Data processing for point-based in situ metrology of freeform optical surface

Parallel unambiguous generalized phase-shifting and T-spline fitting algorithms for optical micro-structured surface 3D topography metrology

3D topography metrology of optical micro-structured surfaces is critical for controlled manufacturing and evaluation of optical properties. Coherence scanning interferometry technology has significant advantages for measuring optical micro-structured surfaces. However, the current research faces difficulties of designing high accuracy and efficient phase shifting, and characterization algorithms for optical micro-structured surface 3D topography metrology. In this paper, parallel unambiguous generalized phase-shifting and T-spline fitting algorithms are proposed. To avoid phase ambiguity and improve the accuracy of the phase-shifting algorithm, the zero-order fringe is determined by the iterative envelope fitting with Newton's method, and the accurate zero optical path difference is determined by a generalized phase-shifting algorithm. In particular, the calculation procedures of the multithreading iterative envelope fitting with Newton's method and generalized phase shifting are optimized with the graphics processing unit-Compute Unified Device Architecture kernel function. Additionally, to fit the base form of optical micro-structured surfaces and characterize the surface texture and roughness, an effective T-spline fitting algorithm is proposed by optimizing the preimage of the T-mesh with image quadtree decomposition. Experimental results show that the surface reconstruction of optical micro-structured surfaces using the proposed algorithm is more accurate, and the efficiency is 10 times higher than that of current algorithms; the time of the surface reconstruction is less than 1 s. Compared with the current B-spline method, the accuracy of roughness characterization using the proposed T-spline algorithm is improved by more than 10%.

Freeform optics characterization with surface registration and fitting algorithms for optical point-based spatial path 3D topography metrology

Accurate characterization of the form error for freeform optics is critical for controlled manufacturing and evaluation of optical properties. To solve the difficulty of current surface registration and fitting algorithms, and improve characterization accuracy of the form error of freeform optics for optical point-based spatial path 3D topography metrology, in this paper, improved surface registration and fitting algorithms are proposed, including a B-spline surface description of freeform optics, point orthogonal projection, registration parameter optimization, and B-spline fitting. Limited by the angular characteristics of an optical point-based sensor, the slope and reference frame of freeform optics must be flexibly adjusted, and polynomial surfaces are described and fitted as B-spline surfaces based on B-spline geometric invariance. To efficiently determine corresponding points on B-spline surfaces, the point orthogonal projection algorithm without Bezier subdivision is proposed using the first-order Newton method. Then, the iteration procedure of coordinate adjustment in sphere space using Lie algebra registration parameters is proposed to solve the difficulty of the current registration parameter optimization procedure. To fit a spatial path form error, the least squares B-spline fitting method is proposed to improve the Zernike method. Through simulation experiments, the proposed registration algorithm with good convergence can improve accuracy by one to two orders of magnitude compared with current registration algorithms. Through repeated experiments of a freeform prism, the proposed method can significantly improve the peak-to-valley and RMS accuracies compared with the stylus method, and characterize the mid-high frequency form error (about 200 nm) of a freeform prism.

Steep freeform measurement method based on a normal transverse differential confocal

A normal transverse laser differential confocal freeform measurement (NTDCFM) method was proposed to address the high-precision measurement difficulty of steep freeform surfaces with large variations in inclination, scattering, and reflectance. Using D-shaped diaphragm technology, the freeform surface under test (FSUT) axial variation transformed into a spot transverse movement on the detection focal plane. Meanwhile, a 2D position sensitive detector (PSD) was used to obtain the normal vector of the sampling points so that the measuring sensor's optical axis could track the FSUT normal direction. The focus tracking method extended the sensor measurement range. Theoretical analysis and experimental results showed that the axial resolution of the NTDCFM was better than 0.5 nm, the direction resolution of the normal vector was 0.1°, the maximum surface inclination could be measured up to 90°, the sensor range was 5 mm, and the measurement repeatability of the FSUT was better than 9 nm. It provides an effective new anti-inclination, anti-scattering, and anti-reflectivity method for accurately measuring steep freeform surfaces.

Design and error calibration of an on-axis deflectometric microscope system

An on-axis deflectometric microscope system (ODMS) is proposed for the microscopic surface measurement with high accuracy and a large slope dynamic range. To reduce the geometry sensitivity, a beam splitter is employed to build the coaxial configuration among the illumination screen, camera, and tested sample, which facilitates the calibration of system geometrical parameters. Due to the small working distance, the system model miscalibration in the model-ray-tracing-based "null" testing could cause obvious geometrical aberrations. In this paper, the geometrical aberrations due to the system model miscalibration are analyzed, and the corresponding calibration method based on computer-aided reverse optimization is applied to achieve accurate measurement. In addition, the systematic error introduced by the system components in the ODMS are also discussed. Both the simulation and experiment have been carried out to demonstrate the feasibility and high accuracy of the proposed measurement method. The proposed system is compact in structure, large in measurable slope range, and high in spatial resolution, providing a viable metrological tool for the microscopic testing of various freeform surfaces, microstructural elements, and micro-devices.

