INVESTIGATION OF INJECTION MOLDING PROCESS FOR HIGH PRECISION POLYMER LENS MANUFACTURING DISSERTATION. the Degree Doctor of Philosophy in the Graduate

Transcription

1 INVESTIGATION OF INJECTION MOLDING PROCESS FOR HIGH PRECISION POLYMER LENS MANUFACTURING DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Chunning Huang, M.S. * * * * * The Ohio State University 2008 Dissertation Committee: Professor Allen Y. Yi, Adviser Approved by Professor Jose M. Castro Professor L. James Lee Adviser Industrial and Systems Engineering Graduate Program

2 ABSTRACT Injection molding polymer optical components have long been used for its high volume, low cost and lightweight capability over traditional glass optics. However, the process has not been readily accepted in precision optical fabrication industry because several difficult issues such as geometry deviation, inhomogeneous index distribution, birefringence and freeform fabrication have hindered the implementation of injection molding process in high precision optical applications. This dissertation research was an attempt to create a methodology for injection molding process for high precision polymer lens manufacturing. The study included both experimental approach and numerical modeling in order to identify the proper polymer lens manufacturing processes. The scope of this research involved in both fundamental and systematic investigation in optical design, mold and lens fabrication, as well as optical metrology issues related to polymer lens manufacturing to obtain precision macro and micro polymer freeform optics with accurate geometry and proper optical performance by the state-of-the-art mold fabrication and molding technology. With the aid of DOE (design of experiment) and DEA (data envelopment analysis) methods, the critical process parameters were narrowed down and the optimal conditions ii

3 were determined for lens geometry compensation. The mold compensation methodology was developed based on advanced freeform measurement and data analysis technology and STS (slow tool servo) freeform mold fabrication. The effects of the process parameters on optical performance such as birefringence, index distribution and surface scattering were carefully studied by theoretical and empirical analysis. Due to the complexity of the injection molding process, single process condition cannot fulfill all the requirements for lens quality, therefore balanced process parameters need to be selected as a compromise for desired specifications. Moreover, fabrication of macro Alvarez lens, micro Alvarez lens array, diffractive lens and Fresnel lens has proven that the advanced mold fabrication and injection molding process can provide an easy and quick solution for freeform optics. In addition, simulation with Moldflow Plastic Insight 6.1 was implemented to verify the experiment results and the prediction of the simulation results was validated using experiment results. Experimental results also showed that injection molding process is capable for precision optics manufacturing with accurate mold compensation and process control. iii

4 Dedicated to my parents iv

5 ACKNOWLEDGMENTS I would like to express my sincere gratitude to my advisor, Professor Allen Yi, for his guidance and support throughout my PhD study and during the completion of this dissertation. I have learned a great deal from his intellectual insight and knowledgeable expertise. It was an invaluable opportunity to work with him and this experience will enrich me for the rest of my life. I also would like to thank Professor Jose M. Castro, Professor L. James Lee and Professor Rebecca B. Dupaix for their service and suggestions on my doctoral committee. I also appreciate the assistance from Professor Thomas Raasch on SHS (Shack-Hartmann Sensor) and Alvarez lens research. I sincerely thank Dr. Nelson Claytor for his valuable discussions during a visit to his company, Fresnel Technologies, Inc. and at CAPCE meetings and for his generous financial support. I would like to thank the members of Professor Yi s group, for their suggestions and help to my dissertation research. Lei Li helped me in ultraprecision machining and measurement setup. He never hesitated to share with me his invaluable experience. Dr. Chunhe Zhang helped me with machining setup. Greg Firestone taught me how to use CMM (Coordinate Measuring Machine) and thermocouples. Thanks also go to Dr. Anurag Jain, Yang Chen and Lijuan Su for their advice to my research. Special thanks v

6 go to Denia R. Coatney for our cooperation on geometry measurement study and friendship. I also want to thank for the help from the machine shop supervisors in Department of Industrial, Welding and Systems Engineering. Bob Miller provided assistance in setting up the injection molding process which is very important for my research. Mary Hartzler taught me and allowed me use the machines in the basement. appreciated. The financial support from the graduate school and CAPCE of OSU is gracefully Last, but not the least, I would like to thank my parents, Xuye and Xiuhua, and my husband, Jianqing, for their encouragement and support. Without their support, I would not have accomplished what I have. vi

7 VITA April 19, 1977 Born Anshan, China B.S. Precision Instruments, Measurement and Control Technology, Tsinghua University, Beijing, China 2002 M.S. Optical Engineering, Tsinghua University, Beijing, China Engineer, Nuctech Company Limited, Beijing, China University Fellow, The Ohio State University Graduate Fellow, Center for Advanced Polymer and Composite Engineering, College of Engineering, The Ohio State University PUBLICATIONS Research Publication 1. L. Li, A. Y. Yi, C. Huang, D. A. Grewell, A. Benatar, and Y. Chen, Fabrication of Diffractive Optics by Use of Slow Tool Servo Diamond Turning Process, Optical Engineering, Vol.45, No.11, , November, vii

