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Library of Congress Cataloging-in-Publication Data

Kress, Bernard C., author.

Digital micro-optics / Bernard C. Kress.

pages cm. – (The field guide series; FG33)

Includes bibliographical references and index.

ISBN 978-1-62841-183-6

1. Optoelectronic devices–Design and construction.

2. Optical MEMS. 3. Integrated optics. 4. Digital

electronics. 5. Diffraction gratings. I. Title.

TK8360.O68K74 2014



Published by


P.O. Box 10

Bellingham, Washington 98227-0010 USA

Phone: 360.676.3290

Fax: 360.647.1445


The content of this book reflects the thought of the author(s). Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon.

Printed in the United States of America.

Last updated 11/20/2014.

Introduction to the Series

Welcome to the SPIE Field Guides—a series of publications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the SPIE Field Guides is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series.

Each SPIE Field Guide addresses a major field of optical science and technology. The concept of these Field Guides is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page, and provides full coverage of that topic on that page. Highlights, insights, and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each Field Guide provide additional information such as related material outside the main scope of the volume, key mathematical relationships, and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field.

The SPIE Field Guides are intended to be living documents. The modular page-based presentation format allows them to be updated and expanded. We are interested in your suggestions for new Field Guide topics as well as what material should be added to an individual volume to make these Field Guides more useful to you. Please contact us at

John E. Greivenkamp, Series Editor

College of Optical Sciences

The University of Arizona

The Field Guide Series

Keep information at your fingertips with all of the titles in the Field Guide Series:
  • Adaptive Optics, Second Edition, Robert Tyson & Benjamin Frazier

  • Atmospheric Optics, Larry Andrews

  • Binoculars and Scopes, Paul Yoder, Jr. & Daniel Vukobratovich

  • Diffractive Optics, Yakov Soskind

  • Digital Micro-Optics, Bernard Kress

  • Displacement Measuring Interferometry, Jonathan Ellis

  • Geometrical Optics, John Greivenkamp

  • Holography, Pierre-Alexandre Blanche

  • Illumination, Angelo Arecchi, Tahar Messadi, & John Koshel

  • Image Processing, Khan M. Iftekharuddin & Abdul Awwal

  • Infrared Systems, Detectors, and FPAs, Second Edition, Arnold Daniels

  • Interferometric Optical Testing, Eric Goodwin & Jim Wyant

  • Laser Pulse Generation, Rüdiger Paschotta

  • Lasers, Rüdiger Paschotta

  • Lens Design, Julie Bentley & Craig Olson

  • Microscopy, Tomasz Tkaczyk

  • Nonlinear Optics, Peter Powers

  • Optical Fabrication, Ray Williamson

  • Optical Fiber Technology, Rüdiger Paschotta

  • Optical Lithography, Chris Mack

  • Optical Thin Films, Ronald Willey

  • Optomechanical Design and Analysis, Katie Schwertz & James Burge

  • Physical Optics, Daniel Smith

  • Polarization, Edward Collett

  • Probability, Random Processes, and Random Data Analysis, Larry Andrews

  • Radiometry, Barbara Grant

  • Special Functions for Engineers, Larry Andrews

  • Spectroscopy, David Ball

  • Terahertz Sources, Detectors, and Optics, Créidhe O'Sullivan & J. Anthony Murphy

  • Visual and Ophthalmic Optics, Jim Schwiegerling

Field Guide to Digital Micro-Optics

The term “digital micro-optics” was introduced in the early 1990s to refer to a specific variety of micro-optics. It is now widely accepted by industry and academia. Digital micro-optics can be related to their counterparts in the electronics realm—“digital electronics,” or “integrated electronics” (ICs)—in various ways, from design to modeling, from prototyping to mass fabrication, and eventually system integration. Historically, the term “digital” in digital electronics refers to three aspects:
  • their digital functionality (binary logic),

  • the way they are designed via a digital computer, and

  • the way they are fabricated (through sets of digital or binary masks).

In digital micro-optics, the term primarily refers to how such optics are designed and fabricated, similar to digital electronics, through specific electronic-design-automation (EDA) software packages and sets of digital masks. Traditional macro-optics, such as telescopes, microscopes, and other imaging optics, have been designed without complex design software tools. Digital optics, especially wafer-scale micro-optics, cannot be designed without specific software and tools. Digital layouts for wafer-level fabrication of micro-optics are also often generated by algorithms similar to the ones used in conventional EDA tools (Cadence, Synopsys, Mentor-Graphics, etc.). Because there is often no analytical solution to the micro-optics design problem, complex iterative optimization algorithms may be required to find an adequate solution.

