc. Soc. Jpn.

Steel, W. H.

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]

Tody, D.

D. Tody, “The IRAF data reduction and analysis system,” in Instrumentation in Astronomy VI, D. L. Crawford, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 627, 773 (1986).

Vanasse, G. A.

Wakaki, M.

N. Ebizuka, M. Wakaki, “Trial manufacture of MCFTS with Wollaston prism and analysis of the optical system without collimating lens,” J. Spectrosc. Soc. Jpn. 42, 17–25 (1993).
[CrossRef]

N. Ebizuka, Y. Kobayashi, S. Sato, M. Wakaki, “Development and practical application of the novel type of two dimensional multi-channel Fourier transform spectrometer,” submitted to J. Spectrosc. Soc. Jpn.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), Chap. 14, p. 665.

Yoshiwara, K.

K. Yoshiwara, “Holographic spectra using a triangle path interferometer,” Jpn. J. Appl. Phys. 6, 116 (1967).
[CrossRef]

Appl. Opt.

Appl. Spectrosc.

J. Opt. Soc. Am.

J. Spectrosc. Soc. Jpn.

N. Ebizuka, M. Wakaki, “Trial manufacture of MCFTS with Wollaston prism and analysis of the optical system without collimating lens,” J. Spectrosc. Soc. Jpn. 42, 17–25 (1993).
[CrossRef]

Jpn. J. Appl. Phys.

K. Yoshiwara, “Holographic spectra using a triangle path interferometer,” Jpn. J. Appl. Phys. 6, 116 (1967).
[CrossRef]

Phys. Lett.

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]

Other

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), p. 63.

N. Ebizuka, Y. Kobayashi, S. Sato, M. Wakaki, “Development and practical application of the novel type of two dimensional multi-channel Fourier transform spectrometer,” submitted to J. Spectrosc. Soc. Jpn.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1975), Chap. 14, p. 665.

P. R. Griffiths, J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, New York, 1986), p. 93.

K. Kudoh, Kiso Bussei Zuhyo [Charts and tables of chemistry and physics constants] (Kyoritu Shuppan, Tokyo, 1972), p. 526.

A. M. Prokhorov, Y. S. Kuz’minov, Physics and Chemistry of Crystalline Lithium Niobate (Hilger, New York, 1990), p. 196.

D. Tody, “The IRAF data reduction and analysis system,” in Instrumentation in Astronomy VI, D. L. Crawford, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 627, 773 (1986).

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Figures (10)

Fig. 1
Fig. 1

Optical diagram of the conventional WP, polarizing interferometer MCFTS.

Fig. 2
Fig. 2

Optical diagram of a novel type of MCFTS with a WP, polarizing interferometer.

Fig. 3
Fig. 3

Fundamental optics of the novel type of MCFTS: (a) top and side views of the trace of the rays separated with each of the optical components, in which the optical axis of each crystal is shown by an arrow or a circle; (b) direction of the polarization of the beam through each optical component. Broken arrows have the phase retardation compared with solid arrows caused by the phase-retarding plate.

Fig. 4
Fig. 4

Schematic diagram, showing the relative path difference among four interferograms separated by the MCFTS: (a) original interferogram; (b), (c) in-phase and antiphase interferograms corresponding to path difference ac in the original interferogram; (d), (e) antiphase and in-phase interferograms corresponding to path difference bd in the original interferogram; (f), (g) enhanced interferograms obtained by subtraction of an antiphase interferogram from an in-phase interferogram, where bc shows the overlapping part of the path difference.

Fig. 5
Fig. 5

Schematic diagram of the analytical method of connecting two interferograms, (a) A and (b) B, after phase adjustment by the use of overlapping parts bc in the interferograms. (c) Connected interferogram, utilizing overlapping parts bc and using the developed phase adjustment method, shown by the flow chart (d).

Fig. 6
Fig. 6

Optical diagram of (a) interferometer optics and (b) imaging optics of a trial manufacture of a novel type of MCFTS.

Fig. 7
Fig. 7

Two pairs of in-phase and antiphase interferograms obtained by the novel type of MCFTS for the cadmium emission lamp. The appropriate phase shift is given between the two pairs of interferograms.

Fig. 8
Fig. 8

(a) Interferogram of the mercury emission lamp obtained with the MCFTS. The interferogram is one of four interferograms, corrected by the use of the Forman method. (b) Power spectra around 577 and 579 nm, reconstructed by cosine fast Fourier transform from the interferogram of (a).

Fig. 9
Fig. 9

Resolving power of the manufactured MCFTS.

Fig. 10
Fig. 10

(a) Interferogram of mercury emission lamp obtained with the MCFTS. The interferogram is connected between two of the four interferograms by the use of the developed phase adjustment method and is corrected by the use of the Forman method. (b) Power spectra around 577 and 579 nm, reconstructed by cosine fast Fourier transform from the interferogram of (a).

Equations (15)

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M a ( x ) = - S a ( u ) exp [ - 2 π i u x - i ϕ a ( u ) ] d u = - S a ( u ) exp [ - i ϕ a ( u ) ] exp ( - 2 π i u x ) d u ,
M b ( x ) = - S b ( u ) exp [ - i ϕ b ( u ) ] exp ( - 2 π i u x ) d u ,
m a ( u ) = - M a ( x ) exp ( 2 π i u x ) d x = S a ( u ) exp [ - i ϕ a ( u ) ] ,
m b ( u ) = - M b ( x ) exp ( 2 π i u x ) d x = S b ( u ) exp [ - i ϕ b ( u ) ] .
S b ( u ) = α S a ( u ) ,
ϕ ( u ) = 2 π Δ x u ,
ϕ b ( u ) = ϕ a ( u ) - ϕ ( u ) .
M b ( x ) = α - S a ( u ) exp [ - i ϕ a ( u ) ] exp [ i ϕ ( u ) ] × exp ( - 2 π i u x ) d u .
f ( u ) = exp [ i ϕ ( u ) ] ,
F ( x ) = - exp [ i ϕ ( u ) ] exp ( - 2 π u x ) d u .
M b ( x ) = α M a ( x )     F ( x ) ,
F - 1 [ M a ( x ) M b ( x ) ] = m a ( u ) · m b * ( u ) = S a ( u ) exp [ - i ϕ a ( u ) ] · S b ( u ) exp [ i ϕ b ( u ) ] ,
m a ( u ) · m b * ( u ) = α [ S a ( u ) ] 2 exp [ - i ϕ ( u ) ] .
F * ( x ) = - exp [ - i ϕ ( u ) ] exp ( - 2 π u x ) d u .
M b ( x ) F * ( x ) = α - S a ( u ) exp [ - i ϕ a ( u ) + i ϕ ( u ) ] × exp [ - i ϕ ( u ) ] exp ( - 2 π i u x ) d u = α M a ( x ) .

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