Design and Fabrication of Nonconventional Optical Components by Precision Glass Molding

Home , Crown glass (optics), Crown glass (window), Diamond turning, Master Mold, Slumping

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of the Ohio State University

Peng He

Graduate Program in Industrial and Systems Engineering

The Ohio State University

2014

Dissertation Committee:

Dr. Allen Y. Yi, Advisor

Dr. Jose M. Castro

Dr. L. James Lee

Peng He

2014

Abstract

Precision glass molding is a net-shaping process to fabricate glass optics by replicating optical features from precision molds to glass at elevated temperature. The advantages of precision glass molding over traditional glass lens fabrication methods make it especially suitable for the production of optical components with complicated geometries, such as aspherical lenses, diffractive hybrid lenses, microlens arrays, etc. Despite of these advantages, a number of problems must be solved before this process can be used in industrial applications.

The primary goal of this research is to determine the feasibility and performance of nonconventional optical components formed by precision glass molding. This research aimed to investigate glass molding by combing experiments and finite element method

(FEM) based numerical simulations. The first step was to develop an integrated compensation solution for both surface deviation and refractive index drop of glass optics. An FEM simulation based on Tool-Narayanaswamy-Moynihan (TNM) model was applied to predict index drop of the molded optical glass. The predicted index value was then used to compensate for the optical design of the lens. Using commercially available general purpose software, ABAQUS, the entire process of glass molding was simulated to calculate the surface deviation from the adjusted lens geometry, which was applied to final mold shape modification. A case study on molding of an aspherical lens was

ii conducted, demonstrating reductions in both geometry and wavefront error by more than

60%.

In addition, mold materials and mold fabrications were explored as molds are crucial for fabrication of different freeform optics. The research for the first time demonstrated the use of graphene-coated silicon as an effective and high-performance mold material for precision glass molding. It was shown experimentally that Si-glass adhesion could be completely avoided by using the carbide-bonded graphene coating on Si molds. A glass

Fresnel lens and a micro lens arrays using graphene-coated Si molds were molded and tested. Two other novel mold materials, i.e., bulk material glass and copper nickel alloy, were also investigated. Prototypes of optical components were molded using these two materials. The molded lens glass samples were measured by 3D profiler, and the optical performance of the molded lens was also evaluated by lab optical setup. The applications of both of the mold materials were also discussed.

Finally, precision glass molding techniques are discussed for two different applications, a diffractive hybrid lens molded by a visible optical glass and a micro lens array molded by infrared (IR) glass. The diffractive hybrid lens was designed to compensate for chromatic aberration. The diffractive efficiency and achromatic focal shift of the molded lens were measured using lab setup, demonstrating a match between the molded lens and optical design. On the other hand, an infrared glass micro lens array and optical gratings were also molded and evaluated using similar approach. The geometry and optical evaluation

iii of these molded glass applications showed that precision glass molding are capable of fabricate non-convectional optical components with designed functionality.

Dedication

This document is dedicated to my family.

Acknowledgments

I would like first to thank my advisor, Dr. Allen Y. Yi, for providing me the opportunity to work in the field of precision optical engineering. I appreciate his insight, suggestions and assistance during my research work. I want to thank Dr. Yi for his patient guidance on my publications, where his attitude of striving for excellence has given tremendous influence to me. Also, I am indebted to my dissertation committee members, Prof. Jose

M. Castro and Prof. L. James Lee for their suggestions, comments and support of my research.

I want thank my previous senior lab fellows, Dr. Yang Chen and Dr. Lijuan Su, who unreservedly taught me the knowledge of glass forming science and simulation related skills. Special thanks should be addressed to Dr. Lei Li, who collaborated with me and provided great help on Graphene project. Without the help of those senior lab fellows, my research project wouldn’t have a good start.

I sincerely give my appreciations to my two 9-year classmates, Likai Li and Hui Li, who collaborated with me on various projects in the past few thousands of days and nights. I am also grateful to work with other excellent labmates, Dave McCray, Ziwei Zhao, Hao

Zhang, Bo Tao, Neil Naples and Amin Moghaddas.

vi I acknowledge the help from Joshua Hassenzahl, lab supervisor at the department of integrated systems engineering, for assisting in mold fabrication and many fixtures used in my research. I also want to thank Prof. Jerald Brevick, graduate studies chair, for his support on my academic progresses.

I want to thank Prof. Fritz Klocke, Dr. Olaf Dambon, Dr. Fei Wang, Mr. Gang Liu and

Mr. Yang Wang at Fraunhofer Institute for Production Technology (IPT), Aachen,

Germany, for providing experimental support and assistance during my visit to IPT.

Finally, I want to express the deepest appreciation for my wife, Jia Li, for her faith and love to me. The mutual intellectual and moral supports between us are my source of power in pursuit of excellence. I am also indebted to my parents, sister, grandparents and parents-in-law for their endless support in my life.

vii

Vita

July, 1986 ...... Born, Xianyang, China

July, 2009 ...... B.S. Mechanical Engineering, University of

Science and Technology of China, Hefei,

China

June, 2011 to July, 2011 ...... Visiting Scholar, Fraunhofer Institute for

Production Technology (IPT), Aachen,

Germany

May, 2014 ...... M.S. Industrial Engineering, the Ohio State

University, Columbus, Ohio

Sep, 2009 to present ...... Graduate Research Associate, Department

of Industrial and Systems Engineering, The

Ohio State University, Columbus, Ohio

viii

Publications

Journal Publications:

 P. He, L. Li, J.Yu, L. J Lee and A. Y. Yi “Compression molding of freeform optics using diamond machined Si mold”, Manufacturing letters, 2014;2:17–20.

 P. He, L. Li, J. Yu, W. Huang, Y.Yen, L. J. Lee, A. Y. Yi “Graphene coated Si mold for molded glass optics”, Optical Letters，2014;53:98–103

 P. He, F. Wang, L. Li, K. Georgiadis, O. Dambon, F. Klocke, and A. Y. Yi, “Development of a low cost high precision fabrication process for glass hybrid aspherical diffractive lenses,” J. Opt., vol. 13, no. 8, p. 085703, Aug. 2011.

 L. Li, P. He, F. Wang, K. Georgiadis, O. Dambon, F. Klocke, and A. Y. Yi, “A hybrid polymer–glass achromatic microlens array fabricated by compression molding,” J. Opt., vol. 13, no. 5, p. 055407, May 2011.

 B. Tao, P. He, L. Shen, “Measurement of Residual Stresses in Molded Glass Lenses”, Advanced Materials Research Vol. 902 (2014) pp 144-147

 B. Tao, P. He, L. Shen, A. Y. Yi “Annealing of Compression Molded Aspherical Glass Lenses”, Journal of Manufacturing Science and Engineering， J. Manuf. Sci. Eng. 136(1), 011008 (2013) doi:10.1115/1.4025395

 L. Su, P. He, and A. Y. Yi, “Investigation of glass thickness effect on thermal slumping by experimental and numerical methods,” Journal of Materials Processing Technology, vol. 211, no. 12, pp. 1995–2003, (2011)

 L. Su, F.Wang, P. He, O. Dambon, F. Klocke, A. Y. Yi “An Integrated Solution for Mold Shape Modification in Precision Glass Molding to Compensate Refractive Index Change and Geometric Deviation” , Optics and Laser in Engineering, 53, 98– 103 (2014).

 B. Tao, L. Shen, P. He, and A. Yi, “Quantitatively Measurement and Analysis of Residual Stresses in Molded Aspherical Glass Lenses” , The International Journal of Advanced Manufacturing Technology, June 24, pp1–8 (2014)

Conference proceedings and presentations:

 P. He, P. Xie, L. J. Lee, and A. Y. Yi. “Rapid Micro-embossing and injection molding.” OSA Technical Digest , Optical Fabrication and Testing, Kohala Coast, Hawaii, June, 2014

 P. He, L. Li,J. Yu,W. Huang, Y-C. Yen, J.L. Lee, A. Y. Yi, “Graphene Coated Si Mold for Precision Glass Optics Molding , ASPE Annual Meeting, St. Paul, MN, Oct, 2013

 P. He, L. Li, J. F. Yu, L. J. Lee, A. Y. Yi, “Ultraprecision Mold Fabrication For Polymer and Glass Molding,” International Symposium on Advanced Molding Technology and Materials Processing, Planery Talk, Ninghai, China, July 2-3 ,2013.

 B. Tao, P. He, L.Shen, “Measurement of Residual Stresses in Molded Glass Lenses”, International Conference on Manufacturing Engineering and Technology for Manufacturing Growth,Miami,FL, Jan, 2014

 P. Xie, E. D. Cabrera, P. Zhang, Y. Yen, P. He, D. Gallego-Perez, L. Chang, A. Y. Yi, J. Castro,and L. J. Lee.“Rapid micro-embossing and injection molding using molds with carbide-bonded graphene coating”, 30th International Conference of the Polymer Processing Society (PPS-30), Cleveland, Ohio, June 8-12, 2014

 F. Klocke, O. Dambon, L. J. Su, F. Wang, P. He, G. Liu, A. Y. Yi, “An Integrated Solution for Compensation of Refractive Index Drop and Curve Change in High Precision Glass Molding,” 12th International Conference of the European Society for Precision Engineering Nanotechnology (Euspen), Stockholm, June (2012).

x Fields of Study

Major Field: Industrial and Systems Engineering

Studies In: Precision glass molding, Optical fabrication, Mold material, Optical design

Table of Content

Abstract ...... ii

Dedication ...... v

Acknowledgments...... vi

Vita ...... viii

Publications ...... ix

Fields of Study ...... xi

Table of Content ...... xii

List of Figures ...... xvii

List of Tables ...... xxiv

Chapter 1 Introduction to Precision Glass Molding ...... 1

xii 1.1 Introduction and Motivation...... 1

1.2 Structure Relaxation and Refractive Index Variation in Molded Glass Optics ... 4

1.3 Precision Glass Molding Process ...... 6

Chapter 2 FEM Simulation Compensation for Both Refractive Index Change and

Geometric Deviation ...... 9

2.1 Introduction ...... 10

2.2 Compensation Procedures for the Mold Shape ...... 12

2.2.1 Original Lens Design ...... 14

2.2.2 Refractive Index Analysis and Compensation ...... 16

2.2.3 Mold Curve Analysis ...... 21

2.2.4 Mold Fabrication and Glass Lens Molding ...... 23

2.3 Experiments and Testing Results ...... 24

2.3.1 Geometry Testing...... 24

2.3.2 Optical Testing ...... 25

xiii 2.4 Conclusion ...... 29

Chapter 3 Investigation of Molding Materials ...... 31

3.1 Graphene Coated Si Mold ...... 32

3.2 Molding Freeform Optics Using Diamond Machines Si Mold ...... 44

3.2.1 Introduction ...... 44

3.2.2 The Fabrication Process ...... 45

3.2.3 Precision Glass Molding ...... 48

3.2.4 Characterization of Molded Freeform Optics ...... 50

3.2.5 Conclusions ...... 52

3.3 Bulk Metallic Glass Mold for High Volume Fabrication of Micro Optics ...... 53

3.3.1 Introduction ...... 54

3.3.2 Fabrication Procedures...... 56

3.3.3 Results and Discussions ...... 67

xiv 3.3.4 Conclusion ...... 71

3.4 Copper Nickel alloy ...... 72

3.4.1 Mechanical Properties of 715 Copper-nickel alloy VS Temperature ...... 72

3.4.2 Mold Materials Consideration for Diffractive Refractive Hybrid Lens ..... 74

3.4.3 Yield Strength and Modulus of Elasticity ...... 76

3.4.4 Thermal Conductivity ...... 76

3.4.5 Machinability and Surface Finish ...... 77

3.4.6 Coefficient of Thermal Expansion (CTE)...... 77

Chapter 4 Glass Molding Examples ...... 79

4.1 Development of a Low Cost High Precision Fabrication Process for Glass

Hybrid Aspherical Diffractive Lenses...... 79

4.1.1 Introduction ...... 80

4.1.2 Optical Design ...... 83

4.1.3 Mold Fabrication ...... 89

xv 4.1.4 Molding Process...... 92

4.1.5 Results and Discussions ...... 96

4.1.6 Conclusions ...... 102

4.2 Precision Molding of Infrared Glass with Graphene Coated Si Wafer ...... 105

4.2.1 Molding of Micro Lens Arrays ...... 105

4.2.2 Molding of Optical Gratings ...... 108

4.2.3 Conclusion ...... 110

References ...... 111

xvi

List of Figures

Figure 1.1 Precision glass molding processes...... 7

Figure 2.1 Flow chart for the integrated compensate scheme ...... 13

Figure 2.2 (a) Geometry of the original lens design. (b) Simulated wavefront of the original lens when a point light source is placed at focal point, d = fb, 0 ...... 15

Figure 2.3 Predicted distribution of refractive index change in the compression molded lens...... 18

Figure 2.4 (a) Simulated wavefront of the uncompensated lens when a point source is placed at the original lens focal point d=fb,0=50.52054 mm (b) Cross section comparison of wavefront between the original lens and the uncompensated lens when the point light source is placed at d = fb,0 in front of the lenses...... 19

Figure 2.5 Mold curve was compensated by FEM predicted geometric deviation ...... 22

Figure 2.6. Picture of a molded compensated Lens...... 23

xvii Figure 2.7 Measured lens geometry compared with index compensated design. (a) Lens upper surface (b) lens lower surface...... 25

Figure 2.8 Schematic of optical measurements on WaveMaster LAB [12] ...... 26

Figure 2.9 (a) Simulated wavefront of index compensated lens when a point source was placed at its focal point. (b) Measured wavefront of the molded lens when a point source was placed at its focal point...... 27

Figure 2.10 (a) Simulated wavefront of index compensated lens when the a point source was placed at d = fb,0. (b) Measured wavefront of molded lens when a point source was placed at d = fb,0 ...... 28

Figure 3.1(a) Schematic of carbide-bonded graphene coating deposition on the Si substrate using nanosheets. (b) Surface scan of an uncoated Si wafer. Surface roughness was 0.53 nm (Ra). (c) Surface scan of a graphene coated Si wafer, surface roughness was

0.50 nm...... 34

Figure 3.2 (a) Cross-section view of the molding experiment set up. (b) Temperature and load history of glass molding. (c) Glass molding using a carbide-bonded graphene coated

Si wafer. (d) Glass molding using a Si wafer without graphene coating...... 36

Figure 3.3(a) Surface profile of a coated Si mold. (b) SEM image of Si mold with microwells after molding. (c) Surface scan of a molded glass with micro pillars. The inset

xviii is an SEM picture of the molded glass. (d) Comparison of line scans between the Si mold and the molded glass part (The profile of the Si mold was flipped for comparison)...... 38

Figure 3.4(a) Surface scan of the molded glass Fresnel lens. (b) Comparison of line scans between the molded glass lens and the Si mold (The profile of the molded glass lens was flipped for comparison)...... 40

Figure 3.5 (a) Optical setup for testing the imaging quality of molded Fresnel lens. LS: light source, LD: light diffuser, d1=690 mm, d2=86 mm, d3 is about 127 mm. (b) Image of the target with both Fresnel lens and commercial lens. (c) Image of the target on CCD with commercial lens alone. The molded lens was removed and CCD was placed on the focus plane of the commercial lens in this measurement...... 41

Figure 3.6 Three silicon molds were diced off the silicon wafer ...... 47

Figure 3.7 Schematic of molding configuration. In this setup, glass is compression molded between a movable upper mold and a fixed lower mold...... 49

Figure 3.8 (a) Picture of the molded 20 x 24 micro lens array. (8.24 mm x 7.20 mm). (b)

3D profile of the molded 6 x 6 glass microlens array. (2.16 mm x 2.16 mm)...... 51

Figure 3.9 (a) 3D profile of the center of the molded glass kinoform lens. (b) Close-up view of the edge of the kinoform surface...... 52

xix Figure 3.10 Replication of plastic micro optics using molded BMG insert as secondary mold. (a) Fabrication of BMG insert using precision glass molding (b) Hot embossing of plastic micro optics with BMG inserts (c) Injection molding of plastic micro optics with

BMG inserts...... 57

Figure 3.11 (a) DSC graph of Zr based BMG. Tg of this BMG is identified as 407 °C.

