Use of Compound Microlens Arrays as a Magnifier in Near-to-eye Head-up Displays

115 Pages·2015·2.65 MB·English

by  Sam Park

USE OF COMPOUND MICROLENS ARRAYS AS A MAGNIFIER IN NEAR-EYE
HEAD-UP DISPLAYS
by

Hongbae Sam Park

B.A.Sc., Simon Fraser University, 2012

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF APPLIED SCIENCE
in
THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES
(Electrical and Computer Engineering)

THE UNIVERSITY OF BRITISH COLUMBIA
(Vancouver)

April 2015

© Hongbae Sam Park, 2015
Abstract

This thesis reports a new approach for making a very compact near-eye display (NED) using two
microlens array (MLA) layers. The two MLAs will work in conjunction as a magnifying lens
(MLA magnifier). The purpose of the MLA magnifier is to aid the eye accommodate on a
display that is positioned within several centimeters from the eye, by generating a virtual image
of the display at optical infinity. While there are recently developed techniques for similar
purposes such as waveguides [17, 18], and retinal scanning methods [21], using a magnifying
lens has been the most exploited avenue for generating a virtual image due to its rather simple,
tried-and-true optical properties; near-eye display systems that incorporate a magnifying lens,
whether it is a single piece or a compound, has been well-studied since the dawn of head-up
displays. However, magnifying lens-based optics is inherently hard to make compact, because as
the focal length becomes smaller, the thickness of the lens becomes larger.
This thesis presents in detail the method for making a MLA magnifier that retains a thin profile
of about 2 mm in thickness with a system focal length of about 6 mm. Thus the total thickness of
the MLA magnifier system is around 8 mm (excluding the thickness of the display) in non-
folded optics configuration, which is much more compact in comparison to other popular near-
eye displays such as Google Glass or Recon Instrument‘s Snow HUD goggles having folded
optics.

ii
Preface

The materials presented in this thesis resulted from an independent and original research work
undertaken by myself, with the guidance of Prof. Boris Stoeber and aids from Recon Instruments
Inc.
In Chapter 1, Figures 1.1, 1.4, and 1.5, are used with permission from the original composers of
the images. Figures 1.2 and 1.6 are public domain images, and Figure 1.3 is a derivative of an
image originally licensed under the Creative Commons BY-SA 3.0 Unported license.
Chapters 2, 3, and 4 are written primarily by Hongbae Sam Park with feedback from Prof. Boris
Stoeber. In Chapter 2, Figure 2.14 is used with permission from the original composer of the
image. A version of Chapter 2 has been published in a conference paper in the proceedings of the
IEEE MEMS 2015 conference, titled as ―COMPACT NEAR-EYE DISPLAY SYSTEM USING
A SUPERLENS-BASED MICROLENS ARRAY MAGNIFIER.‖
Parts of the optimization study presented in Chapter 3 and part of Chapter 4 have also been
published in the same conference paper.
Based on the findings of the research presented here, a provisional U.S. patent application has
been filed, of which I am the primary inventor.
Except for Figures 1.2, 1.3 and 1.6, as well as where otherwise noted, this thesis is licensed
under the Creative Commons BY-NC-ND 2.5 CA license.

