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Optical Engineering Science

Stephen Rolt

University of Durham

Sedgefield, United Kingdom

This edition first published 2020

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Library of Congress Cataloging-in-Publication Data

Names: Rolt, Stephen, 1956- author.

Title: Optical engineering science / Stephen Rolt, University of Durham, Sedgefield, United Kingdom.

Description: First edition. | Hoboken, NJ : John Wiley & Sons, 2020. | Includes bibliographical references and index.

Identifiers: LCCN 2019032028 (print) | LCCN 2019032029 (ebook) | ISBN 9781119302803 (hardback) | ISBN 9781119302797 (adobe pdf) | ISBN 9781119302810 (epub)

Subjects: LCSH: Optical engineering. | Optics.

Classification: LCC TA1520 .R65 2019 (print) | LCC TA1520 (ebook) | DDC 621.36–dc23

LC record available at https://lccn.loc.gov/2019032028

LC ebook record available at https://lccn.loc.gov/2019032029

Cover Design: Wiley

Cover Images: Line drawing cover image courtesy of Stephen Rolt, Background: © AF-studio/Getty Images

Preface

The book is intended as a useful reference source in optical engineering for both advanced students and engineering professionals. Whilst grounded in the underlying principles of optical physics, the book ultimately looks toward the practical application of optics in the laboratory and in the wider world. As such, examples are provided in the book that will enable the reader to understand and to apply. Useful exercises and problems are also included in the text. Knowledge of basic engineering mathematics is assumed, but an overall understanding of the underlying principles should be to the fore.

Although the text is wide ranging, the author is keenly aware of its omissions. In compiling a text of this scope, there is a constant pre-occupation of what can be omitted, rather than what is to be included. This tyranny is imposed by the manifest requirement of brevity. With this limitation in mind, choice of material is dictated by the author's experience and taste; the author fully accepts that the reader's taste may vary somewhat.

The evolution of optical science through the ages is generally seen as a progression of ideas, an intellectual journey culminating in the development of modern quantum optics. Although some in the ancient classical world thought that the sensation of vision actually originates in the eye, it was quickly accepted that vision arises, in some sense, from an external agency. From this point, it was easy to visualise light as beams, rays, or even particles that have a tendency to move from one point to another in a straight line before entering the eye. Indeed, it is this perspective that dominates geometric optics today and drives the design of modern optical systems.

The development of ideas underpinning modern optics is, to a large extent, attributed to the early modern age, most particularly the classical renaissance of the seventeenth century. However, many of these ideas have their origin much earlier in history. For instance, Euclid postulated laws of rectilinear propagation of light, as early as 300 BCE. Some understanding of the laws of propagation of light might have underpinned Archimedes' famous solar concentrator that (according to legend) destroyed the Roman fleet at the siege of Syracuse in 212 BCE. Whilst the law governing the refraction of light is famously attributed to Willebrord Snellius in the seventeenth century, many aspects of the phenomenon were understood much earlier. Refraction of light by water and glass was well understood by Ptolemy in the second century CE and, in the tenth century, Ibn Sahl and Ibn Al-Haytham (Alhazen) analysed the phenomenon in some detail.

From the early modern era, the intellectual progression in optics revolved around a battle between particle (corpuscular) or ray theory, as proposed by Newton, and wave theory, as proposed by Huygens. For a time, in the nineteenth century, the journey seemed to be at an end, culminating in the all-embracing description provided by Maxwell's wave equations. The link between wave and ray optics was provided by Fermat's theorem which dictated the light travels between two points by the path that takes the least time and this could be clearly derived from Maxwell's equations. However, this clarity was removed in the twentieth century when the ambiguity between the wave and corpuscular (particle) properties of light was restored by the advent of quantum mechanics.

This progression provides an understanding of the history of optics in terms of an intellectual journey. This is the way the history of optics is often portrayed. However, there is another strand to the development of optics that is often ignored. When Isaac Newton famously procured his prism at the Stourbridge Fair in Cambridge in 1665, it is clear that the fabrication of optical components was a well-developed skill at the time. Indeed, the construction of the first telescope (attributed to Hans Lippershey) would not have been possible without the technology to grind lenses, previously mastered by skilled spectacle makers. The manufacture of lenses for spectacles had been carried out in Europe (Italy) from at least the late thirteenth century CE. However, the origins of this skill are shrouded in mystery. For instance, Marco Polo reported the use of spectacles in China in 1270 and these were said to have originated from Arabia in the eleventh century.

So, in parallel to the more intellectual journey in optics, people were exercising their practical curiosity in developing novel optical technologies. In many early cultures, polished mirrors feature as grave goods in the burials of high-status individuals. One example of this is a mirror found in the pyramid build for Sesostris II in Egypt in around 1900 BCE. The earliest known lens in existence is the Nimrud or Layard lens attributed to the Assyrian culture (750–710 BCE). Nero is said to have watched gladiatorial contests through a shaped emerald, presumably to correct his myopic vision. Abbas Ibn Firnas, working in Andalucia in the ninth century CE developed magnifying lenses or ‘reading stones’.

