Freeform Surface

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Fang-jung Shiou - One of the best experts on this subject based on the ideXlab platform.

  • multi beam laser probe for measuring position and orientation of Freeform Surface
    Measurement, 2011
    Co-Authors: Rueytsung Lee, Fang-jung Shiou
    Abstract:

    Abstract This study develops a novel optical non-contact probe that measures the position and orientation (normal vector) of a Freeform Surface. The probe system comprises a five-laser-beam projector and a charge-coupled device (CCD) camera. The probe is integrated on a three-axis platform. Five designed laser beams project onto a measuring Surface, where five light spots are observed. The CCD captures the image of this Surface and processes it. The 3D coordinates of the five light spots can be then computed. The normal direction at the central spot on the measuring Surface is determined from two crossed curves through the coordinates of these five light spots. Two crossed curves are constructed using the Bezier method. The normal vector is the cross-product of two tangent vectors to the two crossed curves at central spot. A scheme for calibrating and making measurements using this five-laser-beam probe is proposed and verified experimentally. Experimental results demonstrate that this five-laser-beam probe system can measure the position and orientation of a Freeform Surface. The range of depths that can be measured using this probe is 2.4 mm and the range of angles is 40°. The positional measuring accuracy of the complete system is approximately 30 μm while the orientational accuracy is 1.8°.

  • calculation of the unit normal vector using the cross curve moving mask method for probe radius compensation of a Freeform Surface measurement
    Measurement, 2010
    Co-Authors: Fang-jung Shiou
    Abstract:

    Abstract This paper proposes a cross-curve moving mask method to calculate the unit normal vector based on 5 or 9 data points of a Freeform Surface measurement for probe radius compensation. This is done in order to simplify the calculation and thus, produce a more efficient and time-saving process. Passing through the middle point and 4 or 8 neighboring points, two crossed curves – longitude and latitude can be constructed. The unit normal vector at the middle point can be determined by calculating the cross product of two tangent vectors along these two crossed curves. Different curve fitting methods for the curves passing through 5 or 9 data points, such as Bezier and B-spline methodologies, have been investigated. Three kinds of Surfaces, namely, a spherical Surface, a cosine-like Surface and a shoe-shaped Surface (hereby termed “shoe last”) are selected for evaluating the accuracy of the calculated unit normal vectors.

  • Surface finishing of hardened and tempered stainless tool steel using sequential ball grinding ball burnishing and ball polishing processes on a machining centre
    Journal of Materials Processing Technology, 2008
    Co-Authors: Fang-jung Shiou, Chihcheng Hsu
    Abstract:

    Abstract The objective of this research aims to improve Surface roughness of the hardened and tempered STAVAX plastic mould stainless steel using the ball grinding, ball burnishing and ball polishing Surface finish processes on a machining centre. The flat Surface optimal ball burnishing and spherical polishing parameters have been determined after conducting the Taguchi's L9 and L18 matrix experiments, analysis of variation (ANOVA), and the full factorial experiment, respectively. The Surface roughness of the ground test specimens could be improved from about Ra = 0.5167 to 0.123 μm on average by using the optimal flat Surface ball burnishing parameters. The Surface roughness of the burnished specimens can be further improved to Ra = 20 nanometers (nm) by using the spherical polishing process with determined optimal parameters. By using the finest available commercial grain size of the abrasive material aluminum oxide (Al2O3, WA) as 1 μm in diameter (grid no. 10,000), the mean Surface roughness value of Ra = 16.7 nm on average was possible. The determined flat Surface optimal burnishing and polishing parameters were then applied sequentially to the Freeform Surface test object of a F-theta scan lens, to improve the Surface roughness. The Surface roughness value Ra of Freeform Surface region on the STAVAX tested part, which was hardened and tempered (HRC = 50), can be improved sequentially from about 1.83 to 0.035 μm on average.

  • ultra precision Surface finish of the hardened stainless mold steel using vibration assisted ball polishing process
    International Journal of Machine Tools & Manufacture, 2008
    Co-Authors: Fang-jung Shiou, Hongsiang Ciou
    Abstract:

