Random transmittance based filter array spectrometers: Sparse spectrum recovery and resolution improvement

In this paper, we introduce filters with random transmittance to improve the resolution of miniature spectrometers. We show that a sparse signal spectrum sensed by such filters when processed by an L₁ algorithm aids in improving the resolution. We also show a way to design the filters with random transmittance using optical thin-film technology. We demonstrate that a resolution of 0.99nm, which is 7-fold compared to using filters in [3], can be achieved with only 40 random filters.