8 2. A. Y. Yi, C. Huang, F. Klocke, C. Brecher, G. Pongs, M. Winterschladen, A. Demmer, S. Lange, T. Bergs, M. Merz, and F. Niehaus, Development of A Compression Molding Process for Three-dimensional Tailored Free-form Glass Optics, Applied Optics, Vol.45, No.25, , September, L. Li, C. Huang, and A. Y. Yi, Fabrication of micro and diffractive optical devices by use of slow tool servo diamond turning process, ASPE Annual Meeting, Norfolk, VA, October 9-14, FIELDS OF STUDY Major Field: Industrial and Systems Engineering viii

9 TABLE OF CONTENTS ABSTRACT ii Page DEDICATION ACKNOWLEDGMENTS... VITA... LIST OF TABLES... LIST OF FIGURES. iv v vii xiii xiv CHAPTER 1 INTRODUCTION Research Motivation Literature Review Theoretical models Research Objective CHAPTER 2 PRECISION MOLD DESIGN AND FABRICATION Lens Design Mold Inserts Fabrication Injection Molding Experiments. 19 CHAPTER 3 GEOMOETERY MEASUREMENT AND COMPENSATION Basic Measurement Surface Geometry and Part Thickness.. 24 ix

10 3.3 Mold Compensation Freeform Measurement Surface Measurement Image Reconstruction CHAPTER 4 OPTICAL MEASUREMENT Birefringence (Residual Stress) Measurement Refractive Index Measurement Optical Effects of Surface Finish Theoretical Analysis Surface Characteristics of a Diamond Machined Surface Scalar Method for Diffraction and Scattering Calculation Experiment and Measurement Results Comparison of Surface Profile Measurement and Direct Scattering Measurement Relationship of Molded Surface Quality and Injection Molding Process Conditions CHAPTER 5 ALVAREZ LENS MANUFACTURING Alvarez Lens Alvarez Lens Design Alvarez Lens Fabrication Alvarez Lens Measurement Zernike Polynomials Wavefront Aberration Measurement x

11 Surface Measurement Micro Alvarez Lens Array Mold Design and Fabrication Measurement Microlens Array Geometry Measurement Surface Roughness Adjustable Focal Length Measurement CHAPTER 6 DIFFRACTIVE LENS MANUFACTURING Diffractive Lens Lens Design DOEs Fabrication Polar Coordinate Spiral Tool Path Cartesian Coordinate Broaching Profile Measurement Fresnel Lens Lens Design Mold Fabrication Profile Measurement Optical Performance Simulation CHAPTER 7 CONCLUSION CHAPTER 8 FUTURE WORK 134 APPENDIX A SPECIFICATION OF MOLDING MATERIAL APPENDIX B SH50M MAIN SPECIFICATION 139 xi

12 APPENDIX C PROCESS CONDITIONS FOR FULL FRACTIONAL FACTORIAL EXPERIMENTS APPENDIX D ANOVA RESULTS FOR FULL FRACTIONAL FACTORIAL EXPERIMENTS APPENDIX E DEA RESULTS FOR FULL FRACTIONAL FACTORIAL EXPERIMENTS REFERENCE xii

13 LIST OF TABLES Table Page 3.1 Thermal Properties of Mold insert materials Thickness Measurement Locations Zernike Polynomials (up to 4 th order) B.1 Main specification of SH50M injection molding machine C.1 Process conditions for full fractional factorial experiments D.1 ANOVA results for full fractional factorial experiments E.1 DEA results for full fractional factorial experiments 147 xiii

14 LIST OF FIGURES Figure Page 1.1 Some applications of injection molding optics. (a) f-θ lenses for laser scanner (b) Projection lenses for television (c) Domes for surveillance camera Narrow gap geometry as analyzed by the Hele-Shaw approximation Advanced Compensation procedure for quality lens injection molding Nanotech 350FG ultra precision machine Schematic drawing of the ultraprecision machine and diamond machining process (a) Ultraprecision machine (b) Close up view of diamond machining process Sumitomo SH50M injection molding machine DEA method for total weight vs. standard deviation Thickness and surface measurement setup Thickness measurement comparison between the molded lenses from nickel inserts and aluminum inserts Thickness distribution on the molded lens First round compensated mold insert surface Lens thickness measurement result Schematic of illumination principle Finished nickel mold MicroGlider profilometer.. 34 xiv

15 3.10 Measurement coordinate system manipulation Measurement result of the freeform molded lens (a) Targeted design surface (b) Molded lens surface (c) error between design and molded lens surface Snell s Law Needed points for refractive ray calculation Image reconstruction using the CMM measurement Image formed by the molded freeform optics Principle sketch of plane polariscope Retardation comparison with different packing pressure Retardation comparison with different mold temperature Retardation comparison with different melt temperature D model and birefringence simulation result from Moldflow Retardation simulation result comparison with different packing pressure Calculation of the slope of the wavefront at individual lenslet Index measurement setup Wavefront error of the molded lens under different mold temperature in fluid (a) Lower mold temperature (b) Higher mold temperature Wavefront error of the molded lens under different packing pressure in fluid (a) Higher packing pressure (b) Lower packing pressure Wavefront error of the molded lens under different packing pressure in air Profile of a typical diamond machined surface Specular reflection, high order diffraction and scattering from the diamond machined surface in Figure Diffraction from a diamond machined surface.. 62 xv

