Abstract

The Multiplex Fabry–Perot Interferometer (MFPI) is a unique instrument, incorporating the wide spectral-bandwidth capability of the Michelson interferometer with the small size and high resolution of the Fabry–Perot interferometer. The MFPI is, structurally, a standard Fabry–Perot in which the scanning distance is allowed to be very large, of the order of centimeters. The signal recorded through this distance is Fourier transformed as would be the interferogram produced by a Michelson interferometer. The result is a spectrum containing very high-resolution information over a moderately large optical bandwidth. The MFPI is much smaller than a Michelson producing the same resolution and covers a much broader bandwidth than a Fabry–Perot used in the usual fashion. We present a basic description of the operating theory for the MFPI in terms familiar to the Michelson spectroscopist.

© 1995 Optical Society of America

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References

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  1. V. G. Cooper, “Analysis of Fabry–Perot interferograms by means of their Fourier transforms,” Appl. Opt. 10, 525–530 (1971).
    [CrossRef] [PubMed]
  2. K. Yoshihara, A. Kitade, “Far infra-red spectroscopy by the Fabry–Perot interferometer,” Opt. Acta 26, 1049–1056 (1979).
    [CrossRef]
  3. K. Yoshihara, A. Kitade, “Far infra-red spectroscopy by the Fabry–Perot interferometer II,” Jpn. J. Appl. Phys. 18, 2327–2328 (1979).
    [CrossRef]
  4. K. Yoshihara, A. Kitade, K. Okada, “Far infra-red spectroscopy by the Fabry–Perot interferometer III,” Jpn. J. Appl. Phys. 19, 2523–2524 (1980).
    [CrossRef]
  5. T. Aoki, “High resolution spectrum by the inverse transformation of the Fabry–Perot interferogram,” Appl. Opt. 29, 2364–2365 (1990).
    [CrossRef] [PubMed]
  6. P. B. Hays, H. E. Snell, “Multiplex Fabry–Perot interferometer,” Appl. Opt. 30, 3108–3113 (1990).
    [CrossRef]
  7. H. E. Snell, W. B. Cook, P. B. Hays, “Multiplex Fabry–Perot interferometer: II. Laboratory prototype,” Appl. Opt. 34, 5268–5277 (1995).
    [CrossRef] [PubMed]
  8. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. 7, p. 364.
  9. J. Chamberlain, Principles of Interferometric Spectroscopy (Wiley, New York, 1979), Chap. 1, pp. 5–8.
  10. J. Chamberlain, Principles of Interferometric Spectroscopy (Wiley, New York, 1979), Chap. 6, pp. 145–150.
  11. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), Chap. 12, pp. 159–166.

1995 (1)

1990 (2)

1980 (1)

K. Yoshihara, A. Kitade, K. Okada, “Far infra-red spectroscopy by the Fabry–Perot interferometer III,” Jpn. J. Appl. Phys. 19, 2523–2524 (1980).
[CrossRef]

1979 (2)

K. Yoshihara, A. Kitade, “Far infra-red spectroscopy by the Fabry–Perot interferometer,” Opt. Acta 26, 1049–1056 (1979).
[CrossRef]

K. Yoshihara, A. Kitade, “Far infra-red spectroscopy by the Fabry–Perot interferometer II,” Jpn. J. Appl. Phys. 18, 2327–2328 (1979).
[CrossRef]

1971 (1)

Aoki, T.

Bell, R. J.

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), Chap. 12, pp. 159–166.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. 7, p. 364.

Chamberlain, J.

J. Chamberlain, Principles of Interferometric Spectroscopy (Wiley, New York, 1979), Chap. 1, pp. 5–8.

J. Chamberlain, Principles of Interferometric Spectroscopy (Wiley, New York, 1979), Chap. 6, pp. 145–150.

Cook, W. B.

Cooper, V. G.

Hays, P. B.

Kitade, A.

K. Yoshihara, A. Kitade, K. Okada, “Far infra-red spectroscopy by the Fabry–Perot interferometer III,” Jpn. J. Appl. Phys. 19, 2523–2524 (1980).
[CrossRef]

K. Yoshihara, A. Kitade, “Far infra-red spectroscopy by the Fabry–Perot interferometer II,” Jpn. J. Appl. Phys. 18, 2327–2328 (1979).
[CrossRef]

K. Yoshihara, A. Kitade, “Far infra-red spectroscopy by the Fabry–Perot interferometer,” Opt. Acta 26, 1049–1056 (1979).
[CrossRef]

Okada, K.

K. Yoshihara, A. Kitade, K. Okada, “Far infra-red spectroscopy by the Fabry–Perot interferometer III,” Jpn. J. Appl. Phys. 19, 2523–2524 (1980).
[CrossRef]

Snell, H. E.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. 7, p. 364.

