Abstract

This paper is concerned with the development of Fourier transform spectroscopy from its beginnings in Michelson’s visibility technique through the present day application using modern digital computers. Methods used in maximizing the efficiency of the computation, as well as the interferometer, are discussed. Means of finding the Fourier transform other than by digital computer are mentioned, and currently available commercial instruments are named.

© 1966 Optical Society of America

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  1. P. B. Fellgett, thesis, U. of Cambridge (1951).
  2. H. Fizeau, Ann. Chim. Phys. (3), 66, 429 (1862).
  3. A. A. Michelson, Phil. Mag. (5), 31, 256 (1891).
  4. M. Born, E. Wolf, Principles of Optics, (The Macmillan Co., New York, 1964), 2nd ed., p. 320 ff.
  5. Rayleigh, Phil. Mag. (5), 34, 407 (1892).
  6. H. Rubens, R. W. Wood, Phil. Mag. 21, 249 (1911).
  7. P. Jacquinot, C. Dufour, J. Rech. du Centre Nat. Rech. Sci. Lab. Bellevue (Paris) 6, 91 (1948).
  8. H. A. Gebbie, G. A. Vanasse, J. Strong, J. Opt. Soc. Am. 46, 377 (1956).
  9. H. A. Gebbie, Phys. Rev. 107, 1194 (1957).
    [CrossRef]
  10. J. Phys. Radium 19, 187 (1958) contains the papers of the 1957 C.N.R.S. Bellevue, Colloquium. They will not be individually referenced.
  11. B. N. Grechushnikov, G. I. Distler, I. P. Petrov, Soviet Phys.-Cryst. 8, 367 (1963).
  12. J. Connes, Rev. Opt. 40, 45, 116, 171, 231 (1961). An English translation is available to Government contractors as a Navy publication NAV-WEPS Rept. No. 8099, NOTS TP 3157, published by the U.S. Naval Ordnance Test Station, China Lake, California.
  13. Rayleigh, Phil. Mag. (6), 24, 864 (1912).
  14. G. A. Vanasse, J. Opt. Soc. Am. 52, 472 (1962).
    [CrossRef]
  15. J. Strong, G. A. Vanasse, J. Opt. Soc. Am. 49, 844 (1959).
    [CrossRef]
  16. P. F. Parshin, Opt. Spectry. 14, 207 (1963).
  17. P. F. Parshin, Opt. Spectry. 14, 156 (1963).
  18. T. Williams, J. Opt. Soc. Am. 50, 1159 (1960).
    [CrossRef]
  19. J. Dowling, J. Opt. Soc. Am. 54, 663 (1964).
    [CrossRef]
  20. J. E. Chamberlain, J. E. Gibbs, H. A. Gebbie, Nature 198, 874 (1963).
    [CrossRef]
  21. J. Connes, V. Nozal, J. Phys. Radium 22, 359 (1961).
    [CrossRef]
  22. M. Forman, W. H. Steel, G. A. Vanasse, J. Opt. Soc. Am. 56, 59 (1966).
    [CrossRef]
  23. A. Filler, J. Opt. Soc. Am. 54, 762 (1964).
    [CrossRef]
  24. P. F. Parshin, Opt. Spectry. 16, 275 (1964).
  25. B. A. Kiselev, P. F. Parshin, Opt. Spectry. 12, 169 (1962).
  26. D. R. Lumb, G. C. Augason, in Infrared Spectra of Astronomical Bodies (Proc. 12th Intern. Astrophys. Symp., Liege, June 1963) (Institute d’Astrophysique, Cointe-Sclessin, Belgium, 1964), p. 132.
  27. J. Strong, G. A. Vanasse, J. Opt. Soc. Am. 50, 113 (1960).
    [CrossRef]
  28. K. F. Renk, L. Genzel, Appl. Opt. 1, 643 (1962).
    [CrossRef]
  29. P. L. Richards, J. Opt. Soc. Am. 54, 1474 (1964).
    [CrossRef]
  30. L. Mertz, in Infrared Spectra of Astronomical Bodies (Proc. 12th Intern. Astrophys. Symp., Liege, June 1963 (Institute d’Astrophysique, Cointe-Sclessin, Belgium, 1964), p. 120.
  31. H. P. Gush, H. L. Buijs, Can. J. Phys. 42, 1037 (1964).
    [CrossRef]
  32. J. Connes, H. P. Gush, J. Phys. Radium 20, 915 (1959).
    [CrossRef]
  33. P. Connes, Rev. Opt. 35, 37 (1956).
  34. L. Mertz, “Heterodyne Interference Spectroscopy”, presented to I.C.O., Conference, Stockholm, 1959.
  35. P. Bouchariene, P. Connes, J. Phys. Radium 24, 134 (1963).
  36. H. Yoshinaga, Appl. Opt. 3, 805 (1964).
    [CrossRef]
  37. R. V. Alves, Mellon Institute Symposium on Far Infrared Transpose Spectroscopy, Pittsburgh (June 1965).
  38. J. Connes, P. Connes, “Near Infrared Planetary Spectra by Fourier Spectroscopy” (private communication).
  39. L. Mertz, Transformations in Optics (John Wiley & Sons, Inc., New York1965), pp. 54 ff.
  40. E. E. Bell (private communication).
  41. W. Sinton, J. Quant. Spectry. Radiative Transfer 3, 551 (1963).
    [CrossRef]
  42. R. Beer, Jet Propulsion Laboratory, Pasadena, Calif. (private communication).
  43. G. Roland “Spectroscopie par le transformation du fourier”, thesis, U. of Liege, Liege, Belgium (April, 1965).

