Abstract: Embodiments of the present invention provide systems and methods for compact birefringent interferometer and Fourier Transform spectrometer which uses rotating birefringent crystal plate to produce variable optical path difference (OPD) between ordinary and extraordinary rays of the incident light travelling through the birefringent crystal plate. In one aspect, the system includes an optical birefringent interferometer and Fourier Transform spectrometer comprising a polarizing beamsplitter, a reflective mirror, a rotating and a fixed compensating birefringent plate. In another aspect, the interferometer and Fourier Transform spectrometer may further include a photodetector in order to obtain a spectrum of the incoming radiation. In yet another aspect, the interferometer and Fourier Transform spectrometer may further include a one-dimensional or two-dimensional photodetector array or in order to obtain a hyper-spectral image of the radiation source or illuminated object.