Analysis of the Sagnac interference imaging spectrometer with a variable optical path difference

The Sagnac interference imaging spectrometer with a variable optical path difference (OPD) is proposed in this paper, which employs two wedge prisms coupled with a modified Sagnac interferometer, and produces a variable OPD through the moving wedge prism. Compared with the conventional imaging spectrometer, the Sagnac interference imaging spectrometer shows its advantages of miniaturization and insensitive to the non-uniform variation of the moving speed and the environment vibration. The exact expression of the OPD as a function of different parameters is derived, and the influences of the moving displacement, wedge angle and acute angles on the OPD are analyzed and discussed within the scope of engineering design. This study provides an important theoretical and practical guidance for the engineering of the Sagnac interference imaging spectrometer.