Unlike digital electronics, digital micro-optics can implement either digital or analog functionality, or a combination thereof. A typical digital function may be a fan-out beam splitter, and an analog function may be an imaging task. A hybrid may result in a complex multifocus imaging lens, a function impossible to implement in traditional analog macro-optics.

Bernard C. Kress

Google [X] Labs, Mountain View, CA

Table of Contents

Glossary xii

Refractive Micro-Optics 1

Digital Micro-Optics 1

Naming Conventions 2

Free-Space and Guided-Wave Micro-Optics 3

Maximizing the Refractive Effect 4

Maximizing the Diffractive Effect 5

Total Internal Reflection 6

Guided-Wave Digital Optics 7

Optical Waveguide Types 8

Modes in Optical Waveguides 9

Coupling Losses in Optical Waveguides 10

Free-Space Micro-Optics 11

Graded-Index Micro-Optics 12

GRIN Lenses 13

Spectral Dispersion in Micro-Optics 14

Imaging with Microlens Arrays 15

Light-Field Cameras 16

Light-Field Displays 17

Beam Steering with MLAs 18

Beam Shaping/Homogenizing with MLAs 19

Diffractive Micro-Optics 20

Digital Diffractive Optics 20

Analytic and Numeric Diffractives 21

Fresnel and Fourier Diffraction Regimes 22

Fourier and Fresnel Diffractive Optics 23

Analytic Diffractive Elements 24

Reflective Gratings 25

Amplitude Gratings 26

Binary Phase Gratings 27

Multilevel Diffractives 28

Diffractive Lens Surface Profiles 29

Diffraction Efficiency 30

Diffractive Fresnel Lens 31

Diffractive Lens Profile Descriptions 32

Microlens Parameters 33

Spectral Bandwidth of Diffractives 34

Broadband Diffractives 35

Achromatizing Hybrid Lenses 36

Athermalizing Hybrid Lenses 37

Hybrid-Lens Surface Descriptions 38

Hybrid Refractive/Diffractive Lens 39

Aberrations in Micro-Optics 40

Beam-Shaping Lenses 42

Vortex Microlenses 43

Extended Depth of Focus Microlenses 44

Aperture and Wavefront Coding 45

Spatially Multiplexed Planar Optics 46

Diffractive Null Lenses 47

Interferogram Lenses 48

Toroidal and Helicoidal Planar Lenses 49

Iterative Optimization Process 50

Numerical Optimization 50

Numeric Diffractives 51

CGH Design Constraints 52

Merit Function Definition 53

IFTA Algorithm 54

Direct Binary Search 55

Simulated Annealing 56

Beam-Shaping CGHs (Numeric) 57

Spot Array Generators 58

MLAs and Multifocus Lenses 59

Dammann Gratings 60

Talbot Self-Imaging 61

From Micro-Optics to Nano-Optics 62

Subwavelength Optics 62

Large- and Small-Period Gratings 63

Zero-Order Gratings 64

Rigorous EM Diffraction Theory 65

Effective Medium Theory 66

EMT Encoding Schemes 67

Form Birefringence 68

Antireflection microstructures 69

Parity-Time Symmetry in Optics 70

PT Grating-Assisted Couplers 71

Nonreciprocal Free-Space PT Gratings 72

Surface Plasmonics 73

Photonic Crystals 74

Metamaterials 75

Metasurfaces and Resonant Antennas 76

Holographic Micro-Optics 77

The Holographic Process 77

Gabor and Leith Holograms 78

Thin and Thick Holograms 79

Reflection and Transmission Holograms 80

Fraunhofer and Fresnel Holograms 81

Holographic Interference 82

The Grating Vector 83

Floquet’s Theorem and the Bragg Conditions 84

Grating Strength and Detuning Factor 85

Kogelnik Theory for Volume Holograms 86

Angular and Spectral Bandwidths in Holograms 87

Two-Step Holographic Recording 88

Surface-Relief Holograms 89

Holographic Recording Media: Applications 90

Holographic Recording Media: Advantages and Drawbacks 91

Dynamic Micro-Optics 92

Dynamic Micro-Optics 92

Liquid-Crystal Optics 93

Liquid-Crystal Microdisplays 94

OLED Micro-Displays 95

Quantum-Dot Displays 96

H-PDLC Switchable Hologram 97

H-PDLC Recording and Playback 98

MEMS/MOEMS Micro-Optics 99

MEMS Gratings 100

MEMS Display Panels 101

MEMS Laser Scanners 102

