Wrapped Phase Values Research Articles

Gamma error correction algorithm for phase shift profilometry based on polar angle average

Phase errors caused by the gamma nonlinear response of the phase shift profilometry (PSP) severely affect 3D measurement accuracy. To tackle this, a simple phase error compensation technique based on polar angle average is presented in this paper to improve the accuracy. Wrapped phase values are regarded as polar angles, and a polar axis distribution map can be obtained in the polar coordinate. Practically, the polar axis distribution (PAD) of the undistorted wrapped phase is uniform. When there are nonlinear effects in an PSP, the polar axis is unevenly distributed. The difference between adjacent polar angles is computed and then rearranged with specifically labels. After that, the even PAD diagram is generated, and the smooth phase can be further recovered. Compared with conventional nonlinearity correction methods, the proposed method corrects the error without any auxiliary conditions. Its effectiveness and robustness are verified in simulations and experiments.

Absolute phase unwrapping for dual-camera system without embedding statistical features

This paper proposes an absolute phase unwrapping method for three-dimensional measurement that uses two cameras and one projector. On the left camera image, each pixel has one wrapped phase value, which corresponds to multiple projector candidates with different absolute phase values. We use the geometric relationship of the system to map projector candidates into the right camera candidates. By applying a series of candidate rejection criteria, a unique correspondence pair between two camera images can be determined. Then, the absolute phase is obtained by tracing the correspondence point back to the projector space. Experimental results demonstrate that the proposed absolute phase unwrapping algorithm can successfully work on both complex geometry and multiple isolated objects measurement.

A Novel Phase Shifting Technique of Coherent Gradient Sensing Method for Measuring Crack-tip K-Dominance

A novel phase shifting method for coherent gradient sensing (CGS) is proposed to automate fringe processing. The phase shifting of CGS interferograms can be simply realized by placing three plane-parallel plates sequentially between the two gratings in the traditional CGS method. The phase shifting method is deduced theoretically and the full-field wrapped phase value can be calculated accurately from four or more interferograms. A calibration test that determines the elasto-optic constant for a polymethyl methacrylate (PMMA) sheet is implemented as a verification experiment. Results show the proposed phase shifting method is valid for transmission CGS measurement. As an application, the proposed phase-shifted CGS method is applied to measure the crack tip K-dominance in a PMMA sheet. In addition, the phase shifting method is shown to be valid for reflective CGS measurement.

Reliability-guided phase unwrapping algorithm following noncontinuous path based on color fringe projection

The intrinsic drawbacks of existing reliability-based algorithms, they often fail to handle wrapped phase data contains error sources, such as phase discontinuities, noise and undersampling. These algorithms often calculate the reliability only relying on the recorded pixel intensity or wrapped phase value, but the intensity of pixel always exist many noises. In this paper, we present a new method to define the reliability of pixel and path of phase unwrapping, the pixel's intensity and color are employed in fringe analysis simultaneously. The reliability function is calculated based on modulation, second difference of wrapped phase, and second difference of modulation, then we present the concept of smoothness of path, the reliability of path is calculated based on reliability of pixel and smoothness of path. Experiment results validate our proposed algorithm is more accurate than many previous algorithms. The proposed algorithm can be used to unwrap the complex phase map with discontinuous jump, and can be implemented with high efficiency without any manual interface.

Demodulation of a single interferogram based on continuous wavelet transform and phase derivative

A novel method based on continuous wavelet transform (CWT) and guidance of phase derivative is developed to measure the phase of a single fringe pattern which contains closed fringes. Wrapped phase values are retrieved by ridge extraction algorithms based on CWT which has the capability of better noise reduction and thus increases the resolution of measurement significantly. To further reduce the noise, the scales detected by maximum ridge algorithm are filtered iteratively before retrieval of wrapped phase. The proposed method also identifies any ambiguous point in a non-monotonous fringe pattern by directly tracking an inflexion point from an unwrapped phase map without the use of a carrier. The algorithm developed is validated by computer simulation and experimental results. Based on micro interferometry the experimental results for both static and dynamic deformations of a micro structure demonstrate that the proposed method is an effective tool for the analysis of closed fringe patterns and subsequent deformation measurement. However, the proposed technique is limited to measurement of surface which is relatively smooth compared to the mean wavelength of the light source. In addition, prior knowledge of the sign of surface slope is required in cases where a spatial carrier is not available or adaptable.

Absolute phase measurements using geometric constraints between multiple cameras and projectors

The method of phase shift with the projection of multiple cyclic patterns enables 3D measurement that is highly accurate, dense, and fast. However, this measurement is only possible for the wrapped phase value, which has ambiguities in its multiples of cycles. Two particular problems are that conventional methods require additional patterns to be projected to determine the absolute phase and that unwrapping the phase tends to fail where depth varies abruptly. Two methods are proposed: the first is to determine the absolute phase without additional patterns being projected by observing the projected pattern with multiple cameras and applying the geometric constraints between them, and the second is to prevent failure in unwrapping the phase by referring to continuities in the relative phases of multiple projected patterns. The proposed methods were achieved with a 3D scanner that can measure approximately a 180 degrees field of view within 0.5 s, with an accuracy of 0.14 mm in depth.

Phase extraction from a single fringe pattern based on guidance of an extreme map

A method for automatic phase extraction from a single fringe pattern based on the guidance of an extreme map is introduced. The method uses an adaptive weighted filter to reduce noise and enhance contrast and to locate the fringe extremes. Wrapped phase values are calculated by use of an arccosine function obtained from the extreme map. With this method, wrapped phase values can be efficiently demodulated from a single fringe pattern without the need for assigning fringe order or interpolating fractional fringe order. The validity of the method is demonstrated by use of closed-fringe patterns generated by digital speckle interferometry.

Phase difference-based multichannel phase unwrapping

This work addresses the derivation of the phase difference-based maximum likelihood (ML) phase unwrapping algorithm. To this end, we derive the joint statistics of the phase differences on a two-dimensional grid for the multichannel case, where several scaled wrapped phase values are available. Subsequently, we determine and study the structure of the phase difference-based ML estimator and compare it to known phase unwrapping techniques. This work allows us to frame single and multichannel algorithms in a common formulation. Moreover, among the known single-channel phase difference-based procedures, we identify those attaining an ML solution. We also show that multichannel phase difference-based and, recently proposed, phase-based ML algorithms achieve equivalent solutions.

A new method for phase extraction from a single fringe pattern

A new technique for phase extraction from a single fringe-pattern image is presented. The algorithm locates the fringe maxima (assigned value 1) and minima (assigned value −1), and converts the intermediate gray-values into values between −1 and 1 using linear interpolation. A wrapped phase map is demodulated from a single fringe-pattern and the phase values are computed using an atan mode rather than an atan2 mode. Using the new algorithm wrapped phase values can be efficiently extracted from a single fringe pattern without the need for phase-shifting or carrier fringes. Phase extraction is carried out without the need for assigning fringe orders and distinction for a peak and a trough. The method can be applied to the study of transient events. Experimental results are presented to demonstrate the validity of the method.