Regularized quadratic cost function for oriented fringe-pattern filtering.

Area of Science:

• Image Processing
• Computational Physics
• Optical Metrology

Background:

• Fringe patterns are crucial in optical metrology but are susceptible to noise.
• Existing denoising methods can blur fringe details, compromising measurement accuracy.

Purpose of the Study:

• To develop an effective fringe pattern denoising technique that preserves fringe details.
• To introduce a novel cost function derived from regularization theory within a Bayesian framework.

Main Methods:

• A Bayesian framework with regularization theory was employed to derive a quadratic cost function.
• A Markov random field model incorporating fringe orientation was used as a prior constraint.
• The cost function enforces smoothness along fringe tangent directions, separating noise in the frequency space.

Main Results:

• The proposed method successfully denoises fringe patterns while avoiding blurring.
• Iterative methods provide an efficient implementation for minimizing the cost function.
• Demonstrated performance on both simulated and real fringe pattern data.

Conclusions:

• The developed technique offers a robust solution for fringe pattern denoising.
• Preservation of fringe orientation and detail is achieved, enhancing measurement reliability.
• The method's efficiency and effectiveness are validated through experimental results.