Spectral microscopy is a method to acquire the spectrum for each point in the image of a sample. The most straightforward technique uses spectral filters to collect a sequence of images at a discrete number of spectral bands. A more complete spectral characterization is hyperspectral microscopy, which acquires the whole continuous spectrum of each point of the image. A powerful approach to this aim is Fourier-transform (FT) spectrometry [1, 2], in which an optical waveform is split by an interferometer in two delayed replicas, whose interference pattern is measured by a detector as a function of their delay. The FT of the resulting interferogram yields the continuous intensity spectrum of the waveform. The FT approach is able to retrieve in parallel the spectra for all pixels in a scene and is hence suited for wide-field microscopy, but it requires controlling the delay with sub-cycle precision, which is very difficult to achieve with Michelson and Mach-Zehnder interferometers. Here we introduce a hyperspectral microscope based on the FT approach and using a compact, highly stable common-path birefringent interferometer, a version of the Translating-Wedge-based Identical pulses eNcoding System (TWINS) [3, 4]. Figure 1(a) shows the schematic setup of the microscope. Light is collected by an infinity-corrected objective, it propagates in the interferometer and it is imaged on the 2D detector (14-bits, silicon monochrome CMOS camera) by a tube lens. The component P1 polarizes the input light at 45°.
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