These two separate histories lie at the heart of the science of optical engineering. On the one hand, there is a desire to understand or analyse and on the other hand there is a desire to create or synthesise. An optical engineer must acquire a portfolio of fundamental knowledge and understanding to enable the creation of new optical systems. However, ultimately, optical engineering is a practical discipline and the motivation for acquiring this knowledge is to enable the design, manufacture, and assembly of better optical systems. For this knowledge to be fruitful, it must be applied to specific tasks. As such, this book focuses, initially, on the fundamental optics underlying optical design and fabrication. Notwithstanding the advent of powerful software and computational tools, a sound understanding and application of the underlying principles of optics is an essential part of the design and manufacturing process. An intuitive understanding greatly aids the use of these sophisticated tools.

Ultimately, preparation of an extensive text, such as this, cannot be a solitary undertaking. The author is profoundly grateful to a host of generous colleagues who have helped him in his long journey through optics. Naturally, space can only permit the mention of a few of these. Firstly, for a thorough introduction and grounding in optics and lasers, I am particularly indebted to my former DPhil Supervisor at Oxford, Professor Colin Webb. Thereafter, I was very fortunate to spend 20 years at Standard Telecommunication Laboratories in Harlow, UK (later Nortel Networks), home of optical fibre communications. I would especially like to acknowledge the help and support of my colleagues, Dr Ken Snowdon and Mr Gordon Henshall during this creative period. Ultimately, the seed for this text was created by a series of Optical Engineering lectures delivered at Nortel's manufacturing site in Paignton, UK. In this enterprise, I was greatly encouraged by the facility's Chief Technologist, Dr Adrian Janssen.

In later years, I have worked at the Centre for Advanced Instrumentation at Durham University, involved in a range of Astronomical and Satellite instrumentation programmes. By this time, the original seed had grown into a series of Optical Engineering graduate lectures and a wide-ranging Optical Engineering Course delivered at the European Space Agency research facility in Noordwijk, Netherlands. This book itself was conceived, during this time, with the encouragement and support of my Durham colleague, Professor Ray Sharples. For this, I am profoundly grateful. In preparing the text, I would like to thank the publishers, Wiley and, in this endeavour, for the patience and support of Mr Louis Manoharan and Ms Preethi Belkese and for the efforts of Ms Sandra Grayson in coordinating the project. Most particularly, I would like to acknowledge the contribution of the copy-editor, Ms Carol Thomas, in translating my occasionally wayward thoughts into intelligible text.

This project could not have been undertaken without the support of my family. My wife Sue and sons Henry and William have, with patience, endured the interruption of many family holidays in the preparation of the manuscript. Most particularly, however, I would like to thank my parents, Jeff and Molly Rolt. Although their early lives were characterised by adversity, they unflinchingly strove to provide their three sons with the security and stability that enabled them to flourish. The fruits of their labours are to be seen in these pages.

Finally, it remains to acknowledge the contributions of those giants who have preceded the author in the great endeavour of optics. In humility, the author recognises it is their labours that populate the pages of this book. On the other hand, errors and omissions remain the sole responsibility of the author. The petty done, the vast undone…

Glossary

AC Alternating current

AFM Atomic force microscope

AM0 Air mass zero

AM1 Air mass one (atmospheric transmission)

ANSI American national standards institute

APD Avalanche photodiode

AR Antireflection (coating)

AS Astigmatism

ASD Acceleration spectral density

ASME American society of mechanical engineers

BBO Barium borate

BRDF Bi-directional reflection distribution function

BS Beamsplitter

BSDF Bi-directional scattering distribution function

CAD Computer aided design

CCD Charge coupled device

CD Compact disc

CGH Computer generated hologram

CIE Commission Internationale de l'Eclairage

CLA Confocal length aberration

CMM Co-ordinate measuring machine

CMOS Complementary metal oxide semiconductor

CMP Chemical mechanical planarisation

CNC Computer numerical control

CO Coma

COTS Commerical off-the-shelf

CTE Coefficient of thermal expansion

dB Decibel

DC Direct current

DFB Distributed feedback (laser)

DI Distortion

E-ELT European extremely large telescope

EMCCD Electron multiplying charge coupled device

ESA European space agency

f# F number (ratio of diameter to focal distance)

FAT Factory acceptance test

FC Field curvature

FEA Finite element analysis

FEL Filament emission lamp

FEL Free electron laser

FFT Fast Fourier transform

FRD Focal ratio degradation

FSR Free spectral range

FT Fourier transform

FTIR Fourier transform infra-red (spectrometer)

FTR Fourier transform (spectrometer)

FWHM Full width half maximum

GRIN Graded index (lens or fibre)

HEPA High- efficiency particulate air (filter)

HST Hubble space telescope

HWP Half waveplate

IEST Institute of environmental sciences and technology

IFU Integral field unit

IICCD Image intensifying charge coupled device

IR Infrared

ISO International standards organisation

JWST James Webb space telescope

KDP Potassium dihydrogen phosphate

KMOS K-band multi-object spectrometer

LA Longitudinal aberration

LCD Liquid crystal display

LED Light emitting diode

LIDAR Light detection and ranging

MTF Modulation transfer function

NA Numerical aperture

NASA National Aeronautics and Space Administration

NEP Noise equivalent power

NIRSPEC Near infrared spectrometer

NIST National institute of standards and technology (USA)

NMI National measurement institute

NPL National physical laboratory (UK)

NURBS Non-uniform rational basis spline

OPD Optical path difference

OSA Optical society of America

OTF Optical transfer function

PD Photodiode

PMT Photomultiplier tube

PPLN Periodically poled lithium niobate