A comparison between data processing techniques for FTS based on high frequency interferogram sampling

This paper compares different data processing techniques for FTS with the aim of assessing the feasibility of a spectrometer leveraging on standard DAC boards, without dedicated hardware for sampling and speed control of the moving mirrors. Fourier transform spectrometers rely on the sampling of the interferogram at constant steps of the optical path difference (OPD) to evaluate the spectra through standard discrete Fourier transform. Constant OPD sampling is traditionally achieved with dedicated hardware but, recently, sampling methods based on the use of common analog to digital converters with large dynamic range and high sampling frequency have become viable when associated with specific data processing techniques. These methods offer advantages from the point of view of insensitivity to disturbances, in particular mechanical vibrations, and should be less sensitive to OPD speed errors. In this work the performances of three algorithms, two taken from literature based on phase demodulation of a reference interferogram have been compared with a method based on direct phase computation of the reference interferogram in terms of robustness against mechanical vibrations and OPD speed errors. All methods provided almost correct spectra with vibrations amplitudes up to 10% of the average OPD speed and speed drifts within the scan up to 20% of the average, as long as the disturbance frequency was lower than the reference signal nominal one. The developed method based on the arccosine function keeps working also with frequencies of the disturbances larger than the reference channel one, the common limit for the other two.