Optical spectrum analysis from zero crossings

Abstract

A practical method of computing the spectral components directly from measured zero crossings of interferograms is presented. The method requires the sampling of only one zero crossing per Nyquist interval and yields results with a normalized mean-square error that is better than 10(-6) with respect to the fast Fourier transformation when the zero crossing is located within the Nyquist interval with an accuracy of one part in 10(6). The method is also robust against error frequencies that may arise owing to the finite range in the floating-point representation of numbers in a computer. The error frequencies appear whenever a large number of crossings is processed. This type of error is not related to the accuracy of locating the zero crossings and limits the operational bandwidth of a zero-crossing-based optical spectrum analyzer.