Sensitive Hadamard transform imaging spectrometer with a simple MEMS

A hyperspectral Hadamard transform imager is presented. It is based on a flat field spectrometer and a spatial light modulator. Compared to a typical dispersive pushbroom imaging spectrometer, the signal-to-noise-ratio can be increased by 1 ... 2 orders of magnitude for typical dimensions of the hyperspectral data cube. Applicable spatial light modulators include individually addressable MEMS based light modulators such as micro mirrors or newly developed micro shutters as well as mechanical slit positioning systems which are characterized by a fixed, movable pattern. In contrast to the individually addressable devices, the number of operational modes of the slit positioning system is constrained by the mask design, but high pixel numbers and high optical quality can be achieved by a mature and relatively simple micro machining technology. A detailed analysis of the relative performance of hyperspectral Hadamard transform, Fourier transform and hypothetical optimal imaging spectrometers with particular respect to the dimensions of the hyperspectral data cube and the composition of the detector noise reveals a considerable signal-to-noise advantage of the Hadamard transform imaging spectrometer over the Fourier transform imaging spectrometer for domination of read noise and a large number of spectral bands. In case the noise is dominated by dark current noise, the Hadamard transform imaging spectrometer can achieve 50% of the maximum possible sensitivity which is given by the hypothetical optimal imaging spectrometer. In contrast to the Fourier transform imaging spectrometer, the Hadamard transform imaging spectrometer is also suitable for use with short wavelengths.