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Encoding of spectral information onto monochrome imaging cameras is ofinterest for wavelength multiplexing and hyperspectral imaging applications.Here, the complex spatio-spectral response of a disordered material is used todemonstrate retrieval of a number of discrete wavelengths over a wide spectralrange. Strong, diffuse light scattering in a semiconductor nanowire mat is usedto achieve a highly compact spectrometer of micrometer thickness, transformingdifferent wavelengths into distinct speckle patterns with nanometersensitivity. Spatial multiplexing is achieved through the use of a microlensarray, allowing simultaneous imaging of many speckles, ultimately limited bythe size of the diffuse spot area. The performance of different informationretrieval algorithms is compared. A compressive sensing algorithm exhibitsefficient reconstruction capability in noisy environments and with only a fewmeasurements.

Speckle-based hyperspectral imaging combining multiple scattering and compressive sensing in nanowire mats