Measurement Of Freeform Surfaces Research Articles

Round robin comparison study on the form measurement of optical freeform surfaces

A round robin comparison of freeform form measurements was carried out by the project partners and stakeholders of a European metrology research project. Altogether six measuring instruments were considered: five different (pointwise and areal) optical devices and one tactile device. Three optical freeform surfaces were used for the comparison measurements, where two specimens were measured by five instruments and one specimen by four instruments. In this paper, the evaluation methods and results of this round robin are presented for the three freeform surfaces made from a temperature-stable material, Super Invar ®. The freeforms had diameters of 40 mm, 50 mm and 100 mm and best-fit radii of 39.75 mm (convex), 40.9 mm (convex) and 423.5 mm (concave). For comparison, the bilateral pointwise differences between the available measurements were calculated. The root-mean-square values of these differences ranged from 15 nm to 110 nm (neglecting spherical contributions) and provided an insight into the status of typical freeform measurement capabilities for optical surfaces.

Determining the strategy of contact measurements based on results of non-contact coordinate measurements

The strategy of contact coordinate measurements of free-form surfaces may include many elements, e.g. methods of the distribution of measurement points, which determine the final accuracy of measurements. Measurement points, at which contact coordinate measurements are conducted, should be located in the parts of surfaces of investigated objects which are characterized by the poor quality of manufacturing in order to decrease the time of measurements and increase the accuracy of a measurement task. The paper presents the algorithm of determining the strategy of contact measurements in the field of distributing measurement points on curvilinear surfaces. The new method is mainly intended for measurements conducted by using coordinate measuring machines. The algorithm takes into account the results of non-contact coordinate measurements. The application of initial non-contact measurements in the mentioned algorithm is aimed at increasing the accuracy of contact coordinate measurements and speeding up the whole measurement process of complex products.

Selection of the Best Model of Distribution of Measurement Points in Contact Coordinate Measurements of Free-Form Surfaces of Products.

The article presents a new method for determining the distribution of measurement points, which can be used in the case of contact coordinate measurements of curvilinear surfaces of products. The developed method is based on multi-criteria decision analysis. In the case of the new method, the selection of the distribution of measurement points on free-form surfaces is carried out based on the analysis of five different criteria. The selection of the best model of the distribution of measurement points results from the accuracy of coordinate measurements, the time needed to complete measurement tasks, the number of measurement points, the accuracy of the substitute surface representing the measured free-form surface and the area where measurement points are located. The purpose of using the developed method of the distribution of measurement points is to increase the performance of coordinate measurements primarily by increasing the automation of strategy planning of measurements of curvilinear surfaces and improving the accuracy of measurements of free-form surfaces of products. The new method takes into account various aspects of coordinate measurements to determine the final model of the distribution of measurement points on measured surfaces of products, thereby increasing the probability of the proper determination (i.e., identifying the highest deviations of a product) of the location of measurement points on the surfaces of a measured object. The paper presents an example of the application of the created method, which concerns the selection of the best model of the distribution of measurement points on a selected free-form surface. This example is based on, among others, the results of experimental investigations, which were carried out by using the ACCURA II coordinate measuring machine equipped with the VAST XXT measuring probe and the Calypso measurement software. The results of investigations indicate a significant reduction in time of coordinate measurements of products when using the new method for determining the distribution of measurement points. However, shortening the time of coordinate measurements does not reduce their accuracy.

A High-Precision Form-Free Metrological Method of Aeroengine Blades

In order to solve the problems in existing methods for blade profile metrology, such as low accuracy and efficiency, poor flexibility, various constraints, a high-precision form-free method for blade profile metrology is proposed. In the paper, the operational principle, key technologies and evaluation methodology are analyzed in detail. A high-precision method for blade profile metrology based on the concept of “Synchronization of Planning and Measurement” is proposed to solve three key problems for blade metrology synchronously: theoretical data acquisition, path planning and sampling strategy analysis, and profile measurement. A form-free evaluation methodology for blade profile based on parametric modeling is also discussed. The results show that the metrology and evaluation for blade profile are executed automatically without theoretical model data, thus improving the efficiency and flexibility greatly. In addition, all the measurements are completed in the positions near the reference distance of the sensor, thus the depth of measurement approaches 0 mm and the measurement error is no more than 10 μm. The method proposed in the paper is a form-free method with a high precision and has a good application prospect in the field of free-form surface measurement.

