Surface profile measurement using heterodyne moiré signals with an adjustable grating period

This paper presents a heterodyne moiré fringe technique with real-time tunable fringe pitch for high-precision surface profilometry. The proposed method combines tunable fringe projection, heterodyne frequency-shifting, and a least-squares sinusoidal fitting algorithm to achieve stable and high-resolution phase extraction and surface reconstruction. A computer-generated dynamic grating pattern is projected onto a spatial light modulator, and the reflected fringe pattern, deformed by the object's surface profile, is captured by a camera. This deformed fringe is then digitally superimposed with a virtual reference grating to generate a time-varying heterodyne moiré signal. Phase information is retrieved through phase analysis and unwrapped when necessary to reconstruct the continuous 3D surface profile. Experimental validation using a coin and a plaster statue demonstrated a height measurement error of approximately 1.4 µm. Compared with conventional physical grating systems, the proposed approach offers real-time pitch tunability, non-contact operation, a simplified setup, and ease of use, demonstrating strong potential for applications in precision optical metrology.