Phase Retrieval from Integrated Intensity of Auto-Convolution

Ultra-fast optical pulses are the most ephemeral sensing paradigm ever devised, examining events over incredibly brief timescales with broadband illumination. A consequence of sensing at timescales lower than a picosecond is that pulse characterization cannot be done with traditional analog-to-digital samplers and must be ascertained from integrating intensity sensors. Techniques for pulse characterization have been constructed using combinations of time-invariant and time-variant filter responses to create non-linear but invertible intensity datasets (Walmsley & Dorrer, 2009). In this paper, we develop a novel high-order phase retrieval technique to perform pulse characterization from a single-pixel integrating sensor measuring integrated intensity of auto-convolution (IIAC). We examine gradient descent’s ability to recover signals as a function of signal dimension and measurement count, and we demonstrate the effective use of iterative hard tensor thresholding as an initializer. Finally, we demonstrate IIAC recovery in a laboratory setting to recover the time profile of a complex laser pulse. We assert that the IIAC recovery solution demonstrated here simultaneously provides the optics community with a pulse characterization technique that scales to low-power microscopy systems and provides the optimization community with a physically motivated high-order phase retrieval problem enhanced by low-rank tensor processing.