Single-mask sphere-packing with implicit neural representation reconstruction for ultrahigh-speed imaging

Single-shot, high-speed 2D optical imaging is essential for studying transient phenomena in various research fields. Among existing techniques, compressed optical-streaking ultra-high-speed photography (COSUP) uses a coded aperture and a galvanometer scanner to capture non-repeatable time-evolving events at the 1.5 million-frame-per-second level. However, the use of a randomly coded aperture complicates the reconstruction process and introduces artifacts in the recovered videos. In contrast, non-multiplexing coded apertures simplify the reconstruction algorithm, allowing the recovery of longer videos from a snapshot. In this work, we design a non-multiplexing coded aperture for COSUP by exploiting the properties of congruent sphere packing (SP), which enables uniform space-time sampling given by the synergy between the galvanometer linear scanning and the optimal SP encoding patterns. We also develop an implicit neural representation-which can be self-trained from a single measurement-to not only largely reduce the training time and eliminate the need for training datasets but also reconstruct far more ultra-high-speed frames from a single measurement. The advantages of this proposed encoding and reconstruction scheme are verified by simulations and experimental results in a COSUP system.