Mingjun Ren

Measurement and characterization of ultra-precision freeform surfaces using an intrinsic surface feature-based method

Ultra-precision freeform surfaces are complex surfaces that possess non-rotational symmetry and are widely used in advanced optics applications. Due to the geometrical complexity of optical freeform surfaces, there is, as yet, a lack of generalized surface characterization methods which measure various types of ultra-precision freeform surfaces with sub-micrometer form accuracy and surface finish in the nanometer range. To make good this deficiency, a generalized approach for the measurement and characterization of ultra-precision freeform surfaces, named the intrinsic surface feature-based method (ISFM), is presented in this paper. The ISFM makes use of intrinsic surface properties (e.g. curvatures, normal vectors, torsion and intrinsic frames) to conduct data matching or uses some algorithms to search for correspondences such as correlation functions. The method is experimentally verified through a series of measurement experiments. The results show that the proposed ISFM is capable of addressing the deficiencies and limitations of traditional freeform surface characterization methods which are susceptible to outliers and to uncertainty due to the geometry of the freeform surfaces. ISFM is a generalized methodology which is not dependent on the type of freeform surface being characterized.

A task specific uncertainty analysis method for least-squares-based form characterization of ultra-precision freeform surfaces

In the measurement of ultra-precision freeform surfaces, least-squares-based form characterization methods are widely used to evaluate the form error of the measured surfaces. Although many methodologies have been proposed in recent years to improve the efficiency of the characterization process, relatively little research has been conducted on the analysis of associated uncertainty in the characterization results which may result from those characterization methods being used. As a result, this paper presents a task specific uncertainty analysis method with application in the least-squares-based form characterization of ultra-precision freeform surfaces. That is, the associated uncertainty in the form characterization results is estimated when the measured data are extracted from a specific surface with specific sampling strategy. Three factors are considered in this study which include measurement error, surface form error and sample size. The task specific uncertainty analysis method has been evaluated through a series of experiments. The results show that the task specific uncertainty analysis method can effectively estimate the uncertainty of the form characterization results for a specific freeform surface measurement.

Estimation of measurement uncertainty caused by surface gradient for a white light interferometer

Although the scanning white light interferometer can provide measurement results with subnanometer resolution, the measurement accuracy is far from perfect. The surface roughness and surface gradient have significant influence on the measurement uncertainty since the corresponding height differences within a single CCD pixel cannot be resolved. This paper presents an uncertainty estimation method for estimating the measurement uncertainty due to the surface gradient of the workpiece. The method is developed based on the mathematical expression of an uncertainty estimation model which is derived and verified through a series of experiments. The results show that there is a notable similarity between the predicted uncertainty from the uncertainty estimation model and the experimental measurement uncertainty, which demonstrates the effectiveness of the method. With the establishment of the proposed uncertainty estimation method, the uncertainty associated with the measurement result can be determined conveniently.

Autostereoscopy-based three-dimensional on-machine measuring system for micro-structured surfaces

Traditional off-line measuring systems find it difficult to measure micro-structured workpieces which have a large volume and heavy weight, such as micro-structured patterned precision roller drums. This paper proposes an autostereoscopy-based three-dimensional (3D) measuring method and develops an innovative measuring system for the 3D on-machine measurement of the micro-structured surfaces, an Autostereoscopy-based Three-Dimensional On-machine Measuring (ATDOM) system. The ATDOM system is compact and capable of fast data acquisition and high accuracy in 3D computational reconstruction of complex surfaces under different measuring environments. A prototype ATDOM system is experimentally verified through a series of measurement experiments conducted on a precision machine tool. The results indicate that the ATDOM system provides an important means for efficient and reliable on-machine measurement of micro-structured surfaces.

Disparity pattern-based autostereoscopic 3D metrology system for in situ measurement of microstructured surfaces

This paper presents a disparity pattern-based autostereoscopic (DPA) 3D metrology system that makes use of a microlens array to capture raw 3D information of the measured surface in a single snapshot through a CCD camera. Hence, a 3D digital model of the target surface with the measuring data is generated through a system-associated direct extraction of disparity information (DEDI) method. The DEDI method is highly efficient for performing the direct 3D mapping of the target surface based on tomography-like operation upon every depth plane with the defocused information excluded. Precise measurement results are provided through an error-elimination process based on statistical analysis. Experimental results show that the proposed DPA 3D metrology system is capable of measuring 3D microstructured surfaces with submicrometer measuring repeatability for high precision and in situ measurement of microstructured surfaces.