    Abstract A vibration-assisted spherical polishing system driven by a piezoelectric actuator has been newly developed on a machining center to improve the burnished Surface roughness of hardened STAVAX plastic mold stainless steel and to reduce the volumetric wear of the polishing ball. The optimal plane Surface ball burnishing and vibration-assisted spherical polishing parameters of the specimens have been determined after conducting the Taguchi's L 9 and L 18 matrix experiments, respectively. The Surface roughness R a =0.10 μm, on average, of the burnished specimens can be improved to R a =0.036 μm ( R max =0.380 μm) using the optimal plane Surface vibration-assisted spherical polishing process. The improvement of volumetric wear of the polishing ball was about 72% using the vibration-assisted polishing process compared with the non-vibrated polishing process. A simplified kinetic model of the vibration-assisted spherical polishing system for the burnished Surface profile was also derived in this study. Applying the optimal plane Surface ball burnishing and vibrated spherical polishing parameters sequentially to a fine-milled Freeform Surface carrier of an F-theta scan lens, the Surface roughness of R a =0.045 μm ( R y =0.65 μm), on average, within the measuring range of 149 μm×112 μm on the Freeform Surface, was obtainable.

  • calculation of the unit normal vector using the cross curve moving mask for measurement data obtained from a coordinate measuring machine
    Journal of Physics: Conference Series, 2006
    Co-Authors: Fang-jung Shiou, Rueytsung Lee
    Abstract:

    This study presents a cross-curve moving mask method to calculate the unit normal vector based on 5 or 9 data points of a Freeform Surface measurement. The middle point and 4 or 8 neighboring points can be constructed as two crossed curves - longitude and latitude. The unit normal vector at the middle point can be determined by calculating the cross product of two tangent vectors along these 2 crossed curves. Different curve fitting methods passing 5 or 9 data points, such as Lagrange, parametric polynomial, Bezier and B-spline methodologies, are investigated. Two kinds of Surfaces, namely, a sphere Surface and a shoe-shaped geometric Surface are selected for evaluating the accuracy of the calculated unit normal vectors.

Fengzhou Fang - One of the best experts on this subject based on the ideXlab platform.

  • highly efficient machining of non circular Freeform optics using fast tool servo assisted ultra precision turning
    Optics Express, 2017
    Co-Authors: Fengzhou Fang, Xiaodong Zhang, Xianlei Liu, Huimin Gao
    Abstract:

    Freeform optics has been regarded as the next generation of the optical components, especially those with non-circular apertures are playing an increasingly significant role in scanning field and specialized optical system. However, there still exist challenges to machine non-circular optical Freeform Surface. This paper is focused on highly efficiently generating Freeform Surfaces with optical Surface quality by ultra-precision turning using a fast tool servo (FTS). A systematic strategy of machining smooth Freeform Surfaces with rectangular aperture is proposed in this paper. The contour of Freeform optics is decomposed and assigned to the motions of slide and FTS back-and-forth. An optimized model is established for deriving the profile of the rotational component to cater for the capacity of FTS. Tool path reconstruction is carried out to generate a smooth tool trajectory and modified the contour to cater for the stroke of FTS. Simulation is adopted to analyze the machining property of a typical rectangular Freeform Surface. A rectangular Freeform Surface is efficiently machined via the proposed method, where a micron level profile error and nanometric finish in Ra are realized. Characteristics of reflection are analyzed via experiment and simulation. Prospects of such machining approach are discussed to provide guidance to future study.

  • machining approach of Freeform optics on infrared materials via ultra precision turning
    Optics Express, 2017
    Co-Authors: Fengzhou Fang, Jinji Che, Xiaodong Zhang
    Abstract:

    Optical Freeform Surfaces are of great advantage in excellent optical performance and integrated alignment features. It has wide applications in illumination, imaging and non-imaging, etc. Machining Freeform Surfaces on infrared (IR) materials with ultra-precision finish is difficult due to its brittle nature. Fast tool servo (FTS) assisted diamond turning is a powerful technique for the realization of Freeform optics on brittle materials due to its features of high spindle speed and high cutting speed. However it has difficulties with large slope angles and large rise-and-falls in the sagittal direction. In order to overcome this defect, the balance of the machining quality on the Freeform Surface and the brittle nature in IR materials should be realized. This paper presents the design of a near-rotational Freeform Surface (NRFS) with a low non-rotational degree (NRD) to constraint the variation of traditional Freeform optics to solve this issue. In NRFS, the separation of the Surface results in a rotational part and a residual part denoted as a non-rotational Surface (NRS). Machining NRFS on germanium is operated by FTS diamond turning. Characteristics of the Surface indicate that the optical finish of the Freeform Surface has been achieved. The modulation transfer function (MTF) of the Freeform optics shows a good agreement to the design expectation. Images of the final optical system confirm that the fabricating strategy is of high efficiency and high quality. Challenges and prospects are discussed to provide guidance of future work.

