Error analysis of Fourier transform spectrometry based on the beam-folding position-tracking method

The translation stage is a critical component in a scanning Fourier Transform Spectrometer (FTS), and its precise alignment is essential for accurate spectral measurement. In the FTS, spectra are obtained by sampling the interferogram and applying a Fourier transform. However, tilt errors in the translation stage during scanning introduce undesired optical path differences, distorting both the interferogram and the resulting spectra. Additionally, retroreflector prisms used in beam-folding configurations are susceptible to deflection errors, causing deviations between the outgoing and incident beams, which further degrade measurement accuracy. In this paper, theoretical analysis and simulations are performed to quantitatively assess how translation stage tilt and retroreflector prism deflection errors influence the measured spectra and overall system resolution. Specifically, the optical path differences induced by these errors are derived theoretically, and their practical implications on the interferogram sampling interval and spectral resolution are discussed in detail. Simulation results demonstrate that by selecting a translation stage with a maximum tilt error below 150 μrad and retroreflector prisms with deflection angle errors not exceeding 10", the detrimental effects on spectral measurements can be effectively controlled within acceptable limits, ensuring optimal system performance.