Fringe pattern demodulation using Zernike polynomials and a l1-norm regularized extended Kalman filter

Area of Science:

• Optics and Photonics
• Signal Processing
• Metrology

Background:

• Absolute phase estimation is crucial in optical metrology.
• Traditional fringe demodulation methods face challenges with noise and convergence.
• Representing phase using Zernike polynomials (ZPs) offers a structured approach.

Purpose of the Study:

• To propose a novel algorithm for closed fringe demodulation and absolute phase estimation.
• To convert phase estimation into Zernike polynomial coefficient estimation.
• To improve the performance and robustness of phase estimation algorithms.

Main Methods:

• Representing the 2D phase as a weighted linear combination of Zernike polynomials (ZPs).
• Employing a state space model for ZP coefficient estimation.
• Utilizing the extended Kalman filter (EKF) for state estimation due to nonlinearities.
• Incorporating a pseudo-measurement model with sparsity constraints to enhance EKF convergence.

Main Results:

• The proposed algorithm successfully performs absolute phase estimation from closed fringes.
• The method demonstrates robustness against noise in both simulations and experiments.
• The EKF with the pseudo-measurement model shows improved convergence performance.

Conclusions:

• The novel algorithm provides an effective approach for absolute phase estimation in optical systems.
• The Zernike polynomial representation combined with EKF offers a powerful framework.
• The method is practically applicable and noise-robust for real-world metrology applications.