Least-squares gamma estimation in fringe projection profilometry.

Area of Science:

• Optical Engineering
• Metrology
• 3D Imaging

Background:

• Fringe projection profilometry is a key 3D measurement technique.
• Optical systems introduce nonlinear gamma distortion, affecting measurement accuracy.
• Existing methods for gamma correction are often complex or require extensive calibration.

Purpose of the Study:

• To introduce a novel method for estimating and compensating nonlinear gamma factor in fringe projection profilometry.
• To enable accurate 3D surface reconstruction by addressing optical system distortions.
• To provide a computationally efficient solution requiring minimal input data.

Main Methods:

• Indirectly determine the gamma factor by fitting a least-squares plane to the estimated phase from a reference plane.
• Utilize a minimal set of three sinusoidal fringe images for gamma factor estimation.
• Apply inverse gamma compensation for generating new fringe patterns and rectifying existing data.

Main Results:

• Successfully estimated the nonlinear gamma factor using only three fringe images.
• Demonstrated the feasibility of correcting gamma distortion in fringe projection profilometry.
• Validated the method's effectiveness through experimental results.

Conclusions:

• The proposed method offers an effective and efficient way to estimate and compensate for gamma distortion.
• This technique enhances the accuracy and reliability of 3D measurements in fringe projection profilometry.
• The approach is applicable for both rectifying legacy data and improving future measurements.