Suping Fang

Quality-guided phase unwrapping algorithm based on reliability evaluation

For optical interferometry, a new quality-guided phase unwrapping algorithm based on the reliability evaluation of each pixel of the wrapped phase is proposed. First, the parameters used as quality measures in the past quality-guided algorithms are classified into the reliability measure and the quality measure, and the intensity of the object image belongs to the reliability measure. Then, by computing and applying a threshold to the intensity of the object image, the valid region (i.e., the interference region) is distinguished into the reliable region and the doubtful region. The wrapped phase in the reliable region is subsequently unwrapped by the way of multipaths integration, and different paths are guided by separate quality measures. Finally, starting from the reliable region, the doubtful region is unwrapped by the way that each path takes in the reliable region. Experimental results have shown that the proposed algorithm not only performs well, but also computes efficiently.

Simulation method for interference fringe patterns in measuring gear tooth flanks by laser interferometry

We present a ray-tracing-based method for simulation of interference fringe patterns (IFPs) for measuring gear tooth flanks with a two-path interferometer. This simulation method involves two steps. In the first step, the profile of an IFP is achieved by means of ray tracing within the object path of the interferometer. In the second step, the profile of an IFP is filled with interference fringes, according to a set of functions from an optical path length to a fringe gray level. To examine the correctness of this simulation method, simulations are performed for two spur involute gears, and the simulated IFPs are verified by experiments using the actual two-path interferometer built on an optical platform.

Analysis of General Characteristics of Transmission Error of Gears With Convex Modification of Tooth Flank Form Considering Elastic Deformation Under Load

The vibrationlnoise of power transmission gears is a serious problem for vehicles including automobiles, and therefore many studies on gear vibration have been reported. These studies, however, were carried out by investigation using numerical simulations in which gears with specific dimensions and tooth flank modifications under specific loading were considered. Therefore, the general characteristics of the transmission error of gears have not been clarified theoretically. In this report, a general model for the tooth meshing of gears is proposed; in which a quasi-infinite elastic model composed of springs with stiffness peculiar to the gear is incorporated. The transmission error of gears is formulated by theoretical equations. An investigation on the factors affecting the general characteristics of transmission error is accomplished using the formulated equations. The qualitative characteristic of the transmission error of gears with convex tooth flank form deviation is determined by the actual contact ratio and qualitative elements of gears, i.e., tooth flank form deviation and the distribution of stiffness. Even if the amplitude of torque, the amount of tooth flank form deviation, and other quantitative elements are not determined, the qualitative characteristic of transmission error can be derived. The peak-to-peak value of transmission error increases proportionately to the amount of tooth flank form deviation.

Object-image-based method to construct an unweighted quality map for phase extraction and phase unwrapping

A method to construct an unweighted quality map for phase extraction and phase unwrapping is proposed, based on an object image pattern. The object image pattern must be recorded under the same conditions as that of the corresponding interference patterns, except that the lights coming from the reference arm of the interferometer are hidden. An unweighted quality map that can represent the valid and invalid regions in the interference patterns is completed successfully, based on two factors: the fact that the object region in the object image pattern is homologous with the valid region (i.e., the interference region) in the interference patterns, and on distinguishing between the object and background regions in the object image pattern using neighbor window threshold filtering and fitting the boundary of the object image. The application of the proposed method to the real measurement shows its feasibility and correctness. This paper might provide an alternative method for constructing an unweighted quality map for phase extraction and phase unwrapping.

High resolution image fusion algorithm based on multi-focused region extraction ☆

Abstract An efficient way to obtain the high resolution image of a scene is using a line scan camera in the manner of macro photography. Due to the limited depth of field, only some portions of the image are focused. A common solution to this problem is utilizing the multi-focus image fusion technique, in which a series of images with different focus settings is acquired and the images are fused to an all focused one. However, it is difficult to register these high resolution images. Firstly, the magnifications of different regions of an image are different because of the depths of the scene. Secondly, the accuracy of feature detection in the region out of focus is difficult to ensure. Misregistration of the multi-focus images leads to the misjudgment of focus measures and the failure of image fusion. In this paper, we propose a novel high resolution multi-focus image fusion algorithm to solve this problem. The focused regions of each image are extracted for image registration and fusion, which improves the accuracy of image registration and the quality of image fusion. Experimental results show the proposed method is superior to the traditional methods in terms of both subjective evaluation and objective evaluation.

