1 Investigation of Optical Effects of Chalcogenide Glass in Precision Glass Molding and Applications on Infrared Micro Optical M

Investigation of Optical Effects of Chalcogenide Glass in Precision Glass Molding

and Applications on Infrared Micro Optical Manufacturing

Dissertation

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy

in the Graduate School of The Ohio State University

Lin ZHANG, M.S.

Graduate Program in Industrial and Systems Engineering

The Ohio State University

2019

Dissertation Committee

Professor Allen Y. Yi, Advisor

Professor Jose M. Castro

Professor Jerald Ralph Brevick

Copyrighted by

Lin Zhang

2019

Abstract

Precision glass molding (PGM) is being considered as an alternative to traditional methods of manufacturing large-volume, high-quality and low-cost optical components. In this process, glass optics is fabricated by replicating optical features from precision molds to glass at elevated temperature. Chalcogenide glasses are emerging as alternative infrared materials for their wide range infrared transmission, high refractive index and low phonon energy. In addition, chalcogenide glasses can be readily molded into precision optics at elevated temperature, slightly above its glass transition temperature (Tg), which in general is much lower compared to oxide glasses.

The primary goal of this research is to evaluate the thermoforming mechanism of chalcogenide glass around Tg and investigate its refractive index change and residual stresses in molded lens in and post PGM. Firstly, a constitutive model is introduced to precisely predict the material behavior in PGM by integrating subroutines into a commercial finite element method (FEM) software. This modeling approach utilizes the Williams-Landel-Ferry (WLF) equation and Tool-

Narayanaswamy-Moynihan (TNM) model to describe (shear) stress relaxation and structural relaxation behaviors, respectively. It is predicted that ‘index drop’ occurred inside the molded prism due to rapid thermal cycling and the cooling rate above Tg can introduce large geometry deviations to the molded optical lens. Secondly, the refractive index variations inside molded lenses are further

ii evaluated by measuring deviation angle through a prism & wavefront changes through molded lens using a Shack-Hartmann wavefront sensor (SHS), while the residual stresses trapped inside the molded lenses are obtained by using a birefringence method. Measured results of the molded infrared lenses combining numerical simulation provide an opportunity for optical manufacturers to achieve a better understanding of the mechanism and optical performance variation of chalcogenide glasses in and post PGM.

Upon completion of the aforementioned research, two typical micro IR optics are designed, fabricated and tested, an infrared SHS and a large field-of-view (FOV) microlens array, as demonstrations. A novel fabrication method combining virtual spindle based high-speed single- point diamond milling and PGM process is adopted to fabricate infrared microlens array. The uniqueness of the virtual spindle based single-point diamond milling is that the surface features can be constructed sequentially by spacing the virtual spindle axis at an arbitrary position based on a combination of rotational and transitional motions of the machine tool. After the mold insert is machined, it is employed to replicate the optical profile onto chalcogenide glass. On the other hand, an infrared compound-eye system consisting of 3×3 channels for a FOV of 48°×48° is developed.

The freeform microlens array on a flat surface is utilized to steer and focus the incident light from all three dimensions (3D) to a two-dimension (2D) infrared imager. Using raytracing, the profiles of the freeform microlenses of each channel are optimized to obtain the best imaging performance.

To avoid crosstalk among adjacent channels, a micro aperture array fabricated by 3D printing is mounted between the microlens array and IR imager. The imaging tests of the infrared compound- eye imaging system show that the asymmetrical freeform lenslets are capable of steering and forming legible images within the design FOV. Compared to a conventional infrared camera, this iii novel microlens array can achieve a considerably larger FOV while maintaining low manufacturing cost without sacrificing image quality.

Finally, two rapid heating processes are explored and demonstrated by using graphene-coated silicon as an effective and high-performance mold material for precision glass molding. One process is based on induction heating and the other one is based on mid-infrared radiation. Since the graphene coating is very thin (~45 nm), a high heating rate of 5~20 C/s can be achieved. The contact surface of the Si mold and the polymer substrate can be heated above the Tg within 20 s and subsequently cooled down to room temperature within tens of seconds after molding. The feasibility of this process is validated by fabrication of optical gratings, micropillar matrices, and microlens arrays on polymethylmethacrylate (PMMA) substrate with high precision. The uniformity and surface geometries of the replicated optical elements are evaluated using an optical profilometer. Compared with conventional bulk heating molding process, this novel rapid localized heating process could improve replication efficiency with better geometrical fidelity.

Dedication

This document is dedicated to my family.

Acknowledgments

The present research work was carried out at Department of Integrated Systems Engineering at the

Ohio State University and with the support of II-IV foundation block-gift research program since

2015. It has been a great honor to have such an opportunity.

I would like first to express my sincere gratitude to my advisor, Professor Allen Y. Yi, who provides me the opportunity to work in the field of precision optical manufacturing. I appreciate his guidance, encouragement and support throughout my Ph.D. study, and also for his careful reviews of my publications and dissertation. I would like to thank Professor Jose M. Castro and Professor Jerald

Brevick for their guidance, suggestions and service on my doctoral committee.

I want to thank previous senior lab fellows, Dr. Lei Li, Dr. Peng He, Dr. Xin Zhao and Dr. Jian

Zhou, who shared the knowledge of glass forming science and simulation related skills without reservation. Special thanks goes to Dr. Hui Li, who collaborated with me and provided great help on chalcogenide glass molding project. Without the help of those senior lab fellows, my research project would not have a good start.

I want to thank my officemate, Wenchen Zhou, who collaborated with me on various projects in the past thousands of days and nights. I am also grateful to work with other excellent labmates, Dr.

Yufeng Yan, Dr. Xiaohua Liu, Dr. Neil Naples, Dr. Dan Zhang, Dr. Min Wu, Tiantong Chen, vi

Kaiyu Cai, Junjie Pan and many other members in Professor Jose M. Castro and Professor James L.

Lee's groups.

I want to thank the assistance from the machine shop supervisors, Joshua Hassenzahl and William

Tullos, in Department of Integrated Systems Engineering. They taught me and allowed me to use most of the machine tools in the workshop and provided me valuable suggestions on machining. I want to thank Derek A. Ditmer and Dave Hollingshead at OSU Nanotech West for their help on photolithography and other related processes.

Finally, I would like to express my sincerest appreciation to my wife, Xue Ji, for her faith and love to me. The same moral and mental understanding support us to pursuit excellence. I am also indebted to my parents, brothers, sisters, grandparents and parents-in-law for their endless and unflagging support in my life.

vii

Vita

August, 1988 ...... Born, China

July, 2011 ...... B.S., College of Mechanical Science &

Engineering, Jilin University, Changchun,

Jilin, China

July, 2014 ...... M.S., College of Mechanical Science &

Engineering, Jilin University, Changchun,

Jilin, China

August, 2015 to present ...... Graduate Research Associate, Department

of Industrial and Systems Engineering, The

Ohio State University, Columbus, Ohio, USA

viii

Publications

Journal Publications:

1. L. Zhang, N. J. Naples, W. C. Zhou, & A. Y. Yi “Fabrication of infrared hexagonal microlens array by novel diamond turning method and precision glass molding”, Journal of Micromechanics and Microengineering 29, 065004 (2019).

2. L. Zhang, & H. Huang “Micro machining of bulk metallic glasses: a review”, The International

Journal of Advanced Manufacturing Technology 100, 637–661 (2019).

3. L. Zhang, W. C. Zhou, & A. Y. Yi “Investigation of thermoforming mechanism and optical properties’ change of chalcogenide glass in precision glass molding”, Applied Optics 57, 6358-

6368 (2018).

4. L. Zhang, W. C. Zhou, N. J. Naples, & A. Y. Yi “Investigation of index change in compression molding of As40Se50S10 chalcogenide glass”, Applied Optics 57, 4245-4252 (2018).

5. L. Zhang, W. C. Zhou, N. J. Naples, & A. Y. Yi “Fabrication of an infrared Shack–Hartmann sensor by combining high-speed single-point diamond milling and precision compression molding processes”, Applied Optics 57, 3598-3605 (2018).

6. L. Zhang, W. C. Zhou, & A. Y. Yi “Rapid localized heating of graphene coating on a silicon mold by induction for precision molding of polymer optics”, Optics Letters 42, 1369-1372 (2017). ix

7. M. Wu, L. Zhang, E. D. Cabrera, J. J. Pan, H. Yang, D. Zhang, Z. G. Yang, J. F. Yu, J. M.

Castro, H. X. Huang, & L. J. Lee “Carbide-bonded graphene coated zirconia for achieving rapid thermal cycling under low input voltage and power”, Ceramics International 45, 24318-24323

(2019).

8. X. Liu, L. Zhang, W. C. Zhou, T. F. Zhou, J. F. Yu, L. J. Lee, & A. Y. Yi “Fabrication of plano- concave plastic lens by novel injection molding using carbide-bonded graphene-coated silica molds”, Journal of Manufacturing Science and Engineering 141, 081011 (2019).

9. W. C. Zhou, L. Zhang, & A. Y. Yi “Design and Fabrication of a Compound-eye System using

Precision Molded Chalcogenide Glass Freeform Microlens Arrays”, Optik 171, 294-303 (2018).

10. X. H. Liu, T. F. Zhou, L. Zhang, W. C. Zhou, J. F. Yu, L. J. Lee, & A. Y. Yi “Simulation and measurement of refractive index variation in localized rapid heating molding for polymer optics”,

Journal of Manufacturing Science and Engineering 140, 011004 (2018).

11. X. H. Liu, T. F. Zhou, L. Zhang, W. C. Zhou, J. F. Yu, L. J. Lee, & A. Y. Yi “Fabrication of spherical microlens array by combining lapping on silicon wafer and rapid surface molding”,

Journal of Micromechanics and Microengineering 28, 075008 (2018).

12. X. H. Liu, T. F. Zhou, L. Zhang, W. C. Zhou, J. F. Yu, L. J. Lee, & A. Y. Yi “3D fabrication of spherical microlens arrays on concave and convex silica surfaces”, Microsystem Technologies

25, 361-370 (2018).

Conference proceedings and presentations:

1. L. Zhang & A. Y. Yi “Precision molding of optics”, APCOM (Asian Pacific Conference on

Optical Manufacturing), Shanghai (2016).

2. L. Zhang, G. Liu, J. Dukwen, O. Dambon, F. Klocke & A. Y. Yi “Precision molding of optics: a review of its development and applications”, SPIE, San Diego (2016).

Fields of Study

Major Field: Industrial and Systems Engineering

Table of Contents

Abstract ...... ii

Dedication ...... v

Acknowledgments...... vi

Vita ...... viii

Publications ...... ix

Table of Contents ...... xii

List of Tables ...... xvii

List of Figures ...... xviii

CHAPTER 1: INTRODUCTION ...... 1

1.1 Precision Glass Molding ...... 1

1.2 Chalcogenide Glass ...... 3

1.3 Glass Properties ...... 4

1.3.1 Viscosity ...... 5

1.3.2 Viscoelasticity ...... 7 xii

1.3.3 Creep Compliance Function ...... 8

1.3.4 Shear Stress Relaxation...... 10

1.3.5 Temperature Dependency ...... 12

1.3.6 Structural Relaxation ...... 12

1.4 Previous Research Work and Motivation ...... 14

1.4.1 Thermo-mechanical Modeling ...... 15

1.4.2 Molding Experiment ...... 16

1.4.3 Motivation ...... 18

1.5 Overview of the Thesis ...... 19

CHAPTER 2: INVESTIGATION OF REFRACTIVE INDEX CHANGE AND

RESIDUAL STRESS ...... 21

2.1 General Refractive Index Change ...... 21

2.1.1 Measurement Principle ...... 24

2.1.2 FEM Simulation Model ...... 26

2.1.3 Fabrication of Wedge-shaped Prism ...... 27

2.1.4 Shape Measurement ...... 31

2.1.5 Optical Measurement Setup ...... 32

2.1.6 Process Method of Image...... 34

2.1.7 Refractive Index Distribution inside Molded Wedge ...... 35

xiii

2.1.8 Measurement Experiment ...... 36

2.1.9 Conclusions ...... 37

2.2 Distribution of Index Change and Residual Stress ...... 38

2.2.1 Methodology ...... 39

2.2.2 FEM Simulation of Glass Molding ...... 43

2.2.3 Fabrication of Infrared Molded Lens ...... 44

2.2.4 Variation of Lens Profile ...... 46

2.2.5 Residual Stresses Prediction and Measurement ...... 48

2.2.6 Refractive Index Prediction and Measurement ...... 52

2.2.7 Conclusions ...... 57

CHAPTER 3: DEMONSTRATIONS OF INFRARED MICRO OPTICS BY

PRECISION GLASS MOLDING ...... 59

3.1 Shack–Hartmann Wavefront Sensor ...... 59

3.1.1 Virtual Spindle Based Single-point Diamond Milling...... 61

3.1.2 Compression Molding Process ...... 67

3.1.3 Optical Setup and Reconstruction ...... 69

3.1.4 Conclusions ...... 74

3.2 Large Field-of-view Microlens Array ...... 75

3.2.1 Optical Design of Freeform Microlenses ...... 78

xiv

3.2.2 Fabrication of Microlens Arrays ...... 88

3.2.3 Ultraprecision Diamond Turning ...... 92

3.2.4 Precision Glass Molding ...... 93

3.2.5 Characteristics of the Machined Surface ...... 95

3.2.6 Characteristics of Imaging Performance ...... 97

3.2.7 Conclusions ...... 103

CHAPTER 4: LOCALIZED RAPID HEATING OF GRAPHENE COATING ON

SILICON WAFER ...... 105

4.1 Rapid Localized Heating of Graphene Coating by Induction ...... 105

4.1.1 Silicon Mold Fabrication ...... 106

4.1.2 Induction Heating Model ...... 107

4.1.3 Heating Characterization ...... 108

4.1.4 Molding Experiment ...... 110

4.1.5 Optical Characterization ...... 113

4.1.6 Conclusions ...... 115

4.2 Rapid Localized Heating of Graphene Coating by Infrared Radiation ...... 116

4.2.1 Micro-feature Fabrication on Silicon Wafer ...... 118

4.2.2 Carbide-bonded Graphene Coating Using CVD ...... 119

4.2.3 Coating Characterization ...... 119

4.2.4 System Characterization ...... 120

4.2.5 Molding Experiment ...... 122

4.2.6 Optical Characterization ...... 125

4.2.7 Conclusions ...... 126

CHAPTER 5: CONCLUSION AND FUTURE WORK ...... 128

5.1 Thesis Summary...... 128

5.2 Recommendations for Future Work...... 131

Bibliography ...... 133

xvi

List of Tables

Table 1-1 Fitted coefficients of creep compliance function J(t) [16] ...... 10

Table 1-2 Coefficients of shear stress relaxation function G(t) [16] ...... 11

Table 1-3 Structural relaxation parameters of As2S3 [20] ...... 14

Table 2-1 Infrared refractive index results for As40Se50S10 glass ...... 37

Table 3-1 Parameters for the Infrared SHS...... 72

Table 3-2 Coefficients for annealing and molding As2Se3 ...... 81

Table 3-3 Configuration of the Freeform Microlens ...... 82

Table 3-4 Design parameters for microlens of central channel A ...... 84

Table 3-5 Design parameters for microlens of side channel B ...... 84

Table 3-6 Design parameters for microlens of corner channel C ...... 85

Table 3-7 Cutting parameters and the tool geometry ...... 93

xvii

List of Figures

Figure 1.1 Schematic presentation of (a) the precision glass molding process, and (b) a generic glass molding process flow...... 2

Figure 1.2 Comparison of specific volume change of glass and metal at different temperature...... 5

Figure 1.3 Typical viscosity-temperature curve with important viscosity points and ranges.

...... 6

Figure 1.4 Structure of the research topics...... 20

Figure 2.1 Refraction in an isotropic prism of refractive index n2 ...... 25

Figure 2.2 (a) FEM model of a compression molding process of a chalcogenide optical wedge from a cylindrical rod, (b) deformed chalcogenide glass in compression process, (c) compression molding during cooling, and (d) the final shape of the molded optical wedge.

...... 28

Figure 2.3 Schematic diagrams of (a) the mold assembly structure, and (b) real machined mold assembly...... 29

Figure 2.4 (a) Schematic diagram of temperature, position and force variation during

As40Se50S10 molding process, and (b) molded wedge (prism)...... 30

xviii

Figure 2.5 Schematic diagrams of (a) 3D surface morphology, and (b) section profile. .. 32

Figure 2.6 (a) Diagram of the optical setup used to measure infrared refractive index, and

(b) measurement setup...... 33

Figure 2.7 The procedure for measuring refractive index...... 34

Figure 2.8 (a) Original image obtained with the infrared detector, (b) intensity of the original image, and (c) monochromatic image with the central point labeled...... 35

Figure 2.9 (a) Mesh volume change of the molded wedge compared with the initial preform

(Vf/V0), refractive index change distribution of the molded wedge (b) 3D view, (c) cross- section view, and (d) statistic result of the refractive index change...... 36

Figure 2.10 Schematic diagrams of simulated stresses and principle stresses in a unit cube.

...... 41

Figure 2.11 Photoelastic model in a modified dark-field plane polariscope...... 41

Figure 2.12 Wavefront reconstruction based on ray tracing method...... 43

Figure 2.13 (a) FEM model for simulation of precision glass molding, and (b) histories of the applied temperature and load during the initial heating, soaking, pressing and cooling.

...... 44

Figure 2.14 Schematic diagram of the glass molding process for infrared optics...... 45

Figure 2.15 (a) Profiles of molded lens obtained from simulation and experiment, (b) deviation with respect to the mold geometry of the final molded lens at two different

xix cooling rates, (c) evolution of a molded lens profile from simulation, and (d) the profiles of lenses with different cooling rates of 360 K/hr and 1,800 K/hr by simulation...... 47

Figure 2.16 (a) Variations of the von Mises stresses with time at the top, middle, and bottom of the lens, (b) the stress profile along the middle line of the lens, and (c) evolution of the von Mises stresses at the middle point with different cooling rates of 360 K/hr and 1,800

K/hr by simulation...... 49

Figure 2.17 Simulated residual stresses inside the molded chalcogenide glass with two different cooling rates of 360 K/hr and 1,800 K/hr (a) stress component σx, (b) stress component σy, (c) stress component τxy, and (d) stress component σz...... 50

Figure 2.18 Residual stresses intensity distribution by simulation and experiment at different cooling rates, (a) simulation results with 360 K/hr, and (b) 1,800 K/hr, experimental results with (c) 360 K/hr, and (d) 1,800 K/hr, (e) the cross-section intensity distribution from center to edge along the 45 degrees radius simulation results, and (f) measured results of a molded glass lens using a plane polariscope...... 51

Figure 2.19 Schematic diagram of the setup of the SHS experiment for wavefront measurement.

...... 52

Figure 2.20 Schematics diagrams of normalized volume distribution (a) after pressing, and final profiles with (b) 360 K/hr, (c) 1,800 K/hr at room temperature, and (d) volume change during the cooling process...... 54

Figure 2.21 Refractive index change distribution inside the molded lens (a) x-y cross- section view, and (b) statistic distribution of the refractive index change...... 55

Figure 2.22 (a) Wavefront calculated based on FEM numerical simulation, (b) reconstructed wavefront variation using an infrared SHS, (c) deviation between the simulation and measured results, and (d) cross-section deviations along A-A and B-B. . 56

Figure 3.1 Schematic of kinematics of the virtual spindle based single-point diamond milling, (a) initialization of the diamond milling, (b) position and axis transfer, and (c) spiral milling...... 62

Figure 3.2 Schematic diagrams of (a) the virtual spindle based single-point diamond milling toolpath generation, and (b) optimization arithmetic by minimum-area fabrication.

...... 65

Figure 3.3 Characteristics of the generated hexagonal microlens array, optical images with amplifications of (a) 2.5×, (b) 2D micro-topography, (c) 3D micro-topography, and (d) 2D profile along the cross-section A-B...... 66

Figure 3.4 Schematic diagrams of the compression molding process (I) preparation, (II) heating, (III) pressing, and (IV) cooling...... 68

Figure 3.5 Characteristics of the molded infrared microlens array, optical images with amplifications of (a) 2.5 X, (b) 2D micro-topography, (c) 3D micro-topography, and (d)

2D profile along the cross-section A-B...... 69

Figure 3.6 Schematic diagram of the optical principle of (a) single lenslet, and (b) microlens array for wavefront measurement...... 70

Figure 3.7 (a) Schematic diagram of the optical setup, and (b) setup of the experiment. 72

xxi

Figure 3.8 (a) Reference image, (b) measurement image from the infrared detector and recognized and used light spots in the (c) reference image, and (d) measurement image.73

Figure 3.9 (a) Displace from original position, (b) reconstructed wavefront with SHS, (c)

MATLAB simulated wavefront, and (d) error between the measurement and simulation.

...... 74

Figure 3.10 Schematic the infrared artificial compound eye system design...... 79

Figure 3.11 Refractive index of As2Se3 glass after annealing and compression molding. 81

Figure 3.12 Viewing directions of the nine microlenslets...... 82

Figure 3.13 Surface profiles of the 3×3 freeform microlens array (a) first side and (b) second side...... 86

Figure 3.14 Layout of the design for three different microlens and the corresponding spot diagrams for various fields (a) central channel A, (b) edge channel B, and (c) corner channel C...... 87

Figure 3.15 Hardware configuration of ultraprecision multi-axis diamond machine for micro/nano optical generation...... 89

Figure 3.16 Schematic of cutting kinematics for side/corner micro/nano optical generation.

...... 91

Figure 3.17 Schematic of cutting kinematics for central micro/nano optical generation. 92

Figure 3.18 Schematic diagrams of the designed mold inserts and assembly structure. .. 94

xxii

Figure 3.19 Schematic diagrams of the compression molding process (I) preparation, (II) heating, (III) pressing, and (IV) cooling...... 95

Figure 3.20 (a) Photography of the mold insert, (b) 3D microscope diagram of the structures, (c) surface profile error and (d) surface micro-topography of a lenslet...... 96

Figure 3.21 (a) Photography of the molded microlens array, (b) 3D microscope diagram of the structures, (c) surface profile error, and (d) surface micro-topography of a lenslet. .. 97

Figure 3.22 (a) Schematic diagram and (b) layout of the infrared optical testing experiment.

...... 98

Figure 3.23 Schematic diagrams of (a) the star target, (b) image obtained from infrared detector, and (c) simulated image from ZEMAX...... 99

Figure 3.24 Schematic diagrams of (a) the batman array, (b) image obtained from the infrared detector, and (c) simulated image from ZEMAX...... 100

Figure 3.25 Design and measurement of normalized MTF contrast in object space as a function of spatial frequency...... 101

Figure 3.26 (a) Raw data captured by the optical setup (b) image captured by the molded microlens array, and (c) by a commercial infrared camera...... 102

Figure 4.1 Schematic of the induction heating compression molding system...... 107

Figure 4.2 (a) Simplified model of the thin conductor film on a strip-shaped Si substrate in

AC magnetic field. (b) Temperature increase for different amplitudes of the applied magnetic field...... 109

xxiii

Figure 4.3 Temperature profiles on graphene coating measured by IR camera at (a) 13 s,

(b) 29 s. (c) Thermal profiles of different temperatures along the diameter of the Si mold.

(d) Heating/cooling response of graphene coating under different heating powers. (Note: the white spots on the left in (a) and (b) are reflection from the camera lens)...... 110

Figure 4.4 (a) Surface profile of a microchannel Si mold. (b) Surface scan of a replicated

PMMA with microchannels. (c) Surface profile of a microwell matrix Si mold. (d) Surface scan of a replicated PMMA with micropillar matrix. Comparison of line scans between the

Si molds and the corresponding molded (e) microchannels, and (f) microwell/pillar matrix.

