Non-rotational Symmetry Research Articles

The effects of the angle between the indenter edge and the scratch direction on the scratch characteristics of Ti–6Al–4V alloy

Ti–6Al–4V alloy has become a crucial raw material in aerospace and other industries owing to its exceptional mechanical properties. However, it is also a typical difficult-to-machine material, and its removal process and mechanism have been widely investigated by scratch testing. Nevertheless, the inherent non-rotational symmetry of the Vickers indenter introduces a crucial parameter, i.e., the angle λ between the indenter edge and the scratch direction, which affects not only the mechanical response of materials but also its surface formation mechanism during scratch. This study systematically characterized the micro/nano scratch characteristics of Ti–6Al–4V alloy under three typical angles λ (0°, 22.5°, 45°) as well as various normal forces and scratch speeds. The coefficient of friction (COF), scratch depth, scratch width, residual scratch morphology, and specific scratch energy were comparatively analyzed. Finite element simulations confirmed that the direction of material flow changed with the change in angle λ. The corresponding deformation mechanisms during scratch were discussed accordingly. The results revealed a significant influence of the angle λ on the scratch behaviors and surface quality of Ti–6Al–4V alloy.

Broadband spectrally selective infrared radiation and its applications of a superstructure film of combined circular patches

Selective infrared radiation is crucial for achieving infrared stealth and heat dissipation. Artificially designed superstructure film (SF) provides several advantages for controlling and modulating infrared radiation, making them a promising solution for these applications. The research described in this work has successfully produced broadband selective infrared radiation by using a surface made up of circular patches that are combined. Numerical simulations show that this SF can achieve broadband selective radiation with 3–5 μm mid-wave infrared (MWIR) suppression and 8–14 μm long-wave infrared (LWIR) emission. The spectral selectivity can be easily switched to high emissivity in MWIR and low emissivity in LWIR by simply changing the basal layer. The resonance mechanism for achieving broadband spectral selectivity in the SF may be due to a combination of multimode plasmon resonances that are induced by the structural nonrotational symmetry of the circular patches. By applying the selective radiation SF on the tail nozzle or the vehicle, the effect of thermal management is very significant. Selective radiation SF can reduce radiant energy in the 3−5 μm band by a significant amount at 500 °C, resulting in a 46 °C cooler temperature than that at the body without the SF. At 80 °C, radiated energy in the 8–14 μm band is also considerably reduced and the temperature is 10 °C lower than that of the body without the SF. There will be obvious advantages in potential applications for infrared stealth and heat dissipation by the designed SF, a simple and convenient manufacturing process.

P‐4.2: An Image Pre‐distortion Algorithm for Near‐eye Display

With the development of near-eye display technology, optical distortion is often introduced into the design of near-eye optical system to meet people's requirements for high definition and large field of view. However, the larger the field of view, the greater the distortion of the projected image. In order to correct distorted images, this paper proposes an image pre-distortion algorithm based on nonlinear fitting and forward mapping interpolation. The radial basis function fitting algorithm is used to get a more precise mapping relationship between the original image and the pre-distorted image. The compactly supported radial basis function (CSRBF) interpolation algorithm based on forward mapping is used for image gray reconstruction to obtain better correction effect of image distortion. The experimental results show that the fitting error of the radial basis function fitting algorithm can be reduced to less than 1 pixel, reaching sub-pixel level. The pre-distortion algorithm has a good correction effect on the non-rotational symmetry distortion produced by the near-eye optical system, which makes the display image clear and complete.

A Novel Approach for Measurement of Free-Form Optical Elements with Digital Holographic Microscopy.

Free-form optical elements face significant challenges in high-precision measurement due to their high complexity and non-rotational symmetry. Digital holographic microscopy (DHM), as one of the methods for the measurement of free-form optical elements, has promising applications due to its ultra-high precision and non-destructive and fast characteristics. Therefore, we have designed a novel measurement method that combines transmission DHM and reflection DHM to obtain thickness information and surface information of elements to deduce the 3D structure. With this method, we completed the measurement of a free-form optical element. The DHM system we built has recorded holograms under 4× and 20× objectives and successfully recovered the 3D surface shape of the element. The measurements are consistent with the designed and manufactured parameters, demonstrating the unique advantages of DHM for measuring special types of optical elements.

