Residue calibrated least-squares unwrapping algorithm for noisy and steep phase maps

Area of Science:

• Image Processing
• Computational Physics
• Optical Metrology

Background:

• Phase maps are crucial in various scientific fields, but noise and steep gradients complicate accurate unwrapping.
• Existing phase unwrapping algorithms often struggle with noisy data and complex phase transitions, limiting their practical use.

Purpose of the Study:

• To develop a robust phase unwrapping algorithm that effectively addresses noise and steep gradients in phase maps.
• To improve the accuracy and reliability of phase unwrapping for both simulated and experimental data.

Main Methods:

• A novel residue calibrated least-squares method is proposed.
• The algorithm calculates and calibrates residues in derivative maps to form a noise-free Poisson equation.
• Iterative compensation for residuals between wrapped and unwrapped phase maps refines accuracy and mitigates smoothing effects.

Main Results:

• The proposed algorithm demonstrates robust performance in unwrapping noisy and steep phase maps.
• Validation using simulated and experimental data confirms the algorithm's effectiveness.
• Comparative analysis shows superior performance over three other typical phase unwrapping algorithms.

Conclusions:

• The residue calibrated least-squares method provides a reliable and effective solution for challenging phase unwrapping scenarios.
• This algorithm offers a significant advancement for practical applications requiring accurate phase map analysis.