...... 111

Figure 4.5 3D surface profile of (a) 6×6 microlens array mold, (b) an individual microlens cavity on the mold, and (c) comparison of line scans of an individual lens on mold and its corresponding molded lens...... 113

Figure 4.6 (a) Normalized PSF intensity profile at wavelength of 632.8 nm for the microchannel. (b) Light intensity along the X axis of the diffractive image by the microchannel. (c) Normalized PSF intensity profile at wavelength of 632.8 nm by the micropillar matrix. (b) Light intensity along the X and Y axes of diffractive image of the micropillar matrix...... 114

Figure 4.7 (a) Spherical wavefront measurement experiment using an SHWFS. (b)

Reconstructed wavefront with the SHWFS. (c) Simulated wavefront using MATLAB.115

xxiv

Figure 4.8 (a) Schematics of atmospheric pressure chemical vapor deposition setup for coating graphene on silicon wafer, and (b) variation of process parameters as a function of coating time...... 120

Figure 4.9 Schematic of the rapid heating precision molding system...... 121

Figure 4.10 (a) Heating/cooling response of graphene coating under various driving power,

(b) heating/cooling cycles of graphene coating at 300 W, (c) temperature profiles at three different points on the surface, and (d) temperature variation with/without graphene coating...... 123

Figure 4.11 (a) 3D surface profile of a microchannel Si mold, (b) 3D surface scan of a replicated PMMA with microchannels, (c) 3D surface profile of a microwell matrix Si mold, (d) 3D surface scan of a replicated PMMA with micropillar matrix, Comparison of line scans between the Si molds and the corresponding molded, (e) microchannels, and (f) microwell/pillar matrix...... 125

Figure 4.12 (a) Illustration of setup for testing molded optical gratings, (b) - (f) diffraction patterns on the screen with different surface patterns...... 126

Figure 5.1 (a) anti-reflection surface model, (b) effective medium optical model, and (3) proposed 3D anti-reflective surface structure...... 132

xxv

CHAPTER 1: INTRODUCTION

The current chapter contains a general description of the precision glass lens molding process. The mechanical and thermal behaviors of general glass materials, such as viscoelasticity, stress relaxation, as well as the structure relaxation in the molding process, are introduced. A review of previous studies in precision glass molding is given and objectives of the current study as well as its outline are presented.

1.1 Precision Glass Molding

As early as in the 1980s, precision compression molding is first introduced into fabrication of glass optics with complicated surface geometries [1]. The demand for large-volume and cost-effective techniques for mass production of precision optical elements attracts great attention to precision glass molding process (PGM), which is a close net-shaping fabrication process. It is being considered as an alternative to traditional methods of manufacturing high-quality and large-volume optical components. In essence, the PGM is a thermal forming technique, including heating, pressing, holding and cooling stages. In this process, the glass preform is heated to a temperature above the glass transition temperature (Tg). The heating process could be performed via conduction or infrared radiation mechanism. After the heating, the glass preform is pressed into the desired shape. Finally, the molded lens is cooled down according to the pre-defined cooling rate. The cooling process can be conducted by a controlled flow of nitrogen or a water flow in channels

1 inside the molds. For high-volume production, PGM is superior to many traditional methods. PGM offers increased efficiency because the molding cycle is much shorter than the process of grinding and polishing or single-point diamond turning [2]. Production costs are also decreased because the molds can be reused for pressing many optics without major wear or deformation. Figure 1.1 (a) gives a schematic presentation of a typical precision molding process.

Figure 1.1 Schematic presentation of (a) the precision glass molding process, and (b) a generic glass molding process flow.

As an alternative to traditional glass lens manufacturing processes, compression molding of glass lenses is a very attractive approach [3]. Figure 1.1 (b) is a schematic of mold temperature and mold position during glass molding process. The solid (red) line represents temperature changes. The dotted (blue) line indicates the position of the lower mold and dotted (green) line shows the load variation during a glass molding cycle. A typical glass molding process can be grouped in three different stages, labeled as stage A, B and C [4]. In stage A, nitrogen gas (N2) may flow through the mold assembly area to purge the chamber. The mold assembly and the glass blanks are heated

2 to a temperature slightly higher than the transition temperature of glass (Tg). In stage B, molding of the glass lens takes place at a constant temperature. In stage C, the heating elements are turned off and N2 may be used to accelerate the cooling of the mold assembly and the finished lens is released at a temperature close to room temperature.

1.2 Chalcogenide Glass

Instruments working in mid-wave infrared to long-wave infrared bands are in high demand in a variety of applications and have achieved great success in the field of defense, security and healthcare [5]. Chalcogenide glasses are emerging as important enabling materials for low-cost infrared imaging by virtue of their transparency in the key short-wave infrared (SWIR) to longwave infrared (LWIR) bands and the ability to be mass produced and molded into near-net shape lenses [6]. These materials are made of chalcogen elements, such as sulfur, selenium and tellurium

(S, Se and Te), instead of oxygen to bond with heavy metals and metalloids by covalent bonds [7].

The infrared transparency can be observed up to 13.0 µm for sulfide glasses, 17.0 µm for selenide glasses, and 20.0 µm for telluride glasses [6]. In recent years, improvements on commercially available infrared detectors result in a strong demand for more affordable and high-volume infrared optics, to large degree rekindled the interest in molding of chalcogenide glass. These materials provide photonics industry with material candidates for low-cost and high-performance optical devices.

Adoption of chalcogenide glasses for molded infrared optics can be difficult as the behaviors of these glasses under molding conditions will vary, sometimes rapidly around molding temperature.

When the molding temperature is slightly above its glass transition temperature (~Tg), chalcogenide 3 glasses are in viscoelastic state, exhibiting both viscous and elastic characteristics when undergoing deformation. In addition, when subjected to a (sudden) temperature drop from the molding temperature, chalcogenide glasses will experience an instantaneous shrinkage of volume.

Mechanical and thermal cycles in PGM can cause molecular topological structure changes and induce further changes to other physical properties of molded chalcogenide glasses, such as optical refractive index and geometrical shape. However, in spite of the rapid development in fabrication techniques, our fundamental understanding of structural changes in and after PGM inside chalcogenide glasses is still lacking, partially due to the difficulties in performing in situ observation of deformation and its evolution inside the materials in a PGM process. Therefore, a number of challenges must be overcome before the new process could be fully implemented in industry.

1.3 Glass Properties

Unlike metals that have stable crystalline structures at room temperature, glass is in a non- equilibrated state, which is lack of crystalline structures inside. Even at low cooling rates, the glass transforms from liquid state to solid state without crystallization, which is generally regarded as a frozen liquid. Figure 1.2 illustrates the variation of specific volume of glass and metal at different temperatures. When the temperature is below the melting point, the metal is an elastic solid if there is not external load, while glass shows some complicated behaviors. Three distinct regions are noticed, the liquid region, the transition region and the solid region. Glass behaves like a viscous fluid in the liquid region, a viscoelastic fluid in the transition region and an elastic solid in the solid region. Important material properties for glass will be discussed and integrated in FEM simulation in the form of constitutive models using user defined subroutines.

Figure 1.2 Comparison of specific volume change of glass and metal at different temperature.

In addition, the glass transition temperatures are affected by cooling rates during transition from liquid to solid state, accordingly, causing variation in glass properties at room temperature, such as non-equilibrium energy and density (volume). For instance, lower cooling rate results in lower glass transition temperature and higher density. In other words, the glass moves closer to equilibrium state at lower cooling rate.

1.3.1 Viscosity

Viscosity is an important physical parameter which determines the flow of material. The knowledge of viscous behavior is one of the key factors for fabrication of glasses. The typical viscosity curve is plotted in Figure 1.3. Important points and ranges are illustrated in this figure.

Figure 1.3 Typical viscosity-temperature curve with important viscosity points and ranges.

The viscosity of glass changes with temperature. Four standard temperature points are employed in glass working to define the viscosity. These points are known as strain point, annealing point, softening point and working point.

The strain point is the maximum temperature at which a glass can serve for structural and mechanical applications without undergoing creep. The majority of glass forming operations occur between the softening point and the working point. Part of the glass molding process is also located inside this range. Beyond softening point, the glass will yield with a small amount of force, while at the working point, the glass has the viscosity similar to paste. The annealing point is the temperature to which a glass may be heated after working to relieve internal stresses that arose as a result of the thermal deformation.

Viscosity varies with temperature, generally becoming smaller when temperature is elevated. This trend occurs because the increased kinetic motion of molecular chains at higher temperatures promotes the breaking of intermolecular bonds between adjacent layers. Based on a considerable amount of research, one relatively simple empirical model assumes that the viscosity obeys an

‘Arrhenius-like’ equation of the form [8].

ƞ = 퐴ƞ푒푥푝(퐸ƞ/푅푇) Equation 1.1

where Aƞ is a constant value, Eƞ/R is ratio between the activation energy and the gas constant.

1.3.2 Viscoelasticity

Viscoelasticity is a study of materials, which have a time-dependence. Glass shows a viscoelastic behavior in its transition region. The response of a viscoelastic material is typically categorized into two cases, creep and stress relaxation.

Linear viscoelasticity is a reasonable approximation to the time-dependent behavior of glass and polymer at relatively low temperatures and under relatively low stress. According to linear viscoelastic theory, stress σ(t) and strain ε(t) can be expressed by the following convolution integral equations, respectively [9,10].

푡 ( ) ( ) 휎(푡) = ∫0 퐸 푡 − 휉 휀̇ 휉 d휉 + 퐸(푡) 휀(0) Equation 1.2

푡 ( ) ( ) 휀(푡) = ∫0 퐽 푡 − 휉 휎̇ 휉 d휉 + 퐽(푡) 휎(0) Equation 1.3

7 where E(t) = σ(t)/ε0 is the stress relaxation modulus function which is used to describe the stress response when the strain ε(t) = ε(0)u(t) is applied (t > 0). J(t) = ε(t)/σ0 is the creep compliance function which is employed to describe the strain response when the stress σ(t) = σ(0)u(t) is applied

(t > 0).

Laplace transform can be used to convert complex convolution integration into simple algebra form.

Applying Laplace transform to Equations 1.2 and 1.3 [11].

휎̅(푠) = s퐸̅(푠)휀(̅ 푠) Equation 1.4

휀(̅ 푠) = s퐽(̅ 푠)휎̅(푠) Equation 1.5

The relationship between Laplace transforms of relaxation modulus function퐸̅(s), and creep compliance function, 퐽(̅ s) can be simplified as the following equation,

1 퐸̅(푠) = Equation 1.6 푆2퐽(̅ 푠)

The relaxation modulus 퐸̅(s) can be derived from creep compliance 퐽(̅ s), and E(t) can be obtained by using inverse Laplace transform.

1.3.3 Creep Compliance Function

The creep compliance is defined as J(t) = ɛ(t)/r0, where the uniaxial stress should be kept constant in compression. However, in the tests, the uniaxial stress does not stay constant but decreases with time because the section area A(t) increases with time when the cylinder deforms and expands in

8 the radial direction. So, the creep compliance cannot be calculated directly by the definition equation J(t) = ɛ(t)/r0. By using discretization form of Equation 1.3, true strain ɛi is comprised by creep compliance Ji and true stress ri as follows [12],

휎 −휎 ε = ∑푖 퐽 ( 푘 푘−1) ∆푡 + 퐽 휎 Equation 1.7 푖 푘=1 푖−푘 ∆푡 푖 0

The creep compliance Ji can be calculated by the following equation:

휀푖 1 푖 휎푘−휎푘−1 퐽푖 = − ∑푘=1 퐽푖−푘 ( ) ∆푡 Equation 1.8 휎0 휎0 ∆푡

The deformation of the specimen is indicated by true strain ɛ(t) = ln(L(t)/L0) due to large deformation occurred under compression, where L0 is the initial thickness, and L(t) = L0-ΔL is the time-varying thickness.

Since the volume of the specimen is considered to be constant during compression, the circular section area A(t) can be calculated by A(t) = A0L0/L(t) = A0 exp(-ɛ(t)). Then, the true stress is the function of true strain by using the relation r(t) = F/A(t) = r0 exp (ɛ(t)). Finally, by solving Equation

1.8 iteratively, the creep compliance functions J(t) can be calculated.

To fit the test data, Kelvin-Voigt (KV) model is employed to characterize the creep compliance function. This model is gifted the capacity to capture the decreasing strain rate and the asymptotical steady-state strain with time [13,14]. For the Kelvin-Voigt model, the creep compliance function

J(t) is expressed as following [15]:

1 푛 1 1 퐽(푡) = + ∑푖=1 (1 − exp (− )) Equation 1.9 퐸0 퐸푖 휆푖

where λi = ηi/Ei, ηi are the viscosity of dashpots, Ei are the elastic modulus of the springs of the model with E0 (with a value of 15.858 GPa) being the Young’s modulus of As2S3. Three exponential terms are employed to accurately describe the creep compliance function curves. The coefficients of creep compliance function used in this study are listed in Table 1-1.

Table 1-1 Fitted coefficients of creep compliance function J(t) [16]

Ei (MPa) λi (s) Temp (°C) E1 E2 E3 λ1 λ2 λ3 220 4000 300.933 5.350 1662 719.4 6798 230 86.430 28.209 7.605 206.9 387.3 1897 240 55.524 18.385 10.583 43.34 276 144.3

1.3.4 Shear Stress Relaxation

Laplace transform of creep compliance function J(t) can be obtained as described as follows,

̅ 1 푛=3 1 퐽(푠) = + ∑푖=1 Equation 1.10 푠퐸0 푠퐸푖(1+푠휆푖)

When material is in viscoelastic state, it is more convenient to use shear stress G(t) rather than

Young’s modules E(t). In complex domain, the relationship between G(t) and E(t) is described as follows,

3퐾̅(푠)퐸̅(푠) 퐺̅(푠) = Equation 1.11 9퐾̅(푠)−퐸̅(푠)

10 where 퐾̅(s) is Laplace transform of bulk modulus K(t). In general, the K(t) is much larger than the shear modulus and with smaller relaxation, it is regarded as a constant in the equation. Therefore,

퐸0 the Laplace transform of K(t) is 퐾(푠) = , where v0 is the Poisson’s ratio of As2S3 in room 3푠(1−2ν0) temperature. It is common to use the generalized Maxwell model to characterize stress relaxation behavior [13,14]. G(t) can be obtained by Equation 1.8-1.10 by expressing in Prony series as follows [16],

푛=3 푡 퐺(푡) = 퐺∞ + ∑푖=1 퐺푖푒푥푝(− ) Equation 1.12 휏푖

where τi = ηi/Gi is shear stress relaxation time. Gi and G∞ are shear modulus component and long- term shear modulus, respectively. The coefficients used in this study to describe the shear stress are listed in Table 1-2.

Table 1-2 Coefficients of shear stress relaxation function G(t) [16]

Gi (MPa) τi (s) Temp(°C) G1 G2 G3 τ1 τ2 τ3 G∞ 220 6390.96 1.607 0.027 1.614 825.082 4672.24 1.74 230 6390.50 1.462 0.523 0.240 761.150 242.584 1.86 240 6391.27 0.923 0.159 0.041 56.897 230.730 1.99

1.3.5 Temperature Dependency

For viscoelastic materials, the stress relaxation behavior at different temperatures can be shifted along the logarithmic time without shape change on the reference master curve. This is so-called

Thermo-Rheological Simplicity (TRS) behavior and the empirical Williams-Landel-Ferry (WLF) equation [17] is used to characterize the shift factor aT(T):

−퐶1(푇−푇푟푒푓) 푙표푔푎푇(푇) = Equation 1.13 퐶2+(푇−푇푟푒푓)

where Tref is the reference temperature, and C1, and C2 are constants adjusted to fit the shift factor.

Here, the shift factor can be calculated from the creep compliance curves or shear relaxation modulus curves along the logarithmic time axis. For As2S3, when the reference temperature Tref is chosen as 220°C, the calculation results of the two constants are C1 = 5.487, C2 = 49.798 [16].

1.3.6 Structural Relaxation

During cooling, glass materials undergo structural relaxation as temperature is decreased. This process is a nonlinear behavior. It not only depends on current temperature but also the thermal history of the cooling process. To describe this behavior, volume relaxation function Mv(t) is expressed as follows [18],

푉(푇2,푡)−푉(푇2,∞) 푇푓(푡)−푇2 푀푣(푡) = = Equation 1.14 푉(푇2,0)−푉(푇2,∞) 푇1−푇2

where Tf is the fictive temperature describing the degree of internal structural deviation from the equilibrium state. The subscripts 0 and ∞ represent the instantaneous and steady state values of the 12 property of the glass material. In most cases, the experimental data are conveniently expressed by means of the stretched exponential relaxation function, and can be expressed by as a sum of exponential series for calculation as follows [18,19],

푡 훽 푛 푡 푀푣 = exp [−( ) ] = ∑푖=1 푤푖exp (− ) Equation 1.15 휏푣 휏푣푖

where τv or τvi is structural relaxation time, and β is a phenomenological parameter that was adopted to fit the response curve. The value of β lies between 0 and 1. wi are called weighting factors for the

푛 relaxation factors ( ∑푖=1 푤푖 ≅ 1 ). The structural relaxation times are strongly temperature dependent and can be calculated using Tool-Narayanaswamy-Moynihan model (TNM) [18]. The relaxation time is defined as a function of fictive temperature Tf and real temperature T.

∆퐻 1 푥 (1−푥) 휏푣 = 휏푣,푟푒푓exp {− [ − − ]} Equation 1.16 푅 푇푟푒푓 푇 푇푓

where tv, ref is the structural relaxation time at reference temperature Tref. ΔH and R are activation energy and gas constant ratio, respectively. x is a nonlinearity parameter. When the reduced time ξ is introduced as [18],

푡 푑푡′ 휉 = ∫ ′ Equation 1.17 0 휏푣(푇,푡 )

Fictive temperature Tf can be predicted by the equation as follows,

푡 푑푇(푡′) 푇 (푡) = 푇(푡) − ∫ 푀 [휉(푡) − 휉(푡′)] 푑푡′ Equation 1.18 푓 0 푣 푑푡′

Volume of the molded chalcogenide glass during cooling stage can be calculated by Equation 1.14-

1.18. Structural relaxation parameters used in the simulation are listed in Table 1-3.

Table 1-3 Structural relaxation parameters of As2S3 [20]

Material properties As2S3 ΔH/ R (K) (32.4 ± 0.5) × 103 x 0.31 ± 0.02 β 0.82 ± 0.02 -6 Coefficient of thermal expansion of solid αg (/K) 22.0 × 10 -6 Coefficient of thermal expansion of liquid αl (/K) 96.0 × 10

Reference temperature Tref (°C) 250

wi τi, ref (s) 0.6329 0.3396 0.3104 0.1145 0.0510 0.0160

1.4 Previous Research Work and Motivation

As an advanced manufacturing technology, precision glass molding (PMG) process has been recognized as a low-cost and high-efficiency manufacturing technology for machining small- diameter optical elements in industrial production. However, some issues, such as the thermal expansion of molds, mold life, residual stress and refractive index variation inside glass after molding, are greatly affected by various key technologies for precision glass molding. These key technical factors, which affect the quality of the glass lens molding process, are systematically discussed and reviewed to solve the existing technical bottlenecks and problems.

1.4.1 Thermo-mechanical Modeling

Precision glass molding is in essence a thermo-mechanical process, accordingly, its simulation, if to be fully simulated or reproduce the process, is a thermo-mechanical coupled model, which coupling thermal and mechanical physics. The mechanical properties such as modulus of elasticity and viscosity are temperature dependent, and the interfacial heat transfer is critically influenced by the contact area. The deformation behavior of the materials at different temperatures as well as residual stress state inside the molded glass are considerably affected by these parameters in molding process. Quantifying these influences at the transition range has been the subjects of some previous research work. This is briefly outlined below.

Yi and Jain (2005) simulated a glass molding process by finite element method (FEM) code

DEFORM-2D assuming a rigid-viscoplastic and elastic-viscoplastic material model for glass during pressing and cooling stages, respectively [4]. In another research work, Jain and Yi (2005) employed a 2D axisymmetric FEM model in the MSC.MARC software to simulate the viscoelastic stress relaxation of a cylindrical glass disc during glass molding process. Similar experiments were performed to evaluate the simulated results and good agreement was observed [21]. In a subsequent research, Jain and Yi (2006) took into account the structural relaxation behavior of glass in a FEM model to predict the geometrical profile deviation of molded glass discs [22]. The glass material was considered as a rigid-plastic material and modeled as a Newtonian fluid represented by a simple dashpot. A good agreement was observed between experimental and predicted geometrical lens profile deviation when structural relaxation was incorporated into the simulation. Wang et al.

(2009) conducted a 2D numerical simulation to predict the geometrical profile deviation of the

15 molded lenses and based on the numerical results, the mold design was compensated for this deviation [23]. The residual stresses inside a molded cylindrical BK7 glass was predicted by Chen et al. (2008) using numerical simulation [24]. The glass was regarded as a Newtonian fluid during pressing and a viscoelastic solid undergoing structural relaxation during cooling. The residual stresses inside the lenses molded at different cooling rates were also measured by the birefringence method, which showed great agreement with the simulation results. Dambon et al. (2009) employed the FEM software to predict the geometrical profile deviation of a molded lens from its desired form and based on the results, compensated for this in the mold design [25]. Su and Yi

(2012) simulated the cooling process of a cylindrical glass sample using a 2D axisymmetric model, taking into consideration the structural relaxation behavior of the glass material to study the effect of the cooling rate on the refractive index change [26].

1.4.2 Molding Experiment

Compression molding process requires the heating of entire bulk glass blank above glass transition temperature (Tg) where the glass behaves like a viscoelastic material. In this arrangement, the glass mold, vacuum chamber where glass blank is placed and other mechanical components are heated up and then cooled down simultaneously. The entire molding process is conducted in a hermetical environment without oxygen, thereby preventing the oxidation and adhesion of the glass preform and the mold at elevated temperature.

Shishido et al. (1995) investigated the fitting degree of the glass and the mold during molding process [27]. It is noted that fitting degree changes with the surface tension of the glass, and that such change in turn affects the replication accuracy after molding. Fischbach et al. (2010) 16 investigated the glass-to-mold sticking force during precision glass molding [28]. Through the use of design of experiment (DOE), it was shown that the factors which significantly affect sticking force were compression holding time, cooling time and compression force, while film composition, surface roughness and substrate type showed no significant effect on sticking force. Zhou et al.

(2016) applied ultrasonic vibration in glass molding process to improve the formability and reduce adhesion between the glass and the mold at elevated temperature [29,30]. Ultrasonic vibration has a significant effect on reducing the interfacial friction force between the glass preform and mold, homogenizing the stress distribution and reduce stress concentration inside the glass and increasing the material formability in the molding process. Manaf and Yan (2016) proposed a hybrid structure of single-crystal silicon (Si) and high-density polyethylene (HDPE) as new substrate for infrared lenses by using precision glass molding [31,32]. The imaging results presented that the hybrid substrate obtained similar image quality as Si itself, which showed that the hybrid substrate is a promising alternative substrate material for IR lens.

On another hand, a few attempts have been made to achieve rapid thermal heating in precision glass molding during the last decade. Large-current surface resistance heating as an effective rapid localized heating method was proposed and demonstrated in both polymer embossing [33] and chalcogenide glass molding [34]. With the aid of low thermal inertia and high thermal conductivity of nanoscale thickness graphene coating, the cycle time of precision molding could be reduced to less than 5 min. Another technique to reduce cycle time was infrared (IR) laser-assisted localized heating process [35]. By employing carbon black filled epoxy/polymer substrate as IR-absorbent to implement rapid and local heating, the heating time could be reduced to ~5 s with heating rates of 20~60 °C/s. 17

1.4.3 Motivation

Chalcogenide glasses are emerging as important enabling materials for their wide range infrared transmission, high refractive indices, high nonlinearity and low phonon energy [36]. In addition, chalcogenide glasses can be readily molded into precision optics [37,38], therefore providing photonics industry with material candidates for low-cost and high-performance photonic devices.

Despite of those advantages of precision glass molding approach for chalcogenide glass, a number of challenges must be overcome before the new process could be fully implemented in industry.

First, it is well-documented that precision glass molding leads to decrease in refractive index of glass during the rapid thermal process [39]. The decrease of refractive index is one of the most important optical property changes that can alter the performance of an optical optics along with geometric deviations. If the refractive index change introduced by molding process cannot be considered properly in the design, the optical performance of the molded lens will be different from the original design. Therefore, a detailed and most importantly, a quantitative investigation on refractive index change of chalcogenide glasses during the molding process is critical. Future more, the distribution of refractive index and residual stress in the molded elements are generally not uniform, especially for large-aperture molded optics, which should be in need of more comprehensive studies. Second, devices for long- and short-wave infrared (SWIR and LWIR) imaging are largely demanded for a number of applications. A great improvement of infrared imaging systems was given after uncooled detectors became available in the market [6]. Micro lenses are a novel group of modern optical elements, which are widely employed in collimation, focusing or imaging of light. Micro lens technology, especially for infrared applications, holds great

18 potential for the miniaturization of components, reduction of production costs and increase in performance of products. To verify the feasibility of precision glass molding for chalcogenide glass optical elements, typical micro optics were demonstrated. Finally, conventional precision glass molding process is a bulk thermal heating process, in which the entire glass blank, the molding assembly and other mechanical parts are heated above glass transition temperature (Tg) and then cooled down after molding simultaneously. The long cycle time of precision glass molding limits its throughput and wide applications in industry. Novel methods of localized rapid heating process should be proposed to improve the efficiency by employing new molding materials.