  • compensation strategy for machining optical Freeform Surfaces by the combined on and off machine measurement
    Optics Express, 2015
    Co-Authors: Xiaodong Zhang, Zhen Zeng, Xianlei Liu, Fengzhou Fang
    Abstract:

    Freeform Surface is promising to be the next generation optics, however it needs high form accuracy for excellent performance. The closed-loop of fabrication-measurement-compensation is necessary for the improvement of the form accuracy. It is difficult to do an off-machine measurement during the Freeform machining because the remounting inaccuracy can result in significant form deviations. On the other side, on-machine measurement may hides the systematic errors of the machine because the measuring device is placed in situ on the machine. This study proposes a new compensation strategy based on the combination of on-machine and off-machine measurement. The Freeform Surface is measured in off-machine mode with nanometric accuracy, and the on-machine probe achieves accurate relative position between the workpiece and machine after remounting. The compensation cutting path is generated according to the calculated relative position and shape errors to avoid employing extra manual adjustment or highly accurate reference-feature fixture. Experimental results verified the effectiveness of the proposed method.

Xiaodong Zhang - One of the best experts on this subject based on the ideXlab platform.

  • highly efficient machining of non circular Freeform optics using fast tool servo assisted ultra precision turning
    Optics Express, 2017
    Co-Authors: Fengzhou Fang, Xiaodong Zhang, Xianlei Liu, Huimin Gao
    Abstract:

    Freeform optics has been regarded as the next generation of the optical components, especially those with non-circular apertures are playing an increasingly significant role in scanning field and specialized optical system. However, there still exist challenges to machine non-circular optical Freeform Surface. This paper is focused on highly efficiently generating Freeform Surfaces with optical Surface quality by ultra-precision turning using a fast tool servo (FTS). A systematic strategy of machining smooth Freeform Surfaces with rectangular aperture is proposed in this paper. The contour of Freeform optics is decomposed and assigned to the motions of slide and FTS back-and-forth. An optimized model is established for deriving the profile of the rotational component to cater for the capacity of FTS. Tool path reconstruction is carried out to generate a smooth tool trajectory and modified the contour to cater for the stroke of FTS. Simulation is adopted to analyze the machining property of a typical rectangular Freeform Surface. A rectangular Freeform Surface is efficiently machined via the proposed method, where a micron level profile error and nanometric finish in Ra are realized. Characteristics of reflection are analyzed via experiment and simulation. Prospects of such machining approach are discussed to provide guidance to future study.

  • machining approach of Freeform optics on infrared materials via ultra precision turning
    Optics Express, 2017
    Co-Authors: Fengzhou Fang, Jinji Che, Xiaodong Zhang
    Abstract:

    Optical Freeform Surfaces are of great advantage in excellent optical performance and integrated alignment features. It has wide applications in illumination, imaging and non-imaging, etc. Machining Freeform Surfaces on infrared (IR) materials with ultra-precision finish is difficult due to its brittle nature. Fast tool servo (FTS) assisted diamond turning is a powerful technique for the realization of Freeform optics on brittle materials due to its features of high spindle speed and high cutting speed. However it has difficulties with large slope angles and large rise-and-falls in the sagittal direction. In order to overcome this defect, the balance of the machining quality on the Freeform Surface and the brittle nature in IR materials should be realized. This paper presents the design of a near-rotational Freeform Surface (NRFS) with a low non-rotational degree (NRD) to constraint the variation of traditional Freeform optics to solve this issue. In NRFS, the separation of the Surface results in a rotational part and a residual part denoted as a non-rotational Surface (NRS). Machining NRFS on germanium is operated by FTS diamond turning. Characteristics of the Surface indicate that the optical finish of the Freeform Surface has been achieved. The modulation transfer function (MTF) of the Freeform optics shows a good agreement to the design expectation. Images of the final optical system confirm that the fabricating strategy is of high efficiency and high quality. Challenges and prospects are discussed to provide guidance of future work.

  • compensation strategy for machining optical Freeform Surfaces by the combined on and off machine measurement
    Optics Express, 2015
    Co-Authors: Xiaodong Zhang, Zhen Zeng, Xianlei Liu, Fengzhou Fang
    Abstract:

    Freeform Surface is promising to be the next generation optics, however it needs high form accuracy for excellent performance. The closed-loop of fabrication-measurement-compensation is necessary for the improvement of the form accuracy. It is difficult to do an off-machine measurement during the Freeform machining because the remounting inaccuracy can result in significant form deviations. On the other side, on-machine measurement may hides the systematic errors of the machine because the measuring device is placed in situ on the machine. This study proposes a new compensation strategy based on the combination of on-machine and off-machine measurement. The Freeform Surface is measured in off-machine mode with nanometric accuracy, and the on-machine probe achieves accurate relative position between the workpiece and machine after remounting. The compensation cutting path is generated according to the calculated relative position and shape errors to avoid employing extra manual adjustment or highly accurate reference-feature fixture. Experimental results verified the effectiveness of the proposed method.

