Fringe phase extraction using windowed Fourier transform guided by principal component analysis.

Area of Science:

• Optical Metrology
• Image Processing
• Computational Imaging

Background:

• The Windowed Fourier Transform (WFT) is a standard technique for phase map extraction from fringe patterns.
• Existing WFT methods can be computationally intensive and struggle with automatic singular point identification.

Purpose of the Study:

• To develop a new WFT-based algorithm for phase map extraction.
• To enhance computational efficiency and automate singular point exclusion in fringe pattern analysis.

Main Methods:

• Utilized Principal Component Analysis (PCA) to guide the Windowed Fourier Transform (WFT).
• Determined the principal frequency direction at each pixel using PCA on fringe pattern gradients.
• Searched a 1D frequency space for the windowed Fourier ridge, significantly reducing computational burden.
• Employed PCA eigenvalues to automatically identify and exclude singular point regions.

Main Results:

• The proposed PCA-guided WFT algorithm significantly alleviates computational burden for phase extraction.
• The method successfully automates the identification and exclusion of singular points within fringe patterns.
• Numerical simulations and experimental validation confirm the algorithm's effectiveness.

Conclusions:

• The novel PCA-guided WFT algorithm offers an efficient and robust solution for phase map extraction.
• This technique improves upon traditional WFT methods by simplifying computation and enhancing accuracy through automatic singular point handling.