Raman spectral estimation via fast orthogonal search

A Fourier transform (FT) spectrometer measures the autocorrelation (interferogram) of radiation emitted from a source and estimates the optical power spectral density through application of the discrete Fourier transform (DFT) to the recorded interferogram. Although a widely used method, FT spectrometry suffers because its frequency resolution is limited to the sampling rate divided by the number of time-series data points. A large number of points are therefore required to resolve an optical spectrum properly. In this paper, it is shown that a noise-resistant technique known as fast orthogonal search (FOS) can be used to achieve accurate optical spectrum estimation. Further, it is shown that frequency accuracy comparable to the DFT applied to the full interferogram can be obtained with FOS even if the original interferogram is contaminated with noise and then reduced by a factor of up to 10 by irregularly spaced sampling. The FOS application presented here is for the estimation of Raman spectra from interferograms acquired with an FT Raman spectrometer.