Enhanced precision inspection of free-form surface with an improved whale optimization algorithm

For precision inspection of free-form surface parts using non-contact measurement methods, the registration between the actual measurement model and the ideal design model is necessary.The traditional iterative closure point (ICP) method requires good initial parameters to obtain the global optimal transformation matrix, which is difficult to guarantee in the actual detection process. In order to improve the accuracy and robustness of free-form surface precision inspection, an Improved Whale Optimization Algorithm (IWOA) is proposed in this study.This algorithm can solve the required registration parameters by constantly updating the population. A measurement experimental system is designed to test the accuracy of blade registration. The performance of IWOA is evaluated by the actual measurement experiment, and the results are verified by a comparative study with Whale Optimization Algorithm (WOA), Lévy flight trajectory-based Whale Optimization Algorithm (LWOA), and Adaptive Whale Optimization Algorithm (AWOA). The surface registration errors are 0.1711mm for IWOA, 2.0015 mm for WOA, 1.2656 mm for LWOA, 2.8132 mm for AWOA and 2.1537 mm for ICP. The results show that the accuracy of IWOA is more than 7 times higher than other four algorithms. In general, the experiments indicate that IWOA has a good registration ability and can meet the needs of industrial measurement.

Data-Driven Intelligent 3D Surface Measurement in Smart Manufacturing: Review and Outlook

High-fidelity characterization and effective monitoring of spatial and spatiotemporal processes are crucial for high-performance quality control of many manufacturing processes and systems in the era of smart manufacturing. Although the recent development in measurement technologies has made it possible to acquire high-resolution three-dimensional (3D) surface measurement data, it is generally expensive and time-consuming to use such technologies in real-world production settings. Data-driven approaches that stem from statistics and machine learning can potentially enable intelligent, cost-effective surface measurement and thus allow manufacturers to use high-resolution surface data for better decision-making without introducing substantial production cost induced by data acquisition. Among these methods, spatial and spatiotemporal interpolation techniques can draw inferences about unmeasured locations on a surface using the measurement of other locations, thus decreasing the measurement cost and time. However, interpolation methods are very sensitive to the availability of measurement data, and their performances largely depend on the measurement scheme or the sampling design, i.e., how to allocate measurement efforts. As such, sampling design is considered to be another important field that enables intelligent surface measurement. This paper reviews and summarizes the state-of-the-art research in interpolation and sampling design for surface measurement in varied manufacturing applications. Research gaps and future research directions are also identified and can serve as a fundamental guideline to industrial practitioners and researchers for future studies in these areas.

Model calibration by multi-null constraint for an optical freeform surface adaptive interferometer

Model calibration is performed for an adaptive freeform surface interferometer (AFI). In view of the non-unique null configuration in AFI, the multi-null constraint (MNC) calibration method is proposed to address error coupling in the null configuration modeling. The final figure error of the tested surface can be extracted together with the coupling parameters. The performance of the MNC method is evaluated in simulations and experiments. The higher accuracy is proved after the MNC calibration. This calibration is preparation for the subsequent system instrumentation.

Internal Adaptation of Implant-Supported, Polymer-Infused Ceramic Crowns Fabricated by Two CAD/CAM Systems

PURPOSE

The aim of this in vitro study was to compare the internal 3D adaptation of polymer-infused ceramic crowns fabricated using two CAD/CAM systems: CEREC inLab MC XL and Ceramill Motion 2 (5X).

MATERIALS AND METHODS

Twenty-five implant-supported metal-ceramic crowns were fabricated conventionally using the lost-wax technique, and the outer contour was scanned to serve as a guide for designing the polymer-infused ceramic CAD/CAM crowns. Twenty-five crowns were fabricated using CEREC, and 25 crowns were fabricated using Ceramill. The cement space was set to 20 μm. The Zeiss Accura Microsystem Coordinate Measuring Machine (CMM), Calypso, and Geomagic software were used to measure the 3D accuracy of fit of all crowns to their respective implant abutments. To test for the statistical significance between groups in terms of 3D total distortion, a one-way ANOVA was conducted. The Kolmogorov-Smirnov test was used to investigate the differences in the x, y, and z coordinates. A p-value of 0.05 or less was considered statistically significant at an alpha level of 0.05.

RESULTS

Comparing the 3D misfit of metal-ceramic crowns to those of CAD/CAM crowns fabricated using CEREC revealed no significant difference (88.20 ± 36.59 μm vs. 102.45 ± 36.58 μm, p = 0.161). Similarly, no significant difference in 3D total distortion was identified between metal-ceramic crowns and crowns fabricated using Ceramill (88.20 ± 36.59 μm vs. 78.40 ± 31.03 μm, p = 0.336); however, the 3D total distortion of polymer-infused crowns made by Ceramill was significantly reduced compared to that of crowns fabricated by CEREC (78.3 ± 31.0 μm vs. 102.4 ± 36.5 μm, p = 0.019).

CONCLUSIONS

Polymer-infused ceramic crowns fabricated using CEREC exhibited the least accurate 3D fit. All misfit values of the tested groups were within clinically acceptable levels.

Integrated manufacture of a freeform off-axis multi-reflective imaging system without optical alignment

Multi-reflective imaging systems find wide applications in optical imaging and space detection. However, it is faced with difficulties in adjusting the freeform mirrors with high accuracy to guarantee the optical function. Motivated by this, an alignment-free manufacture approach is proposed to machine the optical system. The direct optical performance-guided manufacture route is established without measuring the form error of freeform optics. An analytical model is established to investigate the effects of machine errors to serve the error identification and compensation in machining. Based on the integrated manufactured system, an ingenious self-designed testing configuration is constructed to evaluate the optical performance by directly measuring the wavefront aberration. Experiments are carried out to manufacture a three-mirror anastigmat, surface topographical details and optical performance shows agreement to the designed expectation. The final system works as an off-axis infrared imaging system. Results validate the feasibility of the proposed method to achieve excellent optical application.