Efficient modal analysis using compressive optical interferometry

Interferometry is routinely used for spectral or modal analysis of optical signals. By posing interferometric modal analysis as a sparse recovery problem, we show that compressive sampling helps exploit the sparsity of typical optical signals in modal space and reduces the number of required measurements. Instead of collecting evenly spaced interferometric samples at the Nyquist rate followed by a Fourier transform as is common practice, we show that random sampling at sub-Nyquist rates followed by a sparse reconstruction algorithm suffices. We demonstrate our approach, which we call compressive interferometry, numerically in the context of modal analysis of spatial beams using a generalized interferometric configuration. Compressive interferometry applies to widely used optical modal sets and is robust with respect to noise, thus holding promise to enhance real-time processing in optical imaging and communications.