Application of a nonuniform spectral resampling transform in Fourier-transform spectrometry

Details Application of a nonuniform spectral resampling transform in Fourier-transform spectrometry Application of a nonuniform spectral resampling transform in Fourier-transform spectrometry

Feb 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003apopt..42.1122s&link_type=abstract

Applied Optics, Volume 42, Issue 6, pp. 1122-1131 (2003).

Physics

Optics

3

Fourier Transform Spectroscopy, Signal Processing, Fast Fourier Transforms, Spectral Analysis, Remote Sensing, Atmospheric Optics, Astronomical Telescopes

Scientific paper

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 6N log N 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.

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