Compressive Sensing Absorption Spectroscopy based on Photoelastic Modulation and Single-Pixel Detection

Conventional absorption spectroscopy falls short in complexity and measurement speed. Here, a new type of compressive sensing absorption spectroscopy technique employing a photoelastic modulator (PEM) is presented to address these challenges. The PEM is used to modulate the input spectrum and create multiple harmonic orders as the measurement channels. A sensing matrix is formed by randomly selecting elements from the modulation matrix. The measurement results of different frequency channels are simultaneously captured via a single-pixel photodetector without changing the physical parameters (such as PEM configurations or modulation frequencies). In a measurement example, the first five orders of harmonics are selected, and the input optical spectrum is successfully measured with a compression ratio of 1/16. To further verify the utility of our approach, the infrared spectrum with CO2 absorption is successfully reconstructed with low error.