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1. Cosine Error Elimination Method for One-Dimensional Convex and Concave Surface Profile Measurements

   https://doi.org/10.1115  

   Xiangyu Guo, Jaemin Han (February 2020, Journal of manufacturing science and engineering)

   This paper presents a novel method to eliminate cosine error in precision concave and convex surface measurement by integrating a displacement probe in a precision spindle. Cosine error in surface profile measurement comes from an angular misalignment between the measurement axis and the axis of motion and negatively affects the measurement accuracy, especially in optical surface measurements. A corrective multiplier can solve this problem for spherical surface measurement, but cosine error cannot be eliminated in the case of complex optical surface measurement because current tools do not measure such surfaces along the direction normal to the measurement plane. Because the displacement probe is placed on the spindle axis, the spindle error motion will affect the shape precision and surface roughness measurement of optical components such as mirrors and lenses, and the displacement probe will measure a combination of the spindle error motion and the geometry of optical surfaces. Here, the one-dimensional concave, convex, and hollow measurement targets were used, and cosine error was fundamentally eliminated by aligning the probe on the spindle always normal to the measured surface, and compensation was made for the aerostatic bearing spindle rotational error obtained by the reversal method. The results show that this proposed measurement method cannot only eliminate cosine error but also scan the large area quickly and conveniently. In addition, measurement uncertainty and further consideration for future work were discussed. 

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2. Cosine Error-Free Metrology Tool Path Planning for Thickness Profile Measurements

   https://doi.org/10.1115/1.4048433  

   Guo, Xiangyu; Lee, ChaBum (April 2021, Journal of Manufacturing Science and Engineering)

   null (Ed.)

   Abstract This paper presents a novel thickness profile measuring system that measures double-sided thin pipe wall surfaces in a non-contact, continuous, cosine error-free, and fast manner. The surface metrology tool path was developed to align the displacement sensors always normal to the double-sided surfaces to remove cosine error. A pair of capacitive-type sensors that were placed on the rotary and linear axes simultaneously scans the inner and outer surfaces of thin walls. Because the rotational error of the rotary axis can severely affect the accuracy in thickness profile measurement, such error was initially characterized by a reversal method. It was compensated for along the rotational direction while measuring the measurement target. Two measurement targets (circular and elliptical metal pipe-type thin walls) were prepared to validate the developed measurement method and system. Not only inner and outer surface profiles but also thin-wall thickness profiles were measured simultaneously. Based on the output data, the circularity and wall thickness variation were calculated. The thickness profile results showed a good agreement with those obtained by a contact-type micrometer (1-µm resolution) at every 6-deg interval. The uncertainty budget for this measuring system with metrology tool path planning was estimated at approximately 1.4 µm. 

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3. On-axis deflectometric system for freeform surface measurement

   https://doi.org/10.1364/OL.486170  

   Zhu, Shengtai; Wang, Daodang; Kang, Wenjun; Liang, Rongguang (April 2023, Optics Letters)

   We propose an on-axis deflectometric system for the accurate measurement of freeform surfaces with large slope ranges. A miniature plane mirror is attached on the illumination screen to fold the optical path and achieve the on-axis deflectometric testing. Due to the existence of the miniature folding mirror, the deep-learning method is applied to recover the missing surface data in a single measurement. Low sensitivity to the calibration error of system geometry and high testing accuracy can be achieved with the proposed system. The feasibility and accuracy of the proposed system have been validated. The system is low in cost and simple in configuration, and it provides a feasible way for the flexible and general testing of freeform surfaces, with a significant potential of the application in on-machine testing. 

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4. Experimental Studies on Fabricating Lenslet Array with Slow Tool Servo

   https://doi.org/10.3390/mi13101564  

   Kang, Wenjun; Seigo, Masafumi; Xiao, Huapan; Wang, Daodang; Liang, Rongguang (October 2022, Micromachines)

   On the demand of low-cost, lightweight, miniaturized, and integrated optical systems, precision lenslet arrays are widely used. Diamond turning is often used to fabricate lenslet arrays directly or molds that are used to mold lenslet arrays. In this paper, mainly by real-time monitoring position following error for slow tool servo, different fabrication parameters are quantitatively studied and optimized for actual fabrication, then by actual fabrication validation, uniform and high-fidelity surface topography across the actual whole lenslet array is achieved. The evaluated fabrication parameters include sampling strategy, inverse time feed, arc-length, etc. The study provides a quick, effective, and detailed reference for both convex and concave lenslet array cutting parameter selection. At the end, a smooth zonal machining strategy toolpath is demonstrated for fabricating concave lenslet arrays. 

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5. Fast Non-Convex Hull Computation

   https://doi.org/10.1109/3DV.2019.00087  

   Bayardo Spadafora, Julian; Gomez-Fernandez, Francisco; Taubin, Gabriel (September 2019, 2019 International Conference on 3D Vision (3DV))

   3D surface reconstruction usually begins with a point cloud and aims to build a representation of the object producing that point cloud. There are several algorithms to solve this problem, each with different priors over the point cloud, such as the type of object represented, or the method by which it was obtained. In this work, we focus on an algorithm called Non-Convex Hull (NCH), which reconstructs surfaces through a concept similar to the Medial Axis Transform. A new algorithm called Shrinking Planes is proposed to compute the NCH, based on the Shrinking Ball method with a few improvements. We prove that the new method can approximate surfaces to arbitrarily small error, and evaluate its performance on the surface reconstruction task. The new method maintains the same reconstruction quality as the Naïve Non-Convex Hull method, while achieving a large performance improvement. 

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