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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 64, Iss. 4 — Apr. 1, 1974
  • pp: 485–494

Use of chirping to compensate for nonlinearities in Fourier spectroscopy

Thomas P. Sheahen  »View Author Affiliations


JOSA, Vol. 64, Issue 4, pp. 485-494 (1974)
http://dx.doi.org/10.1364/JOSA.64.000485


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Abstract

Chirping introduced into a Michelson interferometer permits correction for nonlinearities, distortion, and intermodulation in the final spectrum. This is because the false harmonics of each frequency carry the characteristic phase of the original frequency, whereas true spectral components at higher frequencies have their own characteristic phase. In an unchirped interferogram, there is no such distinguishing phase. This paper explains how the distinguishing phase occurs, presents two algorithms for carrying out the distortion correction when the form of the distortion is known, and displays results of correcting selected distorted experimental interferograms. This capability is a new advantage of chirping in Fourier spectroscopy.

Citation
Thomas P. Sheahen, "Use of chirping to compensate for nonlinearities in Fourier spectroscopy," J. Opt. Soc. Am. 64, 485-494 (1974)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-64-4-485


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References

  1. T. P. Sheahen, Chirped Michelson Spectroscopy, Bell Telephone Laboratories Report No. RPSR 71-9 (September 1971). Copies obtainable from Bell Laboratories or from Defense Documentation Center, Alexandria, Va. 22314.
  2. L. Mertz, Transformations in Optics (Wiley, New York, 1965).
  3. H. J. Landau, Bell Syst. Tech. J. 39, 351 (1960).
  4. P. Franklin, Differential Equations for Electrical Engineers (Wiley, New York, 1933), p. 275.
  5. G. F. Hohnstreiter, W. R. Howell, and T. P. Sheahen, in Aspen International Conference on Fourier Spectroscopy, 1970, Air Force Cambridge Research Laboratory Special Report No. 114 (1971), Ch. 24. Copies obtainable from National Technical Information Service, Springfield, Va.
  6. T. P. Sheahen, W. R. Howell, G. F. Hohnstreiter, and I. Coleman, in Ref. 5, Ch. 25.
  7. S. Goldman, Frequency Analysis, Modulation and Noise (McGraw-Hill, New York, 1948). Strictly speaking, the presence of harmonics falls within the category of intermodulation; but in this paper, such distortion is called detector nonlinearity and the term intermodulation is restricted to distortion that originates in the electronics, where neither phase nor amplitude can be calculated.
  8. J. F. McManamen (private communication).
  9. I. Coleman and L. Mertz, Experimental Study Program to Investigate Limits in Fourier Spectroscopy, Block Engineering, Report No. AFCRL-68-0050 (National Technical Information Service, Springfield, Va., 1968).
  10. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965). The discussion on p. 110 states the problem quite succinctly.
  11. J. W. Cooley and J. W. Tukey, J. Math. Comput. 19, 297 (1965).

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