Fiducial-aided on-machine positioning method for precision manufacturing of optical freeform surfaces

There are still significant challenges in the accurate positioning of optical freeform surfaces on the machine tool and the measurement instrument due to the high accuracy requirement and their complex shapes. This paper proposes a Fiducial-aided On-machine Positioning method (FAOPM) that combines on-machine measurement and off-machine measurement to precisely position optical freeform surfaces during the precision manufacturing cycle including rough machining, fine machining, measurement, and error compensation. The FAOPM makes use of fiducials which are firstly measured on a coordinate measuring machine with nanometric accuracy to generate a Fiducial-aided Computer Aided Design (FA-CAD) of the designed optical surface, then the developed on-machine measuring device obtains the accurate positions of the fiducials after remounting in the machining coordinate system. Finally the relative position of the workpiece is identified so that the associated cutting paths and compensation tool path can be easily generated. Several optical freeform surfaces were experimentally machined to prove the capability of the proposed method. The results indicate that the positions of the workpiece during the precision manufacturing and measurement cycle were precisely achieved and the form accuracy of the optical freeform surfaces was remarkable improved based on the FAOPM.

A Study of Mechanics in Brittle–Ductile Cutting Mode Transition

This paper presents an investigation of the mechanism of the brittle–ductile cutting mode transition from the perspective of the mechanics. A mechanistic model is proposed to analyze the relationship between undeformed chip thickness, deformation, and stress levels in the elastic stage of the periodic chip formation process, regarding whether brittle or ductile mode deformation is to follow the elastic stage. It is revealed that, the distance of tool advancement required to induce the same level of compressive stress decreases with undeformed chip thickness, and thereby the tensile stress below and behind the tool decreases with undeformed chip thickness. As a result, the tensile stress becomes lower than the critical tensile stress for brittle fracture when the undeformed chip thickness becomes sufficiently small, enabling the brittle–ductile cutting mode transition. The finite element method is employed to verify the analysis of the mechanics on a typical brittle material 6H silicon carbide, and confirmed that the distance of the tool advancement required to induce the same level of compressive stress becomes smaller when the undeformed chip thickness decreases, and consequently smaller tensile stress is induced below and behind the tool. The critical undeformed chip thicknesses for brittle–ductile cutting mode transition are estimated according to the proposed mechanics, and are verified by plunge cutting experiments in a few crystal directions. This study should contribute to better understanding of the mechanism of brittle–ductile cutting mode transition and the ultra-precision machining of brittle materials.

Fiducial-Aided Robust Positioning of Optical Freeform Surfaces

Form characterization of a machined optical freeform surface demands accurate alignment of the sampled measured data points on the machined surface, and they are compared with the designed geometry of the surface through positioning. In this paper, a fiducial-aided robust positioning method (FAPM) is developed which attempts to evaluate freeform surfaces with high efficiency and precision. The FAPM method makes use of fiducials as reference datum to form a fiducial-aided computer-aided design (FA-CAD) of the freeform surface which not only establishes an inherent surface feature, but also links the different coordinate systems among design coordinate frame, machine tool, and measurement instrument. To verify the capability of the proposed method, a series of experiments were conducted. Compared with the traditional freeform measurement method (e.g., least squares method), the results indicate that the robustness and accuracy of the measurement is significantly enhanced by the FAPM.

A defocus-information-free autostereoscopic three-dimensional (3D) digital reconstruction method using direct extraction of disparity information (DEDI)

Autostereoscopy based three-dimensional (3D) digital reconstruction has been widely applied in the field of medical science, entertainment, design, industrial manufacture, precision measurement and many other areas. The 3D digital model of the target can be reconstructed based on the series of two-dimensional (2D) information acquired by the autostereoscopic system, which consists multiple lens and can provide information of the target from multiple angles. This paper presents a generalized and precise autostereoscopic three-dimensional (3D) digital reconstruction method based on Direct Extraction of Disparity Information (DEDI) which can be used to any transform autostereoscopic systems and provides accurate 3D reconstruction results through error elimination process based on statistical analysis. The feasibility of DEDI method has been successfully verified through a series of optical 3D digital reconstruction experiments on different autostereoscopic systems which is highly efficient to perform the direct full 3D digital model construction based on tomography-like operation upon every depth plane with the exclusion of the defocused information. With the absolute focused information processed by DEDI method, the 3D digital model of the target can be directly and precisely formed along the axial direction with the depth information.

A Study of Cutting Strategy in Single-Point Diamond Turning of Micro V-Groove Patterns on Precision Roller Drums

This paper presents a study of cutting strategies on the surface generation in single-point diamond turning of micro V-groove patterns on precision roller drums. An aluminium precision roller drum with a diameter 250mm and 100 long was diamond turned with a V-groove pattern. A series of cutting experiments were designed to study the effect of the variation of various cutting parameters and cutting tool paths on the surface quality in diamond turning of the precision roller drum. The parameters under investigation included the depth of cut, number of steps and the depth for each cut when diamond turning V-grooves on the cylindrical surface of a workpiece. The measurement result indicates that the surface quality of V-grooves machined on the precision roller drums is affected by cutting strategies. The optimal cutting strategy for machining a V-groove pattern on a precision drum with 5µm depth was obtained.