1.5 Overview of the Thesis

The main focus of this dissertation is to seek scientific and fundamental knowledge of thermoforming mechanism and optical properties change of chalcogenide glass in precision glass molding, verify the feasibility of precision molding for infrared optics and improve the precision glass molding efficiency. Overall, this dissertation describes a comprehensive understanding of low-cost and high-volume nonconventional infrared optics manufacturing. The present thesis consists of five chapters:

Chapter 1 presents the precision glass molding process and its numerical simulation model, briefly and based on this, the motivation and objectives of the present work are outlined.

Chapter 2 contains numerical simulations to collect quantitative refractive index change in molded chalcogenide glass, and optical experiments are conducted to verify the optical and mechanical change in molded lens.

Chapter 3 describes typical infrared micro lenses fabrication process by using diamond turning/milling with precision glass molding as demonstration.

Chapter 4 presents rapid localized heating techniques on carbide-bonded graphene coating using induction heating and mid-infrared radiation, and novel surface molding processes are carried out.

Chapter 5 is devoted to the most important conclusions of the dissertation and suggests some future research directions.

The relation of these research topics is shown in Figure 1.4. The optical effects of the precision glass molding are related to both fundamental and process research. The two application examples are both related to process research and application research. The novel approaches further improve the process research and application research.

Figure 1.4 Structure of the research topics.

CHAPTER 2: INVESTIGATION OF REFRACTIVE INDEX CHANGE AND RESIDUAL STRESS

The current chapter is focused on evaluating the thermoforming mechanism of chalcogenide glasses around its glass transition temperature (Tg) and investigating its refractive index change and residual stresses in molded lens in and post PGM. The refractive index and residual stress inside the molded lens are investigated by FEM simulation and experiment, which help manufacturers to achieve better understanding on the mechanism and optical performance of chalcogenide glasses in and post PGM.

2.1 General Refractive Index Change

For high-volume production, compression molding of chalcogenide glass could be a preferred option to traditional diamond turning method for its high efficiency, short cycle time and reusable tooling. However, some physical properties of chalcogenide glasses will change as their thermal history is altered, primarily during the rapid thermal cycles [26]. When the molding temperature is slightly above its glass transition temperature (~Tg), chalcogenide glasses are in viscoelastic state, exhibiting both viscous and elastic characteristics when undergoing deformation. In addition, when subjected to a (sudden) temperature drop from the molding temperature, chalcogenide glasses will experience an instantaneous shrinkage of volume. The refractive index of glass, which directly

21 depends on glass density, is one of the physical properties that will change during such a thermal process.

It is well-documented that precision glass molding leads to decrease in refractive index of glass during the thermal process [39]. The decrease of refractive index is one of the most important optical property changes that can alter the performance of an optical optics along with geometric deviations. If the refractive index change introduced by molding process cannot be considered properly in the design, the optical performance of the molded lens will be different from the original design. Therefore, a detailed and most importantly, a quantitative investigation on refractive index change of chalcogenide glasses during the molding process is critical.

Previously, studies were conducted to investigate the refractive index change of oxide glass in thermal processing, such as cooling and annealing phase. For example, Su et al. (2012) performed a series of numerical simulations to study the relationship between refractive index change at different cooling rates in compression molding [26]. Fotheringham et al. (2008) conducted experiments to investigate the refractive index drop at different cooling rates [40]. In recent years, some researchers attempted to study the structural relaxation of chalcogenide glasses undergoing different reheating-cooling thermal processes. For example, Zhou et al. (2017) investigated the stress relaxation parameters of As2S3 above its Tg and the strain relaxation occurred during the annealing via finite element method [16]. Novak et al. (2013) conducted a series of experiments to study the index change of molded chalcogenide glasses using a commercial optical instrument [41].

Their results demonstrated that the volume of chalcogenide glass had changed due to structural relaxation, leading to refractive index drop just like what occurred in oxide glass molding process.

However, no detailed combination of both experiments and analytical explanation was provided to verify the reliability and accuracy of simulation result in their publications. To the authors’ best acknowledge, the refractive index drop of chalcogenide glass during cooling (

In this section, the refractive index change of chalcogenide glasses was investigated by both experiment and simulation. The test sample for index measurement was designed as a molded wedge-shaped prism made of As40Se50S10 glass. A set of mold inserts were designed and manufactured by high-speed single-point diamond milling, which were detachable, making the molded wedge release after molding process an easy task. The molded wedge was mounted on the precise rotary table in an optical setup to measure the refraction angle. To fully understand the material behaviors and property change of the As40Se50S10 glass, structural relaxation, which is responsible for volume change in compression glass molding process, is simulated by the finite element method (FEM) software ABAQUS. The refractive index of As40Se50S10 was predicted by obtaining simulation results from ABAQUS using the density-index equation. Finally, the predicted results were confirmed by the aforementioned experiments. Furthermore, the focal shift of the molded lenses after the refractive index variation was also demonstrated by calculation and simulation.

2.1.1 Measurement Principle

2.1.1.1 Refractive Index Measurement

Almost all the refractive index measurement methods are based on one of the basic optical properties, such as diffraction [42], internal reflection [43], interference [44], and deflection [45].

Each measurement method has its advantages and disadvantages in different situations and applications. Among them, the prism method is one of the most popular options, because wedge- shaped prism elements can be relatively easily made and its signal easily observed by detectors [44].

It is known that if a light ray passes through an isotropic optical prism the refractive index of the prism can be determined by measuring the refractive angle of the light ray based on the Snell’s law.

푛1 sin(휃1) = 푛2sin (휃2) Equation 2.1

where n1 is the refraction index of the medium in which the light enters, and n2 is the refraction index of the medium in which the light leaves. θ1 and θ2 are the angles of incidence and refractive, respectively.

Using the Keating’s step procedure for calculating the deflection angle of a prism, the refractive index n2 of the prism can be calculated based on the Snell’s law at the front and back surface of the prism as follows,

푛1 sin(푖1) = 푛2sin (푟1) Equation 2.2

푛2 sin(푖2) = 푛1sin (푟2) Equation 2.3

24 where n1 is generally the refractive index of air (refractive index = 1). i1 and i2 are the incident angles to the front and back surface of the prism. r1 and r2 are the refractive angles from the front and back surface of the prism, as shown in Figure 2.1. The geometrical relationships among A, D, r1, i1 and r2 are related by the equation below.

푖2 = 퐴 − 푟1 Equation 2.4

퐷 = 푖1 + 푟2 − 퐴 Equation 2.5 where A is the angle of the prism. D is the deviation angle, which is determined by the rotational angle of the rotary table between the initial and the final position.

Figure 2.1 Refraction in an isotropic prism of refractive index n2

2.1.1.2 Index Change during Structure Relaxation

The refractive index of molded glass material usually presents a lower value than that of its original [26]. Experimental and analytical studies demonstrated that the refractive indices of transparent materials have a quantitative relation with the density. In glass molding, the volume of a glass changes during one or several stages including heating, molding and cooling. Among them, 25 the cooling process have the most direct influence on the refractive index of the molded glass.

According to Su et al. (2012), the refractive index change within a glass sample can be calculated by a function of the volume change [26,46],

(푛2−1)(푛2+2) 푉 ∆푛 = ( 0 − 1) Equation 2.6 6푛 푉푓

where n is the original refractive index (for As40Se50S10, n = 2.7126 at the wavelength of 8.0

m [47]). V0 is the initial volume of the glass sample, and Vf is the volume at the end of cooling.

As mentioned above, the volume of a glass after undergoing a reheating-cooling thermal process generally expand (Vf > V0) dependent on the cooling rate. Therefore, the refractive index of the molded As40Se50S10 optics will decrease according to the index-density relationship in Equation

2.6.

2.1.2 FEM Simulation Model

Finite element method (FEM)-based numerical simulation has been widely employed to investigate the mechanism of viscoelastic and structure relaxation in compression molding process [48]. In this research, the compression molding of As40Se50S10 glass was simulated using the commercial FEM software ABAQUS. As aforementioned, the entire molding process involves heating, molding and cooling.

In this simulation, a cylindrical preform (2.6 mm diameter and 2.3 mm thickness) was placed between two optical mold halves. The top mold insert was flat and the bottom mold insert is a cavity of a precision machined wedge. The symmetrical algorithm was utilized to decrease

26 computation time, as shown in Figure 2.2 (a). A glass cylinder of As40Se50S10 preform was treated as a deformable part and divided into tetrahedron with 0.01 side length. The stiffness of the mold was assumed to be high enough such that its deformation was ignored in the compression process.

The bottom mold was constrained in the vertical direction, and the top mold was applied with constant pressure load (F = 75 N). Predefined temperature (T0 = 20 °C ) condition was applied to the entire model and then heated above Tg. The friction between As40Se50S10 and molds was characterized using the penalty Coulomb friction model with the friction coefficient chosen to be

0.25 using data from reference [49]. The above described simulation process was a thermo- displacement coupled problem and implemented in ABAQUS. With the shear modulus, shift factor and other parameters as the input of the As40Se50S10 viscoelastic material properties, the compression molding simulation process was successfully completed. Figure 2.2 (b)-(d) illustrated the entire FEM simulated molding process to show the deformation of the cylindrical preform and the formation of the optical wedge specimen. From the simulation results, the chalcogenide glass underwent a uniform and stable deformation process. The residual stress inside the finished molded wedge was small in size.

2.1.3 Fabrication of Wedge-shaped Prism

In this research, the mold inserts for compression molding was machined on the 350 FG (Moore

Nanotechnology Systems, Keene, New Hampshire, USA) by high-speed single-point diamond milling. The milling tool was a single flute, ball-end mill made out of single-point diamond cutter.

6061 aluminum alloy was selected for the mold fabrication for its steady mechanical properties at elevated temperature. The design of the mold insert is shown in Figure 2.3 (a). The structure was

27 different from conventional mold design in that all the features are machined out of one single block of aluminum stock. The mold insert contained a mold core with a wedge cavity and two side blocks, which were detachable. The advantage of this detachable structure was that the molded wedge can be easily released from the mold insert, which reduces the chances of breakage of the molded wedge when taking out from the mold after molding.

The mold insert was firstly rough machined on a conventional CNC 3-axis vertical milling machine

(Haas VF-3, Haas Automation, Inc., Oxnard, California, USA) from a 6061 aluminum alloy rod.

Next, the mold surface was diamond machined with two side blocks on the 350 FG. The spindle speed and feed rate chosen for the turning process were 2000 rpm and 5 mm/min. Then the two side blocks were moved from the mold. Considering the large-slope surface of the wedge, high- speed single-point diamond milling was adopted for fabrication of the features. Compared with slow or fast tool servo (S-/FTS), high-speed single-point diamond milling may be a better option for some applications for the following reasons: (1) Experiments showed that high-speed single- point diamond milling was a highly efficient process with flexibility for fabricating complex micro optics. (2) The clearance angles of most common diamond tools limited their applications in single- point diamond turning. In other words, if the slope angle exceeded the clearance angle of the tool, the flank face of the tool would scratch the finished surface. Therefore, high-speed single-point diamond milling was employed in this precision fabrication for better uniformity in surface generation.

(a) (b) Figure 2.3 Schematic diagrams of (a) the mold assembly structure, and (b) real machined mold assembly.

The milling process consists of rough milling and finish milling. For rough-milling cycle, the spindle speed and feed rate were 40,000 rpm and 5 mm/min. While for the finish-milling cycle, the 29 spindle speed and feed rate are 40,000 rpm and 2 mm/min. No post-machining work was done after the finish cycle on the mold inserts.

(a) (b)

Figure 2.4 (a) Schematic diagram of temperature, position and force variation during As40Se50S10 molding process, and (b) molded wedge (prism).

Glass molding experiments were performed on a commercial molding machine, DTI bench top

GP-10000HT glass press. The variation of temperature, position and force during As40Se50S10 molding process is shown in Figure 2.4 (a). The simulation results were also inserted in the Figure

2.4 (a) to verify the thermal conditions inside the chalcogenide. Before molding, a glass preform was placed on the lower mold sitting in the groove. Three cycles of purge between vacuum and nitrogen were conducted to prevent mold oxidization at elevated temperature. The ramp rate of heating was set at 50 °C/min. After the chamber temperature reached the desired temperature

220 °C for 20 mins, the upper mold moves down to press the preform with a constant load of 75

N. Based on the simulation result, it is noted that the preform was uniformly heated up to 220 °C 30 before molding process. After molding is completed, the cooling stage started with both vacuum and fans turned on. The mold chamber was opened when the chamber temperature was lowered to below 60 °C. These conditions were identified based on previous experiences and FEM simulations in molding of similar materials. The final molded wedge, demolded from the molds after molding, is presented in Figure 2.4 (b).

2.1.4 Shape Measurement

After the mold inserts and the wedge are machined, measurements are conducted on Wyko

NT9100 optical profilometer. Only the section at the optical surface of the mold was measured.

The surface topography of the mold and its corresponding surface on the molded wedge were obtained from the measurements as shown in Figure 2.5 (a). The roughness (Ra) values of these surfaces are 15.64 nm and 17.59 nm. Figure 2.5 (b) shows the measurement results of the sectional profile of the two surfaces. As can be seen, compression molding can replicate micro features with high precision. Errors caused by warpage and shrinkage can be reduced by optimization the molding parameters, such as temperature and load. In the inserted local profile, the largest deviation between the mold and the replicated wedge is around 5~6 nm. The angle of the molded wedge is

10.008 degree, versus the design value of 10.00 degree.

Figure 2.5 Schematic diagrams of (a) 3D surface morphology, and (b) section profile.

2.1.5 Optical Measurement Setup

The optical metrology setup was based on deviation measurement of light by a prism molded using chalcogenide infrared optical material. A schematic diagram of the experimental arrangement is shown in Figure 2.6 (a). Figure 2.6 (b) depicted the setup of the measurement experiment. The deviation angle was measured by using a precise rotary stage (ADRT-150, Aerotech Inc.,

Pittsburgh, Pennsylvania) with accuracy of 5 arc sec. An infrared detector is placed at the end of the rotation arm that is mounted on the 3D precision positioning stage (~1 µm). The detector was a longwave infrared (from 8.0 to 12.00 µm) camera module (FLIR Lepton, FLIR Systems Inc.,

Wilsonville, Oregon) which consists of a focal plane array of 80 × 60 active pixels. The light source was a multiple wavelength coil-wound (ranging from 6.0 to 14.00 µm), supported IR source

(HawkEye Technologies, Infrared Source IR-35, Milford, Connecticut) mounted on a TO-5 header combined with a parabolic reflector to collimate the infrared light beam. Several slits were fabricated and placed in the optical path to make sure that the infrared light goes straight toward

32 the camera. The temperature of the prism was measured by a thermocouple. Measurements were conducted at room temperature.

Figure 2.6 (a) Diagram of the optical setup used to measure infrared refractive index, and (b) measurement setup.

The measurement procedure is demonstrated in Figure 2.7. It begins without the infrared glass wedge located at the initial position of the system as shown in Figure 2.7 (a). The infrared monochromatic light passes through the apertures and a light spot was formed on the detector behind the aperture. After that, the molded infrared glass wedge was installed onto the optical stage, which aligned with the axis of the rotary table. Measurement of the refracted beam angle was done by sweeping the detector around the center of the rotary table. When the light spot overlapped the initial position on the detector, the refractive index can be calculated based on Equation 2.2-2.5. An advantage of the method is that the setup was easy to complete and was accurate as demonstrated by previous studies for refractive index measurement [50].

Figure 2.7 The procedure for measuring refractive index.

2.1.6 Process Method of Image

In order to locate the beam spot more precisely, some operations were conducted to obtain the precise position of the light spot in this measurement. Figure 2.8 (a) is an example of an image obtained with the infrared detector. Due to the large noise from the surrounding environment, the pictures from the infrared camera need to be further processed. The first step is to average 20 images shot every ~0.5 s to minimize the random error from surroundings and system. Then transform the image to the grey-scale image based on intensity distribution, as shown in Figure 2.8 (b). After that, setting different threshold values for the intensity, only the central part will be obtained but with different sizes and areas. The threshold value was then determined by the diameter of the infrared light beam. Each pixel of the infrared detector was 17 μm×17 μm. We adopted the threshold value that the central part will be the same size with the beam area. Figure 2.8 (c) showed a monochromatic image based on intensity of the original image after the background noise was filtered out. During this process, the light spot was located and labeled. The resolution was 1/2 pixel based on this method. Its luminance-weighted centroid was obtained and the central spot was indicated in the figure as well.

(a) (b) (c) Figure 2.8 (a) Original image obtained with the infrared detector, (b) intensity of the original image, and (c) monochromatic image with the central point labeled.

2.1.7 Refractive Index Distribution inside Molded Wedge

As aforementioned, the volume of the molded glass after undergoing thermal process will expand and the refractive index decrease according to the Equation 2.6. Based on the simulation results, the volume of each mesh is obtained (Figure 2.9 (a)) and the calculated refractive index change distribution within the wedge is shown in Figure 2.9 (b) and (c). The refractive index change inside the wedge is fairly uniform (variation ~10-2) because the dimensions of the infrared glass are small

(the initial preform volume of the glass was ~12.2 mm3). The non-uniformity is accounted by the residual thermal stresses inside each mesh [26]. Compared with the index change in the reheating- cooling process, the uniformity inside the wedge can be ignored. Therefore, the refractive index change inside the wedge can be regarded as the average index change.

In order to clearly display the refractive index change distribution of the molded wedge, each element with different refractive index change is obtained by Equation 2.6. Statistics showed that the mean value of refractive index change is -0.0226 for As40Se50S10 glass with standard deviation

0.0013.

Figure 2.9 (a) Mesh volume change of the molded wedge compared with the initial preform (Vf/V0), refractive index change distribution of the molded wedge (b) 3D view, (c) cross-section view, and (d) statistic result of the refractive index change.

2.1.8 Measurement Experiment

Based on the assumption that the refractive index inside the wedge is uniform, the experiments were conducted at room temperature to measure the refractive index of the molded wedge. The deviation angle was composed of the initial angle and the final angle. The value was recorded in

Table 2-1. So the refractive index was calculated and recorded. Multiple averages are taken to reduce uncertainty.

Based on the measured deflection angle, the refractive index drop is about -0.0226±0.0027 at a cooling rate of 36 K/h, and the calculated results are comparable with the simulation results and other similar chalcogenide glasses in previous researches [16].

Table 2-1 Infrared refractive index results for As40Se50S10 glass

Initial Angle Final Angle Refractive Angle Calculated Index 1 -5.4152 11.7347 17.1499 2.6885 2 -5.4263 11.7149 17.1412 2.6876 3 -5.4252 11.7497 17.1749 2.6909 4 -5.4202 11.7595 17.1797 2.6913 5 -5.4302 11.7597 17.1899 2.6923 6 -5.4205 11.7595 17.1800 2.6914 7 -5.4192 11.7742 17.1934 2.6926 8 -5.4057 11.7642 17.1699 2.6904 9 -5.4045 11.7381 17.1426 2.6878 10 -5.4214 11.7548 17.1762 2.6910 Average -5.4188 11.7509 17.1499 2.6903

2.1.9 Conclusions

In this article, the refractive index change of As40Se50S10 glass was studied by both experiment and simulation. First, FEM simulation was conducted to investigate the refractive index distribution in a molded wedge. Because the cylindrical preform is quite small in size, the refractive index non- uniformity is relatively small (about 10-3). Second, an optical measurement experiment was performed. High-speed single-point diamond milling was used to fabricate a detachable mold insert and the infrared glass wedge was fabricated using compression molding process. The molding result and numerical simulation both show that the refractive index of As40Se50S10 glass underwent 37 a significant drop during/after the molding process. This index change was measured to be approximately 0.0226 lower than the nominal value, which should be taken into consideration in lens design. The results can serve as reference for optical designers and manufacturing engineers in developing manufacturing processes to fabricate optics by compression glass molding.

2.2 Distribution of Index Change and Residual Stress

As2S3 used in this study is a very common chalcogenide glass often processed by PGM. Previous researches have studied some characteristics, such as tensile strength [51], structural relaxation [20] and stress relaxation under certain conditions [16]. To conduct a reliable and accurate numerical simulation, it is essential to employ appropriate constitutive models that can accurately describe the behavior of chalcogenide glass undergo PGM process. Based on the previous works on chalcogenide glasses, temperature-dependent rheology could be modeled by the classical phenomenological Vogel-Fulcher-Tammann (VFT) equation or the thermo-rheological simple

(TRS) phenomenon. Moreover, the Williams-Landel-Ferry (WLF) equation and the Tool-

Narayanaswamy-Moynihan (TNM) model are commonly adopted to describe shear stress relaxation and structural relaxation behavior in PGM [18], respectively. Thus, a constitutive model based on experiments is used to predict the complex behavior of the chalcogenide glass in this research.

The aim of the study is to investigate the thermal forming mechanism in PGM and evaluate the optical properties changes in and post PGM. To precisely describe the behavior of As2S3 during such a process, a constitutive model is introduced to describe and predict the formation mechanism of PGM. Based on the results, the geometric deviation, residual stress and refractive index variation 38 will be analyzed by the FEM results. Finally, optical experiments are introduced to evaluate the refractive index variation and residual stresses inside the molded optical components. The combined results can serve as reference for optical designers and manufacturing engineers in developing intelligent manufacturing processes to mold infrared optics by PGM.

2.2.1 Methodology

2.2.1.1 Investigation of Photoelasticity in Molded Glass

The measurement of residual stresses is based on birefringence in molded glass, which comes from the photoelastic effect [52]. When a polarized light beam impinges onto the test glass, a stress-free glass without long-range order does not change its isotropic refractive index. However, when a glass element is under stresses, whether undergoes thermal treatment or external loads, the optical properties inside the material is no longer uniform due to stresses [53].

According to previous studies on transparent materials, there is a quantitative relation between residual stresses inside glass and its refractive index. If the principle refractive index of a glass coincides with the principle stresses at a point in the sample, the refractive indices along the principle axes are related to the principle stresses as follows,

푛1 − 푛2 = 퐶(휎1 − 휎2) Equation 2.7

푛1 − 푛3 = 퐶(휎1 − 휎3) Equation 2.8

푛2 − 푛3 = 퐶(휎2 − 휎3) Equation 2.9

39 where C is the stress-optic constant. ni are refractive indices and σi are the principle stresses along the principle axes.

There are three normal stresses (σx, σy and σz,) and two shear stresses (τxy and τyx) inside the cross section of the simulation model as shown in Figure 2.10. The principle stresses can be obtained from the normal stresses and shear stresses as follows [52],

1 휎 = (휎 + 휎 − √휎2 + 휎2 − 2휎 휎 + 4휏2 ) Equation 2.10 1 2 푥 푦 푥 푦 푥 푦 푥푦

1 휎 = (휎 + 휎 + √휎2 + 휎2 − 2휎 휎 + 4휏2 ) Equation 2.11 2 2 푥 푦 푥 푦 푥 푦 푥푦

휎3 = 휎푧 Equation 2.12

휏푥푦 tan 2휃 = (휎 −휎 ) Equation 2.13 푥 푦 ⁄ 2

where θ is the inclination angle between the incident light beam and the principle stress σ1 when the incident polarized light was parallel to x direction as shown in Figure 2.10. The optical retardation of a glass lens under residual stresses can be calculated by the modified Wertherim law as follows [54],

2 2 훿 = 퐶(휎1푠푖푛 휃 + 휎2푐표푠 휃 − 휎3)푑 Equation 2.14 where d is the distance along the light path through the material. C is the stress-optic constant for the chalcogenide glass used [55].

Figure 2.10 Schematic diagrams of simulated stresses and principle stresses in a unit cube.

The principle of the measurement was schematically illustrated in Figure 2.11. The polariscope consists of three major components, including an illustrator or light source and two plane polarizers.

The light intensity behind the polarization lens can be expressed by using the equations, as follows [53],

Δ 퐼 = 퐼 푠푖푛22휑푠푖푛2 Equation 2.15 0 2 where φ is the inclination angle between the principle stress and axis of polarization. The phase difference Δ is related to the wavelength λ of the light wave.

훿 Δ = 2휋 Equation 2.16 휆

Figure 2.11 Photoelastic model in a modified dark-field plane polariscope. 41

2.2.1.2 Wavefront Reconstruction Based on Refractive Index

The infrared beam wavefront cannot be directly obtained from the ABAQUS simulation. However, based on the refractive index of each mesh, the wavefront can be reconstructed, as shown in Figure

2.12. The optical path L(x, y) distribution through the thermally treated glass lens is defined by [56],

퐿(푥, 푦) = 푛(푥, 푦)푡(푥, 푦) Equation 2.17 where n(x, y) is the refractive index distribution of the molded lens. t(x, y) is the thickness of the molded lens. Since the molded lens is deviated from the initial profile, the actual thicknesses at different positions are determined by the simulation results.

It is known that if a light ray passes through an isotropic optical material, the light will be bent on the interface between two different meshes with different refractive index based on the Snell’s law.