16 4.15 Schematic of phase shift interferometry Setup of the scattering measurement device Scattering measurement system Comparison of the mold insert and molded lens (a) 3D surface profile of a 20 μm tool mark spacing mold insert, measured by Veeco white light profilometer (b) 3D surface profile of the molded lens, measured by Veeco white light profilometer (c) Calculated average 1D spectrum of the same mold surface (d) Calculated average 1D spectrum of the same molded lens surface (e) Directly measured surface scattering of the same mold surface (f) Directly measured surface scattering of the same molded lens surface Experimental results of the lens molded under different packing pressure (a) First order diffraction intensity (b) Surface roughness measured by Veeco (c) Measured tool mark depth Experimental results of the lens molded under different mold temperature (a) First order diffraction intensity (b) Surface roughness measured by Veeco (c) Measured tool mark depth Experimental results of the lens molded under different melt temperature (a) First order diffraction intensity (b) Surface roughness measured by Veeco (c) Measured tool mark depth Schematic drawing of Alvarez lens pair Alvarez lens mold insert and molded lens (a) Alvarez lens mold (b) Molded freeform lenses Measurement Setup for Alvarez Lens Low order Zernike coefficients of the molded Alvarez lens pair while the relative x-axis translation RMS value of the molded Alvarez lens pair while the relative x-axis translation RMS value of the molded Alvarez lens pair while the relative x-axis translation under different packing pressure RMS value of the molded Alvarez lens pair while the relative x-axis translation under different mold temperature 93 xvi

17 5.8 Retardation of the molded Alvarez lens under different process parameters Alvarez lens geometry measurement Schematic drawing of Alvarez lens array Broaching CNC tool path Machined micro Alvarez lens array mold insert Design and 3D measurement results (a) Design (b) Measurement result of lenslet in the middle of the array (c) Difference between the lenslet in the middle of the array and design (d) Difference between the lenslet in the middle and at the edge on the molded microlens array Test setup for measuring the focal length of a molded microlens array pair Focal length measurement result General concept of a DOE s function (amplitude type) Design of 256 level DOE SEM picture of the half-radius diamond tool Spiral CNC tool path for DOE fabrication Broaching CNC tool path for DOE fabrication Sectional SEM scan of a 256-level DOE Sectional AFM scan of the 256-level DOE design Sectional AFM line scan of the 256-level DOE design Fresnel lens design Fresnel lens mold insert and molded lens Measurement result from SEM Feature comparison with different mold temperature Feature comparison with different packing pressure. 124 xvii

18 6.14 Feature comparison with different melt temperature Designed lens diffractive pattern distribution Lens 1 which is under higher packing pressure diffractive pattern distribution Lens 2 which is under lower packing pressure diffractive pattern distribution. 128 A.1 Product data sheet for Plexiglas V A.2 Product data sheet for Plexiglas V825 (Figure A.1 continued) xviii

19 CHAPTER 1 INTRODUCTION 1.1 Research Motivation A lens is an optical device that transmits or refracts light to either concentrate or diverge. It is usually formed from a piece of shaped high purity glass or plastic. A high precision lens is manufactured with very high tolerances, and a slight defect in the lens can cause it to focus the light beam improperly, making it completely ineffective for its intended purpose. The optical aberrations can result from geometry deviation, surface roughness, sub-surface defects from fabrication process, physical and mechanical properties of the optical material and optical conditions, etc. Applications that use high precision lens include medical and military equipment, collision-avoidance devices for the transportation industry, and scientific testing devices. High precision lenses are generally made of glass and require high shape accuracy (a few microns or less) and smooth surfaces (R a ~ 2 ~ 20 nanometers) and a minimum subsurface damage (< 50 nm) [Fahnle, 1988]. The performance of a lens therefore largely depends upon the fabrication process which needs to be carefully designed in order to meet optical requirements. 1

20 Due to some theoretical limitation of the traditional symmetrical optical elements, freeform elements are now beginning to be used in more applications, such as photograph, illumination, optometry and many others. Freeform optical surfaces are defined as those that do not have rotational symmetry and sometimes cover those that have rotational symmetry but with aspheric surface. The lens arrays are also included among freeform optics, since they face the same problems in fabrication, alignment and metrology as the general freeform optics. This category of optics has its obvious advantages in reduction of optical aberrations, system components and favorable positioning of optical elements. This means that freeform optics can replace some of the spherical optics if they can be improved with respect to geometry accuracy and ease of production at a comparable cost. However, the design, fabrication (including direct fabrication and molding) and metrology for freeform elements remain a difficult, case by case and complex task. The conventional production of precision lenses is by all means a complicated process and involves progressive material removal from a raw glass blank by grinding, lapping and polishing operations to obtain a finished optical component. This process is more suitable for manufacturing spherical glass lenses because of their simple geometry. However, the grinding and polishing process makes it difficult to produce freeform surface shapes economically other than sphere or flat using glass materials. As compared to glass optics fabrication, the injection molding process makes it feasible to economically produce more complicated optical shapes such as aspheric lenses, diffractive lenses and freeform lenses in plastic when the optical mold is well designed (compensated) and fabricated. Moreover, injection molding process can be used for high 2

