A Modified Equation for the Spectral Resolution of Fourier Transform Spectrometers

The spectral resolution of a Fourier transform spectrometer (FTS) is traditionally expressed as Δν = 0.5/δ_max in which ν is the wavenumber and δ_max is the maximum optical pathlength difference (OPD). This equation is valid for the moving mirror-based FTS whose OPD is independent of wavelength but inapplicable to the FTS with wavelength-dependent OPD. In this paper, by taking into account the wavelength dependence of OPD, the spectral resolution equation was modified as Δν = 0.5/[δ_max + (dδ_max/dν)ν] to make it applicable to both the OPD-dispersive and OPD-nondispersive FTS devices. A prototype stationary FTS was prepared using a LiNbO₃ waveguide Mach-Zehnder interferometer with push-pull electrodes, and its spectral resolutions at different wavelengths were experimentally and theoretically investigated. The excellent agreement between the theoretical and experimental data demonstrates the applicability of the modified equation for accurate evaluation of FTS resolution.