Tutorial on compressed ultrafast photography.

Significance: Compressed ultrafast photography (CUP) is currently the world's fastest single-shot imaging technique. Through the integration of compressed sensing and streak imaging, CUP can capture a transient event in a single camera exposure with imaging speeds from thousands to trillions of frames per second, at micrometer-level spatial resolutions, and in broad sensing spectral ranges. Aim: This tutorial aims to provide a comprehensive review of CUP in its fundamental methods, system implementations, biomedical applications, and prospect. Approach: A step-by-step guideline to CUP's forward model and representative image reconstruction algorithms is presented with sample codes and illustrations in Matlab and Python. Then, CUP's hardware implementation is described with a focus on the representative techniques, advantages, and limitations of the three key components-the spatial encoder, the temporal shearing unit, and the two-dimensional sensor. Furthermore, four representative biomedical applications enabled by CUP are discussed, followed by the prospect of CUP's technical advancement. Conclusions: CUP has emerged as a state-of-the-art ultrafast imaging technology. Its advanced imaging ability and versatility contribute to unprecedented observations and new applications in biomedicine. CUP holds great promise in improving technical specifications and facilitating the investigation of biomedical processes.