21 volume production, thus the unit cost can be very low. For these apparent advantages, injection molded polymer optics become alternative components in many applications. For example, the pickup lenses for DVD (digital video disk) or CD (compact disk) players and micro lenses for cellular phones are injection-molded of plastics. Figure 1.1 shows some examples of injection molded optics. These optics include f-θ lenses used in scanner, projection lenses for rear projection television and plastic domes for camera systems. (a) (b) (c) Figure 1.1: Some applications of injection molding optics. (a) f-θ lenses for laser scanner (b) Projection lenses for television (c) Domes for surveillance camera Although injection molding polymer optics is increasingly used in industry for many applications, the requirements for image quality are not demanding. However, for precision optical components, optical functionality is always the most important concern for producers and consumers. Recently more requirements in product quality for the injection molding optics are expected. For example, at Videolarm corporate ( improvements in domes for surveillance camera are needed for 3

22 both geometry accuracy and residual stress level to match the high resolution cameras that are being introduced to the system. Some of the drawbacks for injection molded optics include geometry deviation from the original mold design and inhomogeneous index distribution during manufacturing. The geometry deviation resulted from volume shrinkage and warpage are strongly dependent on process conditions. The inhomogeneous index distribution resulted from the residual stresses and non-uniform molecular orientation in the injection molded parts. These are the main reasons that injection molded polymer optics are not suited for high precision applications. Therefore, investigation in injection molding process for high precision polymer lenses is critical to solving the technical issues associated with surface conformance to design and ultimately providing an affordable high precision manufacturing process for satisfactory optical performance. This dissertation research is focused on precision polymer optics fabrication by injection molding. The study involves both experimental approach and numerical modeling in order to identify the proper polymer lens manufacturing processes. The scope of this research includes investigation in optical design, mold and lens fabrication, as well as optical metrology related to polymer lens manufacturing. 1.2 Literature Review In previous research involving in polymer injection molding, most of the work was focused on determining of process parameters in order to optimize part quality. 4

23 Many approaches, including mathematical modeling, numerical simulation, process windows, design of experiment, expert systems, artificial neural networks, case based reasoning, genetic algorithms, and evolutionary strategies, have been tested [Isayev, 1987; Mok, 1999; Kwak, 2005; Shen, 2004; Tan, 1997; Kumar, 2002; Lu, 2001]. With an ever increasing demand on molded part quality, more sophisticated studies were carried out. Shape deformation including shrinkage and warpage, residual stress distribution, molecular orientation, and cooling system were performed by many researchers [Young, 2004; Choi, 1999; Wimberger-Friedl, 1995; Kang, 1998; Liou, 1989]. The above mentioned research activities were conducted with great details but did not address the issues concerning mold compensation for high precision polymer lenses. This dissertation research will demonstrate our efforts to modify the mold design and fabrication in order to compensate the geometrical and optical deviation from design. Our investigation will be focused on study of the effects of the process parameters and on development of the process and methodology to fabricate the freeform lenses with high accuracy and efficiency. On a different note, for high precision optical systems, freeform optics can provide a practical solution for some design and manufacturing problems. Notably, microlens arrays or diffractive optical elements can be injection molded in high volume at a low cost. Numerous publications highlighted the contributions to this field such as the effects of the process variables and size of the micro features for the molded parts [Gale, 1997; Sha, 2007]. However the success of the process also relies on the fabrication of the mold inserts. Fewer articles discussed the advanced mold fabrication 5

24 issue. This dissertation research will develop a methodology that is different from the traditional fabrication processes in the sense that not only macro size but micro lenses mold was also simultaneously machined using STS (slow tool servo) process. In addition, contact and non-contact measurement and data analysis methods will be developed for freeform polymer lens replication technology in this dissertation research. 1.3 Theoretical models Because most injection molded polymer products have asymmetrical configurations and the rheological response of polymer melt is generally non-newtonian and non-isothermal, it is difficult to analyze the filling process without simplifications. The GHS (generalized Hele-Shaw) flow model is the most common approximation that provides simplified governing equations for non-isothermal, non-newtonian and inelastic flows in a thin cavity as shown in Figure 1.2 which is recreated from [Dantzig, 2001]. z y V in or P in Polymer melt 2b x Figure 1.2: Narrow gap geometry as analyzed by the Hele-Shaw approximation 6

25 The assumptions [Su, 2004] of the GHS flow model are: (1) The thickness of the cavity is much smaller than the other dimensions. (2) The velocity component in the direction of thickness is neglected, and pressure is a function of x and y only. (3) The flow regions are considered to be fully developed Hele-Shaw flows in which inertia and gravitational forces are much smaller than viscous forces. (4) The flow kinematics is shear-dominated and the shear viscosity is taken to be both temperature and shear rate dependent. The detailed derivation has been developed by Hieber and Shen [Hieber, 1980]. In view of these assumptions and neglecting compressibility during the filling stages, the momentum equation in the Cartesian coordinate system reduces to: υ x P 0 = z η z (1-1) x υ y P 0 = η (1-2) z z y Where υ x and υ y are velocity components in the x and y directions, respectively; P(x, y) is the pressure, η ( & γ, T ) is the shear viscosity, γ& is the shear rate and T is temperature. Under the present assumptions, γ& is given by 7

