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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 68, Iss. 7 — Jul. 1, 1978
  • pp: 915–919

Nonlinear processing of the interferogram in Fourier spectroscopy

C. H. F. Velzel  »View Author Affiliations


JOSA, Vol. 68, Issue 7, pp. 915-919 (1978)
http://dx.doi.org/10.1364/JOSA.68.000915


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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

Citation
C. H. F. Velzel, "Nonlinear processing of the interferogram in Fourier spectroscopy," J. Opt. Soc. Am. 68, 915-919 (1978)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-68-7-915


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References

  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).

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