The crystal temperature (Tx) is about 480 °C, leaving a relatively large processing window. (b) Surface scan of the polished BMG specimens. The surface roughness surface roughness (Ra) was measured to be about 4.2 nm...... 59

Figure 3.12 Configuration of compression molding of BMG using precision glass molding machine. (a) 3 D model of molding configuration (b) Picture of molding setup with added heat shield, which was added to prevent direct heating from IR heaters to

BMG sample...... 60

Figure 3.13 (a) Parameters of precision molding of BMG. (b) Picture of molded BMG samples...... 62

Figure 3.14 The configuration for hot embossing of PMMA with BMG as mold insert. 64

Figure 3.15 Picture of an aluminum insert holder for injection molding. A molded BMG insert was placed in the pocket under a removable cap...... 65

xx Figure 3.16 Surface profile of different micro optical features (a) Optical gratings with

10 µm pitches. (b) Micro dot arrays with 20 µm spacing. (b) Line patterns with different spacing. The horizontal ruler indicates the size of scanned area by profilometer...... 67

Figure 3.17 Optical profiler measurements of (a) fused silica master mold (b) BMG mold insert (c) PMMA part...... 68

Figure 3.18 A detailed comparison between BMG secondary mold and the molded

PMMA part...... 69

Figure 3.19 (a) Schematic of optical test setup. (b) Measurement of monochromatic diffraction pattern of the molded PMMA...... 70

Figure 3.20 Temperature variation of slastic modulus for copper-nickel alloy (C71500).

...... 74

Figure 4.1 (a) The hybrid aspherical diffractive lens design. S1: Planar surface. S2:

Aspherical diffractive surface (diffractive features are exaggerated for clarity). (b) Close up view of the DOE’s profile...... 85

Figure 4.2 (a) PSF of the hybrid lens at aforementioned wavelengths. (b) OPD of the hybrid lens after optical design optimization...... 88

xxi Figure 4.3 Hybrid lens bottom mold (after molding). The outer diameter is 44.45 mm.

The aspherical diffractive surface has a diameter of 20 mm (with color hue) with 1 mm edge...... 91

Figure 4.4 Molding conditions for P-SK57 glass aspherical diffractive lenses...... 95

Figure 4.5 (a) A molded hybrid aspherical diffractive lens. (b) An optical profilometer scan of molded diffractive features...... 97

Figure 4.6 Geometry comparison between mold profile and lens profile (contour removed). T2 to T6 denote 2nd to 6th teeth...... 98

Figure 4.7 Layout of the optical measurement setup 1 laser. 2 and 3 linear polarizers 4 pinhole 5 field lens 6 hybrid aspherical diffractive lens 7 linear translation stage 8 CCD camera...... 100

Figure 4.8 (a) Image of PSF testing at wavelength of 532 nm. (b) Normalized intensity profile the PSF measurement...... 101

Figure 4.9 The measured focal shift was compared with curve predicted by ZEMAX. 102

Figure 4.10 (a) Profile of 2x2 micro lens array. (b) Surface roughness measurement at the bottom of one concave lens...... 106

xxii Figure 4.11 (a) Picture of molded Infrared sphere with 2x2 micro lens arrays on top plane. (b) Optical microscopic image of molded micro lens arrays...... 107

Figure 4.12 Geometry comparison between Si mold and mold infrared glass...... 108

Figure 4.13 (a) 3D Profile graphene coated Si wafer. (b) 3D profile of molded IR glass.

...... 109

Figure 4.14 (a) Illustration of setup for testing of optical gratings on molded IR glass.

(b) Picture of experimental setup and diffraction patterns...... 110

xxiii

List of Tables

Table 2.1 Mechanical and thermal properties of P-SK57 [9] and WC [10] ...... 16

Table 2.2 Structural relaxation parameters of P-SK57 used for simulation [11] ...... 17

Table 3.1 Microinjection molding conditions ...... 66

Table 3.2 Mechanical properties of 715 copper-nickel alloy vs temperature [66] ...... 73

Table 3.3 Coefficient of thermal expansion of several engineering mold materials...... 78

Table 4.1: Hybrid lens technique features ...... 84

xxiv

Chapter 1 Introduction to Precision Glass Molding

1.1 Introduction and Motivation

Since 1980s’, precision glass molding has been studied as a promising approach for fabricating glass optical components with complicated surface geometries [1,2]. Precision glass molding is a thermalforming process, in which a glass blank is initially heated to a desired temperature and subsequently compression molded between two optical polished molds to create designed lens geometries or surface features. After molding, the molded glass component and mold assembly are cooled with shortest cycle time possible while keeping residual stresses and thermal shrinkage in an acceptable range [3,4]. When the temperature of glass lens is lower than a certain value, i.e. 220 °C for P-SK57 glass, the molded glass component is removed from the mold assembly and is ready to be used after natural cooling to room temperature. By use of precision glass molding, high precision glass optics with complicated shape can be manufactured in a cost effective way when compared to more traditional methods such as grinding, polishing and lapping.

As a net-shape forming process, it allows high volume production of optical components

1 without the use of health hazard polishing powder or fluid, therefore it is environmentally friendly. In addition, shorter cycle time is expected since it is a one-step fabrication process.

The advantages of precision glass molding over traditional glass lens fabrication methods make it especially suitable for the production of optical components with complicated geometries, such as aspherical lens, diffractive hybrid lens, micro lens array, etc. Novel optical components are developed as a response to high demand for compact, high performance optical system in optical electronic applications, such as compact digital cameras, high end medical image system, and mobile projector. Compared to conventional optical systems where sphere lenses are utilized, nonconventional optical components have better performance, smaller size while maintaining relatively low cost, thus they are often used in compact optical system in rigorous conditions.

Despite of those advantages of glass molding approach, a number of challenges must be overcome before the new process could be fully implemented in industry. Previously, several researches have been conducted to investigate the problems ranging from thermal expansion of molds, mold life, residual stress inside molded glass to refractive index variation of glass after molding. Yi et al. developed a simple finite element method

(FEM) model to predict the performance of a lens molding process and presented the results of a precision molded glass aspherical lens [1]. Jain et al. investigated the viscoelastic stress relaxation of glass during molding and applied a numerical model

2 based on generalized Maxwell equation to predict relaxation behavior [5]. In order to improve the geometry accuracy of molded glass optics, Dambon et al. investigated geometrical error of a glass lens from thermal shrinkage and glass structural relaxation

[6]. In the study, an FEM assisted mold manufacturing process with efficient geometry compensation was developed. In addition, many other attempts were also made to address issues such as thermal slumping[7] , residual stresses [4,8], refractive index vibration [9] and protective coating on mold surfaces [10].

The primary goal of this research is to determine the feasibility and performance of nonconventional optical components formed by precision glass molding. The design and fabrication of three optical components including diffractive hybrid lens, micro lens arrays and bulk metallic glass (BMG) inserts will be investigated. The first step is to develop an integrated compensation solution for thermal shrinkages and refractive index variation of glass optics. Both geometry deviation and refractive index drop will be considered simultaneously to improve the performance of molded components. Once the compensated design is identified, fabrication of the above mentioned three optical devices will be fabricated. A commercial FEM software package will be employed to visualize the results for both design and fabrication and to optimize the process. In addition, mold materials and mold fabrications were explored as molds are crucial for fabrication of different freeform optics. molds were molded and tested. Two other novel mold materials, i.e., bulk material glass and copper nickel alloy, were also investigated.

Prototypes of optical components were molded using these two materials. Proper glass,

3 mold materials and molding parameters will be evaluated to satisfy pre-defined design criteria for compression molding of glass optical elements. Finally, the performance of molded optical components will be measured to ensure the expected results are established. In general, the proposed process is a net shape, high volume manufacturing method, thus providing industry with economical optical systems utilizing compact, high precision and low cost optical products.

1.2 Structure Relaxation and Refractive Index Variation in Molded Glass Optics

In compression glass molding, glass blanks undergo structural relaxation during cooling.

The structural relaxation behavior is a non-linear time dependent response of glass properties to thermal history, or temperature change. To represent structural relaxation of glass during cooling, TNM (Tool–Narayanaswamy–Moynihan) model was developed and successfully applied in many studies [11–13]. In the TNM model, the structural relaxation time τv at any given time and temperature can be calculated by Equation 1.1

 H  1 x 1 x     v  v,ref exp      Equation 1.1  R Tref T Tf 

where, τv,ref is structural relaxation time at reference temperature Tref. Tf is fictive temperature, H is activation energy, R is ideal gas constant, and x is fraction parameter, which is between 0 and 1. Due to the structural relaxation behavior, the glass properties,

4 (e.g. volume, refractive index) are different from the original sample after compression molding process. Soules et al. developed an algorithm in software MSC Marc to calculate changed material properties caused by structural relaxation during cooling [14]. The volume of glass at a given time during cooling is calculated by Equation 1.2:

1 dV (T)  dTf   3g (T)  3l (Tf )  3g (Tf )  Equation 1.2 V (0) dT  dT 

Where, αg and αl are linear coefficients of thermal expansion (CTE) of glass at solid and liquid states respectively. Tf is fictive temperature at a given time t. T is current temperature. V(T) is volume of a glass at a temperature T. Therefore the density change of glass can be obtained. On the other hand, relation between the refractive index change and the density change of a glass material is given by Equation 1.3 [14]:

dn n 2 1 n 2  2  d 6n Equation 1.3

where, n and ρ are the original refractive index and density of glass sample before compression molding respectively. This equation is obtained by differentiating the

Lorentz-Lorenz equation assuming that the polarizability of glass materials used in this research is independent of the density [15]. For a glass sample, the change of density can

5 be expressed by change of volume. Applying to Equation 1.3, the refractive index change is obtained as Equation 1.4 [14]:

2 2 (n 1)(n  2) Vo  n   1 Equation 1.4 6n Vc 

where, Vo is initial volume of the glass sample before compression molding process. Vc is finial volume at the end of cooling. The final refractive index of the molded glass lens is nc = n-∆n, which can be determined by the initial volume Vo, finial volume Vc , and catalog value of the refractive index of glass, n. [9,16].

1.3 Precision Glass Molding Process

A typical molding process usually consists of 4 steps, i.e., presetting, heating, molding, cooling. The total cycle time is usually less than 20 minutes. For a single lens, molding steps will be conducted under the following processes, as shown in Figure 1.1.

Figure 1.1 Precision glass molding processes.

Presetting: The upper mold is usually mounted to a fixed position and the lower mold is mounted to a linear drive. A glass blank is placed on the lower mold leaving a gap about

2 mm to avoid contact between glass and the upper mold during heating as a result of thermal expansion. Vacuum is firstly applied to remove air in the chamber, protecting the mold from oxidizing. Nitrogen is introduced afterwards to purge the system and also serves as a protective atmosphere.

Heating: Mold assembly and glass blank are heated by surrounding infrared heaters.

Thermal couples imbedded in the molds are used to regulate the temperature. Typically, the selected molding temperature will be 40~70 °C higher than glass transition temperature (Tg). When the molding temperature is achieved, a soaking time is set to minimize the temperature gradient in both the glass blank and the molds.

7 Molding: When the glass blank and molds reaches a homogenous temperature, vacuum is applied again to prevent any bubble left on the surfaces of molded glass lens. The lower mold is set to approach the upper mold at a constant speed to initialize the molding.

When the contact of glass and upper mold is made, pressing speed and directions are automatically adjusted to keep a constant load by an adaptive feedback control. The position of the lower mold and the molding force are monitored and precisely controlled at a sampling frequency of 1 Hz. The lower mold is then held in place to press the lens so the glass could be fully deformed to the desired shape.

Cooling: Cooling is realized by a forced convection flow of nitrogen gas. A slow cooling is first applied to the system. A low initial cooling rate is critical to minimize the thermal stresses inside the glass. When the glass temperature decreases to Tg, higher cooling rate is used to cool the lens to a lower temperature, i.e. 220 °C for P-SK57 glass. No holding force is applied during cooling to ensure free shrinkage and early separation of the molded glass lens from the molds. Higher cooling rate is not desirable because it will affect the refractive index of glass, which may result in deterioration of the optical performance of the molded lens [9].

After cooling, the mold inserts are separated to allow the molded lens to cool freely. The finished lens is then removed from the molding machine and cooled by natural convection to room temperature.

Chapter 2 FEM Simulation Compensation for Both Refractive Index Change and Geometric Deviation

In precision glass molding, refractive index change and geometric deviation (or geometric deviation as often referred to in industry) occurred during molding process can result in substantial amount of aberrations. Previously, refractive index change and geometric deviation were investigated in separate studies by the authors. However, optical performance of a molded glass lens depends on both refractive index and geometry. In order to mold lenses with optimal performance, both refractive index change and geometric deviation have to be taken in consideration simultaneously and compensated. This research presented an integrated compensation procedure for modifying molds to compensate both refractive index change and geometric deviation.

Group refractive index change predicted by finite element method simulation was used to provide a modified geometry design for a desired lens. Geometric deviations of molded glass lenses with the modified design were analyzed with a previously developed numerical simulation approach, which is used to modify the mold shape. This procedure was validated by molding a generic aspherical glass lens. Both geometry and optical

9 measurement results confirmed that the molded lens performed as specified by the original design. It also demonstrated that finite element method assisted compensation procedure can be used to predict the final optical performance of compression molded glass components. This research provided an opportunity for optics manufacturers to achieve better performance lens while maintaining lower cost and a shorter cycle time.

2.1 Introduction

In recent years, growing demand for small size, high performance optical devices has boosted the development of lenses with nonconventional shapes. Yi and Jain [1] investigated the compression molding technique of aspherical glass lens by both numerical analysis and experimental approach. Then a process of molding 3-dimensional microstructure glass optics was developed by Chen et al. [2]. He et al. [3] further developed a process for fabricating hybrid aspherical diffractive glass lenses. These researches proved that precision glass molding process is a fast and cost effective method for fabricating these lenses with complicated geometries, including aspherical, free form and diffractive hybrid shapes.