Investigation on multi-body dynamics based approach to the toolpath generation for ultraprecision machining of freeform surfaces

This article presents an innovative approach to toolpath generation for ultraprecision machining of freeform optic surfaces based on the principle of Automatic Dynamics Analysis of Mechanical Systems. As components with freeform surfaces often have non-rotational symmetry, there are potential challenges facing their ultraprecision machining through single-point diamond turning, such as the projected points in complex large sag surfaces, which likely find it difficult to communicate with the control system and, thus, do not perform successfully. In ultraprecision machining, to achieve the highest performance in freeform surface resolution, the factors of dynamics, material and mechanical stiffness, frictions, tooling and accuracy of the servo component should be considered. The investigation is focused on an integrated approach and the associated scientific understanding of precision engineering design, ultraprecision machining and metrology of freeform surfaces as well as their application perspective. In this approach, the toolpath for very complex freeform surfaces can be generated using the Newton–Raphson method to solve the kinematics and dynamics equations of motion. The effect of friction and contact force are also investigated for accurate toolpath curve generation. Moreover, the Gear stiff (GSTIFF)/ Wielenga stiff (WSTIFF) integrator for solving the non-linear equations of motion is employed, and the result shows the time step size, playing a critical role in generating toolpath curves with a higher accuracy and resolution.

A freeform optics design with limited data for extended LED light sources

This paper proposes an optimization method for designing a freeform lens which can produce a good uniform circular illumination distribution and obtain high efficiency on the target plane. The initial surface profile of the freeform lens is calculated based on the laws of reflection and the energy conservation law, and then is fitted using the non-uniform rational basis spline (NURBS) method. The control points and weights are applied to parameterize the shape of freeform lens. The merit function for the optimization is defined as relative standard deviation (RSD) of the simulated illumination from the desired illumination and the efficiency of the lens. The simulation results indicate that the RSD is shown to be lower than 0.157, and maximum efficiency can be as high as 83.9%. In addition, it is demonstrated that this algorithm can obtain high uniform illumination distribution on the target plane with less variables. Compared with the conventional method, the simulation results show that the modified algorithm converges with less variables, good uniformity and high efficiency. Moreover, a freeform lens with different lighting patterns and non-rotational symmetry can be produced by the proposed method.

Null testing of nonrotational symmetry transmission optical freeform: design, modeling, and inspection on the basis of Fermat principles

We present a general design method for a type of transmission freeforms without rotational symmetry and achieve the null testing by putting a well-designed Fermat reflector on the transmitting optical path. The design principle of the reflector is given, and an eccentric spherical surface with 1-mm deviation is used as an example of testing freeform. We fabricated the reflector and the freeform with the single-point diamond turning machine. Both conventional interference inspection and our approach give consistent results. The design error is less than 10 6 mm, and the measurement accuracy is nearly completely determined by the fabrication precision. This approach can also be applied to the inspections of reflecting freeforms with low costs.©2015Society

Study on Surface Processing of Non-Rotational Symmetry

This paper studies on technology of slow tool servo method and the processing of high efficiency. High precision surface NRS goal is studied for factors affecting theNRSworkability and surface machining accuracy. Including slow tool servo theory, research tools, tool path generation, surface microstructure simulation, slow tool servoNRSsurface machining and simulation systems development, installation errors and adjustment tool,Yto linear turret design,NRSsurface machining experiments.

Sampling Strategy for Free-Form Surface Inspection Using Coordinate Measuring Machines<sup></sup>

Due to the complexity and non-rotational symmetry of free-form surface, it is difficult to achieve accurate and efficient inspection method. In order to solve this problem, three types of sampling sequences are proposed to specify a set of measuring points of free-form surface. For comparing the results of different sampling strategies, the profile errors of free-form surface are calculated based on a quasi particle swarm optimization (QPSO) searching the transformation parameters to implement localization and surface subdivision method finding the closest points on the design model corresponding to measured points. In order to obtain effective sampling strategies, four design models are generated by non-uniform rational basis spline (NURBS) and parts are manufactured on two machining centers to obtain surfaces of different roughness and measured on CMMs by selecting different sampling methods and sample sizes. The profile errors of parts are calculated by the proposed method and CMMs software, respectively. The results show that randomized Hammersley sampling sequence and medium sample size are preferred for the profile error inspection of given parts if accuracy and time are all considered. The research provides a method for free-form surface accurate inspection while minimizing the sampling time and cost.