1966 (1)

1964 (6)

1963 (6)

B. N. Grechushnikov, G. I. Distler, I. P. Petrov, Soviet Phys.-Cryst. 8, 367 (1963).

P. F. Parshin, Opt. Spectry. 14, 207 (1963).

P. F. Parshin, Opt. Spectry. 14, 156 (1963).

J. E. Chamberlain, J. E. Gibbs, H. A. Gebbie, Nature 198, 874 (1963).
[CrossRef]

P. Bouchariene, P. Connes, J. Phys. Radium 24, 134 (1963).

W. Sinton, J. Quant. Spectry. Radiative Transfer 3, 551 (1963).
[CrossRef]

1962 (3)

1961 (2)

J. Connes, Rev. Opt. 40, 45, 116, 171, 231 (1961). An English translation is available to Government contractors as a Navy publication NAV-WEPS Rept. No. 8099, NOTS TP 3157, published by the U.S. Naval Ordnance Test Station, China Lake, California.

J. Connes, V. Nozal, J. Phys. Radium 22, 359 (1961).
[CrossRef]

1960 (2)

1959 (2)

J. Strong, G. A. Vanasse, J. Opt. Soc. Am. 49, 844 (1959).
[CrossRef]

J. Connes, H. P. Gush, J. Phys. Radium 20, 915 (1959).
[CrossRef]

1958 (1)

J. Phys. Radium 19, 187 (1958) contains the papers of the 1957 C.N.R.S. Bellevue, Colloquium. They will not be individually referenced.

1957 (1)

H. A. Gebbie, Phys. Rev. 107, 1194 (1957).
[CrossRef]

1956 (2)

H. A. Gebbie, G. A. Vanasse, J. Strong, J. Opt. Soc. Am. 46, 377 (1956).

P. Connes, Rev. Opt. 35, 37 (1956).

1948 (1)

P. Jacquinot, C. Dufour, J. Rech. du Centre Nat. Rech. Sci. Lab. Bellevue (Paris) 6, 91 (1948).

1912 (1)

Rayleigh, Phil. Mag. (6), 24, 864 (1912).

1911 (1)

H. Rubens, R. W. Wood, Phil. Mag. 21, 249 (1911).

1892 (1)

Rayleigh, Phil. Mag. (5), 34, 407 (1892).

