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Second-harmonic injection for nonlinear phase-ripple suppression in four-step fringe projection profilometry.

Created on 31 Oct 2026

Authors

Haitao Wu, Yiping Cao, Yu Zhang, Jinlong Li, Kai Yang, Jianping Peng, Yingying Wan

Published in

Optics letters. Volume 51. Issue 21. Pages 5942-5945. Nov 01, 2026. Epub Sep 30, 2026.

Abstract

Projector-camera nonlinearity produces carrier-locked phase ripple in four-step fringe projection profilometry. We introduce second-harmonic injection, whose coefficient controls the third-fifth harmonic imbalance through nonlinear intermodulation, while the injected harmonic is rejected by ideal four-step demodulation. A two-stage spatial-reuse calibration selects the coefficient directly from measured ripple, evaluating 22 candidates using eight images. Across eight independent reference-plane projection-capture repetitions, the method achieved a phase RMSE of 0.00617 ± 0.00009 rad (mean ± sample standard deviation), compared with 0.02243 ± 0.00038 rad without correction. Sculpture-model measurements further demonstrated ripple suppression on a complex surface. The method provides efficient active predistortion for repeated four-step profilometry under a stable, calibrated response.

PMID:
42962093
Bibliographic data and abstract were imported from PubMed on 31 Oct 2026.

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