Abstract

The transform method of Bennett and Rice is used to obtain the output spectrum of a nonlinearly processed interferogram. The interferogram of a multi-element spectrum is considered as band-limited Gaussian noise. The theory is applied to nonlinear processing in holographic Fourier spectroscopy and inverse Fourier spectroscopy and to digital processing in conventional Fourier spectroscopy.

© 1978 Optical Society of America

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  1. S. O. Rice, "Mathematical Analysis of Random Noise," Bell Syst. Tech. J. 23, 282 (1944).
  2. W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958).
  3. W. R. Bennett and S. O. Rice, Philos. Mag. 18, 422 (1934).
  4. A. Kozma, J. Opt. Soc. Am. 56, 493 (1966).
  5. H. Dammann, J. Opt. Soc. Am. 60, 1640 (1970); C. H. F. Velzel, Opt. Commun. 3, 133 (1971); J. W. Goodman and G. R. Knight, J. Opt. Soc. Am. 58, 1276 (1968); J. N. Tokarski, Appl. Opt. 8, 151 (1969).
  6. Hon-ming Lai and Shih-yu Feng, J. Opt. Soc. Am. 66, 761 (1976).
  7. A. Aspect, Thèse (Orsay, 1971).
  8. J. C. Perrin, Thèse (Orsay, 1974).
  9. C. H. F. Velzel, Philips Res. Rep. 27, 297 (1972).
  10. C. H. F. Velzel, Philips Res. Rep. 31, 97 (1976).
  11. See Ref. 2, p. 158.
  12. Lord Rayleigh, "Wave Theory of Light," Encyclopaedia Brittannica XXIV, 1888, Sec. 4.
  13. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves by Rough Surfaces (Pergamon, Oxford, 1963), Chap. 7.
  14. See, e.g., E. C. Titchmarch, Introduction to the Theory of Fourier Integrals (Oxford U.P., New York, 1937).
  15. M. J. Lighthill, An Introduction to Fourier Analysis and Generalized Functions (Columbia U.P., New York, 1959).
  16. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, 1968).
  17. C. H. F. Velzel, Opt. Acta 20, 585 (1973).
  18. M. Forman, J. Phys. 28, C2-58 (1967); see also G. A. Vanasse and H. Sakai, "Fourier Spectroscopy," in Progress in Optics VI, edited by E. Wolf (North-Holland, Amsterdam, 1967).
  19. M. de Haan and C. H. F. Veizel, "Nonlinear Frequency Mixing in Optical Video Recording," Philips Res. Rep. 32, 436 (1977).

1977 (1)

M. de Haan and C. H. F. Veizel, "Nonlinear Frequency Mixing in Optical Video Recording," Philips Res. Rep. 32, 436 (1977).

1944 (1)

S. O. Rice, "Mathematical Analysis of Random Noise," Bell Syst. Tech. J. 23, 282 (1944).

Abramowitz, M.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, 1968).

Aspect, A.

A. Aspect, Thèse (Orsay, 1971).

Beckmann, P.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves by Rough Surfaces (Pergamon, Oxford, 1963), Chap. 7.

Bennett, W. R.

W. R. Bennett and S. O. Rice, Philos. Mag. 18, 422 (1934).

Dammann, H.

H. Dammann, J. Opt. Soc. Am. 60, 1640 (1970); C. H. F. Velzel, Opt. Commun. 3, 133 (1971); J. W. Goodman and G. R. Knight, J. Opt. Soc. Am. 58, 1276 (1968); J. N. Tokarski, Appl. Opt. 8, 151 (1969).

Davenport, W. B.

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958).

de Haan, M.

M. de Haan and C. H. F. Veizel, "Nonlinear Frequency Mixing in Optical Video Recording," Philips Res. Rep. 32, 436 (1977).

Feng, Shih-yu

Hon-ming Lai and Shih-yu Feng, J. Opt. Soc. Am. 66, 761 (1976).

Forman, M.

