Radial-mode sensitive probe beam in the rotational Doppler effect.

The rotational Doppler effect (RDE) attracts much attention in various research areas, from acoustics to optics. The observation of RDE mostly depends on the orbital angular momentum of the probe beam, while the impression of radial mode is ambiguous. To clarify the role of radial modes in RDE detection, we reveal the mechanism of interaction between probe beams and rotating objects based on complete Laguerre-Gaussian (LG) modes. It is theoretically and experimentally proved that radial LG modes play a crucial role in RDE observation because of topological spectroscopic orthogonality between probe beams and objects. We enhance the probe beam by employing multiple radial LG modes, which makes the RDE detection sensitive to objects containing complicated radial structures. In addition, a specific method to estimate the efficiency of various probe beams is proposed. This work has the potential to modify RDE detection method and take the related applications to a new platform.

Simulated wrapped phase optimizes phase retrieval in phase-shifting interferometry.

Phase retrieval is crucial in phase-shifting interferometry and other phase measurement techniques. However, in noisy wrapped phase maps with high steepness, discontinuities arise and cause phase unwrapping errors. To solve this problem, this Letter presents a phase retrieval method based on a simulated wrapped phase. By establishing the correspondence between the simulated and measured interferograms, the difference in wrapped phases between them can be obtained. The difference in wrapped phase map, which has sparse and wide interference fringes, has a higher reliability of phase unwrapping. The proposed method not only possesses high phase retrieval accuracy but it also simplifies the processing of interferograms. Furthermore, the layout of all interferometric systems, the parameters of optical components, and the model of the measured object are known, so the proposed method can be used as a reference for phase retrieval.

Fringe direction weighted autofocusing algorithm for gear tooth flank form deviation measurement based on an interferogram.

When measuring the form deviation of the gear tooth flank with laser interferometry, due to the limitation of the depth of field of the lens, focused and defocused regions exist in the interferogram simultaneously. The introduced errors that were generated by these defocused regions decrease the measurement accuracy. Therefore, the evaluation of definition for interferograms is necessary for image processing. However, the gradient of gray, which performs by fringes, makes it difficult for traditional algorithms to evaluate its definition. This paper proposes a method based on nonsubsampled contourlet transformation (NSCT) combined with fringe direction as weighting coefficients to solve the problem. First, the information about the directions of these fringes in interferograms was evaluated. Then, the NSCT method was applied to interferograms so that several sub-images in different scales and directions can be achieved. Based on these sub-images and directions information, an improved function for definition evaluation was conducted. Lastly, a series of simulations and experiments was carried out to verify its feasibility and accuracy.

Phase unwrapping based on adaptive image in-painting of fringe patterns in measuring gear tooth flanks by laser interferometry.

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.

Weighted least-squares phase unwrapping algorithm based on a non-interfering image of an object.

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.

Autofocusing algorithm of interferogram based on object image and registration technology.

Because the depth of field (DOF) of lenses is limited, a captured interferogram usually includes a focused region and defocused region simultaneously when the form deviation of the helical tooth flank is measured with laser interferometry. Because of the impact of the interference fringe, the existing autofocusing algorithms are difficult for identifying the focused region of the interferogram directly. This paper proposes a new autofocusing algorithm based on the object image and registration technology. First, the reliability region is evaluated according to the gray level. Then the corresponding pixels in the image sequence are determined with the registration technology. Next, the focused region is judged by comparing the average gray gradients in object images. Based on the characteristics of measured gear and the DOF of lens, an experiment is designed. The experimental results are given to verify the feasibility and accuracy of the proposed autofocusing algorithm.