Error compensation and accuracy analysis of laser measurement system based on laser-beam calibration

In this paper, a novel measurement strategy, based on a 4D error-compensation model for the measurement of free-form surfaces in laser measurement systems, is presented. To improve the measurement accuracy, effects of the inclination angle and the azimuth angle (including the rotation angle and the deflection angle) on the measurement results are investigated experimentally. Considering the error compensation and the constructing iterative function, a calibration method for arbitrary positions and orientations of the laser-beam is presented, and a corresponding measurement strategy is presented. To verify the effectiveness and accuracy of the proposed measurement strategy, calibration schemes of a check bar geometry center are studied based on a 4-axis measuring platform. The obtained results demonstrate that the proposed strategy can greatly improve the measurement accuracy.

Compact snapshot multiwavelength interferometer.

We propose a snapshot and compact multiwavelength interferometer for real-time testing of optical surfaces with large slopes. A color camera with a micropolarizer array simultaneously captures the phase-shifted interferograms of multiple wavelengths, from which four interferograms with π/2 phase shift at each wavelength are extracted for multiwavelength phase-shifting interferometric measurement. The accuracy of the proposed system is validated experimentally, and the testing of freeform surface with large slopes is also demonstrated. The proposed system provides a feasible way to obtain the instantaneous online measurement of freeform surfaces while minimizing environmental disturbance.

Extra-detection-free monoscopic deflectometry for the in situ measurement of freeform specular surfaces.

Extra detections of feature points conducted by a third-party instrument are indispensable in the monoscopic deflectometry to specify the surface position, but the measuring capability can be limited because most freeform surfaces do not contain any distinguishable and detectable feature points. In this Letter, the behaviors of the position error and form error of the measured surface are discriminated by reverse ray-tracing. A novel iterative optimization strategy is developed to position the workpiece for the in situ deflectometric measurement so that extra detections can be avoided. It is demonstrated that this method can achieve parallel measuring accuracy with conventional deflectometry, but the measuring efficiency and range of freeform surfaces can be greatly improved. A hollow off-axis parabolic mirror is measured, and its departure from the interferometric results is 139.85nm root mean square.

Fast hierarchical fusion model based on least squares B-splines approximation

With manufacturing shifting from traditional products to high value products, the complexity and accuracy of the products are increasing in order to reduce energy costs, create friendly environment and better health care. Structured surfaces, freeform surfaces, and other functional engineering surfaces are becoming the core part of high value manufacturing products. However, measurement of these surfaces is becoming very difficult due to instrumental limitations including measurement range, speed, resolution and accuracy. Multi-instruments/sensors measurement are now being developed for freeform and structured surface assessment, which requires the fusion of the data into a unified system to achieve larger dynamic measurements with greater reliability. This paper discusses the process of combining data from several information sources (instruments/sensors) into a common representational format and the surface topography can be reconstructed using Gaussian processes and B-spline techniques. In this paper the Gaussian process model is extended in order to take into account the uncertainty propagation and a new data fusion model based on least squares B-splines that drastically reduce the computational time are presented. The results are validated by two for freeform surface measurements.

Simultaneous removal of nonrotationally symmetric errors in tilted wave interferometry

The tilted wave interferometer has been developed as a fast and accurate instrument for the measurement of aspheric and freeform surfaces. We present a method for increasing its robustness and flexibility. Tilted wave interferometry crucially depends on accurate calibration and any changes to a calibrated setup require, in general, a recalibration. Therefore, we propose a method for simultaneous topography reconstruction and elimination of errors arising from such changes. An approach to identify trends in systematic errors for the complex non-null setup with a large number of blackbox model parameters is worked out. The procedure allows deriving an error removal scheme for nonrotationally symmetric components based on measurements in different rotational positions. The feasibility and benefit of the error elimination method are shown both by simulation methods and dedicated experiments. A significant reduction of systematic errors even in a miscalibrated state is achieved. Hence, recalibrations are avoided and measurement time and flexibility are improved.

A robust registration algorithm of point clouds based on adaptive distance function for surface inspection

One key issue in the optical measurement of free-form or complex surfaces is the point cloud registration procedure, which aligns the measurement data to the part model for a robust, fast and accurate inspection process. Therefore, a robust registration method for surface inspection is proposed based on an adaptive distance function (ADF) and the M-estimation method. The ADF as the basis error metric can accurately describe the shortest point-surface distance, and the M-estimation method is used to eliminate outliers and enhance the robustness of the registration performance. The registration problem using the M-estimation method can be interpreted as an iterative reweighted least squares (IRLS) minimization. Then, a nonlinear optimization model called IRLS-ADF is established to obtain the transformation parameters. The convergence of the proposed method is also analysed. Moreover, compared to the previous algorithms, the experiments confirm that the proposed method can achieve a combination of good robustness, fast convergence speed and high accuracy.

