The source scans slowly across the scene. Within every exposure, much faster intensity modulation encodes path delay. A spatial phase code and a moving shutter do different jobs.
Scan synchronization selects source–sensor correspondences. Modulation phase measures delay. The spatial carrier supports the Fourier reconstruction used in this project.
One direct path and three explicit indirect returns connect a 28 × 12 perspective-sampled relief surface to a camera. They include a different column, the same column at another row, and an extra-length return to the same pixel. The weights are specified for explanation; visibility, BRDFs, shot noise and absolute optical power are not simulated.
P = Σⱼ AⱼGⱼ exp(iφⱼ), φⱼ = 2πfLⱼ/c + βⱼ
R(θ) = Σⱼ AⱼGⱼ cos(θ−φⱼ), S(θ) = cos(θ+α)
⟨R S⟩ = ½ Re[P exp(iα)]
These are AC components after removing constant offsets from nonnegative emitted intensity and sensor response. They describe MHz intensity modulation and lock-in correlation. They do not represent interference of coherent optical fields. The waveform animation slows the modulation clock independently of the scan clock; their displayed speeds are not a physical timing ratio.
Point and line projectors share a collocated, calibrated camera geometry. Their image-coordinate phase code is therefore the same for direct paths. A point scan addresses N×M positions, a line scan N columns; this count is not an acquisition-speed or efficiency benchmark. The signal is normalized over a complete scan. A pixel gate is modeled only for a raster point source; a line with a column gate still admits paths within the active column.
For scanned sources, G is a Gaussian in source-to-receiver column offset; the point/pixel pairing additionally gates row offset. It selects the endpoints’ correspondence, not every intermediate bounce. Even a path that leaves the plane can return to an accepted pixel. For steady flood or plane-front illumination, G=1 in the integrated comparison: a moving exposure alone cannot identify which source region launched a photon. The blue display is the instantaneous exposure, while the computed amplitude is integrated over the full scan.
A world-coded source uses β=2πd(½+X/10), a calibrated projector uses β=2πd·x/(N−1), and sensor coding uses α=2πd·x/(N−1). Plane-front tilt changes illumination path length to Z cosθ+X sinθ. A spatial carrier is separate from rolling exposure; one need not imply the other. A calibrated offset projector would require a different correspondence model.
Achar et al., Epipolar Time-of-Flight Imaging ↗ describes scanning an epipolar sheet while exposing corresponding sensor pixels. The selected-transport and AMCW principles motivate this schematic; it is not a reproduction of that hardware.