Beam shearing characteristic analysis of interferometric hyperspectral imaging system

A birefringent Fourier transform imaging spectrometer with a new lateral shearing interferometer is presented. The interferometer includes a Wollaston prism and a retroreflector. It splits an incident light beam into two shearing parallel parts to obtain interference fringe patterns of an imaging target, which is well established as an aid in reducing problems associated with optical alignment and manufacturing precision. The proposed method provides a direct technology for robust and inexpensive spectrometers to measure spectral signatures. Formulas for the optical path difference (OPD) produced by the proposed birefringent interferometer are derived by the ray-tracing method. Two experiments are carried out to demonstrate the accuracy of the formulas for OPD in the inner scanning mode and window scanning mode, respectively. A laser of wavelength 650 nm is used as a source of the experimental setup. The experimental estimations of the OPD and a reference OPD curve obtained with theoretical analysis are used for comparison. The match between the two curves is highly consistent, for the maximum deviation of the experimental OPD is less than /4. For the further verification of the imaging performance of the proposed method, another experiment is performed. A scene illuminated by an incandescent lamp is used as an imaging target. The temporal rotating of the retroreflector produces a series of time sequential interferograms, where the target is fixed and fringe patterns move. Performing nonuniform fast Fourier transform of the interferogram data produces a spectral data cube (i.e., the spectral images of the target).A series of recovered spectral images whose center wavelengths range from 450 to 650 nm is presented.In this paper, the principle of the instrument is described, and the OPD distribution formula is obtained and analyzed. The performance of the system is demonstrated through a numerical simulation and three experiments. This work will provide an important theoretical basis and the practical instruction for designing a new type of birefringent Fourier transform spectrometer based on Wollaston prism and its engineering applications.