Traceability of form measurements of freeform surfaces: metrological reference surfaces

Due to the complexity of measurement systems for asphere and freeform surfaces, well-known artifacts are required to characterize the accuracy of the results of their form measurements. We present advancements in manufacturing and characterization of metrological multispherical freeform artifacts. The strong cooperation between the manufacturing and measurement units of Physikalisch–Technische Bundesanstalt (PTB) allows the form of the artifacts to be manufactured very accurately and the root-mean-square deviation from the desired design form to be improved by a factor of >20 compared to former results (e.g., from a value >500 nm to about 20 nm). Furthermore, a nickel/phosphorous coating is added to the copper surface, resulting in greater hardness and allowing the coated surface to be used as a reference for low-force tactile measurement systems. Four Gaussian peak fiducial marker structures are added to the design to improve the evaluation of comparison measurements. In addition to characterizing the radii in the spherical segments using PTB’s radius measurement bench, we also characterize the sphericity of the spherical segments using a Fizeau interferometer. We show form measurement results for a full-field measuring tilted-wave interferometer and compare the form measurement results in the spherical segments with measurement results obtained with the Fizeau interferometer.

An Intelligent Self-Calibrating 4-DOF Parallel Robot for Precise Geometric Data Collection in Digital Manufacturing

Abstract Accurate capture of digital data from a manufactured part is an essential source of information about the quality of the produced part and the health of the corresponding manufacturing processes. The commonly known precise instruments for digitizing work-pieces on Coordinate Metrology Machine (CMM) are contact probes. Although, contact techniques confront difficulties, they lead to higher precisions comparing to non-contact methods. Ball-tip-radius error is one of the significant faults of contact methods. Conventional error compensating approaches of ball-tip-radius error often demand complicated and time consuming post-processes. Furthermore, considering the limitations of typical serial structure in commercial CMMs, adaptive accurate path planning is a very complex task. This paper presents an intelligent combination of a novel 4-DOF parallel mechanism implementing, a linear cost-effective contact probe, and an adaptive path planning method to automatically correct the probing direction. The implemented parallel structure has three translational DOF in X, Y and Z directions and one rotational DOF around X axis. A precise turn-table provides rotation of work-piece around the Z axis. The developed algorithm utilizes a data clustering approach and intelligently generates an automated adaptive probe placement and motion path. Validation process using simulation and actual measurement of free-form surfaces demonstrate highly reliable feasibility for eliminating the ball-tip-radius error resulting in high precision 3D data capturing process.

Rapid and Precise Reverse Engineering of Complex Geometry Through Multi-Sensor Data Fusion

This paper presents an effective multi-sensor approach for improving the accuracy of laser scanner by using a tactile probe to perform rapid and accurate reverse engineering of complex objects. The proposed system is unique in that it includes not only the physical integration of the two digitizers but also their combination at the measurement information level. With the coordinate data acquired using the optical scanner, intelligent data segmentation and feature recognition algorithm are proposed to divide the original point set into geometric elements and free-form surfaces. The tactile probe is guided to re-measure each feature with a small number of sampling points. Then different data fusion algorithms are proposed to compensate the scanned data patches of geometric features and free-form features with the accurate tactile probing data. Finally, the compensated point data can be exploited for accurate reverse engineering of a CAD model. Through the fusion of different sensor’s information, both sensors complement each other with their advantages. Experimental results show that for the measurement of geometric surface, the proposed method can improve the accuracy of optical measurement to the accuracy of contact measurement. For free-form surface measurement, the proposed method reduces the optical measurement error from +0.032/−0.019 mm to ±0.016 mm, and the standard deviation from 0.012 mm to 0.004 mm. The measurement efficiency of proposed method is 4.5 times higher than that of contact measurement alone.

Two-step carrier-wave stitching method for aspheric and freeform surface measurement with a standard spherical interferometer.

Measurement of aspheric and freeform surfaces remains challenging due to the various shapes of the surface under test (SUT), especially when the SUT has a large aperture and strong deviation from the spherical surface. This paper proposes a two-step carrier-wave stitching method to enlarge the measurement bandwidth of a digital Moiré interferometry. Then, measurements of aspheric and freeform surfaces with a standard spherical interferometer without a phase-shifting mechanism are demonstrated. Experimental results with a root-mean-square repeatability of better than 1/200λ present good consistency to UA3P contact measurement results. Further simulation results with different residual wavefronts confirm measurement accuracies of peak-to-valley value of 10-3λ. The method is effective for large residual wavefronts and thus has potential for flexible measurement of aspheric and freeform surfaces.

Pure adaptive interferometer for free form surfaces metrology.

