Phase unwrapping by a maximum cross‐amplitude spanning tree algorithm: a comparative study

When the spatial fringe analysis method based on the moiré technique is applied to a noisy fringe image, problems arise in the processing with, for example, phase unwrapping, accuracy of analysis, and so on. A digital filter technique and a filter based on time series analysis are applied to the spatial fringe analysis method to solve these problems. In a simulation with a model of the fringe image, results show that the spatial fringe analysis method using digital filters is highly robust against a noise in an image, and that the method using a Kalman filter can smoothly and accurately detect the phase map of the object with a continuous phase distribution. Furthermore, the method is applied to analyze a speckle fringe image in ESPI. A new speckle interferometry based on the proposed method can analyze specklegrams with a normal ESPI system. The results show that a spatial fringe analysis method based on the moiré technique can analyze accurately the phase of a speckle fringe image using only a single fringe image. The proposed method can be anticipated to accelerate the use of ESPI in industry.

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“…͑7͒, the quantity of noise in the image can be given as noise signal ratio ͑NSR͒. 22 I͑x,z ͒ϭa͑ x,z ͒ϩb͑ x,z ͒cos͓ cx ϩ͑x,z ͔͒ϩnoise ͑7͒…”

Section: Spatial Fringe Analysis Methods With Filter Processingmentioning

confidence: 99%

Improvement of measuring accuracy of spatial fringe analysis method using a Kalman filter and its application

Arai

Yokozeki

2001

Opt. Eng

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“…The Fourier counterpart of the AC method can be derived using the Fourier power theorem [21], which can be mathematically expressed as (6) where and are Fourier transforms of image domain functions and . If we define and and consider the Fourier shift theorem [21], we have (7) Therefore, the linear coefficient can be estimated as the angle of the centroid of an angular distribution of in k-space as follows: (8) where is the Fourier transform of the complex image .…”

Section: A Review Of the Ac Methodsmentioning

confidence: 99%

“…The phase correction and unwrapping methods developed in the past few years generally fall into two categories: path-following methods and minimum-norm methods [1]. Cut-line methods [2]- [4], disk growing method [5], region growing methods (including maximum [6] and minimum spanning tree methods [7]) and Flynn's minimum discontinuity approach [8] are all path-following methods, which are based on the idea of guiding the integration of the gradient map to avoid any error propagation [2]. Minimum-norm methods are used to minimize the cost function to achieve phase unwrapping [1].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear phase correction with an extended statistical algorithm

Chang

Xiang

2005

IEEE Trans. Med. Imaging

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This paper presents a new magnetic resonance imaging (MRI) phase correction method. The linear phase correction method using autocorrelation proposed by Ahn and Cho (AC method) is extended to handle nonlinear terms, which are often important for polynomial expansion of phase variation in MRI. The polynomial coefficients are statistically determined from a cascade series of n-pixel-shift rotational differential fields (RDFs). The n-pixel-shift RDF represents local vector rotations of a complex field relative to itself after being shifted by n pixels. We have found that increasing the shift enhances the signal significantly and extends the AC method to handle higher order nonlinear phase error terms. The n-pixel-shift RDF can also be applied to improve other methods such as the weighted least squares phase unwrapping method proposed by Liang. The feasibility of the method has been demonstrated with two-dimensional (2-D) in vivo inversion-recovery MRI data.

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“…Among the path-dependent methods, a solution is to select from among all possible paths by using amplitude [43] or phase gradient [44,45] information to increase confidence in the unwrapping path. A statistical approach for path selection using genetic algorithms have also been proposed recently [46].…”

Section: Spatial Approachmentioning

confidence: 99%

Fringe Analysis

Surrel¹

2000

Topics in Applied Physics

105

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Abstract. Fringe analysis is the process of extracting quantitative measurement data from fringe -or line -patterns. It usually consists of phase detection and phase unwrapping. Phase detection is the calculation of the fringes phase from the recorded intensity patterns, and this issue represents the major part of the material in this review. Different techniques for this phase calculation are presented, with special emphasis on the characteristic polynomial method, allows us permits to easily design customized algorithms coping with many error sources. For reference, a table presenting the properties of almost all algorithms which have been in recent years is provided in the Appendix. A generic method allowing us to quantitatively evaluate the phase errors and the effect of noise is presented here for the first time. Finally, some elements regarding the complex problem of phase unwrapping are given.

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Phase unwrapping by a maximum cross‐amplitude spanning tree algorithm: a comparative study

Cited by 58 publications

References 15 publications

Improvement of measuring accuracy of spatial fringe analysis method using a Kalman filter and its application

Improvement of measuring accuracy of spatial fringe analysis method using a Kalman filter and its application

Nonlinear phase correction with an extended statistical algorithm

Fringe Analysis

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