Asphericity and Discrete Phase Calculation for Optical Freeform Surface Test with Computer Generated Holograms

Optical freeform surfaces are complex surfaces with non-rotational symmetry that break through the limitations of conventional optical element, and are widely used in advanced optics application for system configuration simplifying and performance enhancing. Interferometric test with computer generated holograms (CGH) has been widely used in the aspherical surfaces testing for their unique wavefront transformation, as well as the freeform surfaces testing with high precision. As an important parameter, it is different at the definition of asphericity in freeform surfaces manufacture and test. Asphericity for interferometric test which verifies the testing ability of the CGH and determines testing system initial configuration was calculated with minimum maximum angle deviation. Reverse ray tracing could get the optimal solution of CGH local phase at certain location in the CGH design. For the non-rotational symmetry of freeform surfaces, the phase of sample point in CGH surface should be calculated in three-dimensional coordinate system. The calculation method of discrete phase was deduced by ray tracing, as well as the phase distribution on freeform surface were proven by calculating in such way. The results were compared with simulation by optical design software. It shows that the method is right and high accuracy to be used in the CGH design for the freeform surfaces.

Effects of Adsorbate Surface Diffusion in Focused Electron-Beam-Induced-Deposition

The time-dependent continuum model is applied to simulate a growth of structures with a non-rotational symmetry. The surface diffusion of adsorbates, depending on the beam parameters and the deposit size, may lead to the different growth rate along deposited structures. Here, a few conventional patterning strategies have been studied: spiral inwards, spiral outwards and zigzag.

Accurate evaluation of free-form surface profile error based on quasi particle swarm optimization algorithm and surface subdivision

Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for the verification of free-form surface profile are available, the profile parameters of free-form surface are proposed by referring to ISO standards regarding form tolerances and considering its complexity and non-rotational symmetry. Non-uniform rational basis spline(NURBS) for describing free-form surface is formulated. Crucial issues in surface inspection and profile error verification are localization between the design coordinate system(DCS) and measurement coordinate system(MCS) for searching the closest points on the design model corresponding to measured points. A quasi particle swarm optimization(QPSO) is proposed to search the transformation parameters to implement localization between DCS and MCS. Surface subdivide method which does the searching in a recursively reduced range of the parameters u and v of the NURBS design model is developed to find the closest points. In order to verify the effectiveness of the proposed methods, the design model is generated by NURBS and the measurement data of simulation example are generated by transforming the design model to arbitrary position and orientation, and the parts are machined based on the design model and are measured on CMM. The profile errors of simulation example and actual parts are calculated by the proposed method. The results verify that the evaluation precision of freeform surface profile error by the proposed method is higher 10%–22% than that by CMM software. The proposed method deals with the hard problem that it has a lower precision in profile error evaluation of free-form surface.

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.

Measuring optical freeform surfaces using a coupled reference data method

Flat optical freeform surfaces usually possess non-rotational symmetry with a small curvature and lack of strong features for surface alignment. Due to the lack of strong features and small curvature, it is difficult to align the design and measured surfaces for characterizing the surface quality of flat optical freeform surfaces with sub-micrometre form accuracy. The traditional least squares method (LSM) generally produces large errors as there is a lack of strong features as reference for the alignment of the design and measured surfaces. This paper proposes a novel and practical method named the coupled reference data method (CRDM) to evaluate flat optical freeform surfaces with high efficiency and precision in the nanometre scale. The method couples reference data to the workpiece of the freeform surface designed model and the concerning reference features are machined together with the workpiece. By aligning the reference data, the proposed CRDM carries out fast surface matching. This makes good preparation for the next matching optimization which is conducted by the least-squares and minimax zone method. After the precise surface matching, the flat optical freeform surface can be evaluated by 3D form error topography and parameters. As compared with a traditional freeform measurement method such as LSM, it is interesting to note that the accuracy and the stability of the measurement can be significantly enhanced by the CRDM.

Encapsulation shape with non-rotational symmetry designed for extraction of polarized light from unpolarized sources

A non-rotationally symmetric encapsulation shape - which takes advantage of the low reflection coefficient for transverse magnetic polarized light near Brewster's angle - designed to enhance extraction of a particular desired linear polarization from an unpolarized source is reported. The algorithm for optimization of the shape is described. Numerical ray-tracing simulations of the encapsulation shape are performed and predict an integrated enhancement of 8.3% in the ratio of desired polarization to undesired polarization when the refractive index of the encapsulant is 1.5. Experimental measurements of fabricated encapsulant shapes agree well with numerical predictions.

