High-power laser systems, characterized by ultra-high peak power and ultrashort pulse durations, play pivotal roles in inertial confinement fusion, particle acceleration, and ultrafast science. However, their performance is increasingly limited by spatiotemporal coupling effects that distort focal spot quality. Recent advances like STRIPED FISH, enable single-shot measurements but introduce reference-arm errors, while hyperspectral approaches suffer from limited channel capacity. Compressed sensing shows promise through sub-Nyquist sampling, yet conventional implementations (CASSI, CUP) recover only intensity. Phase-sensitive compressed sensing techniques (COFT, CS-CMUI) enable complex-field measurement, whereas hyperspectral compressive wavefront sensing can achieve similar results but requires deep learning-based reconstruction, which demands extensive experimental datasets for neural network training. To address the limitations of conventional measurement methods in spectral bandwidth and channel capacity, we present a spatiotemporal optical field measurement technique based on compressed sensing and quadriwave lateral shearing interferometry, which overcomes the channel number constraints of traditional systems. We aim to develop a robust single-shot technique combining compressed sensing with shearing interferometry to achieve 3D spatiotemporal complex-field characterization of high-power lasers. Multiplexing in the spatial and spectral domains is accomplished through compressed sensing, while complex amplitude reconstruction is achieved via quadriwave lateral shearing interferometry. When an input pulse interacts with a 2D phase grating, it generates wavelength-dependent interference patterns. These patterns are encoded by a random binary mask and spectrally dispersed before camera acquisition, creating a compressed image containing multiplexed spectral and spatial information. The reconstruction process involves two key steps: first, the TWIST-TV algorithm is employed to reconstruct wavelength-specific interference patterns from the compressed image, followed by Fourier-based phase recovery techniques to extract the complete complex field (including both amplitude and phase information) at each wavelength from the decoded interferograms.

We conduct a systematic simulation analysis of the measurement technology based on the combination of compressive quadriwave lateral shearing interferometry. Through mathematical modeling incorporating 38 dB Poisson noise, an imaging system resolution limit of NA=0.1, and a 10 μm defocus, we systematically investigate the effect of critical parameters—including the interference pattern period-to-encoding pixel size ratio, channel number, and frame number—on phase recovery accuracy, providing theoretical guidance for subsequent experimental optimization. The three key parameters—the interference pattern period-to-encoding pixel size ratio (γ), channel number, and frame number—are mutually independent in governing the reconstruction performance, which enables their systematic investigation through controlled-variable simulations. This parametric independence arises because the γ exclusively controls the spatial sampling adequacy of interference fringes, the channel number determines the spectral degrees of freedom without affecting spatial sampling, and the frame number provides additional linearly independent equations without altering the system’s spectral or spatial resolution.

First, to determine the optimal γ value for single-shot 20-channel phase reconstruction under near-experimental conditions, we vary the coding mask’s pixel size to adjust γ and evaluate phase recovery. The results show that γ=6?10 provides robust phase retrieval, with γ=10 yielding the smallest reconstruction error. Secondly, to investigate the influence of channel number on phase reconstruction accuracy in single-shot measurements, we systematically increase the spectral channels while maintaining a 2 nm resolution per channel, and evaluate the phase recovery performance under γ=10. The results demonstrate that approximately 20 channels provide the optimal reconstruction accuracy. Beyond this, additional channels lead to degraded performance due to noise accumulation and increased processing complexity. Thirdly, to assess the influence of frame number on phase reconstruction accuracy in multi-frame compressive sensing, we systematically increase the number of frames (distinct coding patterns) while maintaining 100 spectral channels under γ=10 conditions, and evaluate phase recovery performance. The results show that at least 12 frames are required to achieve reliable reconstruction accuracy, with γ=10 maintaining optimal performance. To validate the feasibility of the measurement technology based on the combination of compressive quadriwave lateral shearing interferometry, we implement an experimental setup featuring a broadband source (40 nm bandwidth centered at 800 nm). The system successfully achieves single-shot spatio-spectral phase measurements, which demonstrates accurate wavefront reconstruction across 20 spectral channels with 2 nm resolution. Key design parameters include a 64 μm-period phase grating, a γ=11.2 pattern sampling ratio, and optimized 5× magnification optics. Quantitative evaluation demonstrates excellent reconstruction accuracy, with a mean RMSE of 0.0078λ and a mean ΔP_PV=0.0128λ.

The experimental results have validated the optimal parameters obtained from the simulations, further confirming the reliability of these simulation parameters. This provides a solid foundation for single-shot broadband spectral measurements. Building upon these validated simulation parameters, future work will focus on extending the measurement bandwidth to progressively achieve ultra-broadband pulse measurement capabilities.