In a typical glass molding process, glass blanks experience three stages: fast heating stage, compression molding stage and controlled cooling stage. During the controlled cooling stage, dramatic changes of temperature in a range of several hundreds of degree within a short time affect the performance of molded lenses, and introduce unexpected

10 aberrations in the optical system where molded glass lenses are employed. On the glass properties, both the report from Schott [4] and the research of Fotheringham et al. [5] showed that the refractive index of an optical glass typically becomes smaller after molding due to glass relaxation during cooling. Another issue is with the geometry accuracy of molded lenses. After pressing, the shape of glass lens continuously changes during cooling as a result of thermal shrinkage, which causes curves of the molded lens to deviate from the design form.

Previously, Dambon et al. [6] investigated geometry error of glass lenses from thermal shrinkage and glass structural relaxation. In that study, an FEM (finite element method) assisted mold manufacturing process with efficient geometry compensation was developed. Su et al. [7] presented a numerical method to predict refractive index changes of optical glass after precision molding. Fotheringham el al. [5] verified the empirical logarithm equation on the relationship between refractive index of glass and cooling rate.

The experiments were however based on a relatively low cooling rate compared to normal practice in glass molding [4].

However, both refractive index change and geometric deviation are coupled with heating, molding and cooling parameters in glass molding process and could not be compensated alone. Therefore, a combined compensation solution is required to fabricate high performance molded lenses. In this research, an integrated scheme for designing the mold contours is presented to compensate for both refractive index change and geometrical

11 deviation. Based on previous studies, two FEM predications, i.e. refractive index prediction based on Tool-Narayanaswamy-Moynihan (TNM) model and curvature prediction based on a generalized Maxwell model, are integrated for the first time to solve the problem discussed above. The optical performance of compensated lens is analyzed by using ZEMAX (3001 112th Avenue NE, Suite 202, Bellevue, WA 98004-

8017). Experiments were performed to mold an aspherical lens and test the performance.

The results verified that proper geometry and optical performances were achieved.

2.2 Compensation Procedures for the Mold Shape

In order to reduce the aberrations of a molded lens due to refractive index and geometry changes, optical design of the lens is compensated by curvature modification of the molds. In the process of establishing the compensation scheme, both refractive index change and geometric deviation are modeled by finite element analysis. Su et al. [7] established a methodology for predicting final refractive index, while Wang et al. [8] presented a methodology for designing of the molds for compression molding process.

Both the refractive index and lens shape changes should be compensated to ensure the optical performance of a compression molded lens from a particular heating-molding- cooling condition. Figure 2.1 illustrates the flow chart of the integrated compensation scheme.

Figure 2.1 Flow chart for the integrated compensate scheme

First, the refractive index analysis is conducted to predict the refractive change. Second, the lens shape is modified to compensating the optical performance degradation caused by the refractive index change. An index compensated mold design is obtained afterwards. Third, the shrinkage of lens using “index compensated mold” is predicted. A corresponding amount of alteration is made to mold to obtain a modified mold design.

After the lens is molded using the modified mold, both its geometry and optical performance will be tested. Process parameters might be adjusted and additional compensation cycles are needed if the geometry and optical performance do not satisfy the requirements. Ideally, the finished lens, which has different refractive index from

13 initial glass material, can fulfill optical performance requirement as long as the final lens shape matches the “index compensated mold.”

2.2.1 Original Lens Design

In order to demonstrate the compensation procedure proposed in this research, the design and molding of an aspherical lens is presented in details for an arbitrarily selected double convex lens design. The presented compensation procedures can be easily applied to other glass lenses. In this research, the original design is a double convex aspherical lens with 25 mm in diameter and 4.8 mm thickness at the center, as shown in Figure 2.2 (a). It has two identical surfaces with a radius of 60 mm and conic coefficient k0 of -3.916735.

Glass material is P-SK57, a special optical glass material formulated for precision glass molding. The back focal length of this lens is fb, 0 = 50.52054 mm at  = 632.8 nm, which is considered to be the original lens design in this research.

(a) (b)

Figure 2.2 (a) Geometry of the original lens design. (b) Simulated wavefront of the original lens when a point light source is placed at focal point, d = fb, 0

Wavefront coming from a lens is often used to evaluate the lens performance. Placing a point light source in front of a lens, the distance between the point source and front surface of the lens is defined as d. If the point light source is placed at the front focal point of the original designed lens, where d = fb, 0, the wavefront coming from the back surface of the original lens is simulated in ZEMAX and as shown in Figure 2.2 (b). The light in all simulation and measurement is based on He-Ne laser at wavelength of 632.8 nm.

15 Table 2.1 Mechanical and thermal properties of P-SK57 [9] and WC [10]

Material Properties P-SK57 WC mold Elastic modulus, E [Mpa] 93,000 570,000 Poisson’s ratio, v 0.249 0.22 Density, ρ [kg/m3] 3,010 14,650

Thermal conductivity, kc [W/m ºC] 1.01 6.3

Specific heat, Cp [J/kg ºC] 760 314

Reference temperature, Tref [ºC] 493 - -1 -6 -6 Solid linear CTE, αg [K ] (20-300 ºC) 8.9x10 4.9x10 -1 -5 Liquid linear CTE, αl [K ] (ºC) 3.77x10 - 6 Viscosity η at Tref [MPa-second] 10 -

Refractive index of this lens is nd = 1.58700, which is the listed value from glass catalog.

Mechanical and thermal properties of P-SK57 glass and mold, tungsten carbide (WC), are listed in Table 2.1Error! Reference source not found. Liquid linear coefficient of thermal expansion (CTE) is chosen as three times of solid linear CTE. The viscosity of

Tref is based on the definition of Tg.

2.2.2 Refractive Index Analysis and Compensation

In glass molding, the volume of a glass blank changes during the heating, molding, and cooling (or annealing) process [17]. The refractive index of a molded glass usually shows a lower value than glass blanks. This "index drop" depends on the cooling rate of molded

16 lenses during molding. Proposed by Su et al. [7] , the change of refractive index can be predicted by equations below,

2 2 (n 1)(n  2) Vo  n   1 Equation 2.1 6n Vc 

Where, Vo is the initial volume of the glass sample before heating. Vc is the final volume of the glass sample after cooling. n is refractive index of glass before heating. The final refractive index of molded glass lens is nc = n + ∆n.

To predict such index drop, the cooling process of a lens with original design shape was simulated in a two dimensional (2D) axisymmetric model. Parameters required for TNM model in the simulation are given in Table 2.2.

Table 2.2 Structural relaxation parameters of P-SK57 used for simulation [11]

Material Properties P-SK57

Reference temperature, Tref [ºC] 494 Activation energy/gas constant, ΔH/R [K] 84,396.5 Fraction parameter, x 0.789

Weighing factor, wg 1

Structural relaxation time, τv,ref [sec] (at Tref) 100.7

Stress relaxation time, τs,ref [sec] (at Tref) 26.88

17 In the simulation, the molded glass lens was assumed to have been cooled to room temperature at a pre-determined cooling rate of 0.55 K/s. As indicated in Schott report[4]

, fabrication of a glass bank usually involves a slow annealing process. Therefore, the initial volume Vo was modeled by uniformly annealing of glass at an extremely low cooling rate, i.e. 2°C/hour. The final volume Vc of each element was calculated by cooling simulation of glass molding. The initial volume of every element is the same while final volume is different from element to element due to non-isothermal cooling.

Then Vc and Vo are plugged in Eq. 1 to calculate the corresponding refractive index change.

Figure 2.3 Predicted distribution of refractive index change in the compression molded lens.

18 Using the above simulation, the refractive index change of each element can be calculated. The distribution of refractive index change of the molded lens is then illustrated in Figure 2.3. Average of refractive index change, ∆nd,average is -0.00282, and

-5 the maximum variation n,max of refractive index change is 7.0x10 . The standard

-5 deviation of refractive index change n is calculated as 1.48x10 . Considering n,max is less than 2.5% of ∆nd,average, the average index drop value of -0.00282 was used to predict the refractive index of lenses after glass molding, which yields to n1=1.58418.

(a) (b)

19 In order to see the influence of refractive index drop on a molded lens, wavefront of an uncompensated lens (initial shape design and changed refractive index) is simulated.

With an average refractive index drop of -0.00282, the back focal length of an uncompensated lens changes to fb,u = 50.76680 mm. If a point light source is placed at the original focal point, where d= fb,0 = 50.52054 mm, the wavefront from the uncompensated lens is shown in Figure 2.4 (a). The peak-to-valley (P-V) value of wavefront is calculated as large as 5.4 wave. The comparison of the wavefront between the original lens and the uncompensated lens is plotted in Figure 2.4 (b).

From Figure 2.4 (a) and (b), it is clear that the index drop affects the optical parameters of molded lens (e.g. focal length, output wavefront), which deviated the optical performance of molded lens from the original design. In order to reduce such optical deviation, geometric parameters of the molded lens (e.g. radius of the lens surfaces, thickness of the lens and the conic coefficient of the aspherical curve) have to be adjusted to compensate for the refractive index change. The new geometric design of the index changed lens is called the compensated lens, which is expected to perform the same as the original lens.

In the compensated design, the refractive index of glass was offset by the amount

∆nd,average=-0.00282 from the initial value of nd=1.58700. The focal length of the compensated lens was set the same as the original design value, i.e., fb,0 = 50.52054 mm.

Radius of the lens surfaces and the conic coefficient were set as variables. The thickness

20 of this lens is the same as 4.8 mm. he compensated lens has two identical surfaces with a radius of 59.7154 mm and a conic coefficient k1 = -3.895206. An index compensated mold shape was subsequently obtained by matching the shape of compensated lens.

2.2.3 Mold Curve Analysis

Due to the nonlinear shrinkage of glass after cooling, the geometry of molded glass lens will be different from the shape of mold. Therefore, mold curve has to be compensated by means of mold modifications. An initial mold design, which is determined before simulation, is imported into the FEM software and used as geometry boundary conditions in the simulation. Lens geometric deviation based on generalized Maxwell model is treated as the feedback value for mold design modification [8].

In this research, initial mold design was index compensated mold, which was obtained from refractive index analysis as described above in Section 2.2. First, the entire glass molding process including heating, pressing and cooling were simulated with consideration of heat transfer and geometry deformation. The difference between shape of molded lens and shape of design is called geometric deviations. After simulation, the geometric deviation was predicted up to 4 m as the indicated in red dashed curve in

Figure 2.5.

Figure 2.5 Mold curve was compensated by FEM predicted geometric deviation

Second, the predicted geometric deviation was used as the feedback for mold modification to minimize geometric deviation of molded lens. The initial mold shape was offset by the predicted geometric deviation. The modified mold was then used as initial mold for new simulation. More simulation cycles may be needed to eliminate the aberration. After the iterated calculation, compensation on mold can be finally determined as the blue solid curve in Figure 2.5. If a lens is perfectly compensated, the geometric deviation on molded lens will be zero, as indicated by the solid green line.

22 2.2.4 Mold Fabrication and Glass Lens Molding

Based on the compensated mold design, a pair of WC mold inserts was fabricated. A Pr-

Ir protective coating layer was applied on mold surfaces. Aspherical lenses were molded using the compensated mold pair on a Toshiba glass molding machine (model GMP-

207V). The actual cooling rate during experiments was recorded by the temperature couple buried inside the molds. For the lens under test, the cooling rate was measured as

0.84 K/s, which is slightly higher than the pre-defined cooling rate. This difference was largely due to difficulty involving in cooling rate control on the Toshiba machine. A picture of molded lens is shown in Figure 2.6 below.

Figure 2.6. Picture of a molded compensated Lens.

23 At cooling rate of 0.84 K/s, the simulation calculated that average refractive index change is -0.00300. Therefore, the refractive index of molded lens is predicted as 1.58700-

0.0030= 1.58400. The back focal length of experimental molded lens with the compensate design is fb,e = 50.53801 mm.

2.3 Experiments and Testing Results

2.3.1 Geometry Testing

The geometry of the molded lens was measured on a stylus profilometer (Form Talysurf

PGI 1250A, http://www.taylor-hobson.com), which was conveniently designed for measuring aspherical molded glass lenses. Both sides of the aspherical surfaces were measured, which are as shown in Figure 2.7 (a) and (b), respectively. The measured lens surfaces showed a good agreement to the index compensated design with the maximum discrepancy less than 1.5 m. These measurements were consistent with the results published earlier [8].

(a) (b) Figure 2.7 Measured lens geometry compared with index compensated design. (a) Lens upper surface (b) lens lower surface.

2.3.2 Optical Testing

The molded lens was tested by using WaveMaster LAB (http://www.trioptics.com), which is a comprehensive wavefront analyzer designed for laboratories. The schematic of optical tests on the WaveMaster LAB is illustrated in Figure 2.8. A point light source from a microscope objective lens was placed in front of the molded lens. The distance between the point light source and the lens under test can be adjusted. Light passing through the molded lens is expanded by a telescope lens assembly, and subsequently captured by the wavefront sensor.

Figure 2.8 Schematic of optical measurements on WaveMaster LAB [12]

If a point light source is placed in front of the experimental molded lens where the distance d equals to fb,e, the wavefront coming from the back surface of the compensated lens is simulated by ZEMAX, as shown in Figure 2.9 (a). The wavefront is slightly different from expected value as shown in Figure 2.2 (b) , because the actual cooling rates were higher than the pre-determined cooling rate used for the compensation design in section 2.1. Experiments were performed to measure the wavefront coming from the molded lenses using the WaveMaster LAB. However, the exact distance between the point light source and the lenses was difficult to determine, all the measurements were performed by adjusting the point light source to the actual front focal point of the experimental molded lens, where d equals fb,e . Figure 2.9 (b) shows the captured

26 wavefront of a molded lens. The P-V value was measured as 0.55 wave, the standard deviation was 0.132 wave. The measurements are close to the simulated value which has a P-V value of 0.3 wave, as shown in Figure 2.9 (a).

(a) (b)

Another measurement was conducted to further validate the performance of the molded lens. In this test, the distance between the point light source and the experimental molded lens was adjusted to the focal length fb,0, (50.52054mm) of the original lens. d = fb,0 was set by shifting the point light source Δf = fb,e - fb,0 =50.53801mm-50.52054mm =17.47

27 m from its actual focal point towards the lens under test. The measured wavefront is shown in Figure 2.10 (b), which is close to the simulated wavefront shown in Figure

2.10 (a). The P-V value of both measured results and simulated results is 1.0 wave.

(a) (b)

Figure 2.10 (a) Simulated wavefront of index compensated lens when the a point source was placed at d = fb,0. (b) Measured wavefront of molded lens when a point source was placed at d = fb,0

The measurements of geometry and optical performance indicated the compensated lens demonstrated good results. For the focal length, if there was no refractive index change compensation, the difference on focal length between uncompensated lens and original lens would be a Δf1= fb,u - fb,0 =50.76680 mm-50.52054 mm=246.26 m. After

28 compensation, the difference on focal length between compensated lens and original lens is only 17.4 m, which is more than 10 times smaller. Geometric deviation was reduced from 4 m to 1.5 m. The optical performance deviation was represented by wavefront reading, which was compensated from 5.4 wave to 1.0 wave in P-V value. In this case, both geometric and optical deviation have been compensated to meet the design requirements, thereby further compensation is not necessary.

2.4 Conclusion

For precision glass molding, a compensation scheme for mold shape modification was developed by integrating both refractive index change and geometric deviation analyses.

