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

Xiaolong Ma¹, Xiaofei Wang¹, Ruizhan Zhai¹

¹Qilu University of Technology (Shandong Academy of Sciences), Laser Institute, Shandong Academy of Scienses, China-Belarus Belt and Road Joint Laboratory on Intelligent Perception in Extreme Environments, Shandong Key Laboratory of Optoelectronic Sensing Technologies, National-Local joint Engineering Laboratory for Energy and Environment Fiber Smart Sensing Technologies, 3501 Daxue Road, Changqing District, Jinan 250353, China.

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|April 14, 2026

Summary

Gamma nonlinearity in fringe projection systems distorts image statistics, impacting defect detection. Correction stabilizes images by reducing variance, improving defect separability rather than just contrast.

Keywords:

computational imaging defect saliency fringe projection profilometry gamma nonlinearity overexposure analysis

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Area of Science:

Optics and Photonics
Image Processing
Metrology

Background:

Phase-shifting fringe projection (PSFP) is crucial for 3D measurement and industrial inspection.
Gamma (γ) nonlinearity in projector-camera systems is typically viewed as a phase error.
This nonlinearity affects modulation stability, overexposure, and defect visibility in fringe imaging.

Purpose of the Study:

To re-evaluate γ nonlinearity not as a phase error, but as a statistical distortion mechanism.
To analyze the interaction between γ nonlinearity, fringe modulation, and frequency transfer.
To clarify the role of γ correction in defect imaging under nonlinear and near-overexposure conditions.

Main Methods:

Analytical modeling based on DC-AC decomposition of phase-shifting demodulation.
Development of modulation-domain saliency formulations and frequency-domain harmonic energy ratio.
Controlled experiments on highly reflective sheet-metal specimens.

Main Results:

γ nonlinearity suppresses fringe fundamentals and introduces harmonics, compressing modulation contrast in bright regions.
γ correction primarily offers statistical stabilization, not necessarily contrast amplification; it can decrease mean-contrast and SNR.
Separability-based defect metrics consistently improve post-correction due to reduced nonlinear and saturation variance.

Conclusions:

γ nonlinearity acts as a statistical distortion, reshaping image properties like modulation and defect saliency.
The main benefit of γ correction is statistical stabilization, enhancing defect separability.
Provides theoretical insight and practical guidance for robust defect imaging in challenging conditions.