푛1 sin(휃1) = 푛2sin (휃2) Equation 2.18

푛2 sin(휃3) = 푛1sin (휃4) Equation 2.19

where n1 is the refractive index of the medium in which the light enters, and n2 is the refraction index of the medium in which the light leaves. θ1, θ3 and θ2, θ4 are the angles of incidence and refraction, respectively.

Assume the refractive index of air is 1 (n1= 1), then the total optical path travels certain distance d in optical axis is as shown in Figure 2.12. 42

Figure 2.12 Wavefront reconstruction based on ray tracing method.

2.2.2 FEM Simulation of Glass Molding

Employing the constitutive model stated above, a numerical platform for PGM was established using ABAQUS with a subroutine (UMAT). Using the axis-symmetry of the set-up, simulation of a quarter of the three-dimensional (3D) model with symmetric boundary conditions was adopted to reduce calculation time while maintaining simulation accuracy, as shown in Figure 2.13 (a). The upper and lower molds were made of an aluminum alloy (Al 6061). They are treated as linearly elastic but with a high Young’s modulus of 68.9 GPa, Poisson’s ratio of 0.33, and thermal conductivity of 15.4 W/(m·s). The upper mold is convex spherical with a radius r = 420 mm, while the lower mold is a plan. The friction coefficient of the contact surfaces between the molds and chalcogenide glass was set as 0.1 and with the thermal conductance coefficient of 2,500 W/(m·s).

In FEM simulation, the set-up was meshed into displacement-temperature coupled elements.

A typical force-control compression molding process consists of four stages, including heating, soaking, pressing and cooling, as shown in Figure 2.13 (b). The whole process was conducted and the temperature variation & loading force were monitored in the simulation. Initially, the entire 43 simulation model was pre-set at room temperature (20 °C). In the heating stage, the entire simulation model was heated evenly from 20 °C to 220 °C in 440 s. After heating is completed, the upper mold moved down and kept near to the preform for 300 s. When the chalcogenide glass preform was heated to 220 °C, the upper mold began pressing on the glass preform. During pressing phase, a constant force 100 N was applied until the desired displacement was reached. The material was driven to contact all the area of the mold completely. The cooling stage was then followed. In this stage, temperature inside the glass was different from temperature of the molds because of different contact thermal conductivity. The cooling stage has taken long time until temperature of the molded lens was cooled down to room temperature. In order to study the effect of cooling rate, two cooling rates, 360 K/hr and 1,800 K/hr, were applied for the cooling process.

Figure 2.13 (a) FEM model for simulation of precision glass molding, and (b) histories of the applied temperature and load during the initial heating, soaking, pressing and cooling.

2.2.3 Fabrication of Infrared Molded Lens

In this paper, the molds were fabricated by single-point diamond turning on the Nanotech 350 FG

(Moore Nanotechnology Systems, Keene, New Hampshire, USA). Aluminum alloy 6061 was selected for mold fabrication for its high machinability, thermal conduction and steady mechanical 44 properties at elevated temperature. The mold surfaces were first diamond turned with 1,000 rpm spindle speed and 10 mm/min feed rate. Then the surface profile was fabricated by slow tool servo.

For rough-cutting cycle, the cutting depth is 10 μm, and the feed rate is 5 mm/min. For finish cutting, the cutting depth and feed rate are 5 μm and 3 mm/min, respectively. No post machining process was performed on the molds after diamond turning.

The molds were mounted on a commercial compression molding machine Model GP-10000HT

(Dyna Technologies, Inc., Sanford, Florida, USA) to form concave infrared lens (r = 420 mm).

The molding process can be divided into four phases, including preparation, heating, pressing and cooling. The entire process was shown in Figure 2.14. A piece of As2S3 chalcogenide glass preform

(double-side polished with 11 mm radius and 2 mm thickness) was placed between the upper and lower mold. After three cycles of purge were conducted, temperature was elevated to 220 °C at

1,800 K/hr and remained at this temperature for 10 min. Then a 100 N load was applied to the upper mold for 6 min to ensure that the molded profile conform to the mold insert.

Figure 2.14 Schematic diagram of the glass molding process for infrared optics. 45

2.2.4 Variation of Lens Profile

Previous studies have proven that the final profile of the molded lens directly influenced the optical behavior [2,57]. The final profiles of the molded lens were extracted from simulation and experiment using white interferometer (Wyko NT9100, Bruker AXS Inc., 5465 East Cheryl

Parkway Madison, WI, USA). Figure 2.15 (a) shows the final profiles of molded lenses during molding with cooling rate of 360 K/hr by both experiment and simulation. The geometry of the replicated features by simulation and experiment matched each other as well as the original design.

The details of deviation of the lens profiles with respect to the original design were illustrated in

Figure 2.15 (b). The largest deviation of the profiles occurs near the center of the molded lens (less than 1 μm) at two different cooling rates of 360 K/hr and 1,800 K/hr.

In order to explain the deviation happened in the molding process, the profile of the lens in the pressing and cooling stages were obtained from FEM simulation with cooling rate of 360 K/hr, as shown in Figure 2.15 (c). During the pressing phase, glass preform was compressed to the shape of the mold. When pressing was completed and the load was removed from the mold, the lens did not move away from the mold shape thus the profile of the lens matched the mold’s curvature. In the cooling stage, a more noticeable deviation appeared near the center of the lens from the mold temperature (220 °C) down to the transition temperature (~185 °C). Then the profile deviation of the molded lens increased slowly from the transition temperature down to room temperature

(20 °C). As explained above, the largest deviation near the center was mainly associated with thermal shrinkage and structural relaxation in cooling phase.

Figure 2.15 (a) Profiles of molded lens obtained from simulation and experiment, (b) deviation with respect to the mold geometry of the final molded lens at two different cooling rates, (c) evolution of a molded lens profile from simulation, and (d) the profiles of lenses with different cooling rates of 360 K/hr and 1,800 K/hr by simulation.

Figure 2.15 (d) showed the final profiles of the simulation results with different cooling rates of

360 K/hr and 1,800 K/hr, respectively. In the inserted figure in Figure 2.15 (d), the profile with large cooling rate of 1,800 K/hr was much closer to the original desired mold shape. Due to the structural relaxation with large cooling rate, the material was much further away from equilibrium state with a larger volume than that after annealing. However, large cooling rate leads to higher inner residual stresses or local stress concentration [58]. Thus, to obtain a precision molded lens profile, accurate compensation in mold design is necessary.

2.2.5 Residual Stresses Prediction and Measurement

2.2.4.1 Experiment Measurement

In the experiment, a plane polariscope (PS-100-SF, Strainoptics Inc. North Wales, PA, USA) was employed to measure the residual stresses inside the molded lens by birefringence method. The principles of the measurement were described above, as illustrated in Figure 2.11. The molded lens was first placed between the polarizers and the analyzer can be rotated around the central axis to adjust the fringe color of the point. Because the axisymmetricity of the molded lens, directions of the two principle stresses at the edge were either parallel or perpendicular to the edge. The polarizer was rotated to a position when the dark fringes appeared on the sample. The dark fringe appeared when the quarter wave plate introduced an equal amount of retardation at the point of interest.

Pseudocolors were used to show light intensity.

2.2.4.2 FEM Prediction

Another factor influences the optical quality of molded lenses is the residual stresses inside the molded components [59]. Large residual stresses inside the molded lenses will lead to deformation and inhomogeneous refractive index in optical elements [60]. Because chalcogenide glass undergoes a sudden thermal change at the instant of forming, the internal stresses are generated inside the molded infrared lens immediately.

In a PGM process, although internal stresses were initially generated in the heating stage, it disappeared quickly as the temperature was above Tg, and subsequently the stresses generated during pressing also dissipated quickly at elevated temperature. The internal stresses remained at very small level (<1.0 MPa), and also relaxed in very few seconds or less. After cooling began, 48 when temperature was decreased to around 185 °C, the internal stresses were moved up sharply and remained around this level until the end of PGM process. The stress along the rotational axis was presented in Figure 2.16 (a) during the entire process. In addition, temperature distribution along the axis was also obtained, as shown in Figure 2.16 (b). It is noted that during pressing, temperature variation is very small, and the glass preform was in viscoelastic state. At round 185 °C in the cooling stage, temperature on the molded lens surface is very different from that of the center of the molded lens. Glass in the center was still in viscoelastic state, while the materials around the edge already solidified. Because temperature variation along the lens rotational axis, the coefficient of temperature expansion was inhomogeneous, leading to uneven volume shrinkage. Figure 2.16

(c) shows the evolution of internal stress at the center of the molded glass with different cooling rate. Due to smaller temperature variation in the cooling stage on the surface and center, lower cooling rate could reduce residual stresses more efficiently.

To verify the simulation results, the optical retardation based on simulated residual stresses through the glass lens can be obtained by the Equation 2.10-2.16. The optical retardation of each mesh was calculated and then integrated into the entire concave lens. Figure 2.17 showed the simulated residual stresses distribution along x-y cross section of the molded chalcogenide lens with different cooling rates of 360 K/hr and 1,800 K/hr. Based on the stresses distribution map, the σyy and σzz were dominant stress components. At the edge of the molded lens, the σxx and τxy were much higher.

In general, the residual stress components inside the molded lens with cooling rate of 1,800 K/hr were much larger than that with 360 K/hr.

The intensity distribution using the numerical simulation results with a monochromatic light of

632.8 nm wavelength [24], as illustrated in Figure 2.18 (a) and (b), which was similar to the images obtained from plane polarizer shown in Figure 2.18 (c) and (d). The light intensity along the radius indicated that the optical retardation varied from center to edge. The dark zone in the center area demonstrated that the direction of principle stresses was parallel to the axis of the polariscope.

Figure 2.18 (e) and (f) showed the normalized intensity along the rotational axis φ = 45 degrees in the molded lenses with different cooling rates and the measured light intensity, respectively. The results showed a good agreement of the simulation and experiment results between two different cooling rates of 360 K/hr and 1,800 K/hr. The deviation between the simulation results and experimental measurements came from the inaccuracy of material model, initial conditions of glass, and surrounding noise in the measurement. The agreement verified that the numerical simulation was a very efficient way to estimate the residual stress inside the molded lenses.

2.2.6 Refractive Index Prediction and Measurement

2.2.6.1 Experiment Measurement

The refractive index change inside the molded lens was calculated by measuring the wavefront out of the concave lens. The wavefront variations were obtained by using an infrared Shark-Hartmann wavefront sensor (SHS) [56]. In this setup, the wavefront image was collected by an infrared microlens array, as illustrated in Figure 2.19 (a). The distance between the infrared detector and the microlens array can be precisely adjusted by the positioning stage. The molded lens was placed in front of the microlenses to generate the focal spots on the infrared detector. The detector used for infrared (IR) SHS is a commercial grade camera (ATOM 640, Sofradir EC, Inc., Fairfield, New

Jersey, USA). The detailed measurement and calculation algorithm will be included in a different publication [61]. Figure 2.19 (b) and (c) presented the reference image and the measurement image with 8.0 µm infrared light with the identified valid feature points, respectively.

Figure 2.19 Schematic diagram of the setup of the SHS experiment for wavefront measurement.

2.2.6.2 FEM Prediction

Refractive index is another important property of precision molded optical lens [9,34]. Refractive index variations in a molded lens will introduce distortion to the wavefront passing through the lens.

Based on Equation 2.6, the index change was related to the density for the transparent material. As density is inversely proportional to volume, the refractive index is also a function of glass’s volume [62]. Because of the sudden temperature change in PGM, volume of the glass will experience an immediate change follow by graduate relaxation. Moreover, the inhomogeneous temperature distribution and variation inside the molded lens, and structural relaxation during cooling lead to different volumes after molding, which further impact the distribution of refractive index in the final molded lens. Up to now, volume change of glass molding process for chalcogenide glasses has not been studied in great length, except some analysis of final refractive index change [63].

In this research, cooling at 2 K/hr is considered the reference annealing rate that the glass sample was initially cooled at [16,46]. Volume of the chalcogenide glass cooled at this cooling rate was predicted by using simulation results. The simulated volume at this low cooling rate was accepted as the original volume or initial volume of the glass for all further calculation.

In order to reveal of the refractive index transformation during molding, the change of glass density was monitored during the pressing and cooling phases, as illuminated in Figure 2.20 (a)-(c). The density distribution inside the molded lens was not uniform during the pressing stage, even above the Tg (~185 °C). The non-uniform density of the surface layer was much larger than that of the center region and then remained so until the end of the PGM process. Figure 2.20 (b) and (c) 53 showed the normalized volume distribution of the molded lens. The mean density changes are around -0.51 % and -0.36 % drop with cooling rates of 360 K/hr and 1,800 K/hr, indicating that the fast cooling rate would lead to smaller volume change. Figure 2.20 (d) presented the volume change of the chalcogenide glass during the cooling stage. The curves also showed that with a faster cooling rate, volume of the glass was larger than that with a slower cooling rate, indicating that the final state deviated from minimum-energy balance further.

The refractive index change distributed inside the molded lens was extracted from the simulation result with 360 K/hr cooling rate, as shown in Figure 2.21 (a). The profile of the refractive index change inside the molded lens was similar to the density distribution. The refractive index variation across the lens varied from -0.05 to 0.01. The formation of refractive index variation is closely

54 related to the structural relaxation, while the uneven distribution of the refractive index change is due to thermal history and heterogeneous deformation of the surface and central zone. The stresses generated in the cooling phase and surface curve further influenced the structure relaxation and refractive index profile in the molded lens. The statistical results of the measurement data also suggested that the refractive index change was concentrated in one small range, as shown in Figure

2.21 (b). The mean value of the refractive index change was -0.0174 with 0.010 standard deviation.

However, the index drop at cooling rate of 360 K/hr is much larger than that of oxide glass and optical polymers, such as polymethylmethacrylate (PMMA) and polycarbonate (PC). It should be considered in the optical design to ensure proper optical performance of the molded lenses.

Figure 2.21 Refractive index change distribution inside the molded lens (a) x-y cross- section view, and (b) statistic distribution of the refractive index change.

Furthermore, an optical experiment was conducted to prove the predicted results from simulation.

Figure 2.22 (a) and (b) showed the reconstructed wavefront variation at the cooling rate of 360 K/hr by simulation results and experimental measurement, respectively. The results from simulation and experiment are very close. Limited by the aperture of the SHS sensor, only 40% central area

(diameter = 8.0 mm) of the infrared wavefront passing through the molded lens is collected. The 55 maximum error is 2.17 × 10−3mm across pupil areas shown in Figure 2.22 (c), which is 0.266 waves since an 8.0 m wavelength of the infrared source was employed. The deviation along A-A and B-

B in Figure 2.22 (d) was also obtained. This error mainly comes from deviation in molding experiments and misalignment of the measurement system as shown in Figure 2.22 (d). In order to validate the accuracy of experiments, five supplemental measurements were conducted to avoid random noise. This part of the research has demonstrated that the performance of the simulation results was accurate in index change prediction.

2.2.7 Conclusions

Precision molding of chalcogenide glass lenses was successfully modeled by integrating viscoelastic, stress relaxation and structural relaxation theories using a commercial FEM software with user defined subroutines. This model was based on classic mechanics and can be easily implemented in FEM simulations to study the deformation mechanism in viscoelastic state in compression molding of chalcogenide glass optics. Furthermore, the simulation results were further conducted to reveal the optical property changes after molding. The experiments under the same molding conditions used in the simulation were performed on a precision glass molding machine to verify the simulation results. Lens profiles, residual stresses and refractive index change in the molded glass lenses were carefully studied by performing both FEM based numerical simulation and direct measurements using interferometry, birefringence method, and wavefront reconstruction.

Some of the key contributions of this work are summarized as follows.

(1) Numerical simulation using a commercial FEM software with user defined subroutines representing constitutive equations was used to study compression molding of chalcogenide glass considering stress relaxation and structural relaxation. The results can be used to predict lens profile, residual stresses and index change of compression molded optical components.

(2) The molded lens profile was measured using an optical profiler. Comparison between design and the numerical simulation results shows a reasonable agreement.

(3) By using birefringence method, the residual stresses inside the molded components can be obtained. The stress distribution closely matches the numerical simulation results, which further verified the use of numerical simulation in chalcogenide glass molding.

(4) The amount of index change and distribution can be accurately predicted by FEM using the

Tool-Narayanaswamy-Moynihan (TNM) model. Due to structural relaxation, volume of glass will change under different cooling rate after a reheat-cooling thermal cycle in a typical molding process.

(5) Also in this research, the refractive index changes of As40S60 were carefully studied by using the TNM model for structural relaxation behavior. Based on the relationship between volume variation and index change, the refracted wavefront of a parallel light beam by a molded lens was further simulated. Comparing the calculation and test measurements, reasonable agreement was obtained and the results demonstrated that the index drop (~0.0174) occurred inside the As40S60 lens that was molded at 360 K/hr cooling rate.

CHAPTER 3: DEMONSTRATIONS OF INFRARED MICRO OPTICS BY PRECISION GLASS MOLDING

The current chapter involves two infrared optical demonstrations of precision glass molding on chalcogenide glass, including a plano-convex microlens array for Shack–Hartmann wavefront sensor (SHS) and a freeform large field-of-view microlens array. Two novel machining strategies are proposed for symmetrical feature fabrication. The molded geometrical profiles and optical performance were obtained.

3.1 Shack–Hartmann Wavefront Sensor

Since its invention from the early seventies, the Shack-Hartmann wavefront sensor (SHS) has been widely employed in a variety of applications and achieved great successes in ophthalmology and adaptive optics [64]. The SHS is a unique but important optical device used for wavefront detection and measurement. However, limited by available manufacturing technologies, most of inventions in SHS is focused on work in visible band in the following areas: collimation [65], arithmetic [66,67], dynamic range [68,69] and manufacturing method [70–76]. The SHS working in the infrared range is rarely reported, especially for affordable SHS systems.

As a key component in precision glass molding tool, the mold insert can be fabricated using several methods. These methods include ultra-violet (UV) lithography [70–72], diamond turning [73], diamond micro-milling [74], diamond flycutting [75], and electroforming process [76]. However, the fabrication methods based on lithography process must be combined with other processes, such as plasma etching and isotropic silicon wet etching. In comparison, ultraprecision diamond turning, milling and flycutting methods do not require other mechanical process with more flexibility and high precision. Our previous work demonstrated that the typical microlens array were fabricated by combining single-point diamond turning and injection molding [61]. There are minor deviations in geometry and surface roughness between the mold insert and the molded microlens array.

However, the single-point diamond turning has drawbacks. A relatively small bandwidth due to the large inertia of the mechanical slides may lead to a low productivity.

Furthermore, with respect to some complex discontinuous geometries, serval innovative diamond turning methods have been proposed. For instance, diamond micro chiseling and special Guilloche machining technique are proposed to generate retroreflective and microstructure array [77], respectively. However, these methods are not suitable to generate structures with variable shapes.

Virtual spindle based tool servo diamond turning is another approach in discontinuous geometry manufacturing [78]. However, even equipped with a fast tool servo, the relatively small traveling range, typically much less than 1 mm [61], limited its manufacturing potentials. In this project, we chose single-point diamond milling to fabricate the microlens array mold insert.

In this section, an infrared plano-convex microlens array is designed and fabricated by combination of virtual spindle based single-point diamond milling and precision glass molding process. Aided

60 by minimum-area tool-path generation arithmetic, the virtual spindle based single-point diamond milling provides a universal and effective solution to the fabrication of microlens array on the mold insert. Chalcogenide glasses, instead of traditional infrared materials such as Ge or ZnSe, are selected for the production of high-precision molded microlens array. The geometries and surface roughness of the molded microlens array are measured and examined. Assembled with an IR detector, the optical property of the microlens array and the validity of the SHS are demonstrated as well.

3.1.1 Virtual Spindle Based Single-point Diamond Milling

3.1.1.1 Kinematics of the Virtual Spindle based Single-point Diamond Milling

The kinematics of moving virtual spindle is illustrated in Figure 3.1. The om-xmymzm and ot-xtytzt are the machine coordinate and working coordinate, respectively. At the initial stage, the machine coordinate is coincident with the working coordinate, as show in Figure 3.1 (a). Meanwhile, the three directions of the local coordinate of lenslet os-xsyszs are set the same with the machine coordinate. During machining, the machine coordinate remains unchanged, while the working coordinate is being shifted from one local coordinate to another one at a time, as shown in Figure

3.1 (b) and (c).

Figure 3.1 Schematic of kinematics of the virtual spindle based single-point diamond milling, (a) initialization of the diamond milling, (b) position and axis transfer, and (c) spiral milling.

In order to generate the geometry of each lenslet on the plane surface, the position of the working coordinate needs to be changed from one place to another and each local machining process to be treated as an independent one. The details of this process can be summarized in the following steps.

Step 1, initialization. Like conventional diamond turning, the working coordinate ot-xtytzt is first moved to the center of the work chuck and coincided with the machine coordinate om-xmymzm. Each local coordinate os-xsyszs of a lenslet was virtually constructed with the same directions of the machine coordinate, as shown in Figure 3.1 (a).

Step 2, position transfer. Transfer the working coordinate ot-xtytzt to the local coordinate os-xsyszs by moving the 2D slides of the machine (Δx and Δy). Because the direction of these three coordinates are the same, the working coordinate and the local coordinate are coincident, as shown in Figure 3.1 (b).

Step 3, rotation around virtual axis. In the local coordinate, the oszs was set as the rotation axis. To make the point os is the fixed point on the os-xsys plane, the rotation motion around the oszs virtual axis was induced by the harmonic oscillations (Δx(t) and Δy(t)) with the same frequency on the xs- and ys-axis, as shown in Figure 3.1 (c).

Step 4, local spiral diamond milling. Since the working coordinate and the local coordinate were coincident, similar to the conventional diamond milling process, the diamond milling tool is moved to the surface and the geometry of each lenslet is generated as an independent process. When the lenslet was finished, repeated the Step 2 and Step 3 for the next lenslet milling until every microlens is completed.

3.1.1.2 Toolpath Generation Arithmetic

In order to have a clear description and understanding of the machining process, further works on toolpath generation should be given. The toolpath for the hexagonal microlens array is generated by MATLAB. The pitch and radius of curvature for each lenslet are 600 µm and 8.845 mm, respectively.

Based on the machining strategy for the microlens array stated above, the toolpath of the diamond tool in the machine coordinate om-xmymzm is illuminated in Figure 3.2 (a). As aforementioned, the toolpath for each lenslet of the microlens array can be treated as an independent machining process.

After one lenslet was finished, the working coordinate ot-xtytzt is transferred to another position and coincided with the local coordinate of the lenslet. By shifting each local coordinate of the lenslet, the entire microlens array can be finished in sequence.

To enhance machining efficiency of the milling process, the servo motion along the zm direction was also optimized by following the principle of minimum fabrication area. As illuminated in

Figure 3.2 (b), similar to the conventional toolpath generation strategy, the toolpath for the diamond milling tool was divided into serval segments with constant cutting depth. However, each segment of the toolpath was different in length and coverage area. In this research, for example, in the first cycle, the material only in the central part was removed from the surface, which covered a very small area. The surface outside the envelope curve remained. After the 1st cycle, the diamond milling tool directly began the 2nd cycle with large coverage. Such process would continue until the entire surface of the lenslet was generated. Unlike the conventional toolpath generation strategy, the minimum-area strategy reduced the machining time by taking out invalid toolpath in surface area.

3.1.1.3 Finish Geometry Measurement

At the start, the mold insert was rough machined on a common Haas VF-3 3-axis vertical machine center (Haas Automation, Inc., Oxnard, California, USA) from a 6061 aluminum alloy rod. For the final finish surface, an ultraprecision lathe (Moore Nanotechnology, Inc., Keene, New Hampshire, 64

USA) with five-axis servo motions was employed to generate the microlens array. The diamond milling tool (K&Y Diamond, Ltd., Diab St-Laurent, Quebec) has a 0.503 mm tool nose radius that was compensated in the generation for spiral tool path trajectory. For all the molds used in this research, initial milling depth was 5-10 µm and finish milling depth was 2.0 µm at 60,000 rpm.

The feedrates for rough and finish milling were set at 10 and 5 mm/min, respectively.

Figure 3.2 Schematic diagrams of (a) the virtual spindle based single-point diamond milling toolpath generation, and (b) optimization arithmetic by minimum-area fabrication.

After machining, the optical surface profiler, white-light interferometer (Wyko NT9100, Brukner.,

Tucson, Arizona, USA) was employed to capture the microstructures of the machined surface, with

2D and 3D features. The microscope photograph of the machined surface is illuminated in Figure

3.3 (a), which shows that the machined microlens array has good uniformity. The 2D surface profile further proved that the finished surface was smooth with really sharp line at the interaction edge, as shown in Figure 3.3 (b). Besides, the surface roughness of the lenslet was around 15.6 nm, adequate for requirements of infrared optics. Moreover, a 3D surface profile was presented in

Figure 3.3 (c) with an area of 3.0×3.2 mm by stitching multiple details. Finally, the cross-section profile on the A-B line was obtained from the 3D surface measurement.