1891 (1)

A. A. Michelson, Phil. Mag. (5), 31, 256 (1891).

1862 (1)

H. Fizeau, Ann. Chim. Phys. (3), 66, 429 (1862).

Alves, R. V.

R. V. Alves, Mellon Institute Symposium on Far Infrared Transpose Spectroscopy, Pittsburgh (June 1965).

Augason, G. C.

D. R. Lumb, G. C. Augason, in Infrared Spectra of Astronomical Bodies (Proc. 12th Intern. Astrophys. Symp., Liege, June 1963) (Institute d’Astrophysique, Cointe-Sclessin, Belgium, 1964), p. 132.

Beer, R.

R. Beer, Jet Propulsion Laboratory, Pasadena, Calif. (private communication).

Bell, E. E.

E. E. Bell (private communication).

Born, M.

M. Born, E. Wolf, Principles of Optics, (The Macmillan Co., New York, 1964), 2nd ed., p. 320 ff.

Bouchariene, P.

P. Bouchariene, P. Connes, J. Phys. Radium 24, 134 (1963).

Buijs, H. L.

H. P. Gush, H. L. Buijs, Can. J. Phys. 42, 1037 (1964).
[CrossRef]

Chamberlain, J. E.

J. E. Chamberlain, J. E. Gibbs, H. A. Gebbie, Nature 198, 874 (1963).
[CrossRef]

Connes, J.

J. Connes, V. Nozal, J. Phys. Radium 22, 359 (1961).
[CrossRef]

J. Connes, Rev. Opt. 40, 45, 116, 171, 231 (1961). An English translation is available to Government contractors as a Navy publication NAV-WEPS Rept. No. 8099, NOTS TP 3157, published by the U.S. Naval Ordnance Test Station, China Lake, California.

J. Connes, H. P. Gush, J. Phys. Radium 20, 915 (1959).
[CrossRef]

J. Connes, P. Connes, “Near Infrared Planetary Spectra by Fourier Spectroscopy” (private communication).

Connes, P.

P. Bouchariene, P. Connes, J. Phys. Radium 24, 134 (1963).

P. Connes, Rev. Opt. 35, 37 (1956).

J. Connes, P. Connes, “Near Infrared Planetary Spectra by Fourier Spectroscopy” (private communication).

Distler, G. I.

B. N. Grechushnikov, G. I. Distler, I. P. Petrov, Soviet Phys.-Cryst. 8, 367 (1963).

Dowling, J.

Dufour, C.

P. Jacquinot, C. Dufour, J. Rech. du Centre Nat. Rech. Sci. Lab. Bellevue (Paris) 6, 91 (1948).

Fellgett, P. B.

P. B. Fellgett, thesis, U. of Cambridge (1951).

Filler, A.

Fizeau, H.

H. Fizeau, Ann. Chim. Phys. (3), 66, 429 (1862).

Forman, M.

Gebbie, H. A.

J. E. Chamberlain, J. E. Gibbs, H. A. Gebbie, Nature 198, 874 (1963).
[CrossRef]

H. A. Gebbie, Phys. Rev. 107, 1194 (1957).
[CrossRef]

H. A. Gebbie, G. A. Vanasse, J. Strong, J. Opt. Soc. Am. 46, 377 (1956).

Genzel, L.

Gibbs, J. E.

J. E. Chamberlain, J. E. Gibbs, H. A. Gebbie, Nature 198, 874 (1963).
[CrossRef]

Grechushnikov, B. N.

B. N. Grechushnikov, G. I. Distler, I. P. Petrov, Soviet Phys.-Cryst. 8, 367 (1963).

Gush, H. P.

H. P. Gush, H. L. Buijs, Can. J. Phys. 42, 1037 (1964).
[CrossRef]

J. Connes, H. P. Gush, J. Phys. Radium 20, 915 (1959).
[CrossRef]

Jacquinot, P.

