Study of process parameters on optical qualities for injection-molded plastic lenses Huai En Lai and Pei Jen Wang* Department of Power Mechanical Engineering, National Tsing Hua University, 101, Sec. 2, Kuangfu Road, Hsinchu 30013, Taiwan, Republic of China *Corresponding author: [email protected] Received 3 January 2008; revised 4 March 2008; accepted 7 March 2008; posted 10 March 2008 (Doc. ID 91177); published 11 April 2008 Numerical simulations for mold-flow analysis and experimental measurements of injection-molded plas- tic lenses have been conducted for investigation of optical qualities, residual birefringence, and form ac- curacy resulting from various pertinent process conditions. First, residual birefringence distributions on the lens have been predicted and verified experimentally. Furthermore, full-scale factorial design of ex- periments was conducted to comprehend the influences of qualities, such as shear stresses, form accu- racy, and volumetric deviation, on the measured primary or Seidel aberrations. In conclusion, residual birefringence induced by stresses represented by photoelasticity measurements agrees well with the nu- merical predictions and the experimental results indicate that the residual birefringence is mainly gen- erated during the mold-filling stage. In addition, spherical aberration of the injection-molded plastic lenses is more sensitive to the pertinent qualities as compared to coma and astigmatism. © 2008 Optical Society of America OCIS codes: 260.1440, 080.1010, 220.3630, 080.2205. 1. Introduction the qualities [1–5], a systematic method based upon In this paper, comprehensive study of injection- factorial design of experiments is adopted for in- molded plastic lenses is presented through both vestigating the effects of residual birefringence, numerical simulations and experimental veri- form accuracy, and volumetric deviations on the fications for illustrating the pertinent optical charac- Seidel aberrations. The conclusions show prominent teristics of the plastic lenses. First, results from results and observations in the injection molding of three-dimensional mold-flow analysis are employed plastic lenses. to simulate the thermomechanical history of molten Since Sir Isaac Newton published basic theories plastics inside the mold cavity in terms of stresses for light and optics in the 18th century, optical instru- and shrinkage. Then, individual effects from the ments have been invented and manufactured for flow-induced and thermal-induced birefringence exploring minute bioorganisms, distant planets, are investigated by photoelasticity measurements and even mysterious galaxies. As progress in optical on thermally annealed lenses. Furthermore, with engineering technology was made in the past few the help of Taguchi methods as design of experiment decades, optical lenses are commonly adopted by (DOE) steps for comprehending the processing influ- various consumer products for either capture or dis- ences of processing conditions on qualities including play of images. For examples, 3G mobile phones, di- residual birefringence, form accuracy, and volu- gital still cameras, and digital video projectors all are equipped with modern optical lenses. Since consu- metric deviations. For further study of the effects mer products are mass produced in thousands or of processing conditions and interactions among millions of units monthly, cost reduction has become the major research objective in industries recently. 0003-6935/08/122017-11$15.00/0 In modern manufacture processes, the injection- © 2008 Optical Society of America molding process has been widely accepted because 20 April 2008 / Vol. 47, No. 12 / APPLIED OPTICS 2017 of its ability to meet stringent production require- as cycloolefin polymer (COP), has recently merged ments. However, compared to the glass lenses made into mass production of plastic lenses in consumer by the grinding and polishing process, injection- products. Among the commercialized COP polymers, molded plastic lenses have been known for poor ZEONEX, produced by Zeon Chemicals, Japan, is production yields because the lenses are made by specially tailored for optical lenses because of very complex manufacture procedures which require ther- low water absorption, low density, low impurity, high mal annealing for enhancing dimensional stability deflection temperature, and high transmittance. afterward. It has been noted that the quality of op- From the literature, most published works in the tical images in plastic lenses is influenced by two manufacture of plastic lenses have been conducted groups of crucial factors, namely, the one contribut- for polymethyl-methacrylate (PMMA) and polycarbo- ing to residual birefringence and the other to chan- nate (PC), but