Femtosecond lasers are powerful in studying matter’s ultrafast dynamics within femtosecond to attosecond time scales. Drawing a three-dimensional (3D) topological map of the optical field of a femtosecond laser pulse including its spatiotemporal amplitude and phase distributions, allows one to predict and understand the underlying physics of light interaction with matter, whose spatially resolved transient dielectric function experiences ultrafast evolution. However, such a task is technically challenging for two reasons: first, one has to capture in single-shot and squeeze the 3D information of an optical field profile into a two-dimensional (2D) detector; second, typical detectors are only sensitive to intensity or amplitude information rather than phase. Here we have demonstrated compressed optical field topography (COFT) drawing a 3D map for an ultrafast optical field in single-shot, by combining the coded aperture snapshot spectral imaging (CASSI) technique with a global 3D phase retrieval procedure. COFT can, in single-shot, fully characterize the spatiotemporal coupling of a femtosecond laser pulse, and live stream the light-speed propagation of an air plasma ionization front, unveiling its potential applications in ultrafast sciences.

Fourier-transform spectral imaging captures frequency-resolved images with high spectral resolution, broad spectral range, high photon flux, and low stray light. In this technique, spectral information is resolved by taking Fourier transformation of the interference signals of two copies of the incident light at different time delays. The time delay should be scanned at a high sampling rate beyond the Nyquist limit to avoid aliasing, at the price of low measurement efficiency and stringent requirements on motion control for time delay scan. Here we propose, what we believe to be, a new perspective on Fourier-transform spectral imaging based on a generalized central slice theorem analogous to computerized tomography, using an angularly dispersive optics decouples measurements of the spectral envelope and the central frequency. Thus, as the central frequency is directly determined by the angular dispersion, the smooth spectral-spatial intensity envelope is reconstructed from interferograms measured at a sub-Nyquist time delay sampling rate. This perspective enables high-efficiency hyperspectral imaging and even spatiotemporal optical field characterization of femtosecond laser pulses without a loss of spectral and spatial resolutions.