P. Jacquinot, C. Dufour, J. Rech. du Centre Nat. Rech. Sci. Lab. Bellevue (Paris) 6, 91 (1948).

Kiselev, B. A.

B. A. Kiselev, P. F. Parshin, Opt. Spectry. 12, 169 (1962).

Lumb, D. R.

D. R. Lumb, G. C. Augason, in Infrared Spectra of Astronomical Bodies (Proc. 12th Intern. Astrophys. Symp., Liege, June 1963) (Institute d’Astrophysique, Cointe-Sclessin, Belgium, 1964), p. 132.

Mertz, L.

L. Mertz, Transformations in Optics (John Wiley & Sons, Inc., New York1965), pp. 54 ff.

L. Mertz, in Infrared Spectra of Astronomical Bodies (Proc. 12th Intern. Astrophys. Symp., Liege, June 1963 (Institute d’Astrophysique, Cointe-Sclessin, Belgium, 1964), p. 120.

L. Mertz, “Heterodyne Interference Spectroscopy”, presented to I.C.O., Conference, Stockholm, 1959.

Michelson, A. A.

A. A. Michelson, Phil. Mag. (5), 31, 256 (1891).

Nozal, V.

J. Connes, V. Nozal, J. Phys. Radium 22, 359 (1961).
[CrossRef]

Parshin, P. F.

P. F. Parshin, Opt. Spectry. 16, 275 (1964).

P. F. Parshin, Opt. Spectry. 14, 156 (1963).

P. F. Parshin, Opt. Spectry. 14, 207 (1963).

B. A. Kiselev, P. F. Parshin, Opt. Spectry. 12, 169 (1962).

Petrov, I. P.

B. N. Grechushnikov, G. I. Distler, I. P. Petrov, Soviet Phys.-Cryst. 8, 367 (1963).

Rayleigh,

Rayleigh, Phil. Mag. (6), 24, 864 (1912).

Rayleigh, Phil. Mag. (5), 34, 407 (1892).

Renk, K. F.

Richards, P. L.

Roland, G.

G. Roland “Spectroscopie par le transformation du fourier”, thesis, U. of Liege, Liege, Belgium (April, 1965).

Rubens, H.

H. Rubens, R. W. Wood, Phil. Mag. 21, 249 (1911).

Sinton, W.

W. Sinton, J. Quant. Spectry. Radiative Transfer 3, 551 (1963).
[CrossRef]

Steel, W. H.

Strong, J.

Vanasse, G. A.

Williams, T.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, (The Macmillan Co., New York, 1964), 2nd ed., p. 320 ff.

Wood, R. W.

H. Rubens, R. W. Wood, Phil. Mag. 21, 249 (1911).

Yoshinaga, H.

Ann. Chim. Phys. (3) (1)

H. Fizeau, Ann. Chim. Phys. (3), 66, 429 (1862).

Appl. Opt. (2)

Can. J. Phys. (1)

H. P. Gush, H. L. Buijs, Can. J. Phys. 42, 1037 (1964).
[CrossRef]

J. Opt. Soc. Am. (9)

J. Phys. Radium (4)

J. Phys. Radium 19, 187 (1958) contains the papers of the 1957 C.N.R.S. Bellevue, Colloquium. They will not be individually referenced.

J. Connes, V. Nozal, J. Phys. Radium 22, 359 (1961).
[CrossRef]

J. Connes, H. P. Gush, J. Phys. Radium 20, 915 (1959).
[CrossRef]

P. Bouchariene, P. Connes, J. Phys. Radium 24, 134 (1963).

J. Quant. Spectry. Radiative Transfer (1)

W. Sinton, J. Quant. Spectry. Radiative Transfer 3, 551 (1963).
[CrossRef]

J. Rech. du Centre Nat. Rech. Sci. Lab. Bellevue (Paris) (1)

P. Jacquinot, C. Dufour, J. Rech. du Centre Nat. Rech. Sci. Lab. Bellevue (Paris) 6, 91 (1948).

Nature (1)