In this approach, an FEM simulation based on TNM model was applied to predict index drop of the optical glass after precision molding. The predicted index value was then used to adjust the geometric design of the lens. Using commercially available general purpose software, ABAQUS, the entire process of glass molding was simulated to calculate the deviation from the adjusted lens geometry, which is applied for final mold shape modification. A case study on molding of an aspherical lens was conducted. The geometry variation was confirmed to be less than 1.5 m by using the Talysurf profiler.

Wavefront of the molded lens was measured on WaveMaster LAB. The captured PV value of the wavefront of the compensated lens was about 1.0 wave, compared to the uncompensated lens of 5.4 wave.

29 FEM assisted compensation procedure was found to be effective in predicting the final optical performance of compression molded precision glass lenses. Two FEM models can successfully predict refractive index and geometry variations. The integrated results were used for mold shape modification for compensating the refractive index and geometry change. This method can be used in design to achieve higher performance of the glass lenses at a lower manufacturing cost and a shorter production cycle.

In the future, this integrated compensation procedure can be applied to special cases of precision molded glass devices, such as microlens arrays, freeform optics. In addition, other glass relaxation material models on index drop prediction may be tested to further improve the accuracy. For lenses with high center-to-edge thickness ratios, non- uniform index distribution compensation instead of group index compensation to the lens may be needed if there is an even larger refractive index variation.

Chapter 3 Investigation of Molding Materials

Mold materials for precision glass molding require sufficient strength and hardness at high temperature and pressure. Considering the harsh environment where the molds are used, good resistance to oxidation and corrosion, chemical stability are also required. It is preferred to have a mold material with high thermal conductivity and low thermal expansion which help maintain good geometry accuracy during the thermal cycles.

However, it is not always obtainable to find materials with all those properties while maintaining a low fabrication cost for varieties of molding condition. Therefore, the selection of mold materials largely depends the specific glass material, molding conditions and mold geometries. For example, for molding of a low Tg (glass transition temperature) glass, stainless steel mold with nickel nitride coating can be used [18].

However, for the vast varieties of other regular glass, mold may work at a molding temperature up to 850°C. In this case, tungsten carbide (WC) mold with platinum coating are usually required. Another concern is about the machinability of materials respect to the required geometries. For example, WC mold is processed by precision grinding, which is difficult to create micro scale features. In this chapter, three different mold

31 materials, i.e., Graphene coated Si wafer, bulk metallic glass and copper nickel alloy are investigated for different applications.

3.1 Graphene Coated Si Mold

Silicon is one of the most widely used materials in micro fabrication because of its material properties, available processing methods, and low manufacturing cost [19].

Various features and structures have been fabricated on Si substrates, such as microlens arrays [20] and optical gratings [21]. On the other hand, these types of features are often encountered in precision glass molding, a net-shaping process for glass optics fabrication by replicating optical features from precision molds to glass at elevated temperature [6,22,23]. However, Si cannot be used directly as mold material due to severe adhesions between Si and glass. The adhesions are either caused by anodic bonding or chemical bonding at elevated temperature [24].

A few attempts have been made to use silicon molds for glass molding. For example,

Albero et al. demonstrated the molding of glass microlens arrays on a Si mold, which however had to be completely etched after molding to release the glass lens array [25].

This Si-sacrifice molding method consisted of multiple steps and the Si mold could only be used once, thus it is not an economical approach. Hirai et al. used a Si3N3/SiO2/Si mold for imprinting fine patterns to glass surfaces, but the mold had limited feature depth because they were created on a thin layer of SiO2 instead of directly on the Si

32 substrate [26]. Chen et al. fabricated a micro machined silicon mold for a Fresnel lens glass molding [27], however the process was limited to low glass-transition temperature

(Tg) glasses therefore the molded optics had poorer quality as compared to regular glass.

In this research, we developed a technique that can be used to prevent adhesions between

Si molds and the molded glass optics by utilizing a thin layer of carbide-bonded graphene, a two dimensional material with extraordinary mechanical properties [28]. The building of a strong graphene coating as a protective layer on silicon substrates [29] provides the surface with a unique combination of many advantages, such as high thermal conductivity, high hardness, and low surface friction. This newly developed technology makes it possible to use micro/nano patterned Si wafers for high volume precision glass optics fabrication thus resulting in a process with low manufacturing cost. Although other materials, such as glassy carbon, CVD diamond and nitride ceramics were also used as mold materials [30,31], most of these materials cannot match Si in terms of versatility of micro/nano scale fabrication, material availability, and manufacturing cost [19].

In this research, we demonstrated precision molding of glass micro optics with graphene coated Si molds. As described below, the coating process requires the heating of high- temperature silicone rubber, a piece of GP-SO3H nanopaper [32] as well as Si substrates inside a quartz tube. First, the quartz tube was heated in vacuum from room temperature to 500 °C in 30 min. Vacuum was applied to remove air in the system. Then vacuum line was turned off and the sealed system was further heated from 500 °C to 1,000 °C in 20

34 min. At elevated temperature, silicone rubber was thermally degraded into silicon or silicon oxide radicals. At the same time, benzenesulfonic acid groups in the nanopaper were thermally decomposed to form gases like SO2 and CO2. Because of the formation of gas bubbles inside the nanopaper layers, graphene sheets exfoliated and eventually flew away from the nanopaper. Reactive sites like carbon radicals were formed at the edge of graphene or on the basal plane, possibly at which the functional groups were bonded before degradation [29]. Third, the system was kept at 1,000 °C for 30 min. At this temperature, silicon substrate surface was activated to produce –Si and –SiO active groups. As the vacuum was released due to formed gases, nitrogen gas was introduced to maintain an atmospheric pressure. As illustrated in Figure 3.1(a), the exfoliated graphene nanosheets were deposited to Si surface and reacted with thermally activated Si-, SiO- or

OSiO-, radicals, eventually built robust C-Si and C-O-Si bonds between the graphene nanosheets and the substrate and also between neighboring graphene nanosheets. Finally, the system was naturally cooled to room temperature. The coated sample was washed with water and acetone to remove ash on the coated surface, followed by drying in vacuum oven at 100 °C overnight. The surface roughness of an uncoated Si wafer and a coated Si wafer were measured using a white light optical profilometer (Wyko, NT

9100). As shown in Figure 3.1(b) and (c), no notable differences were found in surface roughness between the uncoated and coated Si wafer.

Figure 3.2 (a) Cross-section view of the molding experiment set up. (b) Temperature and load history of glass molding. (c) Glass molding using a carbide-bonded graphene coated Si wafer. (d) Glass molding using a Si wafer without graphene coating.

The carbide-bonded graphene coatings on silicon substrates provide a unique combination of many attractive properties for glass molding. Graphene is an excellent thermal conductor that enhances heat transfer from the Si substrate to glass and can also help generate a uniform temperature distribution during glass molding. The analysis and testing of the thermal conductivity of this carbide-bonded graphene coating will be discussed in a separate research. The friction coefficient of the graphene coating is found

36 to be only 0.029, which is more than 60% lower than that of a silicon wafer (0.076) [29].

The low friction coefficient can improve the filling ability of glass into small features on molds. The graphene coated Si mold has also greatly increased Young’s modulus and hardness that can minimize the wear of molds during compression molding. In addition, a robust anti-scratching capability is also an indicator of a long mold life [29].

The graphene coating works as an isolation layer on Si molds to prevent the direct bonding between Si and glass. A few preliminary molding experiments have been conducted to test the performance of graphene coated Si molds. As illustrated in Figure

3.2 (a), a glass blank was placed between two Si wafers in a sandwich style. The blank is

P-LASF47 (Schott Glass Inc.), a glass formulated for precision glass molding with a Tg of

530 °C. Glass blanks were polished into cylinder shape with a height of 5 mm and a diameter of 10 mm. Molding process parameters are illustrated in Figure 3.2(b). The glass blank was heated by four 500 w Watlow cartridge heaters to 640 °C in vacuum and subsequently compression molded with a molding force of 220 N. After controlled cooling, the molded glass part was released from the Si mold.

Figure 3.2 (c) and (d) show the glass molding results using a carbide-bonded graphene coated silicon wafer and an uncoated silicon wafer as molds, respectively. As demonstrated in Figure 3.2(c) and (d), the silicon wafer with carbide-bonded graphene coating has successfully molded a glass part without any contamination and mold/part failure. However, both the molded glass and the uncoated silicon wafer were broken due

37 to thermal stresses from adhesion. After molding, glass blanks were pressed into disks with a height of about 3 mm. The surface roughness of the molded glass in Figure 3.2(c) is about 8 nm (Ra). This experiment demonstrated the effectiveness of graphene coating in preventing Si-glass adhesion.

Figure 3.3(a) Surface profile of a coated Si mold. (b) SEM image of Si mold with microwells after molding. (c) Surface scan of a molded glass with micro pillars. The inset is an SEM picture of the molded glass. (d) Comparison of line scans between the Si mold and the molded glass part (The profile of the Si mold was flipped for comparison).

38 In order to test the coatings on non-flat surfaces, a Si mold with microwells was fabricated using standard photolithography and inductively coupled plasma (ICP) - reactive ion etching (RIE) method. A thin film graphene coating was applied to the surface of the Si mold. The surface profile of the coated Si mold, which was measured using a Wyko NT9100 optical profilometer, is shown in Figure 3.3(a) and the scanning electron microscope (SEM) image of the mold is shown in Figure 3.3(b). Each microwell has a width of 11 µm and average depth of 1.5 µm.

A glass blank was molded on the graphene coated mold. The replicated features on glass were scanned and shown in Figure 3.3(c). In this figure, highly uniformed micron pillars were formed on the glass surface with an average height of 1.5 µm, which matches the dimensions of the microwells on the Si mold. This demonstrated that high precision microfeatures can be successfully transferred to glass surfaces using this method.

The good surface finish on the molded glass indicated that it is possible to fabricate high precision glass optics with graphene coated Si molds. As a proof-of-concept, a glass

Fresnel lens was fabricated by precision glass molding using a graphene coated Si mold.

For the molding setup, upper mold was a flat Si wafer while lower mold had a Fresnel lens structure, which was fabricated by a combination of ultraprecision diamond turning and reactive ion etching (RIE) [27]. Again, both the upper and lower Si molds were coated with a thin graphene coating.

The Si mold is a convex Fresnel lens so the molded glass lens becomes a concave

Fresnel. The molded glass Fresnel lens has a diameter of 9 mm and the nominal height of the teeth is 1 µm. As shown in Figure 3.4(a), the microstructure of the molded glass lens was again measured using the Wyko NT 9100 optical profilometer. A comparison between the lens surface and the mold surface is shown in Figure 3.4(b).

The image quality of the molded glass Fresnel lens was tested by using an optical system shown in Figure 3.5 (a). Light source used in this experiment was a white light bulb. A light diffuser was mounted next to the light source to create a uniform illumination. A target (USAF 1951, 3"x3" negative target, Edmunds Optics) was mounted in front of the light diffuser. Because of the molded Fresnel lens is a concave lens, a standard

41 commercial F/4 lens (Double-convex lens of 25 mm diameter and 100 mm FL, Edmunds

Optics) was placed behind the Fresnel lens to form a real image on the CCD. The captured image is shown in Figure 3.5 (b). As a comparison, Figure 3.5 (c) is the image of the target using the commercial lens alone. The two images match nicely, demonstrating the imaging quality of the molded Fresnel lens.

The durability of the carbide-bonded graphene coating was also evaluated. A graphene coated Si wafer has been used for more than 20 times without notable signs of wearing.

In the second experiment, a graphene coated Si wafer was continuously molded at elevated temperature of 640 °C for an extended time (2 hours). After molding, the coating showed no signs of wearing and no changes on surface roughness were found before and after molding. These preliminary experiments have shown that the carbide-bonded graphene has the durability for high precision glass molding applications. A quantitative study on the wear and bonding strength of the carbide-bonded graphene coating is the focus of a current research project.

It is worth to note that the carbide-bonded graphene coating technique is a low cost process compared to other more traditional coating methods. The coating materials are inexpensive and can be obtained rather easily. High-temperature silicone rubber is a standard industrial material and is readily available. GP-SO3H nanopaper is a newly developed material but can also be fabricated in a cost effective way [33]. The cost of the furnace is much lower compared to other coating equipment. Moreover, thickness of the

42 graphene coating can be controlled by adjusting the coating time and the content of coating materials, i.e. high-temperature silicone rubber and GP-SO3H nanopaper. Current available coating thickness can be tuned from nanometers to micrometers. For the coated

Si wafer used in this research, the thickness was about 45 nm. The thickness of coating was measured by AFM (atomic force microscopy) scanning on a partially oxygen etched grapheme coating.

In conclusion, the research reported in this research for the first time demonstrated the use of carbide-bonded graphene as an effective and high performance coating material for precision glass molding. It was shown experimentally that Si-glass adhesion could be completely avoided by using the carbide-bonded graphene coating on Si molds. The coating can be applied to Si molds with or without microfeatures. As a demonstration, a glass Fresnel lens was fabricated and the molded Fresnel lens exhibits good optical performance. By using the carbide-bonded graphene coating, we expect to realize the full potential of Si as a mold material to achieve extremely low -adhesion, low friction, uniform temperature distribution, and low fabrication cost for micro/nano scale precision glass optical component manufacturing.

43 3.2 Molding Freeform Optics Using Diamond Machines Si Mold

With the help of Graphene coated Si wafer, an innovative method to fabricate silicon molds for micro freeform optics using ultraprecision diamond machining was developed.

Specifically, molds for two microlens arrays and a kinoform lens were created on a 5.0 mm thick silicon wafer. The silicon molds were coated with a graphene-like carbon coating using chemical vapor deposition to prevent glass to silicon adhesion. To demonstrate the machined silicon molds, glass optics were fabricated using precision compression molding. Compared with conventional grinding process for tungsten carbide, the proposed method provides a more flexible, faster and affordable alternative to fabricate molds for complex precision glass optics.

3.2.1 Introduction

In recent years, freeform optics are becoming increasingly popular because of the growing demand for high performance, compact but affordable glass optical devices.

Freeform components, or optical elements without rotational symmetry, which often including microlens arrays and kinoform optical elements, see potential applications in head-up displays, LED lighting and remote sensing [34–36]. To fabricate glass freeform optics, precision molding is one of the preferred methods because of its cost- effectiveness, process consistency and short production time. One of the biggest challenges in precision molding is the fabrication of high quality molds, which are required to press glass at elevated temperature [1,22]. Currently, tungsten carbide (WC)

44 is the de facto mold material for large continuous optical surfaces. However, WC molds have to be precision ground thus the process has intrinsic disadvantages due to long cycle time and the associated high fabrication cost. In addition, due to limits on available grinding tool geometries, freeform optics with microstructures are difficult to machine on the WC substrate.

In this research, we proposed a novel process to fabricate freeform optics by combining precision glass molding and diamond machining of single crystalline silicon (Si).

Compared with WC, Si is cost-effective, readily available and can be processed using many well established cleanroom processing methods. Furthermore, since thermal conductivity of Si is about 50% higher than that of WC, a Si mold provides better temperature distribution in a hot forming process. In addition, probably more significant to this research, Si mold can also be fabricated using ultraprecision single point diamond micro machining process as demonstrated in this research. Ultraprecision single point diamond machining is a much faster, more accurate and flexible fabrication method than grinding, making silicon a promising candidate to replace WC in certain applications, particularly where microstructures with sharp or straight edges are involved.