iii
Table of Contents

Abstract .......................................................................................................................................... ii
Preface ........................................................................................................................................... iii
Table of Contents ......................................................................................................................... iv
List of Tables ............................................................................................................................... vii
List of Figures ............................................................................................................................. viii
List of Symbols ........................................................................................................................... xiii
List of Abbreviations ................................................................................................................ xvii
Glossary .................................................................................................................................... xviii
Acknowledgements .................................................................................................................... xix
Dedication .....................................................................................................................................xx
Chapter 1: Introduction ................................................................................................................1
1.1 Background in Head-up Displays ................................................................................... 1
1.2 Background in Near-eye Displays .................................................................................. 4
1.3 Challenges in Designing NED Optics............................................................................. 6
1.4 Objectives ....................................................................................................................... 7
Chapter 2: Design of Microlens Array Magnifier ......................................................................8
2.1 Background in Superlens ................................................................................................ 8
2.2 Design ............................................................................................................................. 8
2.2.1 Analytical Model ........................................................................................................ 9
2.2.2 Light Throughput Analysis ....................................................................................... 17
2.2.2.1 Convex-convex MLA Magnifier ...................................................................... 17
iv
2.2.2.2 Concave-convex MLA Magnifier ..................................................................... 24
2.2.3 Eyebox Formation ..................................................................................................... 25
2.2.3.1 Consideration for Thick Lenses ........................................................................ 28
2.2.4 Optimization ............................................................................................................. 29
2.2.4.1 Design Tradespace Analysis ............................................................................. 30
2.2.5 Modulation Transfer Function for Resolution Estimation ........................................ 34
2.2.6 Simulation ................................................................................................................. 36
2.2.6.1 Simulated Resolution (With Microlens Arrays) ............................................... 42
Chapter 3: Prototyping................................................................................................................46
3.1 Fabrication of the Microlens Arrays ............................................................................. 46
3.1.1 Fabrication Techniques ............................................................................................. 46
3.1.2 Process Overview...................................................................................................... 46
3.1.2.1 Photolithography ............................................................................................... 47
3.1.2.2 Reflow ............................................................................................................... 49
3.1.2.3 Molding and Removal of the Cast MLA .......................................................... 51
3.1.3 Experiments .............................................................................................................. 52
3.2 Making of the Prototype ............................................................................................... 55
Chapter 4: Evaluation of Microlens Array Magnifier .............................................................58
4.1 Experimental Setup ....................................................................................................... 58
4.2 Measurement of the Resolution .................................................................................... 60
4.3 Measurement of the Angular FOV ............................................................................... 68
4.4 Eyebox .......................................................................................................................... 71
Chapter 5: Conclusions and Future Work ................................................................................77
v
5.1 Concluding Remarks ..................................................................................................... 77
5.2 Future Work .................................................................................................................. 78
Bibliography .................................................................................................................................80
Appendices ....................................................................................................................................85
Appendix A ............................................................................................................................... 85
Appendix B ............................................................................................................................... 88
Appendix C ............................................................................................................................... 92

vi
List of Tables

Table 2.1: Combinations of the convex and concave MLA for magnifying condition. ............... 16
Table 2.2: MLA magnifier parameters for the best design option. ............................................... 34
Table 4.1: Horizontal spatial frequency and converted angular resolution of the test patterns. ... 65
Table 4.2: The size of the eyebox from theory, simulation, and measurements........................... 75
vii
List of Figures

