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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 14, Iss. 4 — Apr. 1, 1975
  • pp: 1004–1012

Chirped Fourier Spectroscopy. 2: Theory of Resolution and Contrast

Thomas P. Sheahen  »View Author Affiliations


Applied Optics, Vol. 14, Issue 4, pp. 1004-1012 (1975)
http://dx.doi.org/10.1364/AO.14.001004


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Abstract

When applied to a Fourier spectrometer, chirping raises questions about the resolution and contrast of the device. A theory is presented to show how the nonlinear phase affects the instrument profile and resolution; the penalty for chirping a high resolution interferometer is much smaller than had been believed. An algorithm is presented for recovering contrast; it is shown that the fast Fourier transform is still usable, allowing realization of full contrast. Systems bearing a residual nonlinear phase dispersion (accidental chirping) can take advantage of this theory.

© 1975 Optical Society of America

History
Original Manuscript: August 19, 1974
Published: April 1, 1975

Citation
Thomas P. Sheahen, "Chirped Fourier Spectroscopy. 2: Theory of Resolution and Contrast," Appl. Opt. 14, 1004-1012 (1975)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-14-4-1004


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References

  1. J. W. Cooley, J. W. Tukey, Math. Comput. 19, 297 (1965). [CrossRef]
  2. J. Connes, Rev. Opt. 40, 45, 116, 171, 231 (1961).
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  5. J. Connes, Aspen International Conference on Fourier Spectroscopy, 1970 (Air Force Cambridge Research Laboratory Special Report No. 114, January5, 1971), Chap. 6.
  6. T. P. Sheahen, Appl. Opt. 13, 2907 (1974). [CrossRef] [PubMed]
  7. L. Mertz, Transformations in Optics (Wiley, New York, 1965).
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  13. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic Press, New York, 1972).
  14. Should the detector begin to saturate under high intensity, D must be written as D(ω,I), in which case we have an intractable integral equation for all but the simplest spectra. For a discussion of ways to treat saturation in a chirped interferometer, see T. P. Sheahen, J. Opt. Soc. Am. 64, 485 (1974). [CrossRef]
  15. The use of aliasing has its own difficulties. See D. A. Walmsley, T. A. Clark, R. E. Jennings, Appl. Opt. 11, 1148 (1972). [CrossRef] [PubMed]
  16. An equivalent approach is to add N extra zeros on the right of the digitized interferogram and perform a FFT to obtain the N nonzero real spectral points, ignoring the N imaginary points. This second method uses more computer core.
  17. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).
  18. L. Mertz, Infrared Phys. 7, 17 (1967). [CrossRef]
  19. I. Coleman, L. Mertz, “Experimental Study Program to Investigate Limits in Fourier Spectroscopy,” Block Engineering, Report AFCRL-68-0050 (January1968).
  20. Because the frequency dependence of A in Eq. (14) appears only parametrically through x0, it is tempting to invoke the Fourier shift theorem and the convolution theorem to manipulate Eq. (14) into a form suitable for a Fourier transform. However, the fixed upper limit of L prevents this because the compensating apodizer A[x − x0(ωj)] is not simply a sliding boxcar of constant length and shifting center; it is a boxcar that decreases in length as the phase delay [and x0(ωj)] increases.
  21. J. M. Dowling, Ref. 5, Chap. 4.
  22. G. F. Hohnstreiter, W. R. Howell, T. P. Sheahen, Ref. 5, Chap. 24.
  23. T. P. Sheahen, W. R. Howell, G. F. Hohnstreiter, I. Coleman, Ref. 5, Chap. 25.
  24. C. Flammer, Spheroidal Wave Functions (Stanford University Press, 1957).
  25. A. M. Despain, J. W. Bell, Ref. 5, Chap. 41.
  26. In retrospect, the start and end positions of the mirror scan might have been shifted to the left.

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