Depth Dynamics via One-Bit Frequency Probing in Embedded Direct Time-of-Flight Sensing

Time-of-flight (ToF) sensors with single-photon avalanche diodes (SPADs) estimate depth by accumulating a histogram of photon return times, which discards the timing information required to measure depth dynamics, such as vibrations or transient motions. We introduce a method that transforms a direct ToF sensor into a depth frequency analyzer capable of measuring high-frequency motion and transient events using only lightweight, on-sensor computations. By replacing conventional discrete Fourier transforms (DFTs) with one-bit probing sinusoids generated via oversampled sigma-delta modulation, we enable in-pixel frequency analysis without multipliers or floating-point operations. We extend the lightweight analysis of depth dynamics to Haar wavelets for time-localized detection of brief, non-repetitive depth changes. We validate our approach through simulation and hardware experiments, showing that it achieves noise performance approaching that of full-resolution DFTs, detects sub-millimeter motions above 6 kHz, and localizes millisecond-scale transients. Using a laboratory ToF setup, we demonstrate applications in oscillatory motion analysis and depth edge detection. This work has the potential to enable a new class of compact, motion-aware ToF sensors for embedded deployment in industrial predictive maintenance, structural health monitoring, robotic perception, and dynamic scene understanding.