Stabilizing Defect Visibility Under Overexposure in Fringe-Based Imaging via γ Nonlinearity Analysis

Phase-shifting fringe projection (PSFP) is widely used in industrial inspection and three-dimensional measurement, where γ nonlinearity of the projector-camera system is traditionally treated as a phase-error source to be calibrated or compensated. In this work, γ nonlinearity is reinterpreted from an imaging perspective and shown to act as a statistical distortion mechanism that reshapes modulation stability, overexposure behavior, and defect saliency in fringe-based imaging. Building on the intrinsic DC-AC decomposition of phase-shifting demodulation, we analyze how γ nonlinearity interacts with fringe modulation and frequency-selective transfer. An analytical model reveals that γ nonlinearity simultaneously suppresses the fringe fundamental and introduces harmonic leakage, leading to systematic compression of mean modulation contrast in high-brightness regions. As a result, γ correction does not necessarily enhance mean-based defect contrast and may even reduce it, contrary to common intuition. We further demonstrate that the primary benefit of γ correction lies in statistical stabilization rather than contrast amplification. By introducing modulation-domain saliency formulations and a frequency-domain harmonic energy ratio, a physical link is established between γ nonlinearity, overexposure, and defect separability. Controlled experiments on highly reflective sheet-metal specimens confirm that while mean-contrast- and SNR-based saliency metrics often decrease after γ correction, separability-based metrics consistently improve due to reduced nonlinear- and saturation-induced variance. Cross-channel and cross-condition analyses further show that modulation and reflectance images respond differently to γ correction, yet metric-level separability exhibits consistent improvement across channels. These results clarify the true role of γ correction in fringe-based inspection and provide theoretical insight and practical guidance for robust defect imaging under nonlinear and near-overexposure conditions.