A pure adaptive interferometer is proposed for optical free form surfaces metrology without auxiliary devices such as the wavefont sensors and deflectometry systems for DM monitoring. In this method, the DM surface monitoring and free form surface measurement are achieved simultaneously in only one interferometer. The polarizing optics divide the interferometer into two partial common path interferometric system, which provide the null test for tested free form surface and non-null test for the DM surface. The final figure error of the free form surface is extracted by ray tracing. Experiments proving the feasibility of this interferometer is shown.

Interferometry with flexible point source array for measuring complex freeform surface and its design algorithm

The precision of the measurements of aspheric and freeform surfaces remains the primary factor restrict their manufacture and application. One effective means of measuring such surfaces involves using reference or probe beams with angle modulation, such as tilted-wave-interferometer (TWI). It is necessary to improve the measurement efficiency by obtaining the optimum point source array for different pieces before TWI measurements. For purpose of forming a point source array based on the gradients of different surfaces under test, we established a mathematical model describing the relationship between the point source array and the test surface. However, the optimal point sources are irregularly distributed. In order to achieve a flexible point source array according to the gradient of test surface, a novel interference setup using fiber array is proposed in which every point source can be independently controlled on and off. Simulations and the actual measurement examples of two different surfaces are given in this paper to verify the mathematical model. Finally, we performed an experiment of testing an off-axis ellipsoidal surface that proved the validity of the proposed interference system.

Model-based self-optimization method for form correction in the computer controlled bonnet polishing of optical freeform surfaces.

Freeform surfaces have become increasingly widespread in the optical systems for enhanced performance and compact lightweight packaging. The geometrical complexity and high precision requirements of optical freeform surfaces for various functional optical applications, has posed great challenges in the design, precision machining, and measurement of these surfaces. This paper presents a model-based self-optimization approach for precision machining and measurement of optical freeform surfaces in the computer controlled bonnet polishing (CCBP) process. To realize the technical feasibility, the process parameters and motion control are accurately performed through modelling and simulation of machining processes, error compensation, and on-machine metrology.

Method to Evaluate Measuring Uncertainty of Probe Radius Compensation with Account for Variation in Measuring Surfaces

This article describes a methodology of evaluating the uncertainty of the contact measurement of freeform surfaces with coordinate measuring machines, taking into account the variation in the form of measured surfaces. This variation is due to machining uncertainties, which appear during production using a particular machining method and technology. Probabilistic estimates of errors of determination of contact points for freeform surfaces were obtained. Use of this model makes it possible to obtain interval estimates of errors with the required confidence level of probability and mathematical expectation. The relations of the probabilistic error estimates at any of the measured points on surface are obtained.

A study of a priori knowledge-assisted multi-scopic metrology for freeform surface measurement

The traditional multi-scopic metrology system makes use of a micro lens array to capture a raw 3D-image of the target surface in a single snapshot through a CCD camera under normal illumination. However, the resolution of the system depends on the matching precision and efficiency of disparity information during the processing of the 3D raw data. In this paper, the a priori knowledge-assisted multi-scopic metrology is studied and an a priori knowledge-assisted multi-scopic metrology system is established which makes use of patterned illumination custom-designed based on the a priori knowledge of the target freeform surface profile. The a priori knowledge provides abundant versatile known information for a precise and efficient matching process so as to enhance the measuring performance. A customized disparity matching process based on the a priori knowledge is developed accordingly for high-resolution 3D surface reconstruction. An experimental study for measuring freeform surface is conducted to verify the feasibility of the proposed a priori knowledge-assisted multi-scopic metrology system through the comparison between that using normal illumination and a priori knowledge-assisted patterned illumination.

A Curve Network Sampling Strategy for Measurement of Freeform Surfaces on Coordinate Measuring Machines

One of the essential problems in the measurement of the freeform surfaces on a coordinate measuring machine is to design appropriate sampling plans to improve the industrial practice in terms of the tradeoff between the sampling accuracy and the efficiency. This paper presents a curve network sampling strategy to approximate the measured surface within a required accuracy while minimizing the cost and time for the measurement by adaptively deriving the optimal sampling locations. The method iteratively extracts two sets of iso-planar curves along two different directions on the parts to form a curve network, which is used to reconstruct the measured surfaces based on the Gordon surface fitting method. Two criteria are integrated to determine the locations of the sampled curves in the sampling process, including the surface complexity and the deviation of the reconstructed surfaces from the CAD model. Both the computer simulation and the actual measurement are conducted to verify the superior sampling efficiency of the proposed method to the conventional raster fashion sampling in measuring freeform surfaces.