Drive nonlinearities: their effects in Fourier spectroscopy.
Presented is a comprehensive analysis of spectrum errors due to drive nonlinearities in a Michelson interferometer. The fringe-reference sampling case is treated for both repeatable and random nonlinearities. Partial results are given for the equal-time sampling case. The derived equations for the actual (or meansquare) spectrum error can be evaluated numerically for any choice of drive speed variation (or its power spectrum), input radiation spectrum, apodizing function, and filter response characteristic. Closed form solutions are obtained for special cases to show qualitative features of the spectrum error and to establish bounds on its magnitude. It is shown that when fringe-reference sampling is used with a filter having minimal distortion, the relative rms random error in the measured intensity of spectrum lines is typically of the same order as the rms, relative error in drive speed if the resolving power is about five times greater than needed to just resolve the lines and that this error varies as the square root of the resolved spectral interval.
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