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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 42, Iss. 6 — Feb. 20, 2003
  • pp: 1122–1131

Application of a Nonuniform Spectral Resampling Transform in Fourier-Transform Spectrometry

Edwin Sarkissian and Kevin W. Bowman  »View Author Affiliations


Applied Optics, Vol. 42, Issue 6, pp. 1122-1131 (2003)
http://dx.doi.org/10.1364/AO.42.001122


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Abstract

We describe a nonuniform spectral resampling transform (NUSRT) that resamples a frequency-scaled spectrum that has been measured by a Fourier-transform spectrometer (FTS). Frequency scaling of a spectrum can arise from measurements made with off-axis detectors and Doppler shifts induced by motion of a spaceborne FTS relative to an input radiation source. In addition, a spectrum may need to be rescaled in frequency to match spectral lines for applications such as the retrieval of atmospheric state parameters. The NUSRT is cast as a linear algebraic expression that relates a nonuniformly sampled interferogram to an input spectrum. A polynomial approximation is applied to this expression that reduces the inverse of the NUSRT to a series of Fourier transforms that can be implemented as fast Fourier transforms (FFTs). We show that this NUSRT algorithm requires on the order of 6<i>N</i> log <i>N</i> flops, which reduces the computational cost of rescaling by more than 1 order of magnitude compared with conventional FFT-based Shannon interpolation techniques while comparable accuracy is maintained.

© 2003 Optical Society of America

OCIS Codes
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(070.2590) Fourier optics and signal processing : ABCD transforms
(300.6300) Spectroscopy : Spectroscopy, Fourier transforms

Citation
Edwin Sarkissian and Kevin W. Bowman, "Application of a Nonuniform Spectral Resampling Transform in Fourier-Transform Spectrometry," Appl. Opt. 42, 1122-1131 (2003)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-42-6-1122

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