  Encoding of spectral information onto monochrome imaging cameras is of
interest for wavelength multiplexing and hyperspectral imaging applications.
Here, the complex spatio-spectral response of a disordered material is used to
demonstrate retrieval of a number of discrete wavelengths over a wide spectral
range. Strong, diffuse light scattering in a semiconductor nanowire mat is used
to achieve a highly compact spectrometer of micrometer thickness, transforming
different wavelengths into distinct speckle patterns with nanometer
sensitivity. Spatial multiplexing is achieved through the use of a microlens
array, allowing simultaneous imaging of many speckles, ultimately limited by
the size of the diffuse spot area. The performance of different information
retrieval algorithms is compared. A compressive sensing algorithm exhibits
efficient reconstruction capability in noisy environments and with only a few
measurements.