Figure 1.1: Example of a simple HUD [1]. a) An electronic dot sight. b) A view through the dot
sight. ................................................................................................................................................ 1
Figure 1.2: HUD of a Boeing C-17 Globemaster aircraft [3]. Public domain image. .................... 2
Figure 1.3: Example of an in-car HUD [4]. .................................................................................... 3
Figure 1.4 Waveguide-based aircraft HUD introduced by BAE systems [5]. ................................ 4
Figure 1.5 A transparent OLED HUD for cars introduced by Kolon Neoview Inc. [6]. ................ 4
Figure 1.6: A helmet worn by F-35 fighter jet pilots. The image is projected on the inside of the
visor [7]. Public domain image. ...................................................................................................... 5
Figure 2.1: Definition of the ray height and ray angle for the input and output rays to the MLA
system. The refraction of the rays at the boundaries of the MLA system is arbitrary. ................... 9
Figure 2.2: Ray propagation through a decentered microlens. ..................................................... 11
Figure 2.3: Definition of the variables used in ray transfer analysis of the superlens. ................. 12
Figure 2.4: Light propagation through the N-th microlens on each MLA; the N-th microlens on
the first MLA is assumed to be a pinhole to only consider the principal ray of the first N-th
microlens. ...................................................................................................................................... 18
Figure 2.5: Light propagation through the MLA pair with an off-axis source. The microlenses on
the first array are assumed to be pinholes. .................................................................................... 19
Figure 2.6: Light propagation through the MLA pair with an off-axis source. The microlenses on
the first arrays have full apertures. ................................................................................................ 22
Figure 2.7: Ray diagram of the concave-convex system. ............................................................. 24
Figure 2.8: Eyebox size for a convex-convex MLA magnifier .................................................... 26
viii
Figure 2.9: Eyebox size for a concave-convex MLA magnifier ................................................... 27
Figure 2.10: Ray propagation through a concave and a convex microlens. Solid lines are the
actual refracted rays, and dashed lines are imaginary rays which do not refract at the MLA
surfaces. ........................................................................................................................................ 29
Figure 2.11: Design tradespaces spanned by the focal length of the first MLA f , and F, the focal
1
length of the MLA magnifier. a) Tradespace in terms of the exit angle of the collimated beams. b)
Tradespace for the exit angle with unattainable design options indicated as an area at the bottom.
c) Same tradespace as in b) marked with a line that indicates design options that correspond to
the exit angle of -10°. d) Tradespace in terms of the eye relief, with eye relief that corresponds to
20 mm marked in red lines............................................................................................................ 31
Figure 2.12: Illustration of single microlens and its ROC and θ. ................................................. 32
Figure 2.13: Illustration of the change in eye relief due to the difference in the collimated beam
width. θ ................................................................................................................................. 33
out-max
Figure 2.14: Two stimuli with different spatial frequency having different contrast outcomes
through the same optical component [51]. .................................................................................... 35
Figure 2.15: MTF response of a computer-modelled human eye (inset). ..................................... 36
Figure 2.16: Simulation of the MLA magnifier with light sources at different heights on the
object plane. .................................................................................................................................. 37
Figure 2.17: Close-up view of the two MLA layers ..................................................................... 37
Figure 2.18: Ray-tracing simulation of the MLA magnifier with a model of the eye. a) Image
showing all of the components. b) Image zoomed in on the retina. ............................................. 38
Figure 2.19: Ray-tracing simulation of the inter-lens gap. a) Image showing all of the
components. b) Image zoomed in on the retina. ........................................................................... 40
ix
Figure 2.20: The spot diagrams of the focused light rays on the retina, from the microlenses (left),
and from the inter-lens gaps (right). ............................................................................................. 41
Figure 2.21: Simulated MTF response of the MLA magnifier, with inter-lens gaps blocked. The
color-coded lines represent MTF responses of light sources at different locations on the object
plane, whose coordinates on the object plane are noted in the labels above the plot. Lines labeled
as either T or S respectively represents tangential or sagittal plane MTF responses. .................. 42
Figure 2.22: The tangential and the sagittal planes of a lens produce different focal points for off-
axis sources. .................................................................................................................................. 43
Figure 2.23: Simulated MTF response of light coming from inter-lens gaps, with microlenses
blocked. Although the same light sources are used as in Figure 2.22, the contrast reaches zero at
much lower spatial frequency. Lines labeled as either T or S respectively represents tangential or
sagittal plane MTF responses. The spatial frequency axis is half the scale of that in Figure 2.21.
....................................................................................................................................................... 44
Figure 2.24 Image simulation using Zemax. The input image (one of the Zemax-supplied test
images) used is shown (top). What it would look like through the MLA magnifier (bottom). .... 45
Figure 3.1: Description of each process stages ............................................................................. 47
Figure 3.2: Sections of the MLA mask design. a) A complete array of 70x70 microlenses. The
arrows indicate location of the thickness measurements after the reflow. b) Zoomed into one
corner of the array. The red line shows the scanning path of the profilometer for measuring the
height of the photoresist structure after reflow. ............................................................................ 48
Figure 3.3: Photo of the photoresist islands before and after the reflow. a) The islands have a flat
plateau before the reflow. b) After the reflow, the surface profile of the islands is round. .......... 49
Figure 3.4: Parameters of the photoresist cylinder and the spherical cap. .................................... 50
x