not for COP polymers. It is the goal of ging the mechanical dimensions. In general, the this paper to study the optical qualities in injection- residual birefringence defocuses and blurs the opti- molded ZEONEX plastic lenses with comprehensive cal image of objects designated by the modulation experimental verification. transfer function (MTF) requirements. Based upon the literature [6], the residual birefringence evi- 2. Manufacture Process Analysis dently has become a major design and production In this study, a commercial mold-flow analysis pro- problem in high-density information storage medias gram MOLDEX3D, copyrighted by CoreTech System and high resolution optical systems. at Chupei, Taiwan, has been chosen for simulating In photoelasticity theory for materials with isotro- the thermomechanical history of polymeric materials pic optical properties, residual birefringence is de- inside the mold cavity throughout the complete pro- scribed as linear characteristics between residual cess. The main features of the program are itera- stresses and refractive indices of materials defined tive calculations of flow, pressure, and temperature as follows [7]: values of molded lenses at various stages, such as fill- − ¼ ðσ − σ Þ; ing, packing, cooling, and postcooling, with details n2 n1 c 1 2 described elsewhere [12–16]. More importantly, all n3 − n2 ¼ cðσ2 − σ3Þ; n1 − n3 ¼ cðσ3 − σ1Þ: ð1Þ the calculated results are displayed with the help of graphical postprocessors for thermal-mechanical In Eq. (1), σ1, σ2,andσ3 are the principal residual history and distributions in various locations. stresses at the point of interest; n1, n2, and n3 are the refractive indices of materials associated with A. Mold-Flow Analysis the principal stress directions; and c is the stress In the numerical simulations of the process, poly- optic coefficient. According to the literature [8–10], meric melt is assumed to be incompressible during two mechanisms dominate the residual birefringence the filling stage but compressible at the postfill- phenomena in injection-molded lenses; they are ing stage. And, the polymeric melt is characterized commonly known as the flow-induced and thermal- by the generalized Newtonian fluid model and de- induced residual birefringence, respectively. The scribed by governing equations for nonisothermal former is credited to frozen molecule orientations be- three-dimensional flow inside the mold cavity formu- cause of mechanical shear stresses occurring at the lated as follows [14,15]: filling and holding stage; whereas the latter is attrib- uted to shrinking stresses due to nonuniform cooling ∂ρ ∂ þ ∇:ρ u ¼ 0; ðρ uÞþ∇:ðρ uu − σÞ¼ρg; before part removal. It should be further clarified ∂t ∂t that the residual birefringence phenomena are de- σ ¼ −pI þ ηð∇u þ ∇uTÞ; pendent of time and temperature history because ∂T of the viscoelastic properties in polymeric materials. ρC þ u:∇T ¼ ∇ðk∇TÞþη_γ2; ð2Þ In the past decades, many papers on analyzing the p ∂t residual birefringence in complex injection-molding processes have been published for injection-molded where u is the velocity vector; T is the temperature; disks approximated with the Hele–Shaw model [8– t is the time; p is the pressure, σ the total stress ten- 11]. However, the Hele–Shaw model is insufficient sor, ρ the density, η the viscosity, k the thermal con- for representing the flow characteristics of lenses ductivity, Cp the specific heat, and_γ the shear rate. and moldings with microstructures because it is a Based upon the physical phenomena of fluid me- two-dimensional model. As a result, dimensional chanics, the polymeric melt driven by pressure-head errors of injection-molded lenses are still unpredict- would flow along the path with minimal flow resis- able through numerical simulations, and they contri- tance; that is, the longer the flow distance per unit bute to the primary or Seidel aberrations in object time, the smaller the flow resistance along the flow image; namely, spherical aberration, coma, astigma- path. tism, field curvature, and distortion. Since injection-molded parts would deform after In the progress of development in optical the process, the MOLDEX3D/SOLID-WARP module has materials, a well-known polymeric material de- been adopted for warpage analysis of the three- veloped for optics applications, technically known dimensional injection-molded lenses. Based upon 2018 APPLIED OPTICS / Vol. 47, No. 12 / 20 April 2008 the thermal-elasticity theory of solid structures, the module treats three-dimensional stress–strain defor- mation problems as simple solid structures. In the analysis, pertinent assumptions are made for linear and elastic materials properties (1), small strains (2), and the static equilibrium structure (3). Hence, the