3.2.2 The Fabrication Process

3.2.2.1 Ultraprecision Single Point Diamond Machining of Si Wafer

45 Unlike grinding process using super abrasives, ultraprecision single point diamond machining can provide simplicity and flexibility in creating freeform geometries on silicon surface. In this research, a 100 mm Si wafer with 5.0 mm thickness was machined directly on the Nanotechnology Systems’ 350FG 5-axis ultraprecision machine using ultraprecision single point diamond machining. Two types of optical features, a kinoform lens and two microlens arrays were machined on the Si wafer. For the kinoform lens, conventional ultraprecision diamond turning process was utilized. In this process, a half radius diamond tool with a cutting radius of 14.9 µm was used. In order to decrease micro fracture in machining on brittle material, the diamond tool was tilted -24.95º so that a large negative rake angle was established [37]. Initial cutting depth was 300 nm and finish cutting depth was 100 nm. The feedrate was 2 m/rev.

To machine the microlens arrays, ultraprecision diamond slow tool servo process was used [23]. In this unique approach, a single point diamond tool with relatively large radius of 3.048 mm was utilized in order to achieve a better surface finish quality [38].

Similar to kinoform lens machining, the diamond tool was also setup at a negative rake angle -24.95º. The finish cutting depth was 100 nm and the feedrate was 20 mm/min. The average surface roughness value for the microlens array is about 15 nm (Ra) at the bottom of the concave lens surface.

The micro machined silicon wafer was diced into individual blocks using a diamond saw since the entire wafer was too large for the following coating and molding processes. The

46 diced silicon molds containing both the kinoform lens and the microlens arrays are illustrated in Figure 3.6.

Figure 3.6 Three silicon molds were diced off the silicon wafer

3.2.2.2 Coating of Silicon Mold using CVD

Silicon cannot be used directly as mold material due to adhesion to glass at high temperature. The adhesion can either be caused by a process similar to anodic bonding or chemical bonding. Fortunately, it has been demonstrated that carbide-bonded graphene coating can effectively prevent adhesion between silicon and glass [39]. In this research, a chemical vapor deposition (CVD) coating was developed to produce a covalent-bonded

47 graphene-like network coating on silicon substrate using benzene as carbon source under an inert gas flow at high temperature briefly described below.

The silicon substrate was placed in a nitrogen gas purged furnace. When the temperature in the furnace reached 950 °C, benzene was turned to gas in the form of bubbles outside of the furnace. The bubbling rate was about 3 to 5 bubble/s. The benzene bubbles were blown into the furnace under Ar gas flow (200 ml/ min). After 30 min of reaction, the benzene source was cut off and system was turned off for natural cooling. It is believed that the benzene carbon sources form graphene-like structures on the substrate surface.

The coated silicon mold surface exhibits a silver color.

3.2.3 Precision Glass Molding

Glass molding experiments were performed on a DTI bench top GP-10000HT press. A section view of the molding configuration is illustrated in Figure 3.7. The mold assembly is composed of a fixed lower mold, a moveable upper mold and a carbide sleeve. A glass preform is placed directly on the micro machined silicon mold and the silicon mold is then placed on the lower mold. After the upper mold travels to a preset location, the system is heated by two infrared (IR) heaters to molding temperature. Temperature is monitored by two thermocouples, which are mounted in the blind holes of the upper and lower molds. When the system reaches desired temperature, the upper mold moves down to press the glass preform and the micro features on the Si mold are then replicated to glass.

Figure 3.7 Schematic of molding configuration. In this setup, glass is compression molded between a movable upper mold and a fixed lower mold.

In this research, Schott glass P-SK57 in two different geometries was used. First, a flat glass sheet with a thickness of 0.6 mm was used for molding the microlens arrays.

Second, a cylindrical glass preform with a diameter of 10 mm and thickness of 5 mm was used for molding the kinoform lens. P-SK57 has glass transition temperature (Tg) of

49 493°C. The molding temperature was determined to be 560 °C and molding force was

200 N based on previous experience. Cooling was controlled in order to prevent thermal induced cracks and reduce residual stresses in the molded glass optics . A slow cooling rate of 0.6 °C/s was set initially at the beginning of cooling at 560°C. When temperature was lowered to 490°C, the entire glass molding assembly was cooled at a fast cooling rate down to 200 °C, when the molded glass optics was released from the Si mold.

3.2.4 Characterization of Molded Freeform Optics

The geometry of the molded freeform optics is evaluated by an optical profiler (Wyko

NT9100). As shown in figure 3, two seamless microlens arrays, which have the same geometry of individual lenslet but different number of lenslet, were successfully molded.

Each lenslet has an overall dimension of 360 x 360 m. The radius of curvature of each lenslet is 7.1119 mm which gives the effective focal length of 12.1157 mm. Figure 3.8

(a) is a picture of the 20 x 24 micro lens array. The microlens array was originally designed to be used with a charge-coupled device (CCD) camera to form a Shark

Hartmann sensor. Figure 3.8 (b) shows 3D profile of a molded 6 x 6 microlens array.

Figure 3.8 (a) Picture of the molded 20 x 24 micro lens array. (8.24 mm x 7.20 mm). (b) 3D profile of the molded 6 x 6 glass microlens array. (2.16 mm x 2.16 mm).

The molded kinoform lens was evaluated using the Wyko NT9100 profiler as well.

Figure 3.9 (a) shows the measurements of the molded glass kinoform lens surface. A close-up view of the edge of the molded kinoform lens surface is shown in Figure 3.9

(b). It is clear from the measurements that the micro structures of the kinoform lens surface have been transferred to the glass surface.

Figure 3.9 (a) 3D profile of the center of the molded glass kinoform lens. (b) Close-up view of the edge of the kinoform surface.

3.2.5 Conclusions

We proposed a glass molding process to fabricate freeform optics using micro machined silicon mold. Two types of micro freeform structures were firstly machined on a 5.0 mm thick silicon wafer to be used as molds. These silicon molds were then coated using CVD method with graphene-like carbon to prevent glass from sticking to silicon during molding. Two micro freeform glass optical components were then fabricated by using precision glass molding. Compared with the glass molding process using tungsten carbide molds by grinding process, the presented method provides a more flexible, fast and cost effective process to fabricate complex but precise freeform optics.

52 3.3 Bulk Metallic Glass Mold for High Volume Fabrication of Micro Optics

Suitable mold materials are critical for successful high volume replication of micro optical components. As one of the emerging new materials, bulk metallic glass (BMG) can serve as high-quality mold material to overcome the existing challenges with current mold materials. Zr-based BMG does not have the intrinsic structural defects and can be precisely formed into desired shape at elevated temperature. Therefore, the unique combination of good forming ability at elevated temperature and sufficient strength at working temperature make it perfect as high quality mold material for optics fabrication.

This research investigated the fabrication and use of BMG mold inserts to create micro optics on PMMA (polymethylmethacrylate) substrate. BMG mold inserts were replicated from a fused silica master mold using precision glass molding techniques. The molded

BMG inserts with optical features were used next as secondary molds to manufacture of polymer micro optics. High volume production methods, i.e., hot embossing and injection molding, are investigated. In order to evaluate the performance of BMG inserts, the geometry of the gratings on PMMA part were verified with fused silica master mold and

BMG inserts using a non-contact profilometer. In addition, an instrument designed to measure surface scattering was used to measure the light distribution from the gratings.

By using this process, high performance and BMG mold inserts for hot embossing and injection molding can be prepared cost-effectively for high volume production of plastic micro optical components.

53 3.3.1 Introduction

With the development of miniature optical systems, micro optical components such as micro mirrors [40], optical gratings [41], waveguides [42] and optofluidic devices [43] are in greater demands. By using high volume replication processes, such as injection molding and hot embossing, plastic micro optical components can be fabricated in large quantity. However, the successful high volume replication of such micro optical features relies on suitable mold materials. For optical applications, a mold must be fabricated to the desired profile with nanometer surface finish. The mold should also be durable enough to stand up thousands of repeated replication cycles. Currently, stainless steels or nickel plated over steel substrate are the most widely used mold materials for injection molding[44–46]. However, due to the finite grain size, it is challenging to fabricate features smaller than 10 microns [47]. Silicon-based semiconductor materials such as silicon [48], silicon carbide [49] and some ceramic based mold can be used for replicating nano scale fine features, but they are often too brittle thus not suitable to work as a mold been used repeatedly [50] or too difficult to fabricate.

Bulk metallic glasses (BMGs), on the other hand, are group of amorphous metallic materials can be fabricated with nano scale fine features as they do not have grain boundaries and associated structural defects. Therefore, it is a promising candidate as a mold material for high volume replication of polymer micro optics. BMG is extremely strong and exhibits superior properties compared to its crystalline counterpart in tensile strength, elastic deflections and wear resistance [51,52]. More importantly, when heated

54 above its glass transition temperature (Tg) in a supercooled liquid region [53], BMG will soften into a viscous state, where BMG can be precisely formed into desired shape with the proper surface roughness. This unique property makes it a high-strength material with good processability. Therefore, the combination of good forming ability at elevated temperature and sufficient strength at working temperature make it perfect as high quality mold material for optics fabrication.

Previously, a few investigations were carried out to study the replication of micro optical features using BMG molds. Pan et al. demonstrated the fabrication of PMMA microlenses with Mg58Cu31Y11 BMG. This material has a low Tg of 140 °C which limited its working temperature for many polymer materials [54] . Chu et al. replicated the nanostructured gratings from a Pd-based BMG and tested the diffraction patterns

[55]. However, the grating area was relatively small (600×600 m2) thus not suitable for high volume production runs.

The motivation of research is to overcome the above mentioned difficulties by leveraging precision glass molding techniques on a Zr based BMG. The Zr based BMG used in this research has a high Tg , enabling it to process most of plastic materials up to 400 °C . By using precision glass molding technology, which is a net-shaping thermal forming process, large area of micro features can be transferred from master mold to BMG samples with high fidelity. The research discussed the entire process of fabricating BMG inserts, including fabrication of master mold, BMG preparation, configuration and

55 molding parameters, which are important to overcome the challenges. By using molded

BMG inserts, polymer (PMMA) micro optics are successfully fabricated using both injection molding and hot embossing. Finally, in order to evaluate the performance of the molded PMMA micro optics, both the surface geometry and diffraction patterns were tested. This new approach offers new possibilities of fabricating multiple, high-quality

BMG mold inserts for high volume replicating plastic micro optics.

3.3.2 Fabrication Procedures

As mentioned above, BMGs can be formed at high temperature and work as high-quality mold inserts for optical applications at working temperature. The fabrication procedure of making a BMG mold is shown in Figure 3.10. First, a Zr based BMG specimen was heated to a temperature higher than its glass transition temperature (Tg) then was molded off a fused silica master mold. Optical features from fused silica master mold were transferred to BMG surface. Second, the molded BMG insert was subsequently used as secondary mold at a temperature much lower than the Tg of BMG for hot embossing and injection molding of PMMA. The molded PMMA parts are expected to have the same micro gratings as the fused silica master mold.

Figure 3.10 Replication of plastic micro optics using molded BMG insert as secondary mold. (a) Fabrication of BMG insert using precision glass molding (b) Hot embossing of plastic micro optics with BMG inserts (c) Injection molding of plastic micro optics with BMG inserts.

3.3.2.1 Materials and Preparation

The bulk metallic glass used in the research is a Zr based BMG system (Zr-Ni-Cu-Al-

Nb). This BMG is selected as mold material because its combination of desirable properties, i.e., high glass transition temperature (Tg) and good mechanical properties.

Figure 3.11 (a) shows the DSC (differential scanning calorimetry) graph of this BMG, the

Tg of this BMG is identified as 407 °C, which is much higher than the processing temperature of most plastic. For example, PMMA, PC (polycarbonate) and PS

57 (Polystyrene), the most commonly used optical plastics, have injection molding temperatures around 215°C, 320°C, and 230°C, respectively [56–58]. The hot embossing temperatures of plastics are even lower. As a result, the Zr based BMG has sufficient serving temperature range for most plastics. On the other hand, Tg of this Zr based BMG is close to some conventional optical glasses so precision glass molding technology can be adopted for the molding of BMG. The crystal temperature (Tx) of this BMG is about

480 °C, leaving a relatively large processing window (73 °C) for molding. The yield strength is around 1.8 to 2.0 GPa, which is about the same as quenched tool steel [59].

The fracture toughness is about 20 MPa m1/2 and the density is in the range of 6,000-

6,500 kg/m3.

BMG stock is a flat plate, which was cut with diamond saw into square specimens of 10 mm ×10 mm ×3 mm in dimension for molding. The BMG specimens were first mechanically grinded with increasing grit size of the sandpapers (P500, P1000, P2500,

P5000). Next, they were mounted to an automatic polishing machine and polished with 3

µm diamond slurries for 2 min followed by 1 µm diamond slurries for 2 min. The polished BMG specimens show a mirror like silver color finish. As shown in Figure 3.11

(b), surface roughness (Ra) of the polished BMG was measured to be about 4.2 nm.

(a) (b)

Figure 3.11 (a) DSC graph of Zr based BMG. Tg of this BMG is identified as 407 °C. The crystal temperature (Tx) is about 480 °C, leaving a relatively large processing window. (b) Surface scan of the polished BMG specimens. The surface roughness surface roughness (Ra) was measured to be about 4.2 nm.

3.3.2.2 Precision Molding of BMG

Precision glass molding is a hot forming process of replicating optical features from mold to softened glass at elevated temperature [22,39,60,61]. Because of its amorphous nature,

BMG can be molded like oxide glass at temperature between its Tg and Tx. In this research, BMG specimens were molded on a fused silica master mold, which was etched by standard lithography techniques. A fused silica wafer with 50.8 mm in diameter and 1 mm thick was deposited with a 10 µm thickness of photoresist (SPR220-7.0) and then micro machined using reactive ion etching. Various micro optical features were patterned on the master mold. Detailed fabrication parameters can be found elsewhere [62].

(a) (b)

Precision glass molding of BMG was conducted on a commercial molding machine

(Toshiba GMP-207V). The schematic of molding configuration is shown in Figure 3.12

(a). The molding machine has a fixed lower die supported by a lower flange. A flat upper die is connected with an upper flange that can move vertically. Before molding, BMG specimen was placed on fused silica master mold with its polished side facing down. A small gap between the BMG specimen and upper die was left to prevent contact during heating. The entire system was heated by infrared heaters located around the mold assembly. However, it is found in earlier experiments that surface of the BMG specimen

60 would get overheated due to strong radiation directly from the heaters, resulting in surface crystallization problem on the BMG specimen. In order to solve this problem, as shown in Figure 3.12 (b), a stainless steel heat shield was added as heat barrier to prevent direct heating from IR heaters to the BMG surface in later experiments.

Temperature history is the most critical processing parameters for BMG as its physical properties are strongly temperature dependent [63]. As mentioned previously, BMG is very strong at room temperature but becomes soften when its temperature above its glass transition temperature (Tg). However, BMG has a tendency to become crystalized if heated to temperature higher than its crystal temperature (T > Tx). In addition, BMG has to be cooled below a critical cooling rate to avoid crystallization. In this research, the temperature profile was determined by adjustment of a few molding tests.

