## Chirped Fourier Spectroscopy. 2: Theory of Resolution and Contrast

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

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- 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]
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- 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.
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- 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.
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- In retrospect, the start and end positions of the mirror scan might have been shifted to the left.

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