Hilbert-Huang processing for single-exposure two-dimensional grating interferometry.

Area of Science:

• Optics and Photonics
• Signal Processing
• Metrology

Background:

• Fringe pattern analysis is crucial in optical metrology.
• Existing methods struggle with complex, single-shot crossed fringe patterns.
• Robust and efficient processing techniques are needed.

Purpose of the Study:

• To propose a novel single-shot method for processing crossed-type fringe patterns.
• To enhance the accuracy and efficiency of fringe analysis.
• To develop a versatile technique applicable to various fringe pattern types.

Main Methods:

• Hilbert-Huang grating interferometry (HHGI) combines empirical mode decomposition and Hilbert spiral transform.
• Orthogonal empirical mode decomposition separates crossed fringe families.
• Modified automatic selective reconstruction with enhanced fast empirical mode decomposition and mutual information detrending filters fringe sets.
• Hilbert spiral transform performs fringe phase demodulation.

Main Results:

• HHGI successfully resolves crossed fringe patterns into two families.
• Adaptive filtering effectively processes complex and defected patterns.
• Numerical and experimental studies validate the technique's robustness and versatility.
• The method accurately demodulates phases for multiplicative and additive patterns with sinusoidal and binary structures.

Conclusions:

• The proposed HHGI technique offers a valid, versatile, and robust solution for single-shot crossed fringe pattern analysis.
• Efficient adaptive filtering enables fast processing of complex fringe data.
• HHGI advances optical metrology by providing a powerful tool for phase demodulation.