J. E. Chamberlain, J. E. Gibbs, H. A. Gebbie, Nature 198, 874 (1963).
[CrossRef]

Opt. Spectry. (4)

P. F. Parshin, Opt. Spectry. 14, 207 (1963).

P. F. Parshin, Opt. Spectry. 14, 156 (1963).

P. F. Parshin, Opt. Spectry. 16, 275 (1964).

B. A. Kiselev, P. F. Parshin, Opt. Spectry. 12, 169 (1962).

Phil. Mag. (1)

H. Rubens, R. W. Wood, Phil. Mag. 21, 249 (1911).

Phil. Mag. (5) (2)

A. A. Michelson, Phil. Mag. (5), 31, 256 (1891).

Rayleigh, Phil. Mag. (5), 34, 407 (1892).

Phil. Mag. (6) (1)

Rayleigh, Phil. Mag. (6), 24, 864 (1912).

Phys. Rev. (1)

H. A. Gebbie, Phys. Rev. 107, 1194 (1957).
[CrossRef]

Rev. Opt. (2)

J. Connes, Rev. Opt. 40, 45, 116, 171, 231 (1961). An English translation is available to Government contractors as a Navy publication NAV-WEPS Rept. No. 8099, NOTS TP 3157, published by the U.S. Naval Ordnance Test Station, China Lake, California.

P. Connes, Rev. Opt. 35, 37 (1956).

Soviet Phys.-Cryst. (1)

B. N. Grechushnikov, G. I. Distler, I. P. Petrov, Soviet Phys.-Cryst. 8, 367 (1963).

Other (11)

D. R. Lumb, G. C. Augason, in Infrared Spectra of Astronomical Bodies (Proc. 12th Intern. Astrophys. Symp., Liege, June 1963) (Institute d’Astrophysique, Cointe-Sclessin, Belgium, 1964), p. 132.

L. Mertz, in Infrared Spectra of Astronomical Bodies (Proc. 12th Intern. Astrophys. Symp., Liege, June 1963 (Institute d’Astrophysique, Cointe-Sclessin, Belgium, 1964), p. 120.

P. B. Fellgett, thesis, U. of Cambridge (1951).

M. Born, E. Wolf, Principles of Optics, (The Macmillan Co., New York, 1964), 2nd ed., p. 320 ff.

L. Mertz, “Heterodyne Interference Spectroscopy”, presented to I.C.O., Conference, Stockholm, 1959.

R. V. Alves, Mellon Institute Symposium on Far Infrared Transpose Spectroscopy, Pittsburgh (June 1965).

J. Connes, P. Connes, “Near Infrared Planetary Spectra by Fourier Spectroscopy” (private communication).

L. Mertz, Transformations in Optics (John Wiley & Sons, Inc., New York1965), pp. 54 ff.

E. E. Bell (private communication).

R. Beer, Jet Propulsion Laboratory, Pasadena, Calif. (private communication).

G. Roland “Spectroscopie par le transformation du fourier”, thesis, U. of Liege, Liege, Belgium (April, 1965).

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Equations (9)

Equations on this page are rendered with MathJax. Learn more.

I ( x ) = 0 G ( ν ) cos 2 π ν x d ν .
G ( ν ) = 0 L I ( x ) cos 2 π ν x d x .
S 0 ( ν ) = L [ sin ( 2 π ν L ) / 2 π ν L ] = L sinc ( 2 π ν L ) .
A 1 = 1 - x / L ,             x L ,
A 2 = [ 1 - ( x / L ) 2 ] 2 ,             x L ,
S 1 = ( L / 4 ) sinc 2 ( π ν L ) ,
S 2 = J 5 / 2 ( 2 π ν L ) ( 2 π ν L ) 5 / 2 .
ν = ν ( 1 - Ω / 4 π ) .
ϕ ( ν ) = arctan [ S ( ν ) / C ( ν ) ] ,

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