Fig. 1. Schematic diagram of TRSPI. (a) Transient events at different instants are indicated as ti. (b) Different illumination patterns Pj; (c) coded transient event in one period under a certain illumination pattern; (d) under each illumination pattern, a single-pixel detection histogram is measured. By applying different illumination patterns over repetitive events, a series of pattern-encoded histograms are obtained. (e) By extracting signals at the same ti from different histograms, a reconstruction at that instant can be achieved.

Fig. 2. Classic and reciprocal SPI configurations of FTP. (a) Classic configuration of the conventional FTP; (b) according to the Helmholtz reciprocity, a grating is added into SPI configuration for 3D imaging based on FTP theory. (c) The principle of height calculation with the phase difference between the surface of the object and the reference plane.

Fig. 3. Experimental setup of TRSPI for 2D and 3D imaging. (a) Complete TRSPI experimental configuration for 2D imaging; (b) detection module of TRSPI for 3D imaging.

Fig. 4. Measure period of a dynamic scene and digital calibration. (a) Regular checkerboard pattern loaded on the DMD when measuring the period of the dynamic scene; (b) continuous signal recorded by a single-pixel detector when the scene is illuminated by pattern (a), whose length exceeds a period of the dynamic scene. The red dashed box represents the time length of one period of the dynamic scene. (c) Digital calibration scheme when there is a slight mismatch between the period of the dynamic scene and exposure time of each illumination pattern.

Fig. 5. Selected 12 instantaneous frames from 2D TRSPI results (see Visualization 1 for more details).

Fig. 6. 3D TRSPI process based on FTP. (a) One reconstructed frame from detector 1; (b) reconstructed frame from detector 2 at the same time as in (a); (c) Fourier spectrum of (a) after background normalization; (d) positive first-order component of (c), selected with a Hann window; (e) wrapped phase obtained by inverse Fourier transform of (d); (f) reconstructed 3D shape corresponding to current frame (see Visualization 2 for more details). (g) Evaluation of the measurement uncertainty.