Modelling and simulation of freeform surface generation in ultra-precision raster milling

Optical freeform surfaces are large-scale surface topologies with shapes generally possessing non-rotational symmetry with submicrometric form accuracy and nanometric surface finish. Due to the geometrical complexities, the prediction of form accuracy in ultraprecision raster milling of ultra-precision freeform surfaces is more difficult than conventional machining. Nowadays, the achievement of submicrometre form accuracy still depends largely on the experience and skills of the machine operators through an expensive trial-and-error approach. This paper presents a model-based simulation system for the prediction of form accuracy in ultra-precision raster milling of optical freeform surfaces. The system takes into account the cutting mechanics, cutting strategy, and the kinematics of the cutting process. Experimental work has been undertaken to verify the system and the predicted results agree well with the experimental results. The successful development of the model-based simulation system allows the optimum cutting parameters and cutting strategies to be determined without the need to conduct massive and costly trial-and-error cutting tests.

An integrated form characterization method for measuring ultra-precision freeform surfaces

Ultra-precision freeform surfaces are complex surfaces that possess non-rotational symmetry. Currently, there is a lack of definitive international standards and techniques for the characterization of form accuracy and surface quality of ultra-precision freeform surfaces. This paper presents an integrated form characterization method (IFCM) to measure the form accuracy of ultra-precision freeform surfaces. The IFCM is developed based on the five-point pre-fixture, dual cubic B-spline and an iterative precision adjustment algorithm with coordinate transfer. To verify the capability of the proposed method, a series of computer simulation and measurement experiments were undertaken. The results indicate that the IFCM can realize the precise alignment of measured and normal surfaces with accuracy in nanometer range which provides adequate base for good form characterization of ultra-precision freeform surfaces with form accuracy down to below sub-micrometer range.

Measuring ultra-precision freeform surfaces using a robust form characterization method

Ultra-precision freeform surfaces are complex surfaces that possess non-rotational symmetry and are widely used in advanced optics applications. However, there is a lack of a surface characterization method that measures the form accuracy of the ultra-precision freeform surfaces with micrometre to sub-micrometre form accuracy. Due to the high precision requirement of the ultra-precision freeform surfaces, this inevitably involves the outliers in the measured data that would significantly affect the accuracy and the performance of the form characterization method. Although some research work has been found in the development of the form characterization method, most workers have not considered the influence of outliers. It is vital to incorporate robust estimation in the surface characterization method for catering for the influence of outliers. In this paper, a robust form characterization method (RFCM) is presented to characterize the form accuracy of the ultra-precision freeform surfaces. A series of computer simulation and experimental analyses were undertaken to verify the RFCM. The theoretical results agree well with the simulation and experimental results.

HIGH PRECISION RING LOCATION FOR A NEW ROTATIONALLY SYMMETRIC TRIANGULATION SENSOR

For a growing range of optical measurement task, like gap measurement in automotive industry, traditional triangulation sensors have several disadvantages due to the fact that the measurement result is dependent on the orientation of the sensor because of the non-rotational symmetry of the optics. Consequently a design method was proposed recently for a new class of rotationally symmetric triangulation sensors. Such designs can be realized with aspheric reflection optics and area detectors, such as CCD or CMOS. The optics of the sensor can be extended by an imaging optics which allows at the same time image capturing and distance measurement. In this paper we show the first prototype. This system is based on an optical system of one part manufactured by commercially available diamond turning. The layout of the optical system for distance measurement consists of two reflecting aspheric surfaces. The high precision algorithm for ring location was needed because the performance of the sensor is based on the detection of ring, especially the radius of the ring. In this paper, we try to give the different evaluation function for high precision location of ring. Then we used various methods to solve it and got optimized result. The comparison of algorithms for simulation was listed in the paper. And the measurement result for the real image got by the prototype was also presented. It seems the algorithm meets the precision demand of the sensor.

Vectorial nonparaxial propagation equation of elliptical Gaussian beams in the presence of a rectangular aperture.

Based on the vectorial Rayleigh-Sommerfeld diffraction integrals, an analytical propagation equation of vectorial, nonparaxial, elliptical Gaussian beams through a rectangular aperture is derived. Unlike in previous work, the aperture effect and nonrotational symmetry of the beam and aperture are considered in our theoretical model. The results of the far-field and paraxial approximation for the apertured case are treated as special cases of our general expression. It is found that two f parameters fx, fy and two truncation parameters deltax, deltay in the x and y directions, respectively, have to be introduced that affect the beam nonparaxial evolution behavior in both the near field and the far field.