(a) (b)

Figure 3.13 (a) Parameters of precision molding of BMG. (b) Picture of molded BMG samples.

After a few attempts, based on best available experiment conditions, the temperature profile as well as molding force was determined as plotted in Figure 3.13 (a). In this molding test, , vacuum (0.1 Pa) was applied during heating and molding to prevent BMG from oxidation. It takes about 460 sec to heat the mold assembly to the molding temperature of 465 °C. Due to the absence of N2 flow in heating and molding, slightly larger temperature gradient between thermal couple and BMG was expected. As a result, the actual temperature of BMG should be lower than the reading on this curve. The reading of 0.5 kN on the molding force was also the result of vacuum used in the

62 experiment. After a soaking time of 70 sec, a molding force of 3kN was applied to BMG specimen then BMG was subsequently pressed against the fused silica mold. After

molding, the mold assembly was immediately cooled by a maximum N2 gas flow to about

100 °C. Finally, the molded BMG part was released from the mold assembly. Figure

3.13 (b) shows two molded BMG samples with different molding conditions and different micro optics patterns.

3.3.2.3 Hot Embossing of PMMA Using Molded BMG Mold Insert

The hot embossing process was performed on a homemade glass molding machine [64].

The configuration of the machine is illustrated in Figure 3.14. Compared to the commercial machine in section 2.2, this system is heated by four cartridge heaters embedded in upper and lower blocks. Thermal couples are mounted close to the surface of the mold blocks. The PMMA blank was placed between a flat nickel-copper alloy mold and molded BMG insert. During hot embossing, softened PMMA were pressed by the flat mold to BMG insert, filling into micro optical features on BMG insert at temperature higher than Tg of PMMA. The hot embossing can be conducted in air.

However, it is found that air can be trapped in the micro structures of BMG insert which hinder the filling of PMMA. Therefore hot embossing in vacuum was used in the experiment to help the filling of the micro features.

Figure 3.14 The configuration for hot embossing of PMMA with BMG as mold insert.

Process cycle started from heating the system from room temperature to 130°C in 5 min, followed by a soaking time of 5 min to provide a homogeneous temperature distribution. Then the lower mold moved up at a constant speed to press the

PMMA part. When the molding force increased to 890 N, the lower mold was stopped and held at that position. After 300 seconds holding, the system was cooled to 80 °C by

N2 gas.

3.3.2.4 Injection Molding of PMMA Using Molded BMG Mold Insert

Injection molding is a preferred method for high volume fabrication of plastic parts. With proper selected processing parameters, such as melt temperature, injection velocity and packing pressure, high quality plastic micro optics can be fabricated with low cost. In

64 order to use molded BMG as mold inserts for injection molding, a holder was fabricated to secure BMG inserts. As shown in Figure 3.15, the aluminum holder has a removable cap covering small pocket, where the molded BMG insert can be placed. The aluminum holder was mounted to stainless steel die of injection molding machine.

Figure 3.15 Picture of an aluminum insert holder for injection molding. A molded BMG insert was placed in the pocket under a removable cap.

65 The microinjection molding machine (LD30EH2, Sodick Plustech) used in this study can inject plastic melt at a maximum injection velocity of 250 mm/s and generate up to 30 ton of clamping force. The injection system of this machine has a separate screw plasticizing unit and a plunger injection unit. Independent controls of these two units enable precise control of the amount of plastic melt that can be injected into the mold cavity to transfer high quality micro features from the BMG mold insert to molded plastic parts. An optical grade PMMA (Plexiglas V825) was used in the experiment. The molding conditions were summarized in Table 3.1.

Table 3.1 Microinjection molding conditions

Molding parameters Values Melt temperature (°C) 250 Mold temperature (°C) 40 Injection velocity (mm/s) 220 Maximum injection pressure (MPa) 150 Velocity/pressure switch (vol %) 90 Packing pressure (MPa) 100 Packing time (sec) 3 Cooling time (sec) 40 Coolant temperature C 25

66 3.3.3 Results and Discussions

3.3.3.1 Geometry Measurement

The geometry of the molded BMG inserts was measured by a noncontact optical surface profilometer (Wyko NT9100). Figure 3.16 shows the 3D surface profiles of various molded micro features on BMG inserts. The BMG inserts contain several gratings with different pitches but of the same depth. All of the optical micro features have a depth of

650 nm. It is seen that highly uniform gratings can be transferred from fused silica master mold to the BMG samples.

(a) (b) (c)

Figure 3.16 Surface profile of different micro optical features (a) Optical gratings with 10 µm pitches. (b) Micro dot arrays with 20 µm spacing. (b) Line patterns with different spacing. The horizontal ruler indicates the size of scanned area by profilometer.

67 In order to compare the shape transferability using the BMG inserts, the geometry of the fused silica master mold, the BMG insert and the PMMA part made using hot embossing were measured using the Wyko profilometer. The measurement results are shown in

Figure 3.17, where the gratings features on the fused silica master mold, the BMG secondary mold and the molded PMMA part are plotted side by side.

(a) (b) (c)

Figure 3.17 Optical profiler measurements of (a) fused silica master mold (b) BMG mold insert (c) PMMA part.

For the hot embossing process, a detailed comparison between the BMG insert and the molded PMMA part was shown in Figure 3.18. In this comparison, it is clear that the micro features on the BMG mold was successfully transferred to PMMA part with nanometer accuracy.

Figure 3.18 A detailed comparison between BMG secondary mold and the molded PMMA part.

3.3.3.2 Diffraction Scanning Test

In order to analyze the functionality of the optical gratings of the molded PMMA parts, an instrument designed to measure scattering was modified slightly to perform the measurements. The description of the instrument can be found elsewhere [62]. As shown in Figure 3.19 (a), a He-Ne laser beam (632.8 nm) was projected onto the molded

PMMA grating, which was mounted with a fixed angle to the laser. When the laser beam hit the optical gratings on the PMMA, it was split and scattered into different directions.

By using a photodiode scanning across the range of diffraction pattern, the intensity and associated angle of diffraction beam were recorded. As shown in Figure 3.19 (b), the

69 scattering spots diagram is symmetric and the central spot has largest intensity. The secondary max intensity spots are located next to the central area. The intensity and position of each spot represent the performance of the grating. By analyzing the scattering spot diagram, the information of surface properties of molded PMMA gratings can be determined [65]

(a) (b)

Figure 3.19 (a) Schematic of optical test setup. (b) Measurement of monochromatic diffraction pattern of the molded PMMA.

70 3.3.4 Conclusion

This research investigated the manufacturing processes of fabrication and using of BMG inserts as secondary mold for high volume replication of micro optics. With precision glass molding techniques, BMG inserts with large area of micro optical features (5mm x

5mm) were successfully replicated from fused silica master mold. The Zr based BMG used in this research has a high working temperature up to 400°C, which provides sufficient temperature range to process most optical polymers. The molded BMG inserts were proven have worked well as secondary mold to replicate PMMA micro optics for both injection molding and hot embossing. Furthermore, the geometry of fabricated plastic micro optics was compared with BMG inserts as well as master mold. In order to evaluate the performance of the molded PMMA micro optics, both the surface geometry and diffraction patterns were tested. The results showed that the micro optical features that were originally created on the fused silica mold were successfully duplicated to the

PMMA part with high fidelity.

This research validated an efficient and reliable method to employ precision molded, Zr- based BMG as secondary mold in replicating polymer optics. The advantage of fabricating BMG inserts using precision glass molding replies on the idea of replication, where molded part is expected to transfer all fine features from master mold in a short cycle time. In addition, molded of BMG inserts from the same master mold should have the same geometry for a stable replication process. By utilizing multi cavity molding, dozens of BMG inserts can be fabricated in a few cycles. Therefore, this unique method

71 provides the new possibility to fabricate low cost, durable mold inserts for high volume reproduction of precision plastic micro optical components. In the future, the work will continue on molding BMG inserts with more complicated geometry. The wear ability and life time cycle of the Zr-based BMG inserts will also be investigated.

3.4 Copper Nickel alloy

715 copper nickel alloy (C71500) is a copper based alloy with an addition of 30% nickel.

By adding of nickel, the strength and durability of this alloy are largely improved. In addition, there is up to 0.5% of iron in this alloy which provides superior resistance to general corrosion and stress corrosion cracking.715 Copper-nickel alloy is used as the mold material because it offers a good balance between preferred mechanical properties at high temperature, and relatively low fabrication cost.

3.4.1 Mechanical Properties of 715 Copper-nickel alloy VS Temperature

The mechanical properties of 715 copper-nickel alloy enable its application in areas of high temperature and high pressure with destructive turbulence. Table 3.2 lists several mechanical properties, i.e. tensile strength, proof stress and elongation versus temperature up to 550 °C. Those data are based on a test of an annealed rod with 27 mm in diameter

[66]. It reveals that C71500 copper-nickel alloy maintains good mechanical properties at

72 glass molding temperature where it was used. The relation between elastic modulus and temperature (up to 320 °C) is depicted in Figure 3.20 [67].

Table 3.2 Mechanical properties of 715 copper-nickel alloy vs temperature [66]

Proof stress Temperature Tensile strength (0.2% offset) Elongation (%) (°c) (kg/mm2) (kg/mm2)

20 41.5 13.7 56

250 35 10.9 45

350 34 10.4 39

450 31.5 10.7 42

550 26.5 11.8 33

Figure 3.20 Temperature variation of slastic modulus for copper-nickel alloy (C71500).

3.4.2 Mold Materials Consideration for Diffractive Refractive Hybrid Lens

For the mold used in diffractive refractive hybrid lens, a saw teeth shaped features in submicron scale on curved surface is required. The use of regular molding glass requires a molding temperature of 550 °C.

Aluminum bronze shows high strength with excellent resistance to corrosions under service conditions. It is typically used as mold for sand casting, gravity die casting, forgings, extrusions etc [68]. However, aluminum bronze is usually machined from large

74 castings then hand grinded and polished. It is more difficulty to machine aluminum bronze for the fabrication of micron-scale features [69].

Invar is a nickel steel alloy with 36% of nickel which has a extremely low thermal expansion coefficient, typically 1.2 × 10−6 K−1. The low thermal expansion rate is a desirable property for mold to keep geometry while undergoing heating and cooling.

However, the thermal conductivity of invar (10.15 W m−1 K−1) is pretty low, , which is only a fraction of some other mold materials, such as copper-nickel alloy (40 W m−1 K−1) and WC (84.02 W m−1 K−1) [70].

Stainless steel has been used many years as an economical mold material for making glass ware, such as wine cups and glass bottles. However, for the molding of precision glass optics, stainless steel is not ready available for cutting by single point diamond turning. Poor machinability of stainless steel for single-point diamond turning is observed

[71]. The same problem is with tool steels. Ferrous materials are reacting with the carbon in the diamond tool leading severe tool wear and damage.

High nickel alloys are used because of their outstanding corrosion resistance and strength at high temperature. However, grain of high nickel alloy begins to grows at the pressing temperature about 500 °C, leading to a rough mold surface thus it is not suitable for molding glass optics with high accuracy [72].

75 3.4.3 Yield Strength and Modulus of Elasticity

Yield strength of mold materials must be larger than the maximum pressure under glass molding conditions to maintain desired mold geometry. During molding, the viscosity of glass is typically in a range of 107.6 ~ 109 P, which is far less than the viscosity of polymer during injection molding. The load on mold by pressing is relatively small. For example, it was measured that the maximum loading of a 25-mm-diam glass lens is 500

N [5], which equates a average pressure of 1 Mpa. However, local stress at certain point, such as edge of mold, can still be significantly large. In addition, the sticking behavior between glass and mold surface may lead to large tension force. In this case, yield strength of material have to satisfy the molding condition requirement.

A mold material with large modulus of elasticity is usually preferred because less mold deformation will occur under the same load. When a glass is compression molded between two molds, less mold deformation will improve the geometry accuracy of molded glass optics. However, it has to be noted that severe load condition may arise for mold materials with large modules of elasticity. For example, if a mold is not properly constrained, thermal strain could lead to extreme force on mold resulting in mold fail.

3.4.4 Thermal Conductivity

A good thermal conductivity is required for the heating and cooling of the glass optics.

During heating, a glass blank is place on top of lower mold. When a glass lens is molded, it is cooled between the two mold halves. Therefore, heating and cooling rate of glass is

76 primarily controlled by the conduction between the mold material and glass. Good thermal conductivity of mold material will reduce the heating and cooling time thus more control of the thermal treatment of glass can be achieved. In addition, good thermal conductivity could reduce the extent of thermal stress inside a mold during non- homogenous heating and cooling.

3.4.5 Machinability and Surface Finish

As mentioned in section 3.4.2, machinability also limits the selection of mold materials.

For molded glass optics, no post-molding processes such as grinding or polishing is needed as the desired geometry and surface finish of glass optics is achieved by the glass molding process. Therefore, the surface finish of mold must satisfy the precision molding requirements. Typically, the roughness of mold surface of 4 to 10 nm (Ra) is needed.

3.4.6 Coefficient of Thermal Expansion (CTE)

Table 3.2 lists the coefficient of thermal expansion of mentioned alloy and 715 copper- nickel alloy. Invar is the alloy with smallest CTE while copper based alloys, i.e. copper- nickel and aluminum bronze, have larger CTE value. A small CTE value will reduce mold shape variation and thermal strain due to thermal expansion. For glass mold with small CTE value, fewer mold compensation iterations will be needed.

Table 3.3 Coefficient of thermal expansion of several engineering mold materials

Coefficient of thermal Evaluation range Alloy Name Alloy Type expansion (10-6/°C) (°C) UNS C71500 [73] Copper-nickel 16.2 20-300 Aluminum UNS C62400 [74] 16.5 20-300 bronze 1.3 93 Carpenter Invar 36 Invar 4.18 260 [75] 7.6 371 Crucible Steel PM Tool steels: 12.1 20-540 M2 [76] UNS S40900 [77] Stainless steels 12.9 20-650 MONEL alloy R- Nickel alloys 13.9 20-100 405 [78]

Chapter 4 Glass Molding Examples

4.1 Development of a Low Cost High Precision Fabrication Process for Glass

Hybrid Aspherical Diffractive Lenses

The hybrid aspherical diffractive singlet achromat design can be used to reduce chromatic aberration in compact optical systems. In this research, development of a compression molded, low cost and high precision hybrid diffractive glass lens is described.

Specifically, an aspherical diffractive lens designed to compensate for chromatic aberration was fabricated by precision glass molding. The diffractive features are integrated on the aspherical surface to avoid mold alignment during fabrication. As part of the effort to lower manufacturing cost, the diffractive profiles were directly fabricated by single-point diamond turning without polishing. A thin layer of platinum-iridium coating was applied to the mold surfaces to protect the mold inserts from degradation during the molding process. In order to reduce thermal shrinkage error, the hybrid lens was fabricated using a two-step precision molding process on a commercial glass- molding machine. The geometry of the molded hybrid aspherical diffractive lens was

79 measured using an optical profilometer and the results demonstrated a match to the design mold profile with a replication error of 0.16% in the radial direction and 6.3% in the axial direction. In addition, an optical metrology system to evaluate the diffraction efficiency and chromatic focal shift was constructed and the measured results showed that the hybrid lenses indeed function as designed.