As illustrated in Figure 3.3 (d), the 2D cross-section profile of the A-B line, the aperture of the machined lenslet is 605.2 µm. Compared with the designed value 600 µm, the profile of the machined surface matched the initial design well. The depth of each lenslets is 5.503 µm, close to its theoretical value 5.089 µm. The microscope photo also showed that the central machined surface of each machined lenslet was rough and dim, which indicated that the quality of this local area was worse than the surface around it. This was mainly due to two reasons. One was the sampling frequency on the spiral curve near the center got lower than that on the spiral with large radius.

Even the incensement is reduced to half of the initial one, the quality of the machined surface almost

66 did not improve in response. The other reason could be that the tangiental cutting speed became smaller when the milling tool approached to the center of the lenslet. Based on the tool compensation strategy stated in section 3.1.1, when the milling tool moved to the central point, the contact point gradually transferred to the central rotation axis of the milling tool, leading to cutting speed decline. However, the quality of the surface near the center of the lenslet only introduced minor effect for infrared molds.

3.1.2 Compression Molding Process

After the mold inserts were fabricated, the compression molding process was employed to replicate the geometry on the molds to the infrared glass at elevated temperature. The glass compression molding process was conducted on a commercial molding machine Model GP-10000HT (Dyna

Technologies, Inc., Sanford, Florida). A small piece of chalcogenide glass (As2S3) disk with double faces polished was placed between the upper and lower molds. After three cycles of purge with nitrogen, the temperature monitored by thermal couples reached 220 °C and the upper mold pressed onto the chalcogenide glass disk with 350 N load. To ensure the cavity was fully filled, the upper mold was continuously pushed until the position was unchanged for ~5 min. Then the external fan was on and the temperature dropped to ~40 °C. The molded microlens array was demolded from the insert. The entire process is shown in Figure 3.4.

Figure 3.4 Schematic diagrams of the compression molding process (I) preparation, (II) heating, (III) pressing, and (IV) cooling.

Further measurement was conducted to obtain the surface profile and quality after molding. As the measurement tests in mold fabrication, the surface microscope photos, 2D, 3D, and cross-section profile were completed on the Wyko optical profiler. The microscope photos of the molded surface with large area presented the uniformity of microlens array, as shown in Figure 3.5 (a). A 2D and

3D local area with 2.7×3.0 mm profile of the microlens array is shown in Figure 3.5 (b) and (c).

Apart from the central area of each lenslet, the molded surface of the microlens was as smooth as the mold surface with the sharp ridge at the interaction edge. However, the central area of each lens appears to be replicated with small pits, most like due to the local surface near the central part on the mold left by the fabrication process. Finally, the cross-section of the molded geometry showed that the pitch was about 603.8 µm, which was close to the mold geometry 605.2 µm. The measurement result showed that the geometry on the mold had successfully transferred to the chalcogenide glass.

Figure 3.5 Characteristics of the molded infrared microlens array, optical images with amplifications of (a) 2.5 X, (b) 2D micro-topography, (c) 3D micro-topography, and (d) 2D profile along the cross-section A-B.

3.1.3 Optical Setup and Reconstruction

The SHS is a common optical device used in adaptive optics systems, lens testing and increasingly in ophthalmology [61], which is employed to measure the aberrations of an optical wavefront. If the microlens array, the critical component of the SHS assembly, can be molded, it will provide an alternative for low cost optics with high fidelity.

3.1.3.1 Principle of Shack–Hartmann Wavefront sensor

The basic principle of wavefront measurement is by integrating several small lenslets to overfit the incident light. As illustrated in Figure 3.6 (a), the detection plane is on the focal plane of the micro lenslet. When the incident light has a plane wavefront passes through the micro lenslet, the focal point will fall on the light axis, as the black line in Figure 3.6 (a). However, when a distorted wavefront passes through the micro lenslet, the focal point will deviate from the central point. Due

69 to the deviation of the focal point was proportional to the slope of the wave plane, the slope angles

푔푥푖 and 푔푦푖of the waveplane can be determined by [61],

∆푥 푔 = Equation 3.1 푥푖 푓

∆푦 푔 = Equation 3.2 푦푖 푓 where f is the focal length of the micro lenslet, and Δx and Δy are the displacement from the central point of the hexagon.

Figure 3.6 Schematic diagram of the optical principle of (a) single lenslet, and (b) microlens array for wavefront measurement.

Based on measurements from the micro lenslets, the whole wavefront can be divided into small apertures, as shown in Figure 3.6 (b). Then by getting all the slopes of sub-wave plane from each lenslets, the wavefront can be reconstructed by modal reconstruction method. Employing Zernike

70 polynomials to describe the reconstructed wavefront, the partial derivatives of Zernike polynomials are equal to the slopes on x and y directions from each lenslet [67],

1 푛 ∂Z푗(푥,푦) 푔 = ∬ ∑ 푎푗 푑푥푑푦 i=1,2,3…, m Equation 3.3 푥푖 퐴푖 퐴푖 푗=1 ∂푥

1 푛 ∂Z푗(푥,푦) 푔 = ∬ ∑ 푎푗 푑푥푑푦 i=1,2,3…, m Equation 3.4 푦푖 퐴푖 퐴푖 푗=1 ∂푦

3.1.3.2 Optical Setup and Wavefront Measurement

To prove the accuracy and precision of the infrared SHS constructed using a molded lens, a spherical wavefront measurement test was conducted. The core components of the infrared measurement system were an IR microlens array, an IR detector and an IR light source. The optical principle and experimental setup are illustrated in Figure 3.7 (a). The microlens array was mounted on the camera at a distance from the focal plane equals to its focal length. A standard Germanium

(Ge) plano-convex lens (Thorlabs Inc., Newton, NJ, USA) with anti-reflective (AR) film coated was mounted on a two-axis microstage. It was employed to generate a spherical wavefront with focal length 50 mm. The spherical wavefront passed the microlens and focused on the infrared detector imaging plane. The infrared camera (Sofradir EC, Inc., Fairfield, NJ, USA) incorporated a 640×480 microbolometer detector (spectral range 8~14 µm) array, delivers highly quality images in a VGA format. The light source was a multiple wavelength coil-wound (ranging from 6.0 to

14.00 µm), supported IR source (HawkEye Technologies, Infrared Source IR-35, Milford,

Connecticut) mounted on a TO-5 header combined with a parabolic reflector to collimate the infrared light beam. The whole optical setup was shown in Figure 3.7 (b). Some detailed parameters of the self-made SHS are listed in Table 3-1. 71

Figure 3.7 (a) Schematic diagram of the optical setup, and (b) setup of the experiment.

In the experiment, the distance between the spherical lens and the microlens array was set 90 mm.

Figure 3.8 (a) and (b) presented the reference image and the measurement image with 8.0 µm infrared light, respectively. In the photos from the infrared detector, the intensity of the surrounding noise is low when compared with the intensity of the focal spots of the lenslets. In order to reduce the influence of the surrounding noise to the accuracy of the measurement, several options are utilized. One is to setup a threshold for the image to filter out the light spots. After that, small part near the center of the image was employed due to large contrast of light intensity. Then, multiple images were token with the same conditions every ~0.5s and average the background noise. The light spots that were used in the measurement were marked in Figure 3.8 (c) and (d).

Table 3-1 Parameters for the Infrared SHS

Property Parameter Pitch (µm) 600 Curvature radius (mm) 8.845 Pixel size (um) 17 Pixel array 640×480 Focal length (mm) 5 Number of spots 216 72

Figure 3.8 (a) Reference image, (b) measurement image from the infrared detector and recognized and used light spots in the (c) reference image, and (d) measurement image.

Based on the recognized feature points on the reference image and measurement image, the deviations along x and y directions can be obtained for each feature points, as shown in Figure 3.9

(a). Then the Zernike polynomials are used to reconstruct the wavefront. Figure 3.9 (b) and (c) presented the reconstructed and simulated wavefront profiles, respectively. The depth of the curvature is 0.2050 mm over the 8.085 mm pupil diameter in the measurement, and the estimated theoretical value is about 0.2048 mm. The deviation is 0.0012 mm about 15% of the incident light

(8.0 µm), indicating that the measured profile matches well with the theoretical simulation profile, as shown in Figure 3.9 (d). The main error comes from misalignment of the measurement system and imprecise displacement measurement between the spherical lens and the SHS. The

73 measurement results demonstrated that the fabrication of infrared method used to create the microlens array was adequate for the precise infrared optics manufacturing.

Figure 3.9 (a) Displace from original position, (b) reconstructed wavefront with SHS, (c) MATLAB simulated wavefront, and (d) error between the measurement and simulation.

3.1.4 Conclusions

In summary, this research provides a new manufacturing method by combining virtual spindle single-point diamond milling and compression molding for infrared SHS system. In the virtual spindle based single-point diamond milling, the rotation axis was transferred the working coordinate ot-xtytzt from one local coordinate os-xsyszs to another one and rotated around the virtual axis by combining x and y harmonic oscillations motion. By using this configuration, the fabrication of each lenslets can be treated as an independent process. The minimum-area fabrication strategy toolpath generation largely reduced the manufacturing time by taking off the invalid

74 toolpath in the air. Further analysis was conducted to release the manufacturing error in the diamond milling process. After the mold insert was fabricated, the infrared microlens array was molded and measured. At last, the molded microlens array was assembled in the SHS with an IR source and a detector. Experiments show that the SHS can perform accurate wavefront measurement. The same manufacturing strategy, combining diamond milling and compression molding, can be applied to other micro- and nano-scale optics to improve production efficiency and product quality.

3.2 Large Field-of-view Microlens Array

Inspired by the ommatidia, which are tiny independent photoreception units present in insects and crustaceans, artificial compound eyes are one approach towards more compact optical imaging systems from classical imaging concepts [79]. This leads to an enormous volume reduction and an increase in field-of-view of the optical system. It is now attracting ever-increasing attention in a variety of fields, including wide-angle imaging [73,80–82], biological sensing [83,84] and chemical analysis [85–87], to mention just a few. Moreover, artificial compound eyes with the capability to serve in the infrared band can significantly extend novel applications and performance of micro/nano-optical devices.

Currently, serval fabrication techniques have been developed to fabricate microlens arrays, which can be classified according to material removal mechanism as physical [82,88,89], chemical [90–

92], and mechanical in nature [80,81,89,93]. A detailed review of recent fabrication methods for microlens can be found in Ref. [94] for the generation of these micro-optics. In general, most of the physical and chemical processes are often limited by: (a) specific materials and complex processes 75 with high manufacturing cost [93]; (b) hard for these methods to obtain lenslets with well-defined intricate shapes, especially with superimposition of surface nanostructures; (c) a lack of potential for mass industrial replications [36].

More recently, the bottom up three-dimensional (3D) printing technique was adopted in fabrication of meso/micro/nano-optics with complex profile [95,96]. Although the high precision process is superior to other fabrication methods in fast prototyping, the low production efficiency limited working dimension impedes its wider applications in optical manufacturing, especially in large- area micro-optics and quantum optics. Generally, mechanical machining is more universal and deterministic for the generation of complex, smooth, and successive profiles [73,97]. Among the popular methods, single-point diamond turning and high-speed diamond milling are the lead choices for the generation of microlens array on various engineering materials. With high-speed diamond milling, versatile microlens arrays with complicated surface profiles can be rapidly generated, mainly attributing to its unique advantages on ultra/high-speed spindle, flexible programming, and adaptability on materials. However, challenges still exist when it comes to the fabrication of small features, such as microlens arrays. For instance, the non-uniform finished surface quality close to symmetry axis largely deteriorated surface finish qualities due to the inherent kinematics of milling operations [36]. Moreover, the size of diamond milling tools limits its potential on fabrication of smaller structures. Although AFM-tip based micro/nano-milling process can achieve very accurate sub-micron structures, it suffers from low efficiency and high tip wear rate [98]. Today such fabrication processes are still restricted to laboratory environments.

Compared with micro-milling, slow-tool-servo diamond turning, equipped with single-crystalline diamond tip, is more appropriate for complex optical profiles with/without micro/nano-structures.

Additionally, computer numerical servo control has enabled synchronizing of the tool movements with the spindle rotation, thus allowing better flexibility and reliability. However, the inherent spiral trajectory of diamond turning makes it extremely difficult to generate discontinuous optical surfaces, especially for the combination of discrete elements. In general, an ideal strategy is to fabricate each discrete optical element separately, locally, and then combine them together, like in high-speed diamond milling, which treats each element individually. On the other hand, the outline of each optical element is often changed into irregular shape instead of circular boundaries. Spiral trajectory is the best solution for scanning the whole surface. Considering these requirements, a diamond broaching trajectory virtual-axis-based slow-tool-servo diamond turning is often selected for fabricating such complex discrete micro-optics. However, due to the relatively low-efficiency and high cost of diamond turning, this method is typically only suitable for single piece or small batch production.

On the selection of optical materials, chalcogenide glasses are emerging as alternative infrared materials for their wide infrared transmission and easiness to be shaped into micro/nano optical elements by precision glass molding (PGM), a near net-shape fabrication process [99]. For mass production, PGM of chalcogenide glass is preferred over other manufacturing methods due to its high efficiency, short cycle times and reusable tools. In a typical PGM process, a softened glass preform is pressed into the molds and conformed to the desired shape. Around molding temperature, glass is in viscoelastic state, allowing it to be easily shaped under pressure. Therefore,

77 the applications of chalcogenide glasses in optical fabrication provide the photonics industry with excellent material candidates for low-cost and high-performance devices.

Based on the combination of infrared materials and available fabrication processes, a combination fabrication method was proposed to fabricate infrared artificial compound eyes. In this paper, both the micro aperture and profiles of each lenslet were optimized by ZEMAX [100]. Then a virtual- axis-based diamond broaching trajectory and adaptive slow-tool-servo diamond turning technique were introduced to fabricate the mold inserts, which were further employed in the rapid precision glass molding of chalcogenide glass lenses. In order to simplify the assembly process, the aperture together with the fixture structure was created by precision 3D-printing. Finally, the last part of the paper summarizes the optical performance of the artificial compound eyes.

3.2.1 Optical Design of Freeform Microlenses

A 3D infrared artificial compound eye system, which consisted of a pair of microlens arrays and a micro aperture, was earlier designed and fabricated by the authors [101]. However, the artificial compound eye system with two pieces of microlens array was not suitable for compact infrared imaging system. Even coated with an anti-reflective layer on both sides, the performance suffered from a complex assembly process and manufacturing errors. Moreover, the index change in rapid thermal process was not carefully considered in optical design. To this end, a novel optical design was proposed with one single layer integrated asymmetric freeform lenslets on both sides.

The proposed compact design of the infrared camera-based artificial compound eye system is illustrated in Figure 3.10. The compound eye imaging system has three components, involving an

78 asymmetric freeform microlens array, a micro aperture and an infrared detector. The proposed microlens array was divided into 3×3 channels, which can be further classified into 3 different kinds of profiles due to different viewing angles. The incident ray of each channel comes from different spatial directions, and then they were steered by freeform lenslets such that the axis of each channel became perpendicular to the surface of the imaging sensor. Compared to spherical or aspheric profiles, the freeform offers more flexibility and capability to improve the optical performance.

Figure 3.10 Schematic the infrared artificial compound eye system design.

3.2.1.1 Refractive Index in Precision Molding

It is well-documented that precision glass molding leads to a decrease in the refractive index of glass during the thermal process [63]. The refractive index decrease is one of the most important optical property changes that can degrade the performance of an optics along with geometric deviations. If the refractive index change introduced by molding process is not considered properly in the design, the optical performance of the molded lens would be different from the original design. Therefore, a detailed and most importantly, a quantitative and accurate data on refractive index change of chalcogenide glasses is critical for optical design.

As2Se3 is very common in the chalcogenide glass family. Previous studies have reported its physical and optical properties, such as tensile strength [51], structural relaxation [102], and refractive index under certain conditions [16,103]. Thus, in this study, the refractive index change of As2Se3 after compression molding was referenced from [104]. For comparison, the refractive index after annealing and compression molding for the wavelength region of 2-12 µm, is presented in Figure 3.11. Furthermore, the Sellmeier equation was adopted to fit and calculate the refractive index (n) for As2Se3 chalcogenide glass, which is an empirical relationship between refractive index and wavelength for infrared-transparent medium. The usual form of the equation for chalcogenide glasses is listed as follows,

2 2 2 2 퐾1휆 퐾2휆 퐾3휆 푛 − 1 = 2 + 2 + 2 Equation 3.5 휆 −퐿1 휆 −퐿2 휆 −퐿3

where n is the refractive index, λ is the wavelength, and K1,2,3 and L1,2,3 are Sellmeier coefficients that can be experimentally determined. These coefficients are usually quoted for λ in micrometers.

The coefficients for the annealing and compression molding of As2Se3 are summarized in Table

3-2, which are further employed in ZEMAX software for optical optimization. A good fit between the reference and calculated data was confirmed.

Figure 3.11 Refractive index of As2Se3 glass after annealing and compression molding.

Table 3-2 Coefficients for annealing and molding As2Se3

Coefficient Annealing Molding

K1 6.25667E-02 -2.25768E05

L1 9.99402E-04 8.01377E-06

K2 6.73251 2.25775E05

L2 1.02926E-01 1.11336E-05

K3 9.22736E-01 8.06908E-01

L3 1.51326E03 1.37102E03

3.2.1.2 Microlens Profile Design

This novel infrared freeform microlens array has 3 × 3 channels, and each channel was designed to form an aberration-corrected image for a specific spatial direction. Due to different viewing angles of each channel, the surface profile of each microlens was different and needed to be designed individually. The configuration and direction of the viewing angle of each channel are schematically shown in Figure 3.12. Since the viewing directions of the microlenses were symmetric to X and Y directions, the viewing directions for the microlenses were illustrated in

Figure 3.12. The whole field-of-view of the designed microlens array, while the angular incremental step for each microlens was 16° in both the X and Y directions. The design parameters, summarized in Table 3-3, such as the size, pitch, image dimension and field-of-view, have major impacts on the machining process, which will be further discussed in next section.

Table 3-3 Configuration of the Freeform Microlens

Parameters Value Effective microlens dimension 2.5 mm × 2.5 mm Microlens array pitch 2.6 mm Imaging plane length (X direction) 10.88 mm Imaging plane width (Y direction) 8.16 mm Imaging pixel size 17 μm Imaging plane distance 7.6 mm FOV of the entire compound-eye camera ± 24˚

Figure 3.12 Viewing directions of the nine microlenslets.

For microlens profile optimization, polynomial surfaces were utilized to approximately describe the lens profiles. In this research, extended polynomials were employed to optimized the microlens profiles, and the whole process was finished using the commercial optical design software

ZEMAX [25]. The extended polynomial of an optical surface consists of a regular conic aspheric surface and extended polynomial terms, which can be expressed as follows [100],

2 푐푟 푁 푧(푥, 푦) = + ∑ 퐴푖퐸푖(푥, 푦) Equation 3.6 1+√1−(1+푘)푐2푟2 푖=1

2 2 where rxy = √푥 + 푦 , k and c are the conic constant and curvature of the conic surface

th respectively, N is the number of polynomial coefficients and Ai is the coefficient of the i extended polynomial term. The extended polynomial terms can be expressed as follows [100],

푁 1 0 0 1 2 0 1 1 0 2 ∑푖=1 퐴푖퐸푖(푥, 푦) = 퐴1푥 푦 + 퐴2푥 푦 + 퐴3푥 푦 + 퐴4푥 푦 + 퐴5푥 푦 + ⋯ Equation 3.6

In the optimization process, the number of terms affected the accuracy and efficiency in optimization. In another word, more terms gave the system a greater degree of freedom in optimization but increased calculation time and resulted in instability. In this research, 20 items were employed after balancing both the number of variables (freedoms) and the cost of simulation.

On the other hand, the initial conditions had a larger influence on the rate and efficiency on convergence. Based on previous experiences [105], the initial surface profiles were set as prisms on one side with a pre-calculated apex angle to steer the rays from the specific viewing direction, while the other side was set as a convex spherical surface to focus the rays to the detector. The

83 optimized data of these three different microlens were presented in Table 3-4 to Table 3-6, and the final design of the freeform microlens array is shown in Figure 3.13.

Table 3-4 Design parameters for microlens of central channel A

Parameter* First side Second side c -803.8718635581 -0.1428692571526 k -0.051514527096 -0.1192577398273

r2 0 0

r4 -0.011768622725 -0.0033220939168

r6 0.001221282690 0.0000002195557

*where rn is the coefficient for n-power of variable in aspheric formula.

Table 3-5 Design parameters for microlens of side channel B

Parameter First side Second side c 159.476717647 12854.4267692 k -34.1017680598 -0.00434183422 X1Y0 0.00061981387 0.00062892656 X0Y1 0.07915844776 -0.07712794745 X2Y0 -0.00628900792 -0.05471972825 X1Y1 -0.00027079484 -0.00027356155 X0Y2 0.01586379814 -0.03219161032 X3Y0 0.00003767526 0.00001609666 X2Y1 -0.00806568288 -0.00594627099 X1Y2 -0.00000895008 -0.00001552628 X0Y3 -0.00632493986 -0.00493737359

Continued

Table 3-5 Continued

Parameter First side Second side X4Y0 -0.00422749190 -0.00350576176 X3Y1 -0.00001213204 -0.00000191408 X2Y2 -0.00839385779 -0.00752184891 X1Y3 -0.00001111373 -0.00000063383 X0Y4 -0.00345523911 -0.00345523911 X5Y0 -0.00000005710 0.00000395022 X4Y1 -0.00048854366 0.00005027372 X3Y2 0.00000419941 0.00001617964 X2Y3 -0.00239646287 -0.00131813156 X1Y4 -0.00000496769 -0.00000128463 X0Y5 -0.00025226286 0.00008140112

Table 3-6 Design parameters for microlens of corner channel C

Parameter First side Second side c 1.12955961510 -1.70400892445 k -0.23491596735 0.23491596735 X1Y0 -6.42233105731 0.08550000000 X0Y1 0.11650000000 -0.03707997810 X2Y0 0.11972717496 -0.15033062499 X1Y1 -0.01967273043 -0.02162314067 X0Y2 0.12829323333 -0.14246911168 X3Y0 0.00530090786 0.00464659735 X2Y1 0.00002073497 -0.00002073497 X1Y2 0.00049357278 -0.00049357278 X0Y3 -0.00026668015 0.00026668015

Continued 85

Table 3-6 Continued

Parameter First side Second side X4Y0 0.00095654290 -0.00095654290 X3Y1 -0.00032319762 0.00032319762 X2Y2 0.00209368171 -0.00209368171 X1Y3 -0.00025792915 0.00025792915 X0Y4 0.00111038888 -0.00111038888 X5Y0 0.00025890938 -0.00025890938 X4Y1 -0.00000773315 0.00000773315 X3Y2 0.00040026458 -0.00040026458 X2Y3 -0.00008257110 0.00008257110 X1Y4 0.00010157329 -0.00010157329 X0Y5 -0.00002282183 0.00002282183

Figure 3.13 Surface profiles of the 3×3 freeform microlens array (a) first side and (b) second side.

The layout of three different freeform microlens based on ray-tracing and the spot diagrams obtained by steering from a parallel incident light is shown in Figure 3.14. The calculated RMS

(root mean square) spot radius of the center field was within 15.112 μm, 15.884 μm and 15.826

μm for three different freeform microlenses. Although the maximum RMS spot radius for corner channel C with field 3 (X = 0° and Y = -8°) was as large as 16.128 μm, it was still smaller than the

86 pixel size of the uncooled far-infrared detector used in this experiment. The simulation spot diagram was based on pure ray tracing without considering the diffraction effect, but the simulation result was still considered appropriate for optimization in microlens design.

Figure 3.14 Layout of the design for three different microlens and the corresponding spot diagrams for various fields (a) central channel A, (b) edge channel B, and (c) corner channel C. 87

3.2.2 Fabrication of Microlens Arrays

Compared with other microlens fabrication methods, such as thermal reflow, ultraprecision diamond turning has the advantage on well-defined freeform surfaces fabrication on flat or even curved workpieces with optical finish surface quality. In this research, ultraprecision diamond turning was adopted to fabricate mold inserts, which were further employed in precision glass molding process.

3.2.2.1 Motion modulation for complicated profile generation

For freeform profile fabrication, there are several machining strategies, such as slow-tool- servo [73], fast-tool-servo [106], broaching [61], high-speed diamond milling [36]. However, based on the optical layout, straight, steep and derivative-discontinuity edge, restrained the application of conventional slow/fast-tool-servo and high-speed diamond milling in this study, because the spiral-toolpath based conventional turning process resulted in unexpected defects on machined surface. Considering these requirements, a diamond broaching trajectory virtual-axis- based slow-tool-servo diamond turning is possible for fabricating such complex, discrete micro- optics.