Compensation method for the alignment angle error of a gear axis in profile deviation measurement

In the precision measurement of involute helical gears, the alignment angle error of a gear axis, which was caused by the assembly error of a gear measuring machine, will affect the measurement accuracy of profile deviation. A model of the involute helical gear is established under the condition that the alignment angle error of the gear axis exists. Based on the measurement theory of profile deviation, without changing the initial measurement method and data process of the gear measuring machine, a compensation method is proposed for the alignment angle error of the gear axis that is included in profile deviation measurement results. Using this method, the alignment angle error of the gear axis can be compensated for precisely. Some experiments that compare the residual alignment angle error of a gear axis after compensation for the initial alignment angle error were performed to verify the accuracy and feasibility of this method. Experimental results show that the residual alignment angle error of a gear axis included in the profile deviation measurement results is decreased by more than 85% after compensation, and this compensation method significantly improves the measurement accuracy of the profile deviation of involute helical gear.

Image-inpainting and quality-guided phase unwrapping algorithm

For the wrapped phase map with regional abnormal fringes, a new phase unwrapping algorithm that combines the image-inpainting theory and the quality-guided phase unwrapping algorithm is proposed. First, by applying a threshold to the modulation map, the valid region (i.e., the interference region) is divided into the doubtful region (called the target region during the inpainting period) and the reasonable one (the source region). The wrapped phase of the doubtful region is thought to be unreliable, and the data are abandoned temporarily. Using the region-filling image-inpainting method, the blank target region is filled with new data, while nothing is changed in the source region. A new wrapped phase map is generated, and then it is unwrapped with the quality-guided phase unwrapping algorithm. Finally, a postprocessing operation is proposed for the final result. Experimental results have shown that the performance of the proposed algorithm is effective.

Positioning the actual interference fringe pattern on the tooth flank in measuring gear tooth flanks by laser interferometry

In measuring form deviation of gear tooth flanks by laser interferometry, the collected interference fringe pattern (IFP) is badly distorted, in the case of shape, relative to the actual tooth flank. Meanwhile, a clear and definite mapping relationship between the collected IFP and the actual tooth flank is indispensable for both transforming phase differences into deviation values and positioning the measurement result on the actual tooth flank. In order to solve these problems, this paper proposes a method using the simulation tooth image as a bridge connecting the actual tooth flank and the collected IFP. The mapping relationship between the simulation tooth image and the actual tooth flank has been obtained by ray tracing methods [Fang et al., Appl. Opt. 49(33), 6409-6415 (2010)]. This paper mainly discusses how to build the relationship between the simulation tooth image and the collected IFP by using a matching algorithm of two characteristic point sets. With the combination of the two above-mentioned assistant mapping relationships, the mapping relationship between the collected IFP and the actual tooth flank can be built; the collected IFP can be positioned on the actual tooth flank. Finally, the proposed method is employed in a measurement of the form deviation of a gear tooth flank and the result proves the feasibility of the proposed method.

Improvement of the oblique-incidence optical interferometric system to measure tooth flanks of involute helical gears.

We put forward a plan of improving the oblique-incidence optical interferometric system applied in the measurement of tooth flanks of an involute spur gear in order to expand its capability to measure an involute helical gear. On the basis of the features of an involute helical tooth flank, we discuss how to realize the parallelism between the optical axis of the object arm of the optical system and the straight lines constructing the involute helical tooth flank. This parallelism helps the optical system produce an interference fringe pattern as clear as the one of an involute spur gear [Appl. Opt.49, 6409 (2010).]. A numerical simulation is then performed to examine the correctness of the improvement. During simulating, we unify the equation of difference tooth flanks by means of importing two parameters in relation to the left or right side of a tooth flank and the helical direction of teeth, respectively. Finally, the actual experiment is fulfilled through the real optical system built on an optical table. The simulation and experiment results verify the correctness and feasibility of the proposed improvement.

Eccentricity error compensation for geometric camera calibration based on circular features

Circular features are very common in geometric camera calibration. The projection of a circular feature is generally a deformed ellipse, not a true ellipse, due to the presence of lens distortion. The center of the deformed ellipse, obtained by fitting the boundary points with an ellipse, does not necessarily coincide with the distorted point corresponding to the center of the undistorted projection of the circular feature. An eccentricity error will be introduced if the two points are considered to be coincident. In this study three main factors that affect the amount of the eccentricity error are discussed, including the form and amount of lens distortion, the size of the circular feature and the tilt of the supporting plane. Then, an effective geometric camera calibration method is proposed where the eccentricity error is compensated by establishing the correspondence between the estimated model position and the real position of the fitted center of the deformed ellipse. Both simulation and measurement data verify the existence of the eccentricity error and the effectiveness of the proposed method.