Particle-filter-based phase estimation in digital holographic interferometry.

Area of Science:

• Optical Metrology
• Signal Processing
• Image Analysis

Background:

• Digital holographic interferometry (DHI) is crucial for precise measurements.
• Accurate phase estimation from DHI fringes is challenging due to noise and complex patterns.
• Existing methods like unscented Kalman filters struggle with highly noisy or rapidly varying fringe data.

Purpose of the Study:

• To introduce a robust particle-filter-based technique for direct phase estimation from reconstructed interference fields.
• To enhance the analysis of digital holographic interferometric fringes, particularly under adverse noise conditions.
• To provide a superior alternative to current methods for phase and derivative estimation in DHI.

Main Methods:

• Application of particle filters for tracking phase and its derivatives in DHI.
• Utilizing a signal-tracking approach with a Taylor series expanded state model.
• Employing a polar-to-Cartesian conversion for the measurement model and non-Gaussian likelihood for sample weight computation.

Main Results:

• The proposed particle-filter approach demonstrates high robustness against noise.
• It significantly outperforms state-of-the-art methods, especially at low signal-to-noise ratios (e.g., -5 to 20 dB).
• The method successfully estimates phase from severely noisy and rapidly varying fringe patterns with large dynamic ranges.

Conclusions:

• The particle-filter-based technique offers superior performance for direct phase estimation in DHI.
• This method is particularly advantageous for analyzing noisy fringe patterns where traditional approaches fail.
• The approach represents a significant advancement for accurate phase retrieval in challenging interferometric scenarios.