The basic configuration of multi-axis diamond lathe is shown in Figure 3.14, and a close up view of the spatial positions of the diamond tool and the workpiece is illustrated at the right corner in

Figure 3.15. The om-xmymzm and ot-xtytzt were the machine coordinate and working coordinate, respectively. At the initial stage, the machine coordinate is coincident with the working coordinate.

The workpiece was clamped to the vacuum chunk on the airbearing spindle, which rotates around

88 z-axis, as well as the working coordinate ot-xtytzt, while the diamond tool was fixed on the tool post, moving along the z-axis.

Figure 3.15 Hardware configuration of ultraprecision multi-axis diamond machine for micro/nano optical generation.

A two-dimensional (2D) schematic of the desired profile and the relative cutting kinematics is illustrated in Figure 3.16. Because the special symmetric dependency of the machined profiles, the geometry of each lenslet on the mold surface can be fabricated by combining virtual axis strategy and diamond broaching process. To generate each lenslet of the microlens array, a virtual axis of rotation was generated to coincide with the osxs axis and each machining process was treated as an independent operation. Details of this process can be summarized into the following steps,

Step 1. Initialization. Similar to conventional diamond turning process, the working coordinate ot- xtytzt was initially moved to coincide with the machine coordinate om-xmymzm through three linear slides. Each local coordinate of os-xsyszs of the microlenses was virtually constructed with axisymmetric about the omzm axis in the system om-xmymzm as shown in Figure 3.16 (a). 89

Step 2. Position transfer. As shown in Figure 3.16 (b) and (d), to align the working coordinate ot- xtytzt with the local coordinate os-xsyszs through by relative linear motion in xm and ym-axial components or relative rotational motion in cm-axial components to complete the profile fabrication for each lenslet. The point os in the local coordinate was set as a fixed point in the machine coordinate om-xmymzm, while motion of the diamond tool was induced by linear and rotational motion.

Step 3. Localized diamond broaching. When the working coordinate is coincident with the local coordinate, diamond broaching was conducted along the ym-axis direction with a constant feedrate in the xm-axis direction, while tool servo motion along the zm-axis direction was employed to fabricate the complete profiles of each microlens. Each machining process was regarded as one independent process. Figure 3.16 (c) illustrates the linear toolpath parallel to the edge of the microlens.

3.2.2.2 Motion modulation for central profile generation

Considering conventional methods of defining a spiral toolpath, it is not practical for an arbitrary aperture/boundary of a machined surface to deviate considerably from a circle. On one hand, the machining cycle time was elongated substantially due to extensive air cutting. On the other hand, the frequent plunging-in and retraction decrease the tool lifespan and the finished surface quality.

Therefore, for the central microlens, an adaptive spiral method was proposed below to fabricate the surface profile.

Figure 3.16 Schematic of cutting kinematics for side/corner micro/nano optical generation.

When generating a toolpath with consideration of the boundary, it is useful to adopt a parameter that scales the input radial coordinates from conventional spiral toolpath so that they conform to the supplied polar boundary. This way, the angular coordinates of the input spiral remain unchanged, while only the radial coordinates were transferred from a conventional spiral toolpath coordinate, which sufficiently reduced computation in this process. The whole strategy was illustrated using a few boundaries shown in Figure 3.17 (a) and (b), and the ith deformed radial spiral coordinate was given as follows,

푟푑표,푖 푟푑,푖 = × 푟푖 Equation 3.7 푟표,푖

91 where rd,i is the deformed spiral radial coordinate corresponding to ri in the spiral coordinate. rdo,i and ro,i are the outlines of the supplied boundary and spiral boundary.

However, the deformed spiral toolpath reduces efficiency, quality and productivity, especially when the tool moved close to the rotation axis. To further improve the dynamics of the movement, another factor was introduced to change the degree on ‘deformation’ of spiral toolpath. The smoothing parameter value and scaled radial coordinates were shown as follows,

푟푑표,푖 푛 푛 푟푑,푖 = × 푟푖 × + 푟푖 × (1 − ) Equation 3.7 푟표,푖 푁푇푃 푁푇푃

where NPT was the total number of turns in the toolpath, and n is the number of turns corresponding to the ith spiral radial coordinate.

Figure 3.17 Schematic of cutting kinematics for central micro/nano optical generation.

3.2.3 Ultraprecision Diamond Turning

The turning experiments were conducted on an ultraprecision CNC lathe (Moore Nanotechnology,

Inc., Keene, New Hampshire, USA) with five-axis servo motion. The hardware configuration of the experiment setup included a diamond tool clamping on the tool poster and the workpiece 92 installing on the vacuum chunk. The diamond tool with a round cutting edge used in machining was a commercial single-crystalline diamond tool (K&Y Diamond, Ltd., Diab St-Laurent, Quebec,

CA). More details of the turning conditions and the employed tool are shown in Table 3-7. The finished surface was cleaned with acetone and alcohol to remove the residual coolant and attached chips. The finished surface profiles were captured by an optical surface profiler (Wyko NT9100,

Bruckner., Tucson, Arizona, USA).

Table 3-7 Cutting parameters and the tool geometry

Materials Al 6061 Tool nose radius 300 μm Tool rake angle 0° Tool clearance angle 7° Roughing speed 40 mm/s Finishing speed 10 mm/s Contour spacing 5 μm

3.2.4 Precision Glass Molding

The compression molding process was employed to replicate the geometry on the molds to the infrared glass at molding temperature. Since there were requirements on alignment between two sides of the microlens, a set of mold inserts were designed and manufactured with aluminum 6061 material for the molding test. The structure of the mold set was semi-closed and detachable which can make the molded microlens array de-mold easily. The adjoining profile consisted of a semi- circle and a straight line to align and orient the mold inserts. The structure and profiles of the mold inserts are shown in Figure 3.18.

Figure 3.18 Schematic diagrams of the designed mold inserts and assembly structure.

The glass compression molding process was conducted in a commercial molding machine GP-

10000HT (Dyna Technologies, Inc., Sanford, Florida). The entire process is shown in Figure 3.19

(a). A piece of chalcogenide glass (As2Se3) disk (diameter = 25.4 mm and thickness = 2.0 mm) polished on both sides was placed between the upper and lower mold inserts, as shown in Figure

3.19 (b). After three cycles of purge with nitrogen, the chalcogenide glass as well as the entire molding unit were heat up to the molding temperature (225°C) with a heating rate of 1 °C/s. After maintaining the temperature for ~15 min, the upper mold was pressed onto the chalcogenide glass disk with a 350 N load. To ensure the cavity was completely filled, the upper mold was continuously pressed downward until the position remained unchanged for ~5 mins. Then, an external fan was turned on, and the temperature was reduced to ~40 °C with a cooling rate of

0.5 °C/s. The molded microlens array was removed from the insert, as shown in Figure 3.19 (b).

Figure 3.19 Schematic diagrams of the compression molding process (I) preparation, (II) heating, (III) pressing, and (IV) cooling.

3.2.5 Characteristics of the Machined Surface

After slow-tool-servo diamond turning, the machined microlens array was captured by a high- definition digital camera (Canon 80D) with zoom lens (SIGMA 18-35mm F/1.8 DC HSM ART) and shown in Figure 3.20 (a). From the microlens shown in Figure 3.20 (a), each lenslet in the region shared almost the same dimensions without structural and position distortions. For its symmetrical design, it is imported that uniform distribution and finish surface quality of the microlens array over the entire machining area. The central microlens was further captured and stitched by the optical surface profiler with a 10× magnification, as shown in Figure 3.20 (b). The profile error was also obtained by comparing with the optical design, shown in Figure 3.20 (c). For most of the area scan, the surface profile error was limited to ± 0.5 μm. After removing the aspheric surface from the lenslet shown in Figure 3.20 (b), the central part of the surface micro-topography was further illustrated in Figure 3.20 (d). From the analysis modular of the software, the obtained roughness value was about Ra = 22.64 nm. Furthermore, it was noted that along the radius, there were slight fluctuations, which corresponded to the residual tool marks. 95

Figure 3.20 (a) Photography of the mold insert, (b) 3D microscope diagram of the structures, (c) surface profile error and (d) surface micro-topography of a lenslet.

Similar measurement of the molded microlens array was conducted to obtain the surface profile and surface quality after molding process. The surface microscopes photos and 3D geometries were completed on the optical surface profiler, as presented in Figure 3.21. Figure 3.21 (b) and (c) illustrate the three-dimensional (3D) micro structures of the molded central lens and machining deviation in the final microlens array. The observed values are in good agreement with the mold insert as shown in Figure 3.20. The machining deviation was limited to ±2 μm, and the finish surface roughness was about Ra = 28.42 nm. More importantly, the homogeneous features of the molded surface quality as well as the small deviations were obtained, indicating a high fidelity in replication from mold inserts to chalcogenide glass.

Figure 3.21 (a) Photography of the molded microlens array, (b) 3D microscope diagram of the structures, (c) surface profile error, and (d) surface micro-topography of a lenslet.

3.2.6 Characteristics of Imaging Performance

To evaluate the optical performance of the molded microlens array, the compact large field-of- view imaging system was assembled and further tested by a home-made optical imaging test setup.

The imaging system consisted of the molded microlens array, a micro aperture array, an infrared detector and a micro-positioning stage with height adjustable support. The optical layout is illustrated in Figure 3.22. In this setup, the microlens array and the 3D-printed micro aperture array were mounted on a two-axis micro-positioning stage. Both the distance between the microlens array and the infrared camera could be precisely adjusted to one focal length. The infrared camera used for imaging was a commercial grade camera (Sofradir EC, Inc., Fairfield, NJ, USA), which incorporates a 640 × 480 microbolometer detector array with 17 μm × 17 μm pixel pitch, delivering high quality images in VGA format.

Figure 3.22 (a) Schematic diagram and (b) layout of the infrared optical testing experiment.

The light source for optical testing was a home-made hotplate made of an aluminum plate. On one side, it was coated with a thin layer of composite, consisting of a multiple wall carbon nano tube

(CNT) and epoxy resin, which was employed to homogenize temperature distribution on the whole plate. On the other side, a heating circuit was adhered to the plate. The plate temperature could vary between 30~250 °C and be controlled by adjusting the current and voltage, and the targets used in the test were fabricated by wire electrical discharge machining.

To test the quality of the microlens array camera, a test target, as shown in Figure 3.23 (a), was placed in front of the infrared light source as an object, and the object distance was 250 mm. For better illumination uniformity, the temperature of the hotplate was set to 90 °C. Figure 3.23 (b) shows the image formed on the infrared detector. It is observed that all the images from the channels were formed on the detector, and each channel was viewing a specific direction. The target bars were formed in different channels accordingly. However, some crosstalk ghost images and a small amount of overlapping were visible in the images, which can be further improved by the optimization of the shape of the aperture. The same pattern was also introduced into the commercial 98 optical software ZEMAX to simulate the imaging quality, as shown in Figure 3.23 (c). From the comparison between the experiment and simulation, these images were very similar to each other, including geometry and intensity.

Figure 3.23 Schematic diagrams of (a) the star target, (b) image obtained from infrared detector, and (c) simulated image from ZEMAX.

Another infrared target was employed to test the image quality. The object, a batman array, was clearly imaged on the infrared detector, as shown in Figure 3.24 (a) and (b). The batman array target was placed 340 mm away from the imaging detector with 310 mm width. From Figure 3.24 (b), the estimated field-of-view of the infrared microlens was close to ±25.7°, which was in agreement with the design. The formed image was uniform over the detector, but the sub-images presented a small amount of overlapping along the edge. In addition, the sub-images formed by the corner channel showed slightly more aberrations due to a larger angle of view, and this issue can be corrected by image processing and stitching. A similar simulation result was also obtained from

ZEMAX, shown in Figure 3.24 (c).

Figure 3.24 Schematic diagrams of (a) the batman array, (b) image obtained from the infrared detector, and (c) simulated image from ZEMAX.

The modulation transfer function (MTF) was an important tool for objective assessment of the imaging performance of optical systems. In the experiment, it can be considered as the ratio of relative image contrast to relative object contrast. The equation for the MTF can be expressed as,

Relative Image Contrast 푀푇퐹 = Relative Object Contrast

When an object is observed with an optical system, the resulting image will be somewhat degraded due to aberrations and diffraction. In this research, the slanted-edge method specified in ISO

Standard 12,233 was adopted, since it was a simple and efficient way to obtain the MTF. The captured slanted edge images, which were parallel to the central view of each lenslet, for different channels were captured, and the calculated MTF curve of each channel is illustrated in Figure 3.25.

It was noted that there was difference between the calculated and measured results. For example, the central channel had a calculated MTF 0.5 value of 14 cycles∙mm−1, whereas the measured MTF

0.5 value was 9.5 cycles∙mm−1 in the single channel A image. The difference between the calculated and the measured values can be explained by the following reasons, (1) For an image 100 sensor, the corresponding Nyquist frequency (Ny), one half of the reciprocal of the center-to-center pixel spacing, limits the spatial sampling rate of the optical imaging system [86]; (2) In addition, the systematic offset and misalignment, which is caused by fabrication errors, such as geometric error of the lens array, uneven residual refractive index distribution and residual stresses, and defocus due to distance variation between each optical element, all could result in decrease in MTF;

(3) Since chalcogenide glasses usually have large refractive indices, the reflection between the interface was much more severe than oxide glasses used for visible light applications. This problem can be improved by employing an antireflection coating on both sides of the molded microlens or antireflective moth eye micro/nano structures instead; (4) the micro aperture between the infrared detector and the microlens array could further cause image degradation due to the reflectivity of the side wall of the aperture.

Figure 3.25 Design and measurement of normalized MTF contrast in object space as a function of spatial frequency.

101

Finally, an imaging trial was conducted using the molded microlens array imaging system and a commercial infrared camera (FLIR Lepton, FLIR Systems Inc., Wilsonville, Oregon, USA), respectively. The white-hot imaging mode was selected for the infrared detector and the raw images were shown in Figure 3.26, which were captured at the distance of 0.7 m. For comparison, the central images of the microlens array was extracted from the entire image, which was listed next to the commercial image with a ±12.5° field of view and 1.6 mm aperture. The commercial camera, equipped with a silicon lens coated with an anti-reflective layer, had a similar dimension of the imaging detector, involving 80 × 60 microbolometers. The image quality from the large field-of- view microlens array was less sharp than that of the commercial one. This could be attributed to the camera’s non-uniformity compensation (NUC) function, which treated the image as a whole to compensate intensity, a lack of an antireflective coating on the interface, and a lack of lens housing to avoid thermal noise from the surrounding.

Figure 3.26 (a) Raw data captured by the optical setup (b) image captured by the molded microlens array, and (c) by a commercial infrared camera.

102

3.2.7 Conclusions

In this research, a compact large field-of-view infrared microlens array with freeform surfaces was developed. The microlens array can achieve a field of view of 48° × 48° with a thickness of only

1.8 mm. Using optical design software ZEMAX, freeform surface profiles were optimized using extended polynomials. This large field-of-view camera has potential applications in thermal position detection, night vision and integrated infrared imaging, for its compact dimension and low- cost.

To achieve a large field-of-view microlens array in compact size, the infrared optical properties were investigated and optimized using optical design software ZEMAX. Due to rapid thermal variations involved in a typical compression molding process, the refractive index of the infrared materials was slightly different from the original value. Based on previous studies, the adjustment in refractive index was introduced into the software. With a pre-calculated prism and convex initial condition, the optimization was highly efficient even with 40 extended polynomial terms.

The freeform microlens array was fabricated by a combination of virtual-spindle-based/adaptive ultraprecision diamond turning process and precision glass molding, in order to achieve both high quality and low cost. To simplify the machining process, the freeform microlens array was split into two identical parts, the surrounding microlens and the central microlens. Because axisymmetric micro-structure was used in this design, the surrounding microlenses could be fabricated virtual-spindle-based diamond broaching process, while the central microlens was fabricated by adaptive toolpath diamond turning. Furthermore, the mold inserts were employed in

103 precision glass molding. The molded surfaces were evaluated by an optical microscope and white light interferometer, both showing good replication fidelity.

The molded microlens array parts were assembled with a 3D printed micro-aperture and a commercial infrared detector to form a large field-of-view compact camera. Several optical tests were carried out to measure the optical performance, including a star target and a batman array.

The measured field-of-view of the camera was ±25.7°, and the measured MTF was close to the simulated results. With this optical setup, a clear image was successfully formed on the infrared detector. Compared with a conventional commercial infrared camera, the method reported in this study could achieve similar optical performance with low-cost and a shorter cycle-time.

104

CHAPTER 4: LOCALIZED RAPID HEATING OF GRAPHENE COATING ON SILICON WAFER

In current chapter, two novel localized rapid heating processes were explored and demonstrated by using graphene-coated silicon as an effective and high-performance mold material for precision glass molding. One process is based on induction heating and the other one is based on mid-infrared radiation. The feasibility of these processes was validated by fabrication of optical gratings, micropillar matrices and microlens arrays on polymethylmethacrylate substrate. The uniformity and surface geometries of the replicated optical elements were also evaluated using an optical profilometer.

4.1 Rapid Localized Heating of Graphene Coating by Induction

Graphene is an intriguing coating material with excellent physical properties, such as high hardness, low friction and high thermal conductivity attracted great attention [107]. In precision glass molding, a comparative molding test was conducted between silicon (Si) wafer with and without graphene coating [3], which demonstrated its non-stick property even at elevated temperature. In addition, its good electrical and thermal conductivity were also utilized in a flexible low-resistant electro-thermal heating element in rapid localized heating process [34]. However, the thermal effect at the joint between the graphene coating and external power circuit limits high continuous power to be transported into the graphene coating.

105

In this research, we developed a novel graphene thin film heater that enables rapid localized induction heating and cooling. The graphene nanosheets were synthesized by chemical vapor deposition (CVD) and cross-linked into a three-dimensional network by siliconoxy carbide and silicon carbide covalent bonds on patterned Si molds [108]. The nanoscale graphene coating, combining many advantages, such as high electrical and thermal conductivity, allows the contact surface temperature to be raised above Tg within seconds, while other part of the mold remained at lower temperature. This process made the molding process unique but more flexible and effective.

4.1.1 Silicon Mold Fabrication

Si wafers were employed for fabrication of mold inserts for its mechanical properties, material availability, and well-developed micro/nanoscale manufacturing techniques [109]. Both ultraviolet

(UV) lithography and ultraprecision diamond turning were applied to Si wafers to fabricate microfeatures. In this experiment, four pieces of Si wafers were used in molding, two of them with thickness of 500 µm and dimensions of 15mm×15 mm, and the other two with thickness of 5 mm and dimensions of 20 mm×10 mm. For the two thin Si wafers, 5 µm×5 µm microchannel and 10

µm×10 µm microwell with 0.5 µm depth were fabricated on Si wafer via standard UV photolithography, while the other two thick Si wafers were machined directly on the

Nanotechnology Systems’ 350FG ultraprecision machine using ultraprecision diamond machining.

The machined optical microlens arrays consist of 6×6 and 16×16 microlens with 360 µm pitch.

Each individual microlenslet has a radius of 7.1 mm. The silicon molds patterned with micro features were coated with a layer of carbide bonded graphene using CVD method. The detailed information for the CVD coating process is described in reference [110].

106

As shown in Figure 4.1, the in situ localized rapid molding apparatus based on induction heating is similar to the conventional glass molding machine, except the induction coil beneath the Si mold insert and the IR camera used in test. In the system, the induction heating system was modified from a handheld microcomputer-based electromagnetic induction sealing machine (GLF-500F).

The maximum power and frequency were 1,200 W at 30 kHz (±5%). A compact IR camera

(Compact XR Extra-Range Thermal Camera., Seek thermal, Santa Barbara, CA, USA) was used to monitor the temperature changes of the Si mold and polymer substrate. During the test a constant pressure was applied to form the polymer material into the desired geometry.

Figure 4.1 Schematic of the induction heating compression molding system.

4.1.2 Induction Heating Model

To model the heating of the graphene coating, we consider a simplified structure of thin conductor film on a strip-shaped Si substrate in a uniform alternating-current (AC) magnetic field normal to the surface, as shown in Figure 4.2 (a). To determine the heating characteristics requires solving the Maxwell equation while taking into account the electrical resistivity, specific heat capacity and heat transfer from the specimen surface. It is assumed that no thermal resistance between the conductive film and the substrate and the conducting film is sufficiently thin so that the temperature is constant over the thickness [111]. 107

Under these assumptions, the task can be simplified into solving the following equations.

∂퐸 휕퐻 = −휇 Equation 4.1 ∂푥 0 휕푡 where E is the electric field intensity and H is the magnetic field intensity. The total loss per unit area of the structure is given by the loss densities of the conductor film and the silicon substrate.

2 W = 퐸 (푑푆푖⁄휌푆푖 + 푑퐺푐⁄휌퐺푐) Equation 4.2

The temperature filed is determined by the solution of the heat transfer equation below.

∂푇 휕 ∂푇 퐶 = (Λ ) + W − ∂ (푇4 − 푇4 ) Equation 4.3 ∂t 휕푥 ∂푥 푆퐵 푟표표푚

where C = dSicpSiγSi+ dGccpGcγGc; Λ = dSiγSi+ dGcγGc; ρSi, dSi, λSi, γSi, cSi and ρGc, dGc, λGc, γGc, cGc are the electrical resistivity, thickness, thermal conductivity, density and specific heat capability of the

Si substrate and conduction film. Troom is the room temperature. The boundary conditions used in simulation are adopted from Ref [111].

4.1.3 Heating Characterization

In order to investigate the feasibility of the model, a calculation was conducted with 0.05 µm graphene coating on 500 µm Si substrate of 2.54 cm in width. The temperature dependence of the specific heat capacities, electrical and heat conductivity were taken approximately as in reference [112]. Figure 4.2 (b) shows temperature distribution along the width versus time. In

Figure 4.2 (b), it was found that temperature of the inner part is slightly lower than the edge of the

108 specimen. However, due to high thermal conductivity of the graphene coating, the difference was found to be within 5 ℃.

Figure 4.2 (a) Simplified model of the thin conductor film on a strip-shaped Si substrate in AC magnetic field. (b) Temperature increase for different amplitudes of the applied magnetic field.

Before molding the polymer optics elements, the characteristics of the graphene coating were investigated to ensure the graphene based localized heating system functions as we predicted using the analytic model. Two of the infrared images of the Si mold were obtained from the IR camera at 13 s and 29 s with external induction coil operated using the 1,200 W power unit running at 30 kHz, as shown in Figure 4.3 (a) and (b). Within the graphene-coated area, no notable differences were found in surface temperature between various sections of the Si wafers. In addition, a line scan of thermal profile with different temperatures along the diameter of the Si mold was conducted and shown in Figure 4.3 (c). Most of the part along the diameter of the Si mold was carefully maintained at the same temperature, which is the optimal condition for forming, except for the circular edge of the mold. A further investigation on heating/cooling response on the graphene coating of the thick Si mold during heating and cooling was shown in Figure 4.3 (d). As shown in

109

Figure 4.3 (d), the graphene coating temperature could be raised above Tg (~101 C/s) of PMMA in less than 30 s and then rapidly cooled down to below 80 C in less than 90 s.

Figure 4.3 Temperature profiles on graphene coating measured by IR camera at (a) 13 s, (b) 29 s. (c) Thermal profiles of different temperatures along the diameter of the Si mold. (d) Heating/cooling response of graphene coating under different heating powers. (Note: the white spots on the left in (a) and (b) are reflection from the camera lens).

4.1.4 Molding Experiment

A typical precision molding process consists of four stages in a single cycle, i.e., heating, forming, holding and cooling. To implement fast heating and efficient forming, heating and forming were conducted simultaneously. In a molding process, compression pressure P0 was applied when the induction heating started. When the graphene coating layer reached the set temperature, cooling was started right away. The substrate used in the experiments was 2 mm thick 10 mm×10 mm

110

PMMA plates. The molding pressure was 0.4 MPa and molding temperature was 120 C for

PMMA.

Figure 4.4 (a) Surface profile of a microchannel Si mold. (b) Surface scan of a replicated PMMA with microchannels. (c) Surface profile of a microwell matrix Si mold. (d) Surface scan of a replicated PMMA with micropillar matrix. Comparison of line scans between the Si molds and the corresponding molded (e) microchannels, and (f) microwell/pillar matrix.

