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Compact Lens-less Digital Holographic Microscope for MEMS Inspection and Characterization

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

J R Buckland, J M Huntley, S R Turner

|November 6, 2010

Summary

A new algorithm uses graph theory to optimally place branch cuts for unwrapping noisy phase maps. This method improves accuracy in speckle interferometry, handling higher source densities effectively.

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.

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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.