A Modified Equation for the Spectral Resolution of Fourier Transform Spectrometers

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The spectral resolution of a Fourier transform spectrometer (FTS) is traditionally expressed as ${\bm \Delta \nu} = {\bf 0.5}/{\bm \delta} _{{\bf max}}$ in which ν is the wavenumber and ${\bm \delta} _{{\bf max}}$ 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 ${\bm \Delta \nu} = {\bf 0.5}/[{\bm \delta} _{{\bf max}} + ({\bf d}{\bm \delta} _{{\bf max}}/{\bf d}{\bm \nu}){\bm \nu} ]$ 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.