To evaluate the quality and repeatability of this unique molding process, Si molds with microchannels and microwells matrix were fabricated using the standard UV lithography

(measured by Wyko NT9100) as shown in Figure 4.4 (a) and (c). Each microchannel has a width

111 of 5 µm with an average depth of ~0.5 µm. Compared with the replicated features in Figure 4.4 (b), the microchannels were uniformly formed on the PMMA surface with an average height of 0.5

µm, which matched the dimensions of the micro structures on the mold. Another demonstration as shown in Figure 4.4 (c), a microwell matrix mold consists of 10 µm×10 µm squares with a depth of 0.5 µm. The replicated micropillar matrix on PMMA was scanned as shown in Figure 4.4 (d).

The surface profile of the microwell matrix on the mold matched well with the replicated features.

As illustrated in Figure 4.4 (e) and (f), the geometry of the replicated features matched those on the

Si mold. This result demonstrated that the high-precision molding technique discussed in this research can be used to successfully transfer optical microfeatures from mold surface to polymer substrates.

Figure 4.5 (a) and (b) illustrated the 3D geometry of the microlens array, the 6×6 microlens array and an individual microlenslet. The measurement of the curvatures of the mold and replicated features indicated that this method can effectively replicate micro features to PMMA samples with high precision. The deviations between two features are due to part warpage and shrinkage but were determined to be less than a few tens of nanometers.

112

4.1.5 Optical Characterization

The optical measurement setup for diffraction performance is illustrated in Figure 4.6 (a). A He-

Ne laser with 632.8 nm wavelength was used to evaluate the diffraction performance of the optical microchannel & micropillar element. The laser beam was first attenuated by two linear polarizers.

The molded diffractive element was mounted on a linear translation stage with a resolution of 1

µm. The image after the diffractive element was projected onto the imaging plane of a charge coupled device (CCD) camera (PL-B957F, pixeLINK, Ottawa, ON, Canada). The point spread function (PSF) of the molded microchannel & micropillars at the wavelength of 632.8 nm was captured and the normalized intensity profile is shown in Figure 4.6 (a) and (b).

113

To evaluate the optical quality of the molded microlens array, a Twyman-Green interferometer was set up to measure the focal length of each individual microlens. The measured focal length for

PMMA is 12.12 mm, which closely matches to the design effective focal length 12.1 mm. It was demonstrated that the optical property of the replicated samples was quite uniform and precise, an important attribute for optical system assembly.

In the last test, a large-area 16×16 microlens array with the same geometry shape was specially designed for a CCD camera to construct a Shack–Hartmann wavefront sensor (SHWFS) as shown in Figure 4.7 (a). A He-Ne laser with a plane wavefront was used as the light source. The test lens 114 is a standard spherical lens (focal length = 200 mm). In this setup, the distance between the microlens arrays and the CCD was precisely adjusted to one focal length. Figure 4.7 (b) and (c) show the reconstructed wavefront and simulated result using MATLAB. The maximum error is

7.3×10-3 mm over the pupil area, which is similar to an SHWFS that was built in this lab earlier using injection molded microlens arrays [61].

Figure 4.7 (a) Spherical wavefront measurement experiment using an SHWFS. (b) Reconstructed wavefront with the SHWFS. (c) Simulated wavefront using MATLAB.

4.1.6 Conclusions

In conclusion, a novel method of rapid localized induction heating is proposed. This method is based on induction heating of a thin conductive coating on a silicon mold placed in a magnetic field.

Experiments performed in this study demonstrated that compression molding using rapid localized induction heating can be a viable process for high-precision replication of micro scale optical features on polymer substrates. Owning to the high electrical and thermal conductivity, the carbide- bonded graphene is an effective and high-performance coating material for non-sticking localized

115 heating process. The experiments show that the micro features on the Si molds were successfully transferred to the polymer surface within a short thermal cycle of only a few min. As demonstrated in this research, the optical gratings molded using the rapid localized heating by induction have uniform geometries and are capable of providing high quality optical performance. In one of the optical assemblies using a molded microlens array, the performance of the SHWFS is similar to an assembly using a replicated sample fabricated using injection molding process. This method provides an alternative method for precision molding of polymer optics, particularly in applications where the need to improve production efficiency, product quality, and to reduce energy consumption is in high demand.

4.2 Rapid Localized Heating of Graphene Coating by Infrared Radiation

Graphene, as a novel kind of 2D material, monatomic layer of carbon atoms composing of sp2- bonded with the honeycomb lattice structure, has fascinated researchers for centuries. It has been employed in many applications because of its unique electric and optical properties [113–115]. The effective mass of carriers and high carrier mobility make graphene a great candidate for ultrafast optoelectronic devices such as transistors [116] and photodetectors [117–120] in the visible and near-infrared. In the long wavelength range (i.e., mid- to far-infrared), the graphene, like those of

Drudetype materials [121,122], presents strong resonance absorption [122–124]. On the other hand, the building of a strong graphene coating as a protective layer on silicon substrates provides the surface with a unique combination of many other advantages, such as low-adhesion, high thermal conductivity, high hardness and low surface friction [3]. The combination of the aforementioned advantages makes graphene an alternative coating material that can be used with micro/nano

116 patterned Si wafers for high-volume precision glass optics fabrication, thus resulting in a rapid localized molding process at low manufacturing cost.

A few attempts have been made to use graphene coating silicon molds in precision glass molding.

For example, He et al. [3] conducted a comparative molding test between a silicon wafer mold with carbide-bonded graphene coating and a silicon wafer mold without graphene coating. Their investigation demonstrated that graphene coating enables silicon to be used as a mold material by preventing silicon to glass adhesions at elevated temperature. Additionally, graphene coating was adopted as a conductive heating layer in hot embossing. Xie et al. [33] developed a rapid hot microembossing technique utilizing micro-patterned silicon stampers coated with a carbide-bonded graphene network to implement rapid heating and cooling. The hot embossing technique was successfully implemented to imprint microchannel and microlens arrays onto thermoplastic polymer substrates with high precision. Li et al. [34] further extended the rapid heating technique to chalcogenide glass molding process with graphene coated fused silica wafer. The feasibility of this process was validated by both experiments and numerical simulation. Zhang et al. [2] employing high-frequency alternative electromagnetic field as an energy input into the ultra-thin conductive graphene coating. The heating and cooling rates were greatly improved and the whole molding process could be finished within several mins. However, the process cycle was still far from wide applications in industry due to operation complexity.

In this section, we demonstrated precision molding of polymer micro-optics with mid-infrared heater and graphene-coated Si molds. The micro-patterned Si stampers were coated with a thin layer of newly developed carbide-bonded graphene using chemical vapor deposition (CVD). A

117 molding process of a chalcogenide glass with relatively lower Tg than the oxide glass was employed.

Due to the high absorption of min-infrared, the ultra-thin layer of graphene can be heated above Tg within several seconds. Finally, the uniformity, surface quality and optical performance of the molded glass samples were validated.

4.2.1 Micro-feature Fabrication on Silicon Wafer

Silicon (Si) wafers were employed to fabricate the micro-structures on precision molds aimed their high mechanical strength and excellent surface quality among nonmetallic materials. Standard photolithography process was conducted to fabricate micro-structures on the silicon wafer surface.

In this study, the initial silicon wafer was 4 inches diameter and 500 µm thick single-crystalline silicon wafer. First, the silicon wafer was cleaned by using acetone and isopropanol, sequentially.

Then, hexamethyldisilazane (HMDS) prime oven was employed to improve the adhesion between the photoresist and silicon wafer. Afterwards, a layer of AZ5214-E image reversal photoresist was deposited on the silicon wafer with a thickness of 1.65 µm. The wafer was exposed with UV radiation (15mW/cm2) with a duration of 0.5 s on an EV Group 620 advanced contact aligner. To reverse the image, the silicon wafer was put on the hotplate for 2 mins with 115 °C. After cooling down, the flood exposure was conducted with a duration of 10 s. Next, the wafer was developed for 1 min in MF-319 solvent and then rinsed in deionized water. After drying, the wafer was etched on PlasmaTherm SLR-770 using CF4 at a flow rate of 20 sccm. Finally, the remaining photoresist was stripped and cleaned by acetone.

118

4.2.2 Carbide-bonded Graphene Coating Using CVD

The micro-patterned silicon wafers were coated with a thin layer of newly developed carbide bonded graphene using chemical vapor deposition (CVD) [125]. As illustrated in Figure 4.8, a liquid catalyzer, tetraethyl orthosilicatemethane (TEOS) with a purity of 99.8% in glass bubbler and a gas carbon source, methane, were used in graphene coating. The silicon wafer was pre-placed inside a quartz tube furnace. A shield gas, argon, was applied to purge air inside the quartz tube with a flow rate of 50 sccm. The temperature increased from room temperature to 1,100 °C at 10 °C

/min heating rate. After the pre-set temperature was reached, the TEOS was introduced into the tube with flow of argon as a carry gas at 15 sccm. At the same time, the methane was also brought into the tube to react with a duration of 20 mins. After deposition, the whole system cools down with 10 °C /min cooling rate to room temperature.

4.2.3 Coating Characterization

Based on the measurement results by atomic force microscopy (AFM), the carbide-bonded graphene coating on silicon wafer with a thickness of approximately 45 nm showed Young's modulus and Hertzian hardness of 165.3 ± 18.6 and 345.2 ± 22.3 GPa, much higher than those of the silicon substrate (43.81 ± 1.75 and 95.9 ± 10.4 GPa) and the nickel mold (53.6 ± 3.4 GPa and

26.2 ± 1.4) [108]. The carbide-bonded graphene coating significantly improved electrical and thermal conduction that that of silicon wafer. The in-plane thermal conductivity of our carbide- bonded graphene on silicon wafer was ∼1,200 W/m · K, much higher than silicon mold (130 W/m-

K) [33]. Furthermore, the graphene coating on silicon stamper exhibited excellent surface smoothness, great anti-adhesion at elevated temperature and low friction coefficient 0.029

119

(compared with 0.076 for silicon wafer). In addition, the carbide-bonded graphene coating is a multi-layer 3D graphene structures on the silicon wafer, which further enhances the absorption on mid-infrared range. For these reasons, our carbide-bonded graphene coating is ideal for replication of microstructures with high aspect ratios.

Figure 4.8 (a) Schematics of atmospheric pressure chemical vapor deposition setup for coating graphene on silicon wafer, and (b) variation of process parameters as a function of coating time.

4.2.4 System Characterization

As shown in Figure 4.9, the mid-infrared heating based rapid localized molding apparatus was similar to the conventional molding setup. The home-built apparatus mainly consisted of four components, upper mold, graphene coated silicon mold, mid-infrared heater and insulator. The vertical movement of the upper mold was powered by a linear actuator with a ball screw drive system. Aided with the linear encoder feedback of the servomotor, the position control accuracy is about 1 µm. The molding pressure system could provide a constant/variable load during the molding process with the flexible and robust control through a Labview interface. Employing NI

DAQ devices and Labview modular programming, the apparatus was able to achieve process 120 setting, motion and temperature control and real time parameter monitoring. The process parameters, involving temperature and press load, were monitored and automatically stored by the logging system.

A Thermalcraft high-current power supply (1-1-35-230-Y07SK) was adopted to provide power for the mid-infrared heater. The maximum voltage and current were 230V and 35A. Multi-channel K- type thermocouples with a stripped lead were attached to the sample surface with a conductive insulating tape to monitor the temperature profiles for both silicon wafer and polymer substrate.

Then the collected data, as feedback parameters, were further used in a LabVIEW program for PID temperature control.

Figure 4.9 Schematic of the rapid heating precision molding system.

Figure 4.10 (a) illustrated the heating/cooling response of the graphene coating under various driving powers. The result showed that the heating rate increased significantly as the power increased. The average heating rate could achieve 4.88 °C/s, 6.73 °C/s, 8.97 °C/s, 11.36 °C/s,

13.98°C/s, 17.54 °C/s and 18.16 °C/s at the driving power of 150 W, 225 W, 300 W, 375 W, 450

W, 525 W and 600 W, respectively. Using this setup, the silicon wafer surface could be heated

121 from 30 °C to 220 °C within 10-40 s with different level of power. When the driving power was turned down, the silicon surface cools quickly due to the low thermal inertia of thin layer graphene coating. Furthermore, repeated heating/cooling cycles were conducted to evaluate the stability of the graphene coating. As shown in Figure 4.10 (b), in about 40 mins continuous testing, the temperature profile exhibited excellent repeatability implying good thermal stability of the graphene coating. The heating/cooling cycle time remains constant after dozens rapid heating-to- cooling cycles, indicating that the graphene bonding strength is sufficient and stable enough to be implemented in repetitive heating/cooling cycles. In addition, three thermocouples were attached to the surface with insulated tape at the center area, middle area and the edge area, as shown in

Figure 4.10 (c). The temperature variation at these three points showed no notable difference, which indicated that the graphene coated silicon mold maintained at the same temperature, which is the optimal condition for precision molding. Furthermore, the temperature profiles of the graphene coated surface were compared with those without graphene coating with the same driving powers.

The measurement shows large difference in heating/cooling rates, in general, several times faster for the graphene coating molds, as illustrated in Figure 4.10 (d).

4.2.5 Molding Experiment

Rapid localized molding involves the following four steps, heating, pressing, cooling and demolding. Before molding, a piece of Poly (methyl methacrylate) (PMMA) was placed on the surface of the silicon mold. To ensure efficient heat transfer between the mold and PMMA, a small initial pressure was applied on the PMMA preform at the beginning of heating. The graphene coating was quickly heated up over the glass transition temperature Tg to the pre-set molding

122 temperature. The PMMA began to soften and deform within seconds near the interface. After that, a holding pressure, which is much larger than the initial pressure, was applied on to the preform for several seconds. Then, the mid-infrared heater was turned off and the pressure was released when temperature was decreased to below the transition temperature. When temperature was reduced to near room temperature through fast cooling, the mold could be removed for demolding.

Figure 4.10 (a) Heating/cooling response of graphene coating under various driving power, (b) heating/cooling cycles of graphene coating at 300 W, (c) temperature profiles at three different points on the surface, and (d) temperature variation with/without graphene coating.

123

As illustrated in Figure 4.11, the micro-patterns of the silicon wafer and molded samples using rapid heating process were investigated by a white light profilometer (NT 9100 Wyko) to evaluate the replication process. The micro patterns were successfully replicated onto the PMMA substrates in around 60 s cycle time using 300 W operation power. Figure 4.11 (a) and (b) presented the three- dimensional (3D) structures of the micro-channel on the silicon mold and molded samples with an amplification of 20 ×, respectively. From the results shown in Figure 4.11 (b), homogeneous features of both the 3D structures and the profile were obtained, indicating the uniformity of the molded micro-structure. Since distortion of the relative positions between the lenslets was a key factor forming the form error of the micro-channel, the corresponding cross-sectional profiles were further captured presented in Figure 4.11 (e). The average height of the molded micro-channel was about 492 nm, and the distance between two successive micro-channel was about 10.01 μm. The observed values were in good agreement with the molds. More importantly, the shapes as well as the sizes of the two profiles along the cross-sectional directions agreed well with each other, showing high consistence and high accuracy of the obtained structures. Another example, shown in Figure 4.11 (c), was a microwell mold with 10 μm × 10 μm squares and a depth of 0.5 μm. The replicated micropillar on PMMA was shown in Figure 4.11 (d). As illustrated in Figure 4.11 (f), the surface profile of the microwells on the mold matched the replicated features on the substrate.

The result further proved that this novel rapid localized molding process successfully transferred these optical features from mold surface to polymer substrates.

124

4.2.6 Optical Characterization

In order to analyze the functionality of the micro-structure of the molded polymer parts, an instrument designed to measure scattering was modified slightly to perform the measurements. As shown in Figure 4.12 (a), a He-Ne laser beam (632.8 nm) was projected onto the molded polymer micro-structure. When the laser beam strikes the microstructures, such as 1D or 2D gratings, it was

125 split and scattered into different directions. By using a large screen, the intensity and associated angle of diffraction beams were presented. As shown in Figure 4.12 (b) - (f), the scattering spots diagram was symmetric and the central spot had the largest intensity. The secondary max intensity spots were located next to the central area. The intensity and position of each spot represented the performance of the grating. By analyzing the scattering spot diagram, the information of surface properties of molded samples can be determined [126].

Figure 4.12 (a) Illustration of setup for testing molded optical gratings, (b) - (f) diffraction patterns on the screen with different surface patterns.

4.2.7 Conclusions

A new rapid localized precision molding system was developed by utilizing a novel carbide- bonded graphene coating and mid-infrared heater. The silicon wafer provides great mechanical strengths and uniform surface quality. Due to lower thermal conductivity of silicon wafer and great absorption of multi-layer graphene coating, relatively low power to the mid-infrared heater could

126 be applied to achieve rapid heating on graphene coating. As a result, the contact surface temperature could quickly reach softening point within seconds for precise replication of microstructures with very low energy consumption. The heating rate can be increased up to 18.16 °C/s by employing a driving power of 600 W, which could be further improved by utilizing more powerful mid-infrared heater. In addition, the graphene coating also provided very low surface friction, which maybe valuable for de-molding of microstructures with high aspect ratios. This rapid heating strategy was successfully demonstrated in precision molding for both micro-channels and micro-pillar arrays on thermoplastic polymer substrates with high efficiency, uniform surface quality and low energy consumption.

127

CHAPTER 5: CONCLUSION AND FUTURE WORK

5.1 Thesis Summary

Chalcogenide glasses are increasingly being studied for their infrared transmission. More recently, the development of uncooled infrared focal plane detectors boosts the applications of molded optics with chalcogenide glasses, which are significantly cheaper than optics made with expensive germanium. Over the last few decades, chalcogenide glass research has experienced tremendous growth. However, research toward fundamentally understanding of the process and modeling was limited. This research seeks a fundamental understanding of the chalcogenide glass molding process, including forming, mold making, and molding process modeling. One of the objectives of this research is to study one or two of these unsolved problems, i.e., the refractive index change and residual stresses of chalcogenide glass after precision glass molding. Another objective is to extend the application of the precision glass molding by focusing on developing new infrared micro optics like Shack-Hartmann wavefront sensor and large field-of-view freeform microlens array. The last objective is to develop a high-efficiency, low-cost and flexible rapid localized heating process for precision glass molding for texture replication.

In chapter two, the thermoforming mechanism of chalcogenide glasses around its glass transition temperature was investigated by numerical simulation and experiments. First, a constitutive model was introduced to precisely predict the material behavior in PGM by integrating subroutines into a commercial finite element method (FEM) software. This modeling approach utilizes the Williams- 128

Landel-Ferry (WLF) equation and Tool-Narayanaswamy-Moynihan (TNM) model to describe

(shear) stress relaxation and structural relaxation behaviors, respectively. Then, the refractive index variations inside molded lenses predicted by the FEM simulation was confirmed by measuring angular deviation produced by a molded glass prism. In the second section of the chapter, the distribution of refractive index change and residual stresses in the molded lens were further investigated by FEM simulation and experiment. The refractive index variations inside molded lenses obtained by the FEM simulation was evaluated by measuring wavefront changes using an infrared Shack-Hartmann wavefront sensor (SHS), while the residual stresses trapped inside the molded lenses were obtained by using a birefringence method. Measured results of the molded infrared lenses were combined with numerical simulation provided an opportunity for optical manufacturers to achieve better understanding on the mechanism and optical performance of chalcogenide glasses in and post PGM.

In chapter three, two infrared optical elements by precision glass molding on chalcogenide glass were demonstrated. First, a plano-convex micro-lens array is designed and fabricated by combination of ultraprecision diamond milling and precision glass molding. The geometries and surface roughness of the molded micro-lens array are measured and examined. Using an infrared detector, the optical property of the micro-lens array and the validity of the Shack-Hartmann wavefront sensor (SHS) are demonstrated as well. In addition, an infrared compound eye system consisting of 3×3 channels for a field of view of 48°×48° with a thickness of 1.8 mm was developed.

The freeform microlens array on a flat surface was employed to steer and focus the incident light from three dimensions to a two-dimension (2D) infrared imager. Using raytracing method, the profile of the freeform microlenses of each channel were optimized to obtain the best imaging 129 performance. To avoid crosstalk among adjacent channels, a micro aperture array fabricated by 3D printing was mounted between the microlens array and IR imager. The imaging tests of the infrared compound-eye imaging system using the molded chalcogenide glass lenses showed that the asymmetrical freeform lenslets were capable of steering and forming legible images within the designed field of view. Compared to a conventional infrared camera, this novel microlens array can achieve a considerably larger field-of-view while maintaining low manufacturing cost without sacrificing image quality.

In chapter four, two new localized rapid heating processes were explored and demonstrated by using graphene-coated silicon as an effective and high-performance mold material for precision glass molding. One process is based on induction heating and the other one is based on mid-infrared radiation. Since the graphene coating is very thin (~45 nm), a high heating rate of 20~40 C/s can be achieved. The contact surface of the Si mold and the polymer substrate can be heated above Tg within 20 s and subsequently cooled down to room temperature within tens of seconds after molding. The feasibility of this process was validated by fabrication of optical gratings, micropillar matrices, and microlens arrays on polymethylmethacrylate substrate with high precision. The uniformity and surface geometries of the replicated optical elements are evaluated using an optical profilometer. Compared with the conventional bulk heating molding process, this novel rapid localized heating process could improve replication efficiency with better geometrical fidelity and much shorter cycle times.

130

5.2 Recommendations for Future Work

The future works of the related research may include two different topics, i.e., fundamental research on improvement of surface quality, geometrical profile, optical performance, etc., and applications of precision glass molding in micro/nano-optical fabrication.

1. Hybrid Infrared Glass Achromatic Microlens: In recent years, various techniques for creating achromatic lenses have been investigated for polychromatic applications in order to correct chromatic aberrations. Achromatic lenses are usually designed in the form of achromatic doublets, in which materials with different optical dispersion characteristics are assembled together to form a hybrid lens or a diffractive optical achromat, where the complementary dispersion characteristics can be considered. This study will verify the feasibility of creating a hybrid achromatic microlens array by using different kinds of chalcogenide glass in precision glass molding.

2. Antireflection Structure Design and Fabrication: Chalcogenide glasses with high refractive indices face excessive transmission loss due to Fresnel reflection. Traditionally, thin film coatings are needed for molded chalcogenide lenses, which is an added process and a source for errors. Past studies on surface structures have shown that a carefully engineered surface with meso/micro/nanometer scale structures can significantly reduce Fresnel reflection. Anti-reflective surfaces, similar to Figure 5.1 (a) can be constructed such that maximum transmission occurs at boundary by precision glass molding. Such a surface is optically equal to multilevel surface-relief profile where the effective medium can be simplified into a film stack with each layer of the film stack corresponds to a distinct level of the surface-relief profile, shown in Figure 5.1 (b). As a

131 demonstration, a surface with submicron feature can be designed and fabricated as shown in Figure

5.1 (c).

ʌ Ɵ i b ni ni

Ɵ eff neff

K ns Ɵ s ns

(a) (b) (c)

Figure 5.1 (a) anti-reflection surface model, (b) effective medium optical model, and (3) proposed 3D anti-reflective surface structure.

3. Multi-level Flat Infrared Lens Design and Fabrication: Ultra-thin flat lens has shown great potential for the development of miniaturized imaging and sensing systems. By replacing traditional lenses of bulky size, the volume of optical systems can be reduced dramatically without satisfying optical performance. Multi-level meso/micro/nano-meter scale structures are presented the great potential on phase profile control of electromagnetic wave. Superior optical performance can be achieved by optimizing the meso/micro/nano-structure on the ultra-thin lens’ surface.

132

Bibliography

1. R. O. Maschmeyer, C. A. Andrysick, T. W. Geyer, H. E. Meissner, C. J. Parker and L. M. Sanford, “Precision molded-glass optics,” Appl. Opt. 22, 2410–2412 (1983).

2. L. Zhang, W. Zhou and A. Y. Yi, “Rapid localized heating of graphene coating on a silicon mold by induction for precision molding of polymer optics,” Opt. Lett. 42, 1369–1372 (2017).

3. P. He, L. Li, J. Yu, W. Huang, Y.-C. Yen, L. J. Lee and A. Y. Yi, “Graphene-coated Si mold for precision glass optics molding,” Opt. Lett. 38, 2625–2628 (2013).

4. A. Y. Yi and A. Jain, “Compression Molding of Aspherical Glass Lenses–A Combined Experimental and Numerical Analysis,” J. Am. Ceram. Soc. 88, 579–586 (2005).

5. L. Dick, S. Risse and A. Tünnermann, “Process influences and correction possibilities for high precision injection molded freeform optics,” Adv. Opt. Technol. 5, 277–287 (2016).

6. A. Ravagli, C. Craig, J. Lincoln and D. W. Hewak, “Ga-La-S-Se glass for visible and thermal imaging,” Adv. Opt. Technol. 6, 131–136 (2017).