Holographic Backlights and Displays 103

Tunable Moiré Micro-Optics 104

Liquid Micro-Optics 105

Electroactive Polymer Microlenses 106

Micro-Optics Modeling Techniques 107

Diffraction Modeling Theories 107

Ray Tracing through Diffractives 108

Fresnel and Fourier Approximations 109

Near- and Far-Field Regions 110

FFT-Based Physical Optics Propagators 111

Oversampling Process in CGH Modeling 112

Physical Optics Modeling: Resolution Increase 113

Physical Optics Modeling with FFT Algorithms 114

Replication of CGHs 115

Numerical-Reconstruction Windows 116

Numerical-Reconstruction Window Scaling 117

DFT-Based Propagators 118

Fresnel Propagator Using a DFT 119

Arbitrary-Reconstruction Windows 120

DFT-Based Numerical Propagator 121

Physical Optics versus Ray Tracing 122

Micro-Optics Fabrication 123

Fabrication Timeline of Micro-Optics 123

Holographic Exposure and Etching 124

Multiple Holographic Exposures 125

Refractive Micro-Optics Fabrication 126

Sag Calculations for Microlenses 127

Diamond Ruling/Turning 128

Binary Lithography 129

Multilevel Optical Lithography 130

Etch Depth: Critical Distance and Groove Depth 131

Etch Depth: Single-Step Height and Diffraction Efficiency 132

Multilevel Lithographic Fabrication 133

GDSII Mask Layouts 134

Wafers for Micro-Optics 135

Optical Lithography 136

Step-and-Repeat Lithography 137

Useful Lithography Parameters 138

Direct-Write Lithography 139

Greyscale Masking Techniques 140

Greyscale Lithography (Binary) 141

Greyscale Lithography (HEBS) 142

Photomask Patterning 143

Optical Proximity Correction 144

Replication Shim 145

Shim Recombination 146

Plastic Replication Technologies 147

Roll-to-Roll UV Embossing 148

Plastics: Acrylic and Polycarbonate 149

Plastics: Polystyrene and Cyclic Olefin Copolymer 150

Plastics: Cyclic Olefin Polymer and Ultem 1010 151

Effects of Fabrication Errors 152

Micro-Optics in Industry 153

Applications of Micro-Optics 154

Equation Summary 155

Bibliography 162

Index 173



Active-matrix organic light-emitting diode


Antireflection surface


Critical dimension


Computer-generated hologram


Caltech Intermediate Format


Direct binary search


Dielectric electroactive polymer


Discrete Fourier transform


Diffractive optical element


Depth of focus


Diamond turning machine


Dense wavelength division multiplexing


Electroactive polymer


Electronic design automation


Extended depth of focus


Effective medium theory


Finite-difference time domain


Fast Fourier transform


Ferroelectric liquid crystal on silicon


Fresnel zone plate


Graphic Data System II


Gradient index


High-energy beam sensitive


Head-mounted display


Holographic optical element


Holographic-polymer dispersed liquid crystal


Integrated circuit


Iterative Fourier transform algorithm


Insertion loss


Indium tin oxide


Light-absorbing film


Liquid crystal


Liquid crystal on silicon


Local grating approximation


Moiré diffractive optical element


Micro-electro-mechanical system


Microlens array


Micro-opto-electro-mechanical system


Numerical aperture


Organic light-emitting diode


Optical proximity correction


Optical path difference


Optical pick-up unit


Polarization beamsplitter


Photonic crystal


Polymer dispersed liquid crystal


Pulse-density modulation


Planar lightwave circuit


Point spread function


Phase-shift mask


Parity time


Pulsewidth modulation


Rigorous coupled-wave analysis


Resolution enhancement technique


Reactive ion etching


Simulated annealing


Space–bandwidth product


Single-point diamond turning


Total internal reflection


Very-high-speed-integrated-circuit hardware description language


Very-large-scale integration


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