Unwrapping noisy phase maps by use of a minimum-cost-matching algorithm.

Area of Science:

• Image processing
• Optical metrology
• Computational imaging

Background:

• Phase map unwrapping is crucial for quantitative analysis in interferometric techniques.
• Existing branch-cut algorithms can struggle with noisy data and high discontinuity source densities.
• Unwrapped phase maps are essential for accurate measurements in applications like digital image correlation and holography.

Purpose of the Study:

• To present a novel, efficient algorithm for phase map unwrapping using branch cuts.
• To demonstrate the effectiveness of a minimum-cost-matching graph-theory approach for branch-cut placement.
• To improve the robustness and applicability of phase unwrapping in challenging conditions, such as unfiltered speckle interferometry.

Main Methods:

• Development of a minimum-cost-matching algorithm based on graph theory.
• Application of the algorithm to identify optimal branch-cut placements in noisy phase maps.
• Testing the algorithm's performance with high source densities in speckle-interferometry data.

Main Results:

• The proposed method successfully unwraps noisy phase maps by optimally placing branch cuts.
• The graph-theory approach achieves global minimum total cut length.
• The algorithm demonstrates capability in handling unfiltered speckle-interferometry phase maps at densities up to 0.1 sources/pixel, surpassing previous methods.

Conclusions:

• The minimum-cost-matching graph-theory method provides an effective solution for phase map unwrapping.
• This algorithm enhances the accuracy and reliability of interferometric measurements, particularly in noisy environments.
• The method offers significant advantages for applications requiring high-resolution phase data from unfiltered sources.