A geometric principle for absolute angular measurement using single-point ToF ranging

Abstract Absolute angular position measurement is critical for automated systems, yet conventional optical and magnetic encoders often suffer from complex alignment, vulnerability to dirty environments, or high cost. This paper proposes a proof-of-concept angular measurement scheme that converts rotational displacement into monotonic distance variations via a helical reference surface, measured by a single-point Time-of-Flight (ToF) distance sensor. A theoretical model incorporating a reference distance and monotonic mapping bounds is formulated to establish the one-to-one angular transformation within a 〖350〗^o interval. To suppress impulsive distance outliers caused by surface reflections and optical transitions, a threshold-based temporal consistency filter is applied. Experimental validation using a VL53L1X-based prototype demonstrates the fundamental feasibility of the approach, achieving degree-level accuracy under controlled in-air and shallow submerged conditions (10 cm depth). Dynamic evaluations across various rotational speeds, direction reversals, and transient regimes highlight both the capabilities and operational limits of the system, particularly regarding filter-induced latency and sample rejection during rapid motion. Rather than competing with high-precision commercial encoders, the proposed method serves as a simple, low-cost feasibility study tailored for moderate-accuracy applications where environmental tolerance and mechanical simplicity are prioritized.