26 1/ υ = x υ γ& y + (1-3) z z Because of the temperature difference between mold and polymer melt and the viscous heating inside the flow, the filling process should be treated as a non-isothermal case. Heat conduction in the direction of flow is neglected based on the assumption that the thickness 2b is much smaller than the other two dimensions. The energy equation in the melt region becomes ρ c T t T x T y T z 2 2 υ υ ηγ& p + x + y = k + (1-4) 2 2 Where the η & γ is the viscous heating term, and ρ, c p and k are density, specific heat and thermal conductivity, respectively. For simplicity, it is assumed that the velocities of polymer melt on the mold surfaces are zero and the temperature of mold remains at T w during filling. The boundary conditions are given by v v x y υ x = υ y = 0 at z = b = = 0 z z T T = T w at z = ± b = 0 z at z = 0 at z = 0 (1-5) Applying the lubrication approximation, the thickness-averaged continuity equation results in 8

27 ( bυ x ) ( bυ y ) + x y = 0 (1-6) Where υ x and υ y are averaged velocities over z, and b is half of the thickness. The velocities and shear rate can be obtained as b υ x = Λ x dz, y = Λ y z ~ z ~ η b ~ υ z d ~ z (1-7) z η & γ = zλ (1-8) η Where P Λ x =, x y P = y 2 2 Λ and = [ Λ + ] 1/ 2 Λ (1-9) x Λ y In addition, the gapwise-averaged velocities are obtained as: υ = (Λ / b S, υ = (Λ / b S (1-10) x x ) y y ) Where S is the flow conductance which is defined as S z dz η 2 b = 0 (1-11) Hence, substituting (1-10) into (1-6) gives: 9

28 P P S + S = 0 x x y y (1-12) As can be seen, the equations of this model are nonlinear and coupled. It is difficult to solve them analytically. In this dissertation research, simulation software Moldflow Plastic Insight 6.1 will be used to simulate the process and experiments will be conducted to verify the theory and simulation results. 1.4 Research Objective Modeling and optimization of injection molding process for polymer optics have been studied extensively for a long time. Previous studies were focused on the effects of the process variables and material properties to obtain the optimal condition and improve the part quality. However, only a few publications showed efforts in modifying mold design and fabrication to compensate the geometry and optical deviation from design. None provided a general strategy for low cost, high precision lens manufacturing. Also fabrication and measurement of macro and micro freeform polymer optics were not systematically studied before. Thus the overall objective of the dissertation research is to develop a methodology to obtain high precision macro and micro polymer freeform optics with accurate geometry and proper optical performance by the state-of-the-art mold fabrication technology. The polymer optics fabricated by injection molding are usually not suitable for high precision applications due to issues related to geometry deviation, inhomogeneous index distribution, birefringence and thermal instability of molded polymer lenses. The 10

29 geometrical deviation of the molded lenses will be used for mold compensation in this dissertation research. In an optical assembly, optical path length is equal to the product of the physical dimension of the medium and the refractive index. Therefore, the index deviation should also be included for mold compensation. By obtaining the index variation in the molded lens under specific process conditions, the modified mold inserts can be designed and fabricated by combining the surface and thickness measurement results and index distribution. The residual stresses and surface scattering will also be optimized under the same process condition. With the modified mold (generally a freeform shape), the molded lens will have improved optical performance. The advanced iteration compensation procedure is shown in Figure

30 Set optimal process condition Freeform Mold design and fabrication Lens molding process Lens OPD (optical path difference) test Lens optical performance test (birefringence and optical scattering) Acceptable? No Yes Quality lens collection Geometry measurement Index variation measurement Figure 1.3: Advanced compensation procedure for quality lens injection molding The specific objectives of this dissertation research can be summarized as: Investigate the feasibility of using injection molding process to manufacture high precision polymer lenses by performing experiments (both axisymmetrical and freeform lenses) and evaluating surface geometry and optical performance. 12

31 Explore the effects of process variables and material property to perform process optimization for specific objective function (surface shape deviation, birefringence, optical retardation, optical scattering). Improve current measurement method to obtain real freeform surface shape, part thickness and optical performance. Develop a methodology to design and fabricate modified mold inserts to compensate geometry error and optical aberration for the molded optics. Design and fabricate multiple freeform mold inserts and obtain functional injection molded freeform optics including compensated lens, Alvarez lens, micro Alvarez lens arrays and diffractive lenses. 13