Yoshihara, K.

K. Yoshihara, A. Kitade, K. Okada, “Far infra-red spectroscopy by the Fabry–Perot interferometer III,” Jpn. J. Appl. Phys. 19, 2523–2524 (1980).
[CrossRef]

K. Yoshihara, A. Kitade, “Far infra-red spectroscopy by the Fabry–Perot interferometer II,” Jpn. J. Appl. Phys. 18, 2327–2328 (1979).
[CrossRef]

K. Yoshihara, A. Kitade, “Far infra-red spectroscopy by the Fabry–Perot interferometer,” Opt. Acta 26, 1049–1056 (1979).
[CrossRef]

Appl. Opt. (4)

Jpn. J. Appl. Phys. (2)

K. Yoshihara, A. Kitade, “Far infra-red spectroscopy by the Fabry–Perot interferometer II,” Jpn. J. Appl. Phys. 18, 2327–2328 (1979).
[CrossRef]

K. Yoshihara, A. Kitade, K. Okada, “Far infra-red spectroscopy by the Fabry–Perot interferometer III,” Jpn. J. Appl. Phys. 19, 2523–2524 (1980).
[CrossRef]

Opt. Acta (1)

K. Yoshihara, A. Kitade, “Far infra-red spectroscopy by the Fabry–Perot interferometer,” Opt. Acta 26, 1049–1056 (1979).
[CrossRef]

Other (4)

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. 7, p. 364.

J. Chamberlain, Principles of Interferometric Spectroscopy (Wiley, New York, 1979), Chap. 1, pp. 5–8.

J. Chamberlain, Principles of Interferometric Spectroscopy (Wiley, New York, 1979), Chap. 6, pp. 145–150.

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), Chap. 12, pp. 159–166.

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Figures (4)

Fig. 1
Fig. 1

Multiple reflections occurring inside a Fabry–Perot étalon. The incident radiation is shown impinging on the plates at an angle to allow separation of the reflecting beams. The plate spacing is t, the refractive index is μ, and the OPD between consecutive beams is x.

Fig. 2
Fig. 2

Calculated MFPI interferogram produced by a Gaussian-shaped input spectrum with center wave number 2600 cm−1 and HWHM = 30 cm−1. The plate reflectivity is 0.9.

Fig. 3
Fig. 3

Comparison of the input Gaussian spectrum with the Airy transfer function at three values for the étalon plate spacing: (a) FSR equal to 4 times the Gaussian HWHM, (b) Airy function for a FSR equal to twice the HWHM, (c) Airy function for a FSR equal to the HWHM. For the example spectrum from Fig. 2, the OPD x for (a), (b), and (c) would be 0.0083 cm, 0.0166 cm and 0.0333 cm, respectively.

Fig. 4
Fig. 4

Portion of the calculated spectrum derived from a Fourier transform of the MFPI interferogram shown in Fig. 2. The interferogram was truncated at x = 0.0075 cm. Note that the two lowest harmonics are not well resolved, but the higher harmonics are clearly Gaussian.

Equations (17)

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N ( t ) = 1 R 1 + R 0 B ( σ ) [ 1 + 2 n = 1 R n cos ( 4 π n μ t σ ) ] d σ ,
N ( x ) = 0 B ( σ ) d σ + 2 0 B ( σ ) n = 1 R n cos ( 2 π n σ x ) d σ .
I ( x ) = n 1 R n n 0 B ( σ n ) cos ( 2 π x σ ) d σ .
[ I ( x ) ] = n = 1 R n n B ( σ / n ) .
B c ( σ / n ) = δ ( σ / n σ 0 ) = δ ( σ n σ 0 ) .
B ( σ ) = exp [ ( σ σ 0 ) 2 σ H 2 ] = exp ( σ 2 σ H 2 ) * δ ( σ σ 0 ) ,
B c ( σ ) = n = 1 R n n exp ( σ 2 n 2 σ H 2 ) * δ ( σ n σ 0 ) .
n σ high < ( n + 1 ) σ low ,
n max σ low σ high σ low .
rect ( x / D ) = { 1 | x | D 0 | x | > D ,
I m ( x ) = I ( x ) rect ( x / D ) ,
B tc ( σ ) = n = 1 R n n B ( σ / n ) * 2 D sinc ( 2 D σ ) .
σ Nyq = 1 2 b ,
b = 1 2 n h σ high .
I m ( x ) = I ( x ) [ rect ( x / D ) rect ( x / d ) ] ,
B c ( σ ) = 2 D n = 1 R n n B ( σ / n ) * sinc ( 2 D σ ) 2 d n 1 R 2 n B ( σ / n ) * sinc ( 2 d σ ) .
S N n = j k R n n [ ( k j ) + 1 ] 1 / 2 .

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