Chien-hua Chen - One of the best experts on this subject based on the ideXlab platform.

  • Freeform Surface finish of plastic injection mold by using ball-burnishing process
    Journal of Materials Processing Technology, 2003
    Co-Authors: Fang-jung Shiou, Chien-hua Chen
    Abstract:

    Abstract The objective of this study is to introduce the possible ball-burnishing Surface finish process of a Freeform Surface plastic injection mold on a machining center. The design and manufacture of a burnishing tool was first accomplished in this study. The optimal plane ball-burnishing parameters were determined by utilizing the Taguchi’s orthogonal array method for plastic injection molding steel PDS5 on a machining center. Four burnishing parameters, namely the ball material, burnishing speed, burnishing force, and feed, were selected as the experimental factors of Taguchi’s design of experiment to determine the optimal burnishing parameters, which have the dominant influence on Surface roughness. The optimal burnishing parameters were found out after conducting the experiments of the Taguchi’s L18 orthogonal table, analysis of variation (ANOVA), and the full factorial experiment. The optimal plane burnishing parameters for the plastic injection mold steel PDS5 were the combination of the tungsten carbide ball, the burnishing speed of 200 mm/min, the burnishing force of 300 N, and the feed of 40 μm. The Surface roughness Ra of the specimen could be improved from about 1 to 0.07 μm by using the optimal burnishing parameters for plane burnishing. Applying the optimal burnishing parameters for plane burnishing to Freeform Surface plastic injection mold, the Surface roughness Ra of Freeform Surface region on the tested plastic injection part could be improved from about 0.842 to 0.187 μm, through a comparison between using the fine milled and using the ball-burnished mold cavity.

Xu Liu - One of the best experts on this subject based on the ideXlab platform.

  • a mathematical model of the single Freeform Surface design for collimated beam shaping
    Optics Express, 2013
    Co-Authors: Peng Liu, Zhenrong Zheng, Yaqin Zhang, Xu Liu
    Abstract:

    Incoherent collimated beam has a wide application, and reshaping the collimated beam with Freeform optics has become a popular and challenging topic of noniamging design. In this paper, we address this issue, embedded in three-dimensional space without any symmetry, with a Freeform Surface from a new perspective. A mathematical model is established for achieving the one-Freeform Surface design based on the problem of optimal mass transport. A numerical technique for solving this design model is disclosed for the first time, and boundary conditions for balancing light are presented. Besides, some key issues in achieving complex illuminations are addressed, and the influence of caustic Surface on this design model is also discussed. Design examples are given to verify these theories. The results show elegance of the design model in tackling complex illumination tasks. The conclusions obtained in this paper can be generalized to achieve LED illumination and tackle multiple Freeform Surfaces illumination design.

  • Freeform illumination design a nonlinear boundary problem for the elliptic monge ampere equation
    Optics Letters, 2013
    Co-Authors: Peng Liu, Zhenrong Zheng, Yaqin Zhang, Xu Liu
    Abstract:

    We propose an approach to deal with the problem of Freeform Surface illumination design without assuming any symmetry based on the concept that this problem is similar to the problem of optimal mass transport. With this approach, the Freeform design is converted into a nonlinear boundary problem for the elliptic Monge-Ampere equation. The theory and numerical method are given for solving this boundary problem. Experimental results show the feasibility of this approach in tackling this Freeform design problem.

  • distortion correction for imaging on non planar Surface using Freeform lens
    Optics Communications, 2012
    Co-Authors: Jia Hou, Zhenrong Zheng, Xu Liu
    Abstract:

    Abstract The method of designing a Freeform lens which can image on a formula describable non-planar Surface with low distortion was proposed aimed on distortion correction. In this method, the Snell's law and the correspondence between the coordinates of object and the distortion free image are used to establish the partial differential equation which characterizes the Freeform Surface, and the partial differential equation can be solved to form the Freeform Surface. Take projection on spherical Surface for example, a Freeform lens is designed. After adding this lens to the ordinary projection lens at a certain position, the system (ordinary projection lens and Freeform lens) can project an image on sphere with absolute distortion about 2 mm for an observer at half of the projection distance, and the MTF on sphere is analyzed in detail after.