Fourier transform spectrometry without Fourier analysis of the interferogram

TL;DR

This paper introduces a method for analyzing interferometric spectra directly from interferograms without Fourier transforming them, reducing errors and improving precision by using a theoretical lineshape model.

Contribution

It presents a novel approach that bypasses Fourier analysis, directly deriving spectra from interferograms through theoretical lineshape calculations.

Findings

Reduces errors associated with Fourier transforms and related processing.

Provides a closed-form expression for spectra in the time domain.

Improves precision in spectrometry measurements.

Abstract

It is shown here that precision is gained by analyzing the interferometric spectra directly from the interferograms, with no previous Fourier transformation to put them in the standard frequency domain. The method is based on the theoretical calculation of the lineshape, which gives a general closed--form expression for the spectrum in the time domain and is directly assimilable to the experimental interferogram. Error sources in Fourier integrals, apodization, peak fitting with standard interpolation functions, choice of background level, Stokes energy shifts, etc., are neatly avoided.