4.1.1 Introduction

Diffractive optical elements (DOEs) are increasingly used in high-precision compact optical systems, such as digital cameras, pocket camcorders and projectors to improve system performance and reduce product size and cost. Historically, DOEs however were only implemented in limited industrial applications, such as bifocal contact lens, beam shaper and barcode reader diffuser [79–83].

Fabrication methods for DOEs basically fall into two categories: cleanroom based lithography techniques and direct ultraprecision process [62]. Bengtsson et al. used chemically assisted ion-beam etching (CAIBE) to fabricate a 4 by 4 fan-out kiniforms on

GaAs substrate [84]. Martinsson et al. applied DOEs as an advanced beam shaper for vertical-cavity surface emitting (VCSEL's). In another study, a two-level surface relief

DOE was fabricated by electron beam lithography [83]. These lithography based processes, which originated in semiconductor industry more than 50 years ago, are established techniques that can provide accurate mold fabrication for designs with sub- micron features. However, lithography is generally limited to planar or near planar

80 surfaces therefore not suitable for optical components with complex geometries. In addition, the cost for cleanroom fabrication is usually high.

Direct fabrication methods include several ultraprecision machining processes. For example, Fu demonstrated the fabrication of a diffractive lens with continuous relief using focused ion beam milling [85]. A direct-writing method by using excimer laser ablation was also reported to fabricate multilevel diffractive structures [86,87]. However, these direct methods are usually limited to low volume production or specific materials.

To reduce cost, replication techniques have to be used. For example optical grade polymers can be injection molded into extremely complex but accurate geometries. These optics however do not perform well under rigorous conditions of high temperature, stress and humidity that are required for many precision applications.

The biggest problem with polymer devices is the issue of thermal stability. Optical polymer devices may work well at room temperature, but the geometry and optical properties of these polymer devices will deteriorate at higher temperature. Except for some special materials such as flouropolymers, the service temperature of most optical polymer materials is lower than 70 °C [88]. In addition, polymer materials tend to absorb water resulting in change of geometry as the moisture of the environment varies. On the other hand, optical glasses have been and will continue to be the materials of choice for high precision imaging optics mainly because the service temperature of typical optical glass materials is high, usually from 400°C to 700°C. In addition, the thermal expansion

81 of glass materials is in general one order of magnitude less than most optical polymers

[88].

However, traditional glass lens manufacturing processes using grinding and polishing is time consuming and costly. Fortunately compression molding of glass optics, including glass DOEs can be a very attractive approach [1,89,90]. Macro and micro scale optical features can be fabricated by precision glass molding in a fast and economical fashion.

Previously, Yi et al. used fused silica as mold, which was fabricated by standard lithography technique, to produce diffractive features by compression glass molding [62].

They evaluated replication accuracy of the mold and compared optical performance between the mold and the molded lenses. Tanaka et al. analyzed the chromatic aberration of objective lens for DVD (digital video disk) and introduced a relatively small hybrid aspherical lens by glass molding [80]. A proprietary coating process was applied to the mold insert before diamond turning.

In a departure from the previous attempts, the primary goal of this research is to develop an economical process for low cost, high quality conventional size glass DOEs that are suitable for industrial productions. The aim of this research is to develop an economically feasible glass diffractive optics fabrication process by precision glass molding. Proper glass and mold materials and process parameters will be evaluated to satisfy pre-defined design criteria for compression molding of glass aspherical diffractive optical elements thus resulting in lower cost and high quality products. The proposed process is a net

82 shape, high volume manufacturing method, which provides industry with low cost optical systems utilizing hybrid precision glass optics, enabling manufacturing of compact, high precision and low cost optical products.

4.1.2 Optical Design

For a single lens, spherical aberration can be eliminated by use of aspherical design.

However, because of dispersion of some glass materials, chromatic aberration of a single lens could not be reduced by geometry manipulation alone. To achieve better performance, additional components are usually added to reduce optical aberrations [91–

93]. The classic approach to compensating for chromatic aberration is to form an achromat, i.e., a doublet. In a doublet design, one of the lenses is convex made from a crown glass with positive dispersion while the other lens is concave made from a flint glass with negative dispersion. Two lenses with opposite dispersion power are mounted together so the overall chromatic aberration of the compound lens is lower than a singlet.

Inadvertently, the introduction of extra lens increases the size as well as the complexity of the optical system. It also raises the issues of alignment during assembly. On the other hand, diffractive optical elements have negative dispersion [94], therefore instead of using another lens, these optical components with micro/nano features can be applied to a lens surface to form a singlet and compensate for the chromatic aberration.

In this research, a hybrid aspherical diffractive glass lens is introduced to compensate for chromatic aberration. Spherical aberration was compensated by the aspheric design. The

83 specifications of this hybrid lens, which represent a typical objective lens in a compact optical system are listed in Table 1. P-SK57 is a Schott glass that is designed specifically for precision glass molding. The wavelength was chosen to allow the lens to work in visible light range. Specifically, D line (=587.5618 nm) was set as the main working wavelength. DOEs on an aspherical surface highlights the singlet design. Figure 4.1 shows the layout of the hybrid lens design. The diffractive features sizes in Figure 4.1 (a) were exaggerated for display purpose.

Table 4.1: Hybrid lens technique features

F/# 4 Lens diameter 18 mm Center thickness 3 mm

Glass type P-SK57 (nd = 1.58700, d = 59.6001) Wavelength F, D, C (486.1327 nm, 587.5618 nm, 656.2725 nm)

(a) (b)

Figure 4.1 (a) The hybrid aspherical diffractive lens design. S1: Planar surface. S2: Aspherical diffractive surface (diffractive features are exaggerated for clarity). (b) Close up view of the DOE’s profile.

In this research, a commercial lens design software, ZEMAX (ZEMAX Development

Corporation, 3001 112th Avenue NE, Suite 202, Bellevue, WA 98004-8017 USA), was used in the optical design. A planar-convex lens was designed to reduce the cost of mold fabrication. DOEs could be designed on either planar surface (first surface) or aspherical surface (second surface). Obviously, DOEs on the aspherical surface was beneficial for sine condition [80], which reduced the spherical and coma aberration. It was also a preferred design for mold fabrication since it eliminated the need for alignment of the cutting tool because there was only one surface needed to be diamond turned. The need for alignment during compression molding was also subsequently eliminated.

85 In this case, the first surface, S1 in Figure 4.1 (a), is a planar surface. The second surface,

S2, is the aspherical diffractive surface, which is modeled using Binary 2 element in

ZEMAX. Binary 2 elements describe an even aspherical surface with diffraction power.

The even aspherical surface can be expressed by a polynomial with even power terms.

For the lens in this study two power terms were used as expressed in Equation 4.1, as terms higher than 4th order were small enough to be safely ignored:

cr2 z   a r2  a r4 2 4 Equation 4.1 1 1(1 k)c2r2

-3 -6 where c = -1/69.312, k = -18.3594, 2 = -3.936369x10 , 4 = -3.179234x10 , r (0 to 9 mm). c is the curvature at the center of the profile. k is conic constant, which is always negative in this design. r is the radius of this lens and 2, 4 are the even aspherical coefficients.

The diffractive power provided a continous phase, in which the diffracitve features can be infinitely small. For a product design, the actual phase variation is decribed by Equation

4.2:

2 4 6   417.418  2.0909  3.0827 Equation 4.2

86 where  (0<<1) is the normalized radial aperture coordinate. The diffractive profile sag d is given by Equation 4.3:

d  d  Equation 4.3 2 (nd 1)

d = 587.5618 nm is the working wavelength and nd = 1.587 is the refractive index with respect to the working wavelength. The diffractive profile has a saw tooth like shape and the angle  was periodically reset to 0 every 2. Figure 4.1 (b) illustrates the details of the diffractive element shape.

During optical design optimization, effective focal length (EFL) was added as an additional operand in the default merit function in ZEMAX. D line (=587.5618 nm) was given the weight of 10 because it was set as the working wavelength. Figure 4.2 shows the point spread function (PSF) and the optical path difference (OPD) results from

ZEMAX after design optimization. Both of them are based on the three aforementioned wavelengths.

(a) (b)

Figure 4.2 (a) PSF of the hybrid lens at aforementioned wavelengths. (b) OPD of the hybrid lens after optical design optimization.

Compared to the DVD pickup lens in Tanaka's design in [80], the singlet lens in this research has a much larger diameter. It should be noted that issues with thermal shrinkage become more prominent for compression molding of large lenses with sub-micron scale features. This is because mold wear due to friction during molding and thermal shrinkage during cooling are more significant at large dimensions. To mitigate these problems, first a noble metal thin film coating technique was developed for the mold inserts and then a two-step molding was implemented as discussed in the following section.

88 4.1.3 Mold Fabrication

Compared to the standard lithography techniques, single point diamond turning can produce continuous relief DOEs on non-planar surfaces. In this research, a robust fabrication process was developed to support the needs for high volume, high precision and low cost optical components in industry. Specifically, diamond turnable 715 copper nickel alloy (Farmers Copper, 202 37th Street, Galveston, TX 77550) was selected because the 715 alloy offers a good balance between robust mechanical properties at high temperature and relatively low fabrication cost.

Mold inserts were first rough cut from a44.45 mm diameter 715 copper nickel alloy stock. The top and bottom mold inserts were designed with features specifically for compression molding production. The inner diameter of the female mold (top mold) was slightly larger than the outer diameter of the male mold (bottom mold). This provided enough tolerance to the molding machine so the need for alignment of the mold pair was eliminated. The thickness of the hybrid lens is determined by the shoulder height of the bottom mold so there was no need to control the pressing distance during compression molding. The rough finished mold insert was then diamond turned on a Moore 350 FG ultraprecision machine (Moore Nanotechnology Systems, Keene, NH) to the finish dimensions.

Instead of using special materials on the mold surface as in reference [80], the diffractive elements were machined on the nickel alloy surface directly without post-machining

89 polishing. For better surface quality and less machining time, the mold fabrication was finished in two steps, i.e., machining of the aspherical profile and then the diffractive features. First, the aspherical substrate was diamond turned by using a 2.54 mm radius cutting tool. This large radius cutting tool removed stock at a fast rate with optical surface quality. Then the diffractive features were machined on the finished aspherical surface by a special tool, namely a single point diamond cutter with 2 m half radius design (Edge

Technology, Indianapolis, Indiana) . This small diamond cutter was critical to achieving proper diffraction efficiency. It is reported that the diffraction efficiency could reach 95% when a 10 m tip radius cutting tool was used [80]. The finished mold is shown in

Figure 4.3 (photo after molding tests).

For high volume production, longer service life of a mold is required, thus a protective thin film coating was applied on the mold surface. During compression molding, mold surfaces are in contact with the glass-blank at high temperature under large loading forces and for a prolonged period of time. The thin film helps reduce the sticking force between mold surfaces and glass during releasing stage and improves the molded lens surface quality [10]. A platinum-iridium (Pt-Ir) thin film coating was deposited on the mold at the Fraunhofer IPT, using a specially modified CemeCon CC800/9 unbalanced magnetron sputtering machine.

Figure 4.3 Hybrid lens bottom mold (after molding). The outer diameter is 44.45 mm. The aspherical diffractive surface has a diameter of 20 mm (with color hue) with 1 mm edge.

Before the deposition of the Pt-Ir film, the substrate surface was cleaned and activated using argon plasma etching for 5 minutes. This also improves adhesion of the coating that was deposited afterwards, The cleaning and activation process does not change the roughness of the substrate surface. Furthermore, for the mold material used in this study, a 50 nm nickel adhesion layer was first deposited on the mold surface to ensure proper coating adhesion. Next, a 250 nm Pt-Ir coating was deposited using a segmented target.

The composition of the coating was 40 % Pt and 60% Ir. The coating temperature was

150 °C in order to minimize structural change or recrystallization in the substrate

91 material. The 300 nm thin film coating not only provides enough protection to the mold surface but also ensures the DOE features and surface roughness remain unchanged.

4.1.4 Molding Process

The lens molding process was performed on a Toshiba GMP-211V machine at

Fraunhofer Institute for Production Technology IPT in Germany, and the details of the machine and glass molding process can be found elsewhere [1,6]. In order to achieve sub- micron scale diffractive features in high volume compression molding, a two-step molding process was introduced. Specifically, before molding, a simple spherical mold of the same size of the hybrid lens mold was prepared. The spherical surface was derived by an RMS (root mean square) fit with hybrid aspherical diffractive lens profile, as in

Equation 4.4:

2 2 z(r)  R fit  R fit  r Equation 4.4

Rfit was calculated to be 45.8 mm. So in the first step, a precision glass-blank of P-SK57 was molded into a plano-convex shape using the spherical mold and a plano mold, which gave a near net shape to the final lens. Next, the molded spherical lens was molded again by the hybrid lens molds to generate the final aspherical diffractive surface. A typical molding process usually consists of heating, molding, controlled cooling and releasing

92 stages. The total cycle time was less than 15 minutes. For the hybrid lens, both molding steps were performed under the following conditions:

(1) Preparation: The top mold was mounted to a fixed position and the bottom mold was mounted to a linear drive. A P-SK57 glass-blank was placed on the bottom mold with a gap about 2 to 3 mm between the glass blank and top mold. The gap was intent to prevent contact between glass and the top mold during heating as a result of thermal expansion.

Air was pumped out and vacuum was firstly applied to remove oxygen in the chamber, protecting the mold from oxidizing. Nitrogen was introduced afterward to purge the system to create a protective atmosphere.

(2) Heating: Infrared heaters were set around the molds and glass blank. The time to heat the molds and glass-blank from the initial temperature to the molding temperature of 550

°C was 250 seconds. The temperature was regulated by thermal couples imbedded in the molds. The selected molding temperature was 57 °C higher than the glass transition temperature (Tg = 493°C) of P-SK57 glass. A 120-second soaking period was then set to minimize the temperature gradient in both the glass blank and the molds.

(3) Molding: After the glass blank and molds reached a homogenous temperature distribution, vacuum was applied again during the entire molding stage to ensure there was no gas between the molds and glass, to prevent any bubble left on the surfaces of molded glass lens. Then the bottom mold was set to approach the top mold at a speed of

93 0.5 mm/s to initialize the molding. When the contact of glass and top mold was made, pressing speed and directions were automatically adjusted to keep a constant load of 500

N by an adaptive feedback control. The position of the bottom mold and the molding force were monitored and precisely controlled at a sampling frequency of 1 Hz. However, the thickness of the hybrid lens was independent of the traveling distance of the bottom mold. It was set by the distance between the mold pair. When the shoulders of bottom mold and top mold made contact, the thickness of the lens was determined and the bottom mold stopped moving. The bottom mold was then held in place to press the lens so the glass could be fully deformed to the desired shape.