7. A. R. Hilton, “Nonoxide Chalcogenide Glasses as Infrared Optical Materials,” Appl. Opt. 5, 1877–1882 (1966).

8. K. J. Laidler Chemical Kinetics, 3rd ed., Prentice Hall (1987).

9. E. H. Lee and T. G. Rogers, “Solution of Viscoelastic Stress Analysis Problems Using Measured Creep or Relaxation Functions,” J. Appl. Mech. 30, 127–133 (1963).

10. L. W. Morland and E. H. Lee, “Stress Analysis for Linear Viscoelastic Materials with Temperature Variation,” Trans. Soc. Rheol. 4, 233–263 (1960).

133

11. A. H. Corneliussen and E. H. Lee, “Stress Distribution Analysis for Linear Viscoelastic Materials,” in Creep in Structures, pp. 1–20, Springer (1962).

12. M. Arai, Y. Kato and T. Kodera, “Characterization of the Thermo-Viscoelastic Property of Glass and Numerical Simulation of the Press Molding of Glass Lens,” J. Therm. Stress. 32, 1235–1255 (2009).

13. W. N. Findley, J. S. Lai and K. Onaran, Creep and Relaxation of Nonlinear Viscoelastic Materials, Revised ed., Dover Publications (2011).

14. J. D. Ferry, Viscoelastic Properties of Polymers, 3rd ed., Wiley (1980).

15. Roylance D, Engineering Viscoelasticity, Cambridge (2001).

16. J. Zhou, J. Yu, L. J. Lee, L. Shen and A. Yi, “Stress Relaxation and Refractive Index Change of As2S3 in Compression Molding,” Int. J. Appl. Glass Sci. 8, 255–265 (2017).

17. M. L. Williams, R. F. Landel and J. D. Ferry, “The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-forming Liquids,” J. Am. Chem. Soc. 77, 3701–3707 (1955).

18. O. S. Narayanaswamy, “A Model of Structural Relaxation in Glass,” J. Am. Ceram. Soc. 54, 491–498 (1971).

19. C. T. Moynihan, A. J. Easteal, M. A. D. Bolt and J. Tucker, “Dependence of the Fictive Temperature of Glass on Cooling Rate,” J. Am. Ceram. Soc. 59, 12–16 (1976).

20. J. Málek, “Structural relaxation of As2S3 glass by length dilatometry,” J. Non-Cryst. Solids 235–237, 527–533 (1998).

21. A. Jain and A. Y. Yi, “Numerical Modeling of Viscoelastic Stress Relaxation During Glass Lens Forming Process,” J. Am. Ceram. Soc. 88, 530–535 (2005).

22. A. Jain and A. Y. Yi, “Finite Element Modeling of Structural Relaxation During Annealing of a Precision-Molded Glass Lens,” J. Manuf. Sci. Eng. 128, 683–690 (2006).

134

23. F. Wang, Y. Chen, F. Klocke, G. Pongs and A. Y. Yi, “Numerical Simulation Assisted Curve Compensation in Compression Molding of High Precision Aspherical Glass Lenses,” J. Manuf. Sci. Eng. 131, (2009).

24. Y. Chen, A. Y. Yi, L. Su, F. Klocke and G. Pongs, “Numerical Simulation and Experimental Study of Residual Stresses in Compression Molding of Precision Glass Optical Components,” J. Manuf. Sci. Eng. 130, (2008).

25. O. Dambon, F. Wang, F. Klocke, G. Pongs, B. Bresseler, Y. Chen and A. Y. Yi, “Efficient mold manufacturing for precision glass molding,” J. Vac. Sci. Technol. B Microelectron. Nanometer Struct. Process. Meas. Phenom. 27, 1445–1449 (2009).

26. L. Su and A. Y. Yi, “Finite Element Calculation of Refractive Index in Optical Glass Undergoing Viscous Relaxation and Analysis of the Effects of Cooling Rate and Material Properties,” Int. J. Appl. Glass Sci. 3, 263–274 (2012).

27. K. Shishido, M. Sugiura and T. Shoji, “Aspect of glass softening by master mold,” in: Proc. SPIE 2536, Optical Manufacturing and Testing, San Diego, CA, USA, September 8, 1995.

28. K. D. Fischbach, K. Georgiadis, F. Wang, O. Dambon, F. Klocke, Y. Chen and A. Y. Yi, “Investigation of the effects of process parameters on the glass-to-mold sticking force during precision glass molding,” Surf. Coat. Technol. 205, 312–319 (2010).

29. J. Xie, T. Zhou, Y. Liu, T. Kuriyagawa and X. Wang, “Mechanism study on microgroove forming by ultrasonic vibration assisted hot pressing,” Precis. Eng. 46, 270–277 (2016).

30. T. Zhou, J. Xie, J. Yan, K. Tsunemoto and X. Wang, “Improvement of glass formability in ultrasonic vibration assisted molding process,” Int. J. Precis. Eng. Manuf. 18, 57–62 (2017).

31. A. R. Abdul Manaf and J. Yan, “Press molding of a Si–HDPE hybrid lens substrate and evaluation of its infrared optical properties,” Precis. Eng. 43, 429–438 (2016).

32. A. R. Abdul Manaf and J. Yan, “Improvement of form accuracy and surface integrity of Si-HDPE hybrid micro-lens arrays in press molding,” Precis. Eng. 47, 469–479 (2017).

135

33. P. Xie, P. He, Y.-C. Yen, K. J. Kwak, D. Gallego-Perez, L. Chang, W. Liao, A. Y. Yi and L. J. Lee, “Rapid hot embossing of polymer microstructures using carbide- bonded graphene coating on silicon stampers,” Surf. Coat. Technol. 258, 174–180 (2014).

34. H. Li, P. He, J. Yu, L. J. Lee and A. Y. Yi, “Localized rapid heating process for precision chalcogenide glass molding,” Opt. Lasers Eng. 73, 62–68 (2015).

35. C. Lu, Y.-J. Juang, L. J. Lee, D. Grewell and A. Benatar, “Analysis of laser/IR- assisted microembossing,” Polym. Eng. Sci. 45, 661–668 (2005).

36. L. Zhang, W. Zhou, N. J. Naples and A. Y. Yi, “Fabrication of an infrared Shack– Hartmann sensor by combining high-speed single-point diamond milling and precision compression molding processes,” Appl. Opt. 57, 3598–3605 (2018).

37. J. H. Choi, Y. J. Jang, D. H. Cha, J.-H. Kim and H.-J. Kim, “Chalcogenide glass with good thermal stability for the application of molded infrared lens,” in: Proc. SPIE 9253, Optics and Photonics for Counterterrorism, Crime Fighting, and Defence X; and Optical Materials and Biomaterials in Security and Defence Systems Technology XI, Amsterdam, Netherlands, October 31, 2014.

38. D. Gibson, S. Bayya, J. Sanghera, V. Nguyen, D. Scribner, V. Maksimovic, J. Gill, A. Yi, J. Deegan and B. Unger, “Layered chalcogenide glass structures for IR lenses,” in: Proc. SPIE 9070, Infrared Technology and Applications XL, Baltimore, Maryland, USA, July 1, 2014.

39. W. Zhao, Y. Chen, L. Shen and A. Y. Yi, “Refractive index and dispersion variation in precision optical glass molding by computed tomography,” Appl. Opt. 48, 3588– 3595 (2009).

40. U. Fotheringham, A. Baltes, P. Fischer, P. Höhn, R. Jedamzik, C. Schenk, C. Stolz and G. Westenberger, “Refractive Index Drop Observed After Precision Molding of Optical Elements: A Quantitative Understanding Based on the Tool– Narayanaswamy–Moynihan Model,” J. Am. Ceram. Soc. 91, 780–783 (2008).

41. J. Novak, R. Pini, W. V. Moreshead, E. Stover and A. Symmons, “Investigation of index of refraction changes in chalcogenide glasses during molding processes,” in: Proc. SPIE 8896, Electro-Optical and Infrared Systems: Technology and Applications X, Dresden, Germany, October 25, 2013.

136

42. S.-H. Lu, S.-P. Pan, T.-S. Liu and C.-F. Kao, “Liquid refractometer based on immersion diffractometry,” Opt. Express 15, 9470–9475 (2007).

43. E. R. Van Keuren, “Refractive index measurement using total internal reflection,” Am. J. Phys. 73, 611–614 (2005).

44. S. F. O. Silva, O. Frazão, P. Caldas, J. L. Santos, F. M. Araujo and L. A. Ferreira, “Optical fiber refractometer based on a Fabry-Pérot interferometer,” Opt. Eng. 47, 054403 (2008).

45. S. G. Kaplan and J. H. Burnett, “Optical properties of fluids for 248 and 193 nm immersion photolithography,” Appl. Opt. 45, 1721–1724 (2006).

46. L. Su and A. Y. Yi, “Investigation of the effect of coefficient of thermal expansion on prediction of refractive index of thermally formed glass lenses using FEM simulation,” J. Non-Cryst. Solids 357, 3006–3012 (2011).

47. E. Guillevic, X. Zhang, T. Pain, L. Calvez, J.-L. Adam, J. Lucas, M. Guilloux-Viry, S. Ollivier and G. Gadret, “Optimization of chalcogenide glass in the As–Se–S system for automotive applications,” Opt. Mater. 31, 1688–1692 (2009).

48. D. Krause and H. Loch, Mathematical Simulation in Glass Technology, Schott Series on Glass and Glass Ceramics, 1st ed., Springer (2002).

49. J. Zhou, P. He, J. Yu, L. J. Lee, L. Shen and A. Y. Yi, “Investigation on the friction coefficient between graphene-coated silicon and glass using barrel compression test,” J. Vac. Sci. Technol. B 33, 031213 (2015).

50. L. Gampel and F. M. Johnson, “Index of Refraction of Single-Crystal Selenium,” JOSA 59, 72–73 (1969).

51. D. J. McEnroe and W. C. LaCourse, “Tensile Strengths of Se, As2S3, As2Se3, and Ge30As15Se55 Glass Fibers,” J. Am. Ceram. Soc. 72, 1491–1494 (1989).

52. H. Aben and C. Guillemet, Photoelasticity of Glass, Springer (1993).

53. J. F. Orr and J. B. Finlay, “Photoelastic stress analysis,” Opt. Meas. Methods Biomech. 1–16 (1997).

137

54. J. Lubliner and P. Papadopoulos, Introduction to Solid Mechanics: An Integrated Approach, Springer (2014).

55. P. C. Anderson and A. K. Varshneya, “Stress-optic coefficient of Ge-As-Se chalcogenide glasses,” J. Non-Cryst. Solids 168, 125–131 (1994).

56. L. Su, Y. Chen, A. Y. Yi, F. Klocke and G. Pongs, “Refractive index variation in compression molding of precision glass optical components,” Appl. Opt. 47, 1662– 1667 (2008).

57. L. Su, F. Wang, P. He, O. Dambon, F. Klocke and A. Y. Yi, “An integrated solution for mold shape modification in precision glass molding to compensate refractive index change and geometric deviation,” Opt. Lasers Eng. 53, 98–103 (2014).

58. B. Ananthasayanam, P. F. Joseph, D. Joshi, S. Gaylord, L. Petit, V. Y. Blouin, K. C. Richardson, D. L. Cler, M. Stairiker and M. Tardiff, “Final Shape of Precision Molded Optics: Part II—Validation and Sensitivity to Material Properties and Process Parameters,” J. Therm. Stress. 35, 614–636 (2012).

59. A. Y. Yi, B. Tao, F. Klocke, O. Dambon and F. Wang, “Residual stresses in glass after molding and its influence on optical properties,” Procedia Eng. 19, 402–406 (2011).

60. B. Tao, L. Shen, A. Yi, M. Li and J. Zhou, “Reducing Refractive Index Variations in Compression Molded Lenses by Annealing,” Opt. Photonics J. 3, 118–121 (2013).

61. W. Zhou, T. W. Raasch and A. Y. Yi, “Design, fabrication, and testing of a Shack- Hartmann sensor with an automatic registration feature,” Appl. Opt. 55, 7892–7899 (2016).

62. H. N. Ritland, “Relation Between Refractive Index and Density of a Glass at Constant Temperature,” J. Am. Ceram. Soc. 38, 86–88 (1955).

63. L. Zhang, W. Zhou, N. J. Naples and A. Y. Yi, “Investigation of index change in compression molding of As40Se50S10 chalcogenide glass,” Appl. Opt. 57, 4245–4252 (2018).

64. J. W. Cha and P. T. C. So, “A Shack-Hartmann Wavefront Sensor Based Adaptive Optics System for Multiphoton Microscopy,” J. Biomed. Opt. 15, 046022 (2008).

138

65. D. Dayton, B. Pierson, B. Spielbusch and J. Gonglewski, “Atmospheric structure function measurements with a Shack-Hartmann wave-front sensor,” Opt. Lett. 17, 1737–1739 (1992).

66. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” JOSA 70, 998–1006 (1980).

67. R. Cubalchini, “Modal wave-front estimation from phase derivative measurements,” JOSA 69, 972–977 (1979).

68. C. Leroux and C. Dainty, “A simple and robust method to extend the dynamic range of an aberrometer,” Opt. Express 17, 19055–19061 (2009).

69. N. Lindlein and J. Pfund, “Experimental results for expanding the dynamic range of a Shack-Hartmann sensor by using astigmatic microlenses,” Opt. Eng. 41, 529–534 (2002).

70. F. T. O’Neill and J. T. Sheridan, “Photoresist reflow method of microlens production Part I: Background and experiments,” Optik 113, 391–404 (2002).

71. F. T. O’Neill and J. T. Sheridan, “Photoresist reflow method of microlens production Part II: Analytic models,” Optik 113, 405–420 (2002).

72. V. Lin, H. -c. Wei, H. -t. Hsieh, J. -l. Hsieh and G. -d. j. Su, “Design and fabrication of long-focal-length microlens arrays for Shack-Hartmann wavefront sensors,” Micro Nano Lett. 6, 523–526 (2011).

73. A. Y. Yi and L. Li, “Design and fabrication of a microlens array by use of a slow tool servo,” Opt. Lett. 30, 1707–1709 (2005).

74. S. Kirchberg, L. Chen, L. Xie, G. Ziegmann, B. Jiang, K. Rickens and O. Riemer, “Replication of precise polymeric microlens arrays combining ultra-precision diamond ball-end milling and micro injection molding,” Microsyst. Technol. 18, 459– 465 (2012).

75. S. Stoebenau and S. Sinzinger, “Ultraprecision machining techniques for the fabrication of freeform surfaces in highly integrated optical microsystems,” in: Proc. SPIE 7426, Optical Manufacturing and Testing VIII, San Diego, California, USA, August 21, 2009.

139

76. Y.-Q. Fu, N. Kok and A. Bryan, “Microfabrication of microlens array by focused ion beam technology,” Microelectron. Eng. 54, 211–221 (2000).

77. E. Brinksmeier and L. Schönemann, “Generation of discontinuous microstructures by Diamond Micro Chiseling,” CIRP Ann. 63, 49–52 (2014).

78. S. To, Z. Zhu and H. Wang, “Virtual spindle based tool servo diamond turning of discontinuously structured microoptics arrays,” CIRP Ann. 65, 475–478 (2016).

79. K.-H. Jeong, J. Kim and L. P. Lee, “Biologically Inspired Artificial Compound Eyes,” Science 312, 557–561 (2006).

80. L. Li and A. Y. Yi, “Development of a 3D artificial compound eye,” Opt. Express 18, 18125–18137 (2010).

81. H. Zhang, L. Li, D. L. McCray, S. Scheiding, N. J. Naples, A. Gebhardt, S. Risse, R. Eberhardt, A. Tünnermann and A. Y. Yi, “Development of a low cost high precision three-layer 3D artificial compound eye,” Opt. Express 21, 22232–22245 (2013).

82. H. Zhang, S. Scheiding, L. Li, A. Gebhardt, S. Risse, R. Eberhardt, A. Tünnermann and A. Y. Yi, “Manufacturing of a precision 3D microlens array on a steep curved substrate by injection molding process,” Adv. Opt. Technol. 2, 257–268 (2013).

83. M. M. A. Zeinhom, Y. Wang, L. Sheng, D. Du, L. Li, M.-J. Zhu and Y. Lin, “Smart phone based immunosensor coupled with nanoflower signal amplification for rapid detection of Salmonella Enteritidis in milk, cheese and water,” Sens. Actuators B Chem. 261, 75–82 (2018).

84. L.-J. Wang, Y.-C. Chang, X. Ge, A. T. Osmanson, D. Du, Y. Lin and L. Li, “Smartphone Optosensing Platform Using a DVD Grating to Detect Neurotoxins,” ACS Sens. 1, 366–373 (2016).

85. L.-J. Wang, Y.-C. Chang, R. Sun and L. Li, “A multichannel smartphone optical biosensor for high-throughput point-of-care diagnostics,” Biosens. Bioelectron. 87, 686–692 (2017).

86. L.-J. Wang, N. Naudé, Y.-C. Chang, A. Crivaro, M. Kamoun, P. Wang and L. Li, “An Ultra-low Cost Smartphone Octochannel Spectrometer for Mobile Health Diagnostics,” J. Biophotonics 11, e201700382 (2018).

140

87. L.-J. Wang, N. Naudé, M. Demissie, A. Crivaro, M. Kamoun, P. Wang and L. Li, “Analytical validation of an ultra low-cost mobile phone microplate reader for infectious disease testing,” Clin. Chim. Acta Int. J. Clin. Chem. 482, 21–26 (2018).

88. H. Zhang, L. Li, D. L. McCray, D. Yao and A. Y. Yi, “A microlens array on curved substrates by 3D micro projection and reflow process,” Sens. Actuators Phys. 179, 242–250 (2012).

89. A. Y. Yi, C. Huang, F. Klocke, C. Brecher, G. Pongs, M. Winterschladen, A. Demmer, S. Lange, T. Bergs, M. Merz and F. Niehaus, “Development of a compression molding process for three-dimensional tailored free-form glass optics,” Appl. Opt. 45, 6511–6518 (2006).

90. R. Sun, Y. Li and L. Li, “Rapid method for fabricating polymeric biconvex parabolic lenslets,” Opt. Lett. 39, 5391–5394 (2014).

91. K. Lee, W. Wagermaier, A. Masic, K. P. Kommareddy, M. Bennet, I. Manjubala, S.- W. Lee, S. B. Park, H. Cölfen and P. Fratzl, “Self-assembly of amorphous calcium carbonate microlens arrays,” Nat. Commun. 3, 1–7 (2012).

92. S. Tong, H. Bian, Q. Yang, F. Chen, Z. Deng, J. Si and X. Hou, “Large-scale high quality glass microlens arrays fabricated by laser enhanced wet etching,” Opt. Express 22, 29283–29291 (2014).

93. Z. Zhu, S. To and S. Zhang, “Large-scale fabrication of micro-lens array by novel end-fly-cutting-servo diamond machining,” Opt. Express 23, 20593–20604 (2015).

94. T. Hou, C. Zheng, S. Bai, Q. Ma, D. Bridges, A. Hu and W. W. Duley, “Fabrication, characterization, and applications of microlenses,” Appl. Opt. 54, 7366–7376 (2015).

95. T. Gissibl, S. Thiele, A. Herkommer and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10, 554–560 (2016).

96. T. Gissibl, S. Thiele, A. Herkommer and H. Giessen, “Sub-micrometre accurate freeform optics by three-dimensional printing on single-mode fibres,” Nat. Commun. 7, 1–9 (2016).

97. B. McCall and T. S. Tkaczyk, “Rapid fabrication of miniature lens arrays by four- axis single point diamond machining,” Opt. Express 21, 3557–3572 (2013).

141

98. A. A. Tseng, “Removing Material Using Atomic Force Microscopy with Single- and Multiple-Tip Sources,” Small 7, 3409–3427 (2011).

99. L. Zhang, W. Zhou and A. Y. Yi, “Investigation of thermoforming mechanism and optical properties change of chalcogenide glass in precision glass molding,” Appl. Opt. 57, 6358–6368 (2018).

100. Zemax User Manual, [online] https://customers.zemax.com/

101. W. Zhou, L. Zhang and A. Y. Yi, “Design and fabrication of a compound-eye system using precision molded chalcogenide glass freeform microlens arrays,” Optik 171, 294–303 (2018).

102. E. Koontz, P. Wachtel, J. D. Musgraves and K. Richardson, “Characterization of structural relaxation in As2Se3 for analysis of lens shape change in glass press mold cooling and post-process annealing,” in: Proc. SPIE 8884, Optifab 2013, Rochester, New York, USA, October 15, 2013.

103. N. Carlie, N. C. Anheier, H. A. Qiao, B. Bernacki, M. C. Phillips, L. Petit, J. D. Musgraves and K. Richardson, “Measurement of the refractive index dispersion of As2Se3 bulk glass and thin films prior to and after laser irradiation and annealing using prism coupling in the near- and mid-infrared spectral range,” Rev. Sci. Instrum. 82, 053103 (2011).

104. J. Novak, A. Symmons, S. Novak and E. Stover, “Applicability of an annealing coefficient for precision glass molding of As40Se60,” in: Proc. SPIE 9822, Advanced Optics for Defense Applications: UV through LWIR, Baltimore, Maryland, USA, May 17, 2016.

105. L. Li and A. Y. Yi, “Design and fabrication of a freeform microlens array for a compact large-field-of-view compound-eye camera,” Appl. Opt. 51, 1843–1852 (2012).

106. S. Scheiding, A. Y. Yi, A. Gebhardt, L. Li, S. Risse, R. Eberhardt and A. Tünnermann, “Freeform manufacturing of a microoptical lens array on a steep curved substrate by use of a voice coil fast tool servo,” Opt. Express 19, 23938–23951 (2011).

107. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).

142

108. W. Huang, J. Yu, K. J. Kwak, D. Gallego‐Perez, W. Liao, H. Yang, X. Ouyang, L. Li, W. Lu, G. P. Lafyatis and L. J. Lee, “Atomic Carbide Bonding Leading to Superior Graphene Networks,” Adv. Mater. 25, 4668–4672 (2013).

109. S. Franssila, Introduction to Microfabrication, 2nd ed., Wiley (2010).

110. W. Huang, X. Ouyang and L. J. Lee, “High-Performance Nanopapers Based on Benzenesulfonic Functionalized Graphenes,” ACS Nano 6, 10178–10185 (2012).

111. M. Sinder, J. Pelleg, V. Meerovich and V. Sokolovsky, “RF heating of the conductor film on silicon substrate for thin film formation,” Mater. Sci. Eng. A 302, 31–36 (2001).

112. S. M. Sze, K. K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley (2006).

113. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva and A. A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films,” Science 306, 666–669 (2004).

114. F. Xia, H. Yan and P. Avouris, “The Interaction of Light and Graphene: Basics, Devices, and Applications,” Proc. IEEE 101, 1717–1731 (2013).

115. A. Vakil and N. Engheta, “Transformation Optics Using Graphene,” Science 332, 1291–1294 (2011).

116. M. Engel, M. Steiner, A. Lombardo, A. C. Ferrari, H. Löhneysen, P. Avouris and R. Krupke, “Light–matter interaction in a microcavity-controlled graphene transistor,” Nat. Commun. 3, 1–6 (2012).

117. F. Xia, T. Mueller, Y. Lin, A. Valdes-Garcia and P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).

118. T. Mueller, F. Xia and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4, 297–301 (2010).

119. M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser and T. Mueller, “Microcavity-Integrated Graphene Photodetector,” Nano Lett. 12, 2773–2777 (2012).

143

120. Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander and N. J. Halas, “Graphene- Antenna Sandwich Photodetector,” Nano Lett. 12, 3808–3813 (2012).

121. L. A. Falkovsky, “Optical properties of graphene,” J. Phys. Conf. Ser. 129, 012004 (2008).

122. R. Alaee, M. Farhat, C. Rockstuhl and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express 20, 28017–28024 (2012).

123. A. Yu. Nikitin, F. Guinea, F. J. Garcia-Vidal and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85, 081405 (2012).

124. S. Thongrattanasiri, F. H. L. Koppens and F. J. García de Abajo, “Complete Optical Absorption in Periodically Patterned Graphene,” Phys. Rev. Lett. 108, 047401 (2012).

125. M. Wu, L. Zhang, E. D. Cabrera, J.-J. Pan, H. Yang, D. Zhang, Z.-G. Yang, J.-F. Yu, J. Castro, H.-X. Huang and L. J. Lee, “Carbide-bonded graphene coated zirconia for achieving rapid thermal cycling under low input voltage and power,” Ceram. Int. 45, 24318–24323 (2019).

126. H. Husu, T. Saastamoinen, J. Laukkanen, S. Siitonen, J. Turunen and A. Lassila, “Scatterometer for characterization of diffractive optical elements,” Meas. Sci. Technol. 25, 044019 (2014).

144