A method, comprising: determining a set of reference retardances of a polarization interferometer at a point in time, the polarization interferometer comprising a liquid-crystal variable retarder,; determining a set of wavelengths corresponding to spectral slices of a hyperspectral data-cube; forming a reconstruction matrix comprising rows of periodic functions, wherein each row of the reconstruction matrix corresponds to a selected wavelength of the set of wavelengths, and each column of the reconstruction matrix corresponds to a selected retardance of the reference retardances, wherein: the periodic functions have as a parameter the selected wavelength of the corresponding row and are sampled at the selected retardance of each of the corresponding columns; a relative rate of oscillation of the periodic functions in each row is based on a liquid-crystal birefringence of the liquid-crystal variable retarder as a function of at least one of wavelength and temperature; and each of the periodic functions is phase-shifted for each of the selected wavelengths so that a phase of 0 corresponds roughly to a zero-retardance point of the interferometer at each of the selected wavelengths; obtaining an interferogram data-cube comprising an array of one or more simultaneously measured interferograms, wherein each row of the interferogram data-cube corresponds to one of the selected retardances and each column of the interferogram data-cube corresponds to a different interferogram from the simultaneously measured interferograms; and forming a set of matrix-vector products for each of the interferograms, each of the matrix-vector products comprising a matrix multiplication of the reconstruction matrix with a column of the interferogram data-cube, the set of matrix-vector products forming the hyperspectral data-cube. determining a set of reference retardances of a polarization interferometer at a point in time, the polarization interferometer comprising a liquid-crystal variable retarder,; determining a set of wavelengths corresponding to spectral slices of a hyperspectral data-cube; forming a reconstruction matrix comprising rows of periodic functions, wherein each row of the reconstruction matrix corresponds to a selected wavelength of the set of wavelengths, and each column of the reconstruction matrix corresponds to a selected retardance of the reference retardances, wherein: the periodic functions have as a parameter the selected wavelength of the corresponding row and are sampled at the selected retardance of each of the corresponding columns; a relative rate of oscillation of the periodic functions in each row is based on a liquid-crystal birefringence of the liquid-crystal variable retarder as a function of at least one of wavelength and temperature; and each of the periodic functions is phase-shifted for each of the selected wavelengths so that a phase of 0 corresponds roughly to a zero-retardance point of the interferometer at each of the selected wavelengths; the periodic functions have as a parameter the selected wavelength of the corresponding row and are sampled at the selected retardance of each of the corresponding columns; a relative rate of oscillation of the periodic functions in each row is based on a liquid-crystal birefringence of the liquid-crystal variable retarder as a function of at least one of wavelength and temperature; and each of the periodic functions is phase-shifted for each of the selected wavelengths so that a phase of 0 corresponds roughly to a zero-retardance point of the interferometer at each of the selected wavelengths; obtaining an interferogram data-cube comprising an array of one or more simultaneously measured interferograms, wherein each row of the interferogram data-cube corresponds to one of the selected retardances and each column of the interferogram data-cube corresponds to a different interferogram from the simultaneously measured interferograms; and forming a set of matrix-vector products for each of the interferograms, each of the matrix-vector products comprising a matrix multiplication of the reconstruction matrix with a column of the interferogram data-cube, the set of matrix-vector products forming the hyperspectral data-cube.