Single-shot stereo-polarimetric compressed ultrafast photography for light-speed observation of high-dimensional optical transients with picosecond resolution

systems. Thus, the enriched observation to the transient scene and the increased data in measurement assist the reconstruction algorithm to stably and accurately recover the (x, y, t) datacubes from highly compressed measurement38. The details in system settings and characterizations are presented in Supplementary Notes 4 and 5. The second step is to calculate the linear polarization parameters. Inserting polarization components in imaging systems is a commonly used method to passively detect polarization states of light. In general, based on the arrangement of linear polarizers specified by experiments, the recovered (x, y, t) information allows computing the spatiotemporal maps of the first three Stokes parameters (denoted by S0, S1, and S2). For incident light composed of only a linearly polarized component and an unpolarized component, the time-resolved spatial distributions of the AoLP and the degree of linear polarization (DoLP) can be determined (explained in Supplementary Note 6). As the last step, the recovered (x, y, t) datacubes are used to recover the depth information. The scheme of common-main- objective stereoscopy39 is implemented in the dual-channel generation stage (Fig. 1a) to enable depth sensing (see Methods). This method does not rely on active illumination. Rather, it achieves passive detection without adding additional components. It is, therefore, selected to maximally leverage the existing design of the SP-CUP system. The spatial resolution, temporal resolution, and accuracy of polarization measurements are quantified under each setting used in the following experiments (detailed in Supplementary Notes 4–6). Plano-polarimetric ultrafast (x, y, t, ψ) imaging. To detect four photon tags (i.e., x, y, t, ψ), we used SP-CUP to image a dynamic scene: five linear polarizers with different transmission angles were cut into the shapes of printed letters—“L”, “S”, “T”, “U”, and “W”—and were overlaid on top of the corresponding prints. A 7- ps, 532-nm laser pulse illuminated these letters obliquely. The pulse was depolarized by a diffuser. Three 0o polarizers were inserted in Views 1, 3, and 4; three 45o polarizers were inserted in Views 2, 5, and 6. Combining Views 3 and 4 with View 1, we can use two projection angles to sense the transient scene filtered by the 0o polarizers. Similarly, the combination of Views 5 and 6 with View 2 enables reconstructing the same dynamics through the 45o polarizers. If light from the object is linearly polarized, the AoLP can be derived based on the intensity ratio between the recovered datacubes40. Meanwhile, the first Stokes parameter S0, which represents the light intensity reflected by the object, can be readily obtained41 (detailed in Supplementary Note 6). Figure 2a shows the reconstructed ultrafast left-to-right sweeping dynamics at 250 Gfps. Four frames of the reconstructed ψ and S0 are plotted in Fig. 2b–c, and the corresponding movies are presented in Supplementary Movie 1. The laser pulse swept through the sample at a measured apparent speed of 7 × 108 m s−1, closely matching the theoretically expected value based on the pre-set experimental condition. The complete data (i.e., (x, y, t, ψ) information) is also visualized using the point cloud in Fig. 2d, showing that the five letters have distinct AoLPs, ranging across the π angular space. Figure 2e plots mean AoLPs
ψ ð Þ over each letter versus time. The values of
ψ, averaged over time, for “L”, “S”, “T”, “U”, and “W” are 86.9o, –4.6o, 55.7o, –84.2o, and –44.9o, respectively. They are close to the measured ground truths: 84.8o, –1.8o, 53.9o, –83.7o, and –49.5o (black dashed lines in Fig. 2e). The standard deviation, averaged over time, ranges between 1.0o (“L”) and 7.3o (“S”). Additional data are presented in Supplementary Figures 5 and 6. Characterization of early-stage plasma emission. To demon- strate the indispensable utility of the SP-CUP system in ultrafast Dynamic scene Front optics 1x stereoscope objective Diaphra