Generic nonsinusoidal fringe model and gamma calibration in phase measuring profilometry

Area of Science:

• Optical Metrology
• 3D Surface Measurement
• Image Processing

Background:

• Gamma distortion is a primary error source in phase measuring profilometry, affecting sinusoidal waveform accuracy.
• Defocus in projector-camera systems acts as a low-pass filter, attenuating high-frequency harmonics and exacerbating errors.

Purpose of the Study:

• To propose a generic model for gamma-distorted fringes using Fourier series.
• To develop a robust gamma calibration and correction method for phase measuring profilometry.
• To enhance the precision and quality of 3D surface measurements.

Main Methods:

• A generic distorted fringe model expressed as a Fourier series was developed.
• A multifrequency phase-shifting method was employed for gamma calibration, mitigating defocus effects.
• A gamma correction method was introduced to improve signal-to-noise ratio and measurement accuracy.

Main Results:

• Experimental verification confirmed phase error dependency on defocus and pitch.
• The proposed gamma calibration method demonstrated superior robustness against pitch and defocus variations compared to existing techniques.
• Phase precision was significantly enhanced after applying the proposed gamma correction method.

Conclusions:

• The developed generic fringe model accurately represents gamma distortion in phase measuring profilometry.
• The proposed calibration and correction methods effectively reduce phase errors caused by gamma distortion and defocus.
• This research significantly improves the accuracy and reliability of 3D surface measurements using phase measuring profilometry.