Lujie Chen

A quality-guided displacement tracking algorithm for ultrasonic elasticity imaging.

Displacement estimation is a key step in the evaluation of tissue elasticity by quasistatic strain imaging. An efficient approach may incorporate a tracking strategy whereby each estimate is initially obtained from its neighbours’ displacements and then refined through a localized search. This increases the accuracy and reduces the computational expense compared with exhaustive search. However, simple tracking strategies fail when the target displacement map exhibits complex structure. For example, there may be discontinuities and regions of indeterminate displacement caused by decorrelation between the pre- and post-deformation radio frequency (RF) echo signals. This paper introduces a novel displacement tracking algorithm, with a search strategy guided by a data quality indicator. Comparisons with existing methods show that the proposed algorithm is more robust when the displacement distribution is challenging.

Fringe projection profilometry with nonparallel illumination: a least-squares approach

Under a nonparallel illumination condition, fringe patterns projected on an object have unequal fringe spacing that would introduce a nonlinear carrier phase component. This Letter describes a nonlinear carrier removal technique based on a least-squares approach. In contrast with conventional methods, the proposed algorithm would not magnify phase measurement uncertainty, nor does it require direct estimation of system geometrical parameters. The theoretical expression of the carrier phase function on the reference is derived and expanded in a power series. The unknown coefficients in the series are determined by a least-squares method. By subtracting the calculated carrier phase function from the unwrapped phase map, the phase distribution of the object profile is obtained.

Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry

When a continuously deforming object is measured by electronic speckle pattern interferometry (ESPI), the speckle pattern recorded on a camera sensor changes constantly. These time-dependent speckle patterns would provide the deformation history of the object. Various objects are applied with both linearly and nonlinearly varying loads and speckle patterns are captured using a high-speed CCD camera. The temporal intensity variation of each pixel on the recorded images is analyzed by a robust mathematical tool—Morlet wavelet transform instead of conventional Fourier transform. The transient velocity and displacement of each point can be retrieved without the necessity of the temporal or spatial phase unwrapping process. The displacements obtained are compared with those from a temporal Fourier transform, and the results show that the wavelet transform minimizes the influence of noise and provides better results for a linearly varying load. System error in the wavelet analysis for nonlinear load is also discussed.

A hybrid displacement estimation method for ultrasonic elasticity imaging

Axial displacement estimation is fundamental to many freehand quasistatic ultrasonic strain imaging systems. In this paper, we present a novel estimation method that combines the strengths of quality-guided tracking, multi-level correlation, and phase-zero search to achieve high levels of accuracy and robustness. The paper includes a full description of the hybrid method, in vivo examples to illustrate the method¿s clinical relevance, and finite element simulations to assess its accuracy. Quantitative and qualitative comparisons are made with leading single- and multi-level alternatives. In the in vivo examples, the hybrid method produces fewer obvious peak-hopping errors, and in simulation, the hybrid method is found to reduce displacement estimation errors by 5 to 50%. With typical clinical data, the hybrid method can generate more than 25 strain images per second on commercial hardware; this is comparable with the alternative approaches considered in this paper.

Shape measurement by the use of digital image correlation

Digital image correlation DIC using a single camera has been widely used for determination of in-plane displacement. However, in order to obtain shape information on an object, one should employ stereo vision systems with multiple cameras. In this paper, a new method using digital image correlation for shape measurement is developed. In the proposed method, an object with a surface profile is given an in- plane translation, and digital image correlation is employed to measure the image displacement. Since the object has a surface height variation, the magnification at each point is different. Thus the image displacement field obtained from the DIC method contains the shape information of the object, which can be retrieved from a pinhole camera model. Principles of the proposed method are described. Experiments conducted to mea- sure a step change and a light bulb show that the method is simple, effective, and suitable for measurement of a step change or a large object.

Spatial-fringe-modulation-based quality map for phase unwrapping

The quality-guided algorithm is a method widely used in phase unwrapping. The algorithm uses a quality map to guide its unwrapping process, and its validity depends on whether the quality map can truly reflect phase quality. In fringe projection surface profilometry, discontinuous surface structure, low surface reflectivity, and saturation of the image-recording system are sources of unreliable phase data. To facilitate the unwrapping process, we demonstrate an accurate quality map based on spatial fringe modulation, which is extracted from a single fringe pattern. Compared with temporal fringe modulation, the new criterion is more sensitive to spatial structure changes and less dependent on illumination conditions.

Fringe-density estimation by continuous wavelet transform

For many phase extraction algorithms, a priori knowledge of a fringe-pattern density distribution is beneficial for later processing. A fringe-density estimation method based on a continuous wavelet transform (CWT) is proposed. For a one-dimensional signal the instantaneous frequency detected at the CWT ridge is directly adopted as a measure of the local fringe density. For a two-dimensional signal the instantaneous frequency components in both the x and the y directions are detected. Their reliability is evaluated by the CWT coefficient magnitude, based on which an approximate density value is given. The capability for noise reduction and the accuracy of the method are discussed.

Carrier phase component removal: a generalized least-squares approach

In fringe projection profilometry, an object shape is evaluated through phase distribution extracted from a projected fringe pattern. For parallel illumination geometry, the carrier phase component introduced by the fringes is spatially linear, whereas nonparallel illumination would lead to a nonlinear carrier. In this study, a general approach for the removal of a nonlinear-carrier phase component is proposed. A series expansion technique is used to approximate the carrier phase function, and a least-squares method is developed to estimate the unknown coefficients of the series. The theoretical analysis is given on the basis of a divergent illumination geometry with carrier fringes in the x direction. The method is also extended to include a curved surface-fitting approach, which is applicable to various measurement system geometries.

Reply to Comment on "Fringe projection profilometry with nonparallel illumination: a least-squares approach"

We have confirmed that a mathematical expression in our previous Letter [Chen and Quan, Opt. Lett.30, 2101 (2005)] should be modified. The modification, however, does not affect the validity of the method reported, the results obtained and the subsequent conclusions made.

Phase retrieval with a three-frame phase-shifting algorithm with an unknown phase shift.

A three-frame phase-shifting algorithm with a constant but unknown phase shift is proposed. The algorithm is based on background-intensity removal prior to phase retrieval to eliminate an undetermined factor in a fringe pattern. The proposed method is validated on three-dimensional profilometry by fringe projection and on deformation measurement by means of digital speckle shearing interferometry. For a fringe pattern with slow-varying background intensity, the background removal is achieved in the frequency domain. For a speckle pattern, a background removal technique is integrated with the three-frame algorithm. In this process, manual intervention is minimal, and high computational speed is achieved. In addition, high-frequency phase signals would not be removed in the noise-reduction process as is the case in the bandpass-filtering technique. Accuracy of the method is discussed.