Single-shot 2-dimensional optical imaging of transient phenomena is indispensable for numerous areas of study. Among existing techniques

compressed ultrafast photography (CUP) using a chirped ultrashort pulse as active illumination can acquire nonrepetitive time-evolving events at hundreds of trillions of frames per second. However

the bulky size and conventional configurations limit its reliability and application scopes. Superdispersive metalenses offer a promising solution for an ultracompact design with a stable performance by integrating the functions of a focusing lens and dispersive optical components into a single device. Nevertheless

existing metalens designs

typically optimized for the full visible spectrum with a relatively low spectral resolution

cannot be readily applied to active-illumination CUP. To address these limitations

here

we propose single-shot compressed ultracompact femtophotography (CUF) that synergically combines the fields of nanophotonics

optical imaging

compressed sensing

and deep learning. We develop the theory of CUF’s data acquisition composed of temporal–spectral mapping

spatial encoding

temporal shearing

and spatiotemporal integration. We also develop CUF’s image reconstruction via deep learning. Moreover

we design and evaluate CUF’s crucial components—a static binary transmissive mask

a superdispersive metalens

and a 2-dimensional sensor. Finally

using numerical simulations

CUF’s feasibility is verified using 2 synthetic scenes: an ultrafast beam sweeping across a surface and the propagation of a terahertz Cherenkov wave.