32 CHAPTER 2 PRECISION MOLD DESIGN AND FABRICATION Injection molding polymer optical components are used for its high volume and lightweight capability over traditional glass optics. Injection molding is an inherent freeform process thus complex geometry (including aspherical and freeform) can be readily manufactured. However several difficult issues associated with the injection molded optics have hindered the implementation of injection molding process in wider applications. These issues include geometry deviation and inhomogeneous index distribution due to thermal shrinkage; birefringence incurred during the molding process also limited the adoption of polymer optics in certain polarization sensitive optical systems; thermal instability of molded polymer lenses can also render the optics less effective in application where temperature changes become large and frequent (such as optics designed for out door use or high temperature applications). In this research, our goal is to establish a high precision polymer lens manufacturing protocol based on the state-of-the-art ultraprecision machining technologies. Specifically, two focused research subjects were studied: injection molding of macro (imaging optics) and micro optics (including microlens array and diffractive 14

33 optics). In a departure from previous approaches where modifications of process conditions or material properties were the first choice, our aim was to utilize the newly acquired freeform optical fabrication capability using ultraprecision machining process to compensate for optical performance degradation due to injection molding process variability. By precisely measuring the optical retardation and surface deviation resulted from molding process variations, accurate surface geometry of a freeform mold can be constructed. To obtain an injection molded lens for optical applications, three steps need to be completed in sequence. 2.1 Lens Design In this part of the proposed research, two types of optical lenses will be studied. The first type includes precision imaging optics and ophthalmic lenses. The second type is micro optics, specifically issues related to design and fabrication of microlens array and diffractive optics will be studied. For regular lenses, commercial optical design software such as Zemax ( and Code V ( are often used to obtain the surface profile and other dimension information. In this research dissertation, a plano lens is chosen for its simple characteristic since plano lens will simplify the shape measurement, surface diffraction, residual stress and birefringence measurement and 15

34 index measurement. The methodology developed based on the plano lens can be then implemented in other applications without loss of generality. In addition to the plano lenses, lenses with a non axisymmetrical surface profile will also be molded using modified molds in this research. Since traditional fabrication method for freeform elements is difficult or costly, or time consuming, freeform lens manufacturing process has not been used for high volume and low cost production. For this dissertation research, advanced fabrication methods will be developed and precision freeform optics will be fabricated. 2.2 Mold Inserts Fabrication Mold inserts for polymer optics must have optical quality. The inserts used in this research were fabricated on the Moore Nanotech 350FG machine, a state-of-the-art 5-axis ultraprecision diamond machine. The machine is shown in Figure 2.1. Typical applications for this machine include axisymmetric machining of aspheric and toroidal surfaces, raster flycutting of freeform, linear diffractive, and micro-prismatic optical structures, as well as slow tool servo machining of freeform surface ( 16

35 Figure 2.1: Nanotech 350FG ultra precision machine The 350FG (Freeform Generation) ultraprecision machine used in this study was built by Moore Nanotechnology, Inc. It has three linear axes that are equipped with linear laser-scales capable of resolving 8.6 nm at a maximum speed of 1800 mm/min. The straightness on all slides is less than 250 nm over the entire travel up to 350 mm. The work spindle is capable of reaching 6,000 rpm while maintaining axial and radial error motion of less than 25 nm. The work spindle can also maintain angular position to less than 0.5 arc sec in a modulated mode. The main specifications of the ultraprecision machine were detailed elsewhere [Tomhe, 2003]. The C axis was fixed during freeform broaching process while during slow tool servo machining process, the C axis rotated with accurate control. The diamond tool was located on Z axis. Figure 2.2 illustrates the machine operation and the details of the freeform machining process. Arrows in Figure 2.2 (a) indicate positive directions of the linear axes. 17

36 Y Diamond tool Freeform optic X Z(X,Y) (a) (b) Figure 2.2: Schematic drawing of the ultraprecision machine and diamond machining process (a) Ultraprecision machine (b) Close up view of diamond machining process With this machine, the inserts can be fabricated with very low surface roughness (Normally R a is in several nanometers), therefore no post machining polishing is needed. For plano lens mold inserts, the initial inserts can be fabricated by traditional SPDT (single point diamond turning) process. The following modified mold inserts are fabricated by slow tool servo process to create the nonsymmetrical surface profile. The slow tool servo process makes the freeform inserts with accurate geometry and optical finish in one single operation. After the mold inserts are diamond machined, non contact measurement is preferred to measure the surface geometry to protect the optical surface finish. Apart from imaging optical lenses, although individual optical elements in a microlens array or diffractive components may have an axisymmetric curve, multiple 18

37 micro lenses arranged in a matrix format can be treated as a freeform surface and therefore fabrication method used to produce freeform surfaces can be employed to generate the array. The method is different from traditional fabrications processes in the sense that the micro lenses were simultaneously machined using slow tool servo process. A rapid optical manufacturing process from mold making to completed polymer optics based on STS (slow tool servo) will be developed. 2.3 Injection Molding Experiments In the injection molding experiments, PMMA (Polymethyl methacrylate), code named Plexiglas V825, is selected. The specification of this polymer material is shown in Appendix A. Injection molding process is very complicated since more than two hundred variables are involved in the whole process [Greis, 1983]. However, under the conditions that are crucial to our experiments, only several parameters are important to the part quality therefore will be the focus in our study. These parameters include mold temperature, polymer melt temperature, packing pressure, packing time and cooling time. These parameters will be set to different levels to complete a full fractional factorial experiment to optimize the process condition. To evaluate the part quality under each process condition, the collected parts need to be consistent in the concerned specification. For our experiments, the initial ten trial parts will be made and discarded then five or ten parts will be collected for measurement. The room temperature and humidity are also important for the part quality, so any selected experiments will be conducted in one single day to keep the environmental condition consistent. All the experiments in this 19