(4) Cooling: Cooling was realized by a forced convection flow of nitrogen gas. A slow cooling with a rate of 0.8 °C/s was first applied to the system. A low initial cooling rate was critical to minimize the thermal stresses inside the glass [8]. When the glass temperature decreased to below Tg (493 °C), a fast cooling of 1 °C/s was used until the lens cooled to 220 °C. No holding force was applied during cooling to ensure free shrinkage and early separation of the molded glass lens from the molds. Higher cooling rate was not desirable because it would change the refractive index of glass, which may result in deterioration of the optical performance of the molded lens [9,16].

(5) Releasing: After the cooling stage, the mold inserts were released to allow the molded lens to cool freely. The finished hybrid lens was then removed from the molding machine and cooled by natural convection at room temperature.

94 Temperature control and monitored force of the molding steps are shown in Figure 4.4.

Before glass and top mold made contact, the monitored force remains zero with small fluctuation. The negative monitored forces from 35 to 70 second and 420 to 480 second were because of vacuum, which were conducted before heating (to prevent oxidation) and during molding (to prevent bubbles on the glass surface). Considering the effect of vacuum during entire molding stage, the actual molding force from 445 to 465 second was estimated as 1.6 kN, which was the sum of 500 N constant load and 1.1 kN vacuum force. After pressing, force recovered to zero when vacuum pump was stopped. During the fast cooling stage, the monitored force of 50 N with a sharp overshoot was the result of gas pressure by the forced nitrogen flow. Finally, the monitored force decreased to zero when the forced nitrogen flow was stopped.

Figure 4.4 Molding conditions for P-SK57 glass aspherical diffractive lenses.

95 4.1.5 Results and Discussions

4.1.5.1 Geometry and Surface Finish of the Molded Lenses

Figure 4.5 (a) shows a molded hybrid aspherical diffractive lens (18 mm diameter with a thickness of 3 mm). The geometry of the molded lens was scanned by Wyko NT 9100 optical profilometer (Bruker AXS Inc., 5465 East Cheryl Parkway Madison, WI). The curvature of the scanned surface was automatically removed to show only the diffractive features. In Figure 4.5 (b), Wyko highlighted the measured feature using larger scale in the thickness direction than in the radial direction. In order to get a high resolution scan in a large measurement area, stitching was used. This method measured small areas separately and then assembled them into a large scan. A complete profile of the mold and the lens were obtained using this method and part of the profile (between the 2nd and the

6th tooth) was compared. The overall comparison between the design profile and the molded hybrid lens is presented in Figure 4.6.

(a) ! (b)

Figure 4.5 (a) A molded hybrid aspherical diffractive lens. (b) An optical profilometer scan of molded diffractive features.

To compare the DOE geometry between the molds and the molded lens, the curvature of the aspherical surface was removed. As demonstrated in Figure 4.6, diffractive features were successfully transferred from the mold to the glass substrate. The width between the

2nd and the 3rd tooth on the mold was measured to be 414.4 m, compared to the corresponding width 411.8 m on the molded lens. The maximum discrepancy of all five measured teeth demonstrated the replication error in lens radial direction to be less than

0.16%. The burr type artifact that would have been at the tips of the diffractive tooth like features was the result of the measurement error during laser scan, where the surface of the edge point was perpendicular to the incoming light and reflected all the light back.

This would have shown as a sharp edge in the measured profile. In reality, the sharp edge

97 was actually a small flat surface and the assumption was confirmed with a Mitutoyo mechanical stylus profilometer scan. After removing the burr edge effect in the vertical direction, the discrepancy between the molded lens and the mold was measured to be 6.3

%, which was mainly due to the glass thermal shrinkage.

Figure 4.6 Geometry comparison between mold profile and lens profile (contour removed). T2 to T6 denote 2nd to 6th teeth.

Surface finish of the molded hybrid lens was also evaluated after molding using the

Wyko NT 9100 optical profilometer. The Ra value was measured to be 10.16 nm in an evaluation range of 126 m × 94 m.

98 4.1.5.2 Optical Performance

The nth Diffraction efficiency is defined as the power of the nth order diffracted beam to the total power of the incident beam, as in Equation 4.5:

n Pdiff n  Equation 4.5 Pinci

n th where Pdiff can be easily calculated by integration the corresponding n diffraction

pattern of the hybrid lens. For Pinci , however, as a result of the lens surface reflection and transmission absorption, a portion of the power of the incident light will be lost during transmission. Thus, needs to be evaluated without the diffractive pattern on the hybrid lens.

The optical measurement setup for diffraction efficiency is shown in Figure 4.7. A green laser with 532 nm wavelength was used to evaluate the diffraction efficiency at the main working wavelength range. The laser beam was first attenuated by two linear polarizers, then the laser beam was changed into a spherical wave by a pinhole. A plain wave was formed before the light entering the hybrid aspherical diffractive lens. The hybrid lens was mounted on a linear translation stage with resolution of 1 m. The image after the hybrid lens was projected onto the imaging plane of a CCD (charge coupled device) camera (PL-B957F, pixeLINK, 3030 Conroy Road, Ottawa, ON K1G 6C2). According to

99 Eq. (5), the measured first order diffraction efficiency was calculated as 90.86% at the laser wavelength of 532 nm. The diffraction efficiency at two other wavelengths was also measured to be 62.74% at wavelength of 405 nm and 83.74% at 632 nm.

Figure 4.7 Layout of the optical measurement setup 1 laser. 2 and 3 linear polarizers 4 pinhole 5 field lens 6 hybrid aspherical diffractive lens 7 linear translation stage 8 CCD camera.

The PSF of the hybrid lens at wavelength of 532 nm was captured and the normalized intensity profile is shown in Figure 4.8 (a) and (b). In order to reduce noise, ten images were continuously captured and the average was used. In this experiment, the CCD camera imager has a pixel length of 6.75 m. Compared to Figure 4.2 (a), the measured

PSF expands more in radial direction. The measurements are the results of the experimental set up using a 25 m diameter pinhole. A smaller pinhole filter is usually desirable because it creates a better point source for PSF testing. In addition, the discrepancy between the design in ZEMAX and optical test lies in the fact that a 532 nm

100 laser was used in test due to limited selection of laser source while the main working wavelength was 587 nm when the hybrid lens was designed in ZEMAX.

(a) (b)

Figure 4.8 (a) Image of PSF testing at wavelength of 532 nm. (b) Normalized intensity profile the PSF measurement.

Chromatic focal shift describes the corresponding variation of focal length when the wavelength of the incident light changes. The same optical measurement setup as in

Figure 4.7 was employed to measure the chromatic focal shift at three different wavelengths (red 632 nm, green 532 nm, blue 405 nm). During the course of measurement, the position of the hybrid lens on the linear translation stage was carefully adjusted along the optical axis. When the focal point was found on the CCD screen, the

101 position of the hybrid lens on the linear translation stage was recorded. The same procedure was repeated for all three lasers and the focal shifts under these three wavelengths were obtained. Compared with the design data from ZEMAX, the measured results are shown in Figure 4.9. The measured data points were RMS fitted with the design curve and the results showed a good agreement.

Figure 4.9 The measured focal shift was compared with curve predicted by ZEMAX.

4.1.6 Conclusions

To compensate for chromatic aberration, an all glass hybrid aspherical diffractive lens was designed, fabricated and tested. The methodology demonstrated in this research provides a clear economically feasible alternative to the conventional compound doublet

102 lenses, which are usually bigger and heavier than the hybrid lenses. The demonstrated process in optical design, mold fabrication and compression molding proved that large

DOEs optics with sub-micron scale features could be economically produced in high volume for industrial applications.

By use of single point diamond turning, aspherical and diffractive features on the optical mold inserts can be created on the same surface therefore the need for alignment can be eliminated. Without using high hardness thin film coatings, the diffractive features were directly fabricated on the 715 copper nickel alloy using diamond turning. The 715 copper nickel alloy showed sufficient stability during high temperature and high pressure compression molding test. This method reduced the mold fabrication cost and offered an alternative for high efficient mold making.

In this study, a thin film coating was deposited on the finished mold surface. It was determined that a 250 nm Pt-Ir coating with 40 % Pt and 60% Ir to be the most effective condition in protecting the mold for high volume production. In addition, a two-step molding process was developed for large hybrid lenses with micron and sub-micron scale features.

The optical performance of the molded lenses was experimentally evaluated. First the optical profilometer scans showed the geometry discrepancy between the mold and molded lens was 0.16% in radial direction and 6.3% in axial direction. Second the first

103 order diffraction efficiency was measured to be 90.86% at wavelength of 532 nm.

Furthermore the measured achromatic focal shift results showed a match between the molded lenses and the design profile.

The molding experiments also demonstrated that the non-planar profile with sub-micron features can be created on a large glass surface by compression molding, which can be a promising approach to producing high-quality and low-cost all glass hybrid lenses. To reduce the residual stresses and geometry changes due to thermal shrinkage, a two-step molding was developed and proven to be sufficient for this hybrid lens. However, for even larger lenses, thermal shrinkage after molding will significantly affect the geometry thus needs to be compensated.

The refractive index change after heat treatment may also result in deterioration in optical performance. In this case, a well-defined compensation scheme based on numerical simulation of the molded lenses’ properties is critical to improving the quality of final product. To that end, further investigation on the design and the fabrication process to improve the performance of the hybrid aspherical diffractive lens would include FEM

(finite element method) analysis for index variation and the thermal shrinkage compensation during molding of the hybrid lens. Furthermore, applications of DOE optics for specific low cost, high quality products will also be one of the focused research topics in the future.

104 4.2 Precision Molding of Infrared Glass with Graphene Coated Si Wafer

In recent years, infrared optics is becoming increasingly popular because of the growing demands of infrared system in automobiles [95], sensing [96] and communications [97]. One critical component in such systems is infrared glass optics, most of which is manufactured by single point diamond turning (SPDT). However, SPDT of infrared glass is an expensive and time consuming process therefore this manufacturing method limits the applications of infrared optics. With the recent advances in infrared material research, it is promising to use precision molding to fabricate infrared glass.

Precision glass molding is a hot forming process, where glass blanks are heated and compression molded between optical molds [22,81,98]. By using of precision molding technology, infrared glass optics can be manufactured in high volume with a low cost.

The successful replication of infrared glass optics replies surface quality molds, where protective coatings play an important role [39,60]. The graphene coating on Si mold is intended to reduce the friction between glass and mold. As measured using AFM, the graphene coated Si wafer shows significantly reduced friction coefficient compared to uncoated Si wafer[29]. The reduced friction will help the filling of softened infrared glass into micro features on Si mold. Therefore, the replication of optical features is easier. In addition, the graphene coated Si mold has improved wear resistance, providing longer service life of Si mold [39].

4.2.1 Molding of Micro Lens Arrays

We demonstrated the molding of microlens arrays on infrared glass with graphene coated Si wafer. Si wafer was machined using Nanotechnology Systems’ 350FG 5-axis ultraprecision machine, which can provide simplicity and flexibility in creating freeform

105 geometries on silicon surface. Ultraprecision diamond slow tool servo process was used to machine the microlens arrays on a 100 mm Si wafer with 500 µm thickness [60]. In this unique approach, a single point diamond tool with relatively large radius of 3.048 mm was utilized in order to achieve a better surface finish quality[38]. In order to decrease micro fracture in machining on brittle material, the diamond tool was tilted - 24.95º so that a large negative rake angle was established. Initial cutting depth was 300 nm and finish cutting depth was 100 nm. The finish feedrate was 20 mm/min.

(a) (b)

Figure 4.10 (a) Profile of 2x2 micro lens array. (b) Surface roughness measurement at the bottom of one concave lens.

The machined Si mold was coated with graphene to protest its surface. The machined Si mold was measured by a non contact optical profilometer (Wyko, NT9100). As shown in Figure 4.10 (a), there is a 2x2 concave micro lens array. Each lenslet has an overall dimension of 360 x 360 µm. The radius of curvature of each lenslet is 7.1119 mm which gives the effective focal length of 12.1157 mm. The average surface roughness value for

106 the microlens array is about 8 nm (Ra) at the bottom of the concave lens surface. Figure 4.10(b) shows the surface profile at the bottom of one concave lens.

The infrared glass used in this research is BD-2, provided by Lightpath Technologies (2603 Challenger Tech Court, Suite 100, Orlando, FL 32826). BD-2 is a germanium- antimony-selenium glass (Germanium 28%, Antimony 12%, Selenium 60%) with a Tg of 278°C. The Young’s Modulus is 22.1 GPa. Thermal expansion coefficient is 14 x 10-6 / °C [99].

Glass molding experiments were performed on a DTI bench top GP-10000HT press. The molding parameters are based on previous experience and internal communications with LightPath. The pressing temperature of BD-2 was set at 315°C. The molding force was constant at 66N. The cycle time is about 30 min.

(a) (b)

Figure 4.11 (a) Picture of molded Infrared sphere with 2x2 micro lens arrays on top plane. (b) Optical microscopic image of molded micro lens arrays.

107 The BD-2 infrared glass preform was a polished sphere. After molding, a plane surface was molded on top of sphere with concave micro lens arrays. Figure 4.11 (a) shows the picture of a molded IR glass sphere with 2x2 micro lens arrays. Figure 4.11 (b) shows the convex profile of micro lens array measured by an optical microscopic. Surface roughness was measured about 6-9 nm (Ra) on lens and 4-7 nm (Ra) on planer surface.

In order to verify the geometry of molded infrared glass lens, the geometry comparison between Si mold and molded lens is shown in Figure 4.12. The molded lens shows good agreement to Si mold in terms of geometry. Except for some extreme values on the edges, the comparison shows an error map in the order of 100 nm, indicating a good replication of optical features to infrared glass.

Figure 4.12 Geometry comparison between Si mold and mold infrared glass. .

4.2.2 Molding of Optical Gratings

Graphene coating was applied to Si wafer with optical grating, which are periodic micro channels that can diffract light beams. The optical gratings are fabrication using standard photo lithography. Figure 4.13 (a) shows 3D profile of a graphene coated Si wafer. The micro channels have a period of 4 µm and average peak-to-valley depth of 1.58 µm.

108 After glass molding, optical gratings are transferred to IR glass. As shown in Figure 4.13 (b), preliminary results of molded IR glass show an average peak-to-valley depth of 0.6 µm. The depth of gratings on IR glass is smaller than that of Si mold. This is due to insufficient molding force, which can be improved in later experiments.

(a) (b)

Figure 4.13 (a) 3D Profile graphene coated Si wafer. (b) 3D profile of molded IR glass.

In order to demonstrate the functions of optical gratings, molded IR glass were tested using the configuration as shown in Figure 4.14. As shown in Figure 4.14 (a), a beam from He-Ne laser (632.8 nm) travel from right to left until it hits optical gratings on molded IR glass. Because of the periodical structures, the laser beam are reflected and diffracted into several individual beams. Those beams show a diffraction pattern then they are projected on the black screens. The picture of experimental setup and diffraction pattern can be seen in Figure 4.14 (b).

109 (a) (b)

Figure 4.14 (a) Illustration of setup for testing of optical gratings on molded IR glass. (b) Picture of experimental setup and diffraction patterns.

4.2.3 Conclusion

With graphene coated Si wafer, we demonstrated the molding of micro lens arrays and optical gratings on infrared glass. Geometry and optical performance of molded IR glass were tested, demonstrated the functionality of molded IR optics. The graphene coatings works as protective layer on Si wafer is intended to provide longer work life of mold.

110

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