Conventional quality maps for weighted least-squares phase unwrapping are not appropriate in regions of abnormal fringes. In this paper, the use of a non-interfering image of an object for a reliability map is proposed for robust phase unwrapping. First, the conventional weighted least-squares algorithm is applied, and the unreliable region is detected. Then, the unreliable region is unwrapped iteratively using the non-interfering image of the object. Finally, both phase maps are combined and smoothed by a continuity operation. Experimental results show that the proposed algorithm is appropriate for unwrapping phase maps of abnormal fringes.

Phase unwrapping in regions of abnormal fringes remains an unresolved issue. In this paper, we present an approach that combines an image-inpainting strategy based on an adaptive window which is obtained according to the density and orientation of fringe patterns and a quality-guided algorithm for phase unwrapping. First, a threshold is set to a quality map to detect the target region. Second, the target region is filled with new phase values by the adaptive image-inpainting method. Then, a quality-guided phase unwrapping algorithm is applied to this newly generated wrapped phase map. Finally, postprocessing of the unwrapped result is performed. The method is validated through several simulation and experiments. The results demonstrate that the proposed algorithm is effective in the presence of abnormal fringes.

Phase unwrapping in regions of abnormal fringes caused by noise, aliasing, fracturing, and the presence of mass discontinuous phases of unwrapped results remains an unresolved issue. We present an approach that combines an iterated discontinuous phase recovery strategy and a quality-guided algorithm based on mutual information quality maps. First, the quality-guided unwrapping algorithm based on mutual information is applied, and the results of the discontinuous phase region are excluded. Second, the remainder of the continuous phase region is rewrapped and unwrapped iteratively until there are no discontinuities in the result. Finally, the discontinuous region is recovered by a continuity operation. The method is validated through both simulations and experiments, thereby demonstrating that the proposed algorithm is robust in the presence of abnormal fringes and that the discontinuous phase can be reduced significantly.

A measurement datum is crucial in measuring a gear tooth flank by laser interferometry. Manufacturing a physical reference tooth flank as a measurement datum has many drawbacks: many different reference tooth flanks are needed with the changing of the measured gear’s parameters; the reference tooth flank’s manufacturing error lowers the measurement precision; the installation error between the measured and referenced tooth flank lowers the measurement precision also. The drawbacks restrain the practical use of measuring gear by laser interferometry. A construction method of a virtual measurement datum has been proposed to solve the problem. First, a virtual error-free model of the measured tooth flank is built according to its parameters and actual measurement position. Subsequently, the interferogram of the virtual tooth flank is simulated as a measurement datum through the ray tracing. To harvest the actual measurement position of the measured tooth flank, a compensation approach for optical system error and a tracing algorithm for actual installation position are developed. Experimental results prove that a virtual measurement datum can be constructed and used in measuring a gear tooth flank. Furthermore, this research verifies that ray tracing can be used to construct a virtual measurement datum in the relevant comparative measurements processes by laser interferometry.