  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.
