Lateral error correction of fringe projection profilometry via rotational geometry constraint

Fringe projection profilometry is widely employed for high-precision three-dimensional reconstruction. Its accuracy is fundamentally limited by spatial axial ambiguity, namely the non-orthogonality between the physical reference plane normal and the theoretical Z axis, which causes pure depth variations to erroneously map as lateral drift and significantly degrades absolute displacement estimation when global motion and local deformation coexist. To address this, a non-contact lateral correction method is proposed to reconstruct the orthogonal measurement coordinate system at the algebraic level. By quantifying the geometric misalignment between the plane normal and the height direction, a rotation correction matrix is constructed to establish a compensation mechanism that fundamentally eliminates cross-axial projection errors. Experimental validation under coupled displacement deformation conditions demonstrates that the proposed method reduces lateral offset root mean squared error by 83%–90% compared to the uncorrected phase-height model, suppressing step height error to within 0.037 mm and ceramic ball diameter error to within 0.039 mm, with point cloud completeness reaching 86% for planar surfaces and 66% for curved surfaces. By achieving high-precision reconstruction with lower-order fitting models, the proposed method substantially reduces computational overhead while preserving the high point cloud completeness and physical interpretability of the phase-height model.