High speed spectral imaging is useful for a variety of tasks spanning industrial monitoring, target detection, and chemical
identification. To better meet these needs, compact hyperspectral imaging instrumentation, capable of high spectral
resolution and real-time data acquisition and processing, are required. In this paper, we describe the first snapshot imaging
spatial heterodyne Fourier transform spectrometer based on birefringent crystals and polarization gratings. This includes
details about its architecture, as well as our preliminary proof of concept. Finally, we discuss details related to the
calibration of the sensor, including our preliminary investigations into high speed data reconstruction and calibration using
neural networks. With such an approach, it may be feasible to reconstruct and calibrate an entire interferogram cube in
one step with minimal Fast Fourier Transform (FFT) processing.