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Interferometry

Robust unwrapping algorithm for three-dimensional phase volumes of arbitrary shape containing knotted phase singularity loops

[+] Author Affiliations
Olov Marklund

Luleå University of Technology, Department of Computer Science and Electrical Engineering, SE-97187 Luleå, Sweden

Jonathan M. Huntley

Loughborough University of Technology, Wolfson School of Mechanical and Manufacturing Engineering, Loughborough, Leicestershire LE11 3TU, United Kingdom

Rhodri Cusack

MRC Cognition and Brain Sciences Unit, 15 Chauser Road, Cambridge, CB2 7EF, United Kingdom

Opt. Eng. 46(8), 085601 (September 07, 2007). doi:10.1117/1.2771652
History: Received October 23, 2006; Revised February 09, 2007; Accepted February 28, 2007; Published September 07, 2007
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The extension of path-independent 2-D phase unwrapping algorithms, based on placement of branch cut lines between phase singularities of opposite sign, was recently proposed for phase volumes in a paper by Huntley. In 3-D, the singularities were shown to form closed loops, and path independence was achieved by placing branch cut surfaces across the loops. In the current work, we describe in detail an optimized and extended version of Huntley’s algorithm. It deals in particular with two aspects that are essential for practical phase volumes: 1. how to close partial loops that pass through arbitrary boundaries separating valid and invalid phase data, and 2. how to select the set of loops having the shortest length. The second algorithm is necessary to deal with ambiguous cases that can arise when the singularities form knots, i.e., two loops pass through a single phase volume element. The performance of the algorithm is demonstrated on 3-D phase maps from two types of medical imaging data: medical resonance imaging (MRI) and x-ray interferometry.

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© 2007 Society of Photo-Optical Instrumentation Engineers

Citation

Olov Marklund ; Jonathan M. Huntley and Rhodri Cusack
"Robust unwrapping algorithm for three-dimensional phase volumes of arbitrary shape containing knotted phase singularity loops", Opt. Eng. 46(8), 085601 (September 07, 2007). ; http://dx.doi.org/10.1117/1.2771652


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