Significance With the development of fundamental physics, chemistry, materials science, and energy engineering, many processes that occur on the nanosecond (ns, 10(-9) s) to femtosecond (fs, 10(-15) s) time scales, known as ultrafast processes, have become crucial topics in research in related fields. Examples include ultrafast plasma dynamics and X-ray emission dynamics in nuclear fusion investigations. However, observing these ultrafast processes, which aim to record transient dynamics including information from at least two spatial dimensions, remains a significant technical challenge. Current methods for observing ultrafast processes, namely, ultrafast imaging techniques, can be divided into two categories: passive imaging techniques and active imaging techniques. Passive imaging techniques suffer from electronic bottlenecks such as the confinement of carrier movement speed, parasitic capacitance and inductance, and spatial dispersion of electrons, severely restricting their spatial and temporal resolution. Active ultrafast imaging techniques use illumination pulses to observe ultrafast processes, capturing light signals from the observation pulses themselves. This approach overcomes the limitations of electronic bottlenecks on imaging speed and quality in ultrafast imaging technology. With the rapid development of ultrashort pulse generation techniques, ultrafast imaging based on pump-probe, the most commonly applied active imaging technique, can achieve temporal resolutions as fine as a few femtoseconds and spatial resolutions down to sub-micrometer scales. However, pump-probe techniques can only capture a single snapshot of the observed ultrafast process in each observation. To capture the entire ultrafast process, it is necessary to continuously repeat the experiment. The delay between the pump pulse and the probe pulse (observation pulse) must be adjusted accordingly to capture different transient slices. Consequently, pump-probe techniques are not suitable for recording non-repeatable ultrafast processes with significant randomness. In recent years, many single-shot active ultrafast imaging techniques, capable of capturing multiple frames of ultrafast processes in a single observation, have garnered widespread interest. Techniques like FINCOPA, FRAME, and SNAP have emerged as powerful tools for observing critical ultrafast phenomena such as laser-plasma interactions, femtosecond laser ablations, and rapid phase changes. Among these, ultrafast imaging techniques based on spectral-temporal transform utilize different spectral components within a single pulse to record various temporal slices of the observed ultrafast process. Due to their unique ultrafast detection mechanisms, spectral-temporal transform-based techniques can continuously record ultrafast processes at extremely high frame rates exceeding 100 THz, acquiring hundreds of frames in a single shot. These capabilities are unmatched by other active ultrafast imaging methods, which allow for the revelation of transient details within ultrafast processes. In addition, the entire exposure duration of spectral-temporal transform-based ultrafast imaging techniques ranges from femtoseconds to nanoseconds, a wide observation time window unprecedented in other active ultrafast imaging methods. Considering the significance of ultrafast imaging techniques and the impressive capabilities of spectral-temporal transform-based methods in observing ultrafast processes, there is a clear need for a comprehensive review of state-of-the-art techniques. Such a review could inspire further development in ultrafast imaging technology and expand the application domains of single-shot ultrafast imaging techniques. Progress The first work on ultrafast imaging techniques based on spectral-temporal transform was completed by Goda's group at Tokyo University in 2014. They captured 6 pictures with a frame rate exceeding 4.36 THz in a single shot. Since then, considerable advancements have been achieved in two main components: generating observation pulses with spectral-temporal transform characteristics and reconstructing the time-spectral image sequence. For generating observation pulses with spectral-temporal transform characteristics, both glass rods and grating pairs have been widely utilized to generate chirped pulses as observation pulses, with observation time windows ranging from femtoseconds to picoseconds. In 2020, Kannari's group at Keio University broadened the observation time window to a few nanoseconds using a system called free-space angular-chirp enhanced delay (FACED) (Fig. 3). In 2023, Nakagawa's group at Tokyo University further extended the observation time window to over 10 ns through techniques known as "spectral shuttle" (Fig. 4) and "spectrum circuit bridging" (Fig. 5), respectively. Both direct imaging methods, which rely on spatial-spectral mapping, and computational imaging methods, which utilize compression-reconstruction techniques, have been developed for the recovery of spectral-temporal image sequences. The direct imaging methods relying on spatial-spectral mapping were initially pioneered by Goda's group in 2014 (Fig. 6) using a spectral mapping device (SMD), which was further advanced in terms of the number of frames acquired in a single shot by Nakagawa's group in 2020 (Fig. 7). These spatial-spectral mapping methods also encompass spectral filtering introduced by Goda's group in 2015 (Fig. 8), and spatial-point sampling methods initiated by Kannari's group in 2020 (Fig. 9). Computational imaging methods for recovering the spectral-temporal image sequence were first developed by Downer's group from the University of Texas at Austin in 2014 using a single-shot Fourier domain tomography method (Fig. 11). In 2018, Chen's group pioneered computational ultrafast imaging techniques based on spectral-temporal transform using compressed sensing (Fig. 12), which significantly increases the number of pictures acquired in a single shot. Zhang's group developed a single-shot polarization-resolved ultrafast mapping photography (PUMP) by combining spectral-temporal transform with multi-frame computational polarization imaging methods (Fig. 14). Conclusions and Prospects Further development of ultrafast imaging techniques based on spectral-temporal transform should first focus on evaluating the criteria of key parameters, such as the temporal and spatial resolution limits of the ultrafast imaging system, which are still debated. Enhancing temporal resolution further relies on using observation pulses with wider spectra while improving spatial resolution depends on advancements in both the imaging compression system and reconstruction algorithms.
