Local polynomial phase identification and wrapped phase recovery from circular harmonic integrals

Area of Science:

• Optics and Photonics
• Signal Processing
• Image Analysis

Background:

• Fringe analysis is crucial for optical metrology.
• Local polynomial phase modeling offers a robust approach.
• Accurate phase field identification remains a challenge.

Purpose of the Study:

• To develop an algebraic method for relating polynomial phase coefficients to circular harmonic integrals.
• To enable accurate identification of local phase fields in fringe patterns.
• To create an efficient algorithm for denoising and recovering wrapped phase fields.

Main Methods:

• Formulating an algebraic equation connecting polynomial phase coefficients and circular harmonic integrals.
• Transforming circular harmonic integrals into 2D kernel convolutions.
• Deriving a system of equations for estimating local polynomial coefficients across the phase field.

Main Results:

• The proposed method accurately identifies local phase fields.
• An efficient denoising and recovery algorithm for wrapped phase fields is developed.
• Experimental results show model identification accuracy close to the Cramér-Rao lower bound.

Conclusions:

• The developed algebraic approach provides accurate phase field identification.
• The algorithm demonstrates efficiency, adaptability, and high accuracy in fringe analysis.
• Preferred parameter settings for the algorithm are identified through experimentation.