Application of non-uniform Fourier transform to non-uniform sampling Fourier transform spectrometers

TL;DR

This paper compares traditional interpolation and NUFFT methods for processing non-uniformly sampled interferograms, demonstrating NUFFT's advantages in spectral accuracy and computational efficiency, especially under under-sampling and noise conditions.

Contribution

The paper introduces a novel implementation of NUFFT and evaluates its performance against interpolation in high-resolution Fourier transform spectrometry.

Findings

NUFFT matches spectral shape and noise levels of interpolation

NUFFT outperforms in spectral amplitude accuracy

NUFFT offers better computational performance and noise robustness

Abstract

Resampling by interpolation is the traditional method to process interferograms from non-uniformly sampled Fourier transform spectrometers. The non-uniform fast Fourier transform (NUFFT) is an alternative approach that has been mostly overlooked. With the aid of experiments on a high-resolution interferometer with a variety of optical sources, these two methods are compared. It is found that the NUFFT is comparable to interpolation in spectral profile shape and spectral noise levels and is better in spectral amplitude and computer performance. A significant advantage is also found in the case of under-sampling and noise performance by NUFFT due to the unique non-periodic nature of non-uniform sampling. In addition, a novel implementation of NUFFT is presented and analysed.