M. Forman, J. Phys. 28, C2-58 (1967); see also G. A. Vanasse and H. Sakai, "Fourier Spectroscopy," in Progress in Optics VI, edited by E. Wolf (North-Holland, Amsterdam, 1967).

Kozma, A.

A. Kozma, J. Opt. Soc. Am. 56, 493 (1966).

Lai, Hon-ming

Hon-ming Lai and Shih-yu Feng, J. Opt. Soc. Am. 66, 761 (1976).

Lighthill, M. J.

M. J. Lighthill, An Introduction to Fourier Analysis and Generalized Functions (Columbia U.P., New York, 1959).

Perrin, J. C.

J. C. Perrin, Thèse (Orsay, 1974).

Rayleigh, Lord

Lord Rayleigh, "Wave Theory of Light," Encyclopaedia Brittannica XXIV, 1888, Sec. 4.

Rice, S. O.

S. O. Rice, "Mathematical Analysis of Random Noise," Bell Syst. Tech. J. 23, 282 (1944).

W. R. Bennett and S. O. Rice, Philos. Mag. 18, 422 (1934).

Root, W. L.

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958).

Spizzichino, A.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves by Rough Surfaces (Pergamon, Oxford, 1963), Chap. 7.

Stegun, I.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, 1968).

Titchmarch, E. C.

See, e.g., E. C. Titchmarch, Introduction to the Theory of Fourier Integrals (Oxford U.P., New York, 1937).

Veizel, C. H. F.

M. de Haan and C. H. F. Veizel, "Nonlinear Frequency Mixing in Optical Video Recording," Philips Res. Rep. 32, 436 (1977).

Velzel, C. H. F.

C. H. F. Velzel, Philips Res. Rep. 31, 97 (1976).

C. H. F. Velzel, Opt. Acta 20, 585 (1973).

C. H. F. Velzel, Philips Res. Rep. 27, 297 (1972).

Bell Syst. Tech. J. (1)

S. O. Rice, "Mathematical Analysis of Random Noise," Bell Syst. Tech. J. 23, 282 (1944).

Philips Res. Rep. (1)

M. de Haan and C. H. F. Veizel, "Nonlinear Frequency Mixing in Optical Video Recording," Philips Res. Rep. 32, 436 (1977).

Other (17)

W. B. Davenport and W. L. Root, Random Signals and Noise (McGraw-Hill, New York, 1958).

W. R. Bennett and S. O. Rice, Philos. Mag. 18, 422 (1934).

A. Kozma, J. Opt. Soc. Am. 56, 493 (1966).

H. Dammann, J. Opt. Soc. Am. 60, 1640 (1970); C. H. F. Velzel, Opt. Commun. 3, 133 (1971); J. W. Goodman and G. R. Knight, J. Opt. Soc. Am. 58, 1276 (1968); J. N. Tokarski, Appl. Opt. 8, 151 (1969).

Hon-ming Lai and Shih-yu Feng, J. Opt. Soc. Am. 66, 761 (1976).

A. Aspect, Thèse (Orsay, 1971).

J. C. Perrin, Thèse (Orsay, 1974).

C. H. F. Velzel, Philips Res. Rep. 27, 297 (1972).

C. H. F. Velzel, Philips Res. Rep. 31, 97 (1976).

See Ref. 2, p. 158.

Lord Rayleigh, "Wave Theory of Light," Encyclopaedia Brittannica XXIV, 1888, Sec. 4.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves by Rough Surfaces (Pergamon, Oxford, 1963), Chap. 7.

See, e.g., E. C. Titchmarch, Introduction to the Theory of Fourier Integrals (Oxford U.P., New York, 1937).

M. J. Lighthill, An Introduction to Fourier Analysis and Generalized Functions (Columbia U.P., New York, 1959).

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, 1968).

C. H. F. Velzel, Opt. Acta 20, 585 (1973).

M. Forman, J. Phys. 28, C2-58 (1967); see also G. A. Vanasse and H. Sakai, "Fourier Spectroscopy," in Progress in Optics VI, edited by E. Wolf (North-Holland, Amsterdam, 1967).

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