38 research dissertation were conducted on Sumitomo SH50M injection molding machine shown in Figure 2.3. The specification of SH50M is listed in Appendix B. Figure 2.3: Sumitomo SH50M injection molding machine 20

39 CHAPTER 3 GEOMOETERY MEASUREMENT AND COMPENSATION Although optics fabricated by injection molding are increasingly used in industry, requirements for image quality in many applications are not necessarily demanding. However, for precision optical components, optical functionality is the most important factor for producers and consumers. The geometry deviation resulted from volume shrinkage and warpage is one of the drawbacks for injection molded optics. This is the main reason that prevents injection molded optics from being used in high precision applications. Therefore, investigation in injection molding process for high precision polymer lenses is critical to solving the technical issues associated with surface conformance to design and ultimately providing an affordable high precision manufacturing process for satisfactory optical performance. 3.1 Basic Measurement The quality of the injection molded components is strongly dependent on process conditions. For this research, the optimal process conditions were obtained with the aid 21

40 of DOE (Design of Experiments) and DEA (Data Envelopment Analysis) methods according to basic measurement results. The mold inserts were made of copper nickel C715 ( and the design was a plano lens with diameter of 50 millimeters and thickness of 3 millimeters. After initial tuning of the process, five parameters in different levels were set up for a full factorial design of experiments. Seventy-two experiment conditions were listed in Appendix C. For the plano lens, both the diameter and the thickness of the injection molded part were measured. A micrometer was opted for diameter measurement and a precision indicator was used for thickness measurement on specific position. A precision scale was used for part weight measurement. Every part was measured and the average and standard deviations were calculated for each group under the same process condition. The measurement data (total weight and its standard deviation) were processed using ANOVA (analysis of variance) built in MINITAB and DEA to obtain the effects of the process variables and the optimal conditions (Refer to Appendix D and Appendix E). From ANOVA results, melt temperature, mold temperature, packing pressure were found to be the most important variables and cooling time, packing time were less important. The conclusion from ANOVA results just narrowed down the critical process parameters for the following study. From DEA results, four process conditions (Condition 12, 27, 32 and 36) were obtained which means they were better choices for designated objective functions. As optimal process condition, Condition 12 (melt temperature 210 C (450 F), 22

41 mold temperature 65 C (150 F), cooling time 40 sec, packing pressure 76.3 MPa (35%) and packing time 7.5 sec) was chosen for the following study. The result for total weight vs. standard deviation by DEA is shown below and four optimal conditions are marked on Figure Total Weight vs Standard Deviation Standard Deviation Total Weight (grams) Figure 3.1: DEA method for total weight vs. standard deviation These basic measurement results provide qualitative analysis and show the process consistency and comparison of the rough dimension of the molded lens to the design. However, they cannot be used to assess the part optical performance due to the rough measurement and different merit functions. The main benefit from these results is 23

42 to narrow down the critical process parameters and choose one optimal condition for following studies. 3.2 Surface Geometry and Part Thickness The surface geometry accuracy on a lens is critical to its optical performance. The deviation of the molded surface with the design surface will introduce unwanted aberrations in an optical assembly. Each single surface geometry and part thickness need to be measured accurately and the aberration from the geometry can be estimated for the following compensation scheme. The surface geometry and part thickness can be measured by two LVDTs (linear variable difference transformers) mounted on the 350 FG machine (Figure 3.2(b) as viewed in the Z direction). The axial movement accuracy of the 350 FG machine is only several nanometers, much higher than the molded surface geometry deviation. The two LVDTs are coaxially mounted and the molded part surface is perpendicular to the direction between two LVDT tips. This setup provides the accuracy for thickness measurement as shown in Figure

43 (a) 350 Machine Frame (b) LVDT setup Figure 3.2: Thickness and surface measurement setup The molded lens is held on the machine main spindle and the LVDT setup is installed on the Z slide (as shown in Figure 3.2 (b)). Since the valid measurement range of LVDT is only ±100 µm, the spindle and Z slide moving position for each measurement point should be preset on the estimated spot to prevent probe from over-traveling. The geometry of each surface can be obtained from single surface LVDT measurement data on the same side after removing the tilt error. The thickness can be obtained from both surface LVDT measurement data for the corresponding pair of points. By modifying the part holder and keeping a constant environment condition (temperature, noise etc), the measurement repeatability were maintained to less than 0.4 µm. Only selected non-ferrous materials can be machined by diamond turning process to optical quality without polishing, so in this dissertation research aluminum and copper 25

44 nickel alloy were chosen to fabricate mold inserts. The thermal properties of the mold insert materials are listed in Table 3.1. Copper Nickel C715 Aluminum 6061 T6 CTE*, linear 250 C 16.2 µm/m- C 25.2 µm/m- C Specific Heat Capacity J/g- C J/g- C Thermal Conductivity 29.0 W/m-K 167 W/m-K * Coefficient of Thermal Expansion Table 3.1: Thermal properties of mold insert materials Due to the different material thermal properties, even under same process condition, the molded parts by using different mold insert materials also will be different in final shape such as part thickness P-V (peak to valley) value. The thickness of the molded plano lenses from nickel inserts and aluminum inserts but under same process condition was measured in the locations listed in Table 3.2. The center of the molded lens was set as origin of the coordinate system and Y axis and Z axis were in the same direction as the machine coordinate system. The measurement area for surface geometry and thickness was limited by the dimensions of the lens holder and LVDT probes, so the area that is close to the edge of the molded lenses could not be measured by current measurement setup. For this study, the radius of the measurement area was 12 mm to avoid the interference between the lens holder and the probes. 26

45 Location Y (mm) Z (mm) Table 3.2: Thickness measurement locations The measurement results from nickel inserts and aluminum inserts are shown in Figure 3.3. The thickness P-V value of the molded plano lenses with copper nickel C715 inserts was about 20% less than that with aluminum 6061 inserts. Since aluminum is easier to machine, aluminum was again chosen as main mold insert material for the following experiments in this dissertation research. The measurement results from different mold materials also show the same tendency for the thickness distribution on the molded lens, therefore, the conclusions from the following experiments which were based on aluminum inserts can be applied for the molded lenses with copper nickel inserts. 27

46 Figure 3.3: Thickness measurement comparison between the molded lenses from nickel inserts and aluminum inserts With the aluminum flat mold inserts, the P-V value of the thickness deviation of the molded plano lens is about 7 µm from the first experiment round under condition 12 (melt temperature 210 C (450 F), mold temperature 65 C (150 F), cooling time 40 sec, packing pressure 76.3 MPa (35%) and packing time 7.5 sec) on all measurement locations. Figure 3.4 shows the thickness measurement results. From the figure, it can be seen that the square area was measured due to the constraints for measurement point selection. The lens compensation scheme that would be implemented was based on this measurement result. 28

47 Figure3.4: Thickness distribution on the molded lens 3.3 Mold Compensation When lens geometry and thickness measurement are performed, the amount of mold compensation can be determined under the same process condition. First, the difference between the measured molded lens surfaces and design surface profile can be obtained. Second, the surface geometry can be fitted by Zernike polynomials (details will be explained later), which is a convenient tool for wavefront description. The compensated mold surface will be a complex freeform surface. Finally, slow tool servo machining will be used to fabricate the compensation mold with optical surface quality. With this mold insert, the molded lens should have better geometry and optical 29

48 performance that can be quantified using the techniques described in this dissertation research. The first round compensation is based on the molded lens thickness measurement results from aluminum flat mold inserts. The modified mold insert surface is shown in Figure 3.5. The analytical expression for the fitted surface is second order Zernike polynomials. The P-V value for the modified mold surface with 40 mm in diameter is about 11 µm to compensate the uneven thickness of the molded lens with flat mold insert. The first round compensated mold insert surface is also fabricated with Aluminum Figure 3.5: First round compensated mold insert surface The lens thickness measurement results are shown in Figure 3.6. The blue line is the molded lens thickness measurement result from original flat mold insert. The red and 30

49 black lines are two molded lenses from the first round compensated mold insert. The measurement locations can be referred in Table Thickness (mm) flat mold modified mold modified mold Location Figure 3.6: Lens thickness measurement result From the measurement shown in Figure 3.6, it can be seen there is more than 50% improvement on the thickness variation for the molded lens after compensation comparing with the original lens. The compensation method for lens quality improvement has been proven to be effective. The further work will be focused on improvement in compensation results. 3.4 Freeform Measurement Benefiting from continuing research and development, freeform optical surface are now becoming a practical solution to many optomechanical designs. However, because of the asymmetrical geometry of the freeform optics, it is difficult to obtain 31

50 accurate surface curvature information of the freeform components. In this dissertation research, a methodology for freeform measurement and data analysis was introduced. The optical lens used in this research has a 3D tailored free-form surface. Three dimensional tailoring is a constructive method for the design of freeform illumination optics [Ries, 2002]. Light from a point source is transmitted by the freeform lens and redirected to cast a prescribed illumination distribution on an image surface. The exact shape of the lens surface is calculated by solving a set of differential equations that describe a piecewise smooth surface, the desired trimming, and the redirection of radiation defined by the slope and the curvature of the surface. The second surface of the glass lens is flat. Figure 3.7 shows the 3D tailored free-form lens that refracts the light rays from a point light source to form the Fraunhofer Institute for Production Technology (IPT) logo as bright lines on a flat screen (the image plane). The finished lens has a diameter of 20 mm, and the image has a size of 20 mm 20 mm. Projection Molded freeform lens 20 mm 20 mm (Point) Light source Figure 3.7: Schematic of illumination principle 32