We introduce a wide field hyperspectral microscope using the Fourier-transform approach. The interferometer is based on the Translating-Wedge-Based Identical Pulses eNcoding System (TWINS) [Opt. Lett. 37, 3027 (2012)], a common-path birefringent interferometer which combines compactness, intrinsic interferometric delay precision, long-term stability and insensitivity to vibrations. We describe three different implementations of our system: two prototypes designed to test different optical schemes and an add-on for a commercial microscope. We show high-quality spectral microscopy of the fluorescence from stained cells and powders of inorganic pigments, demonstrating that the device is suited to biology and materials science. We demonstrate the acquisition of a 1Mpixel hyperspectral image in 75 seconds in the spectral range from 400 to 1100 nm. We also introduce an acquisition method which synthesizes a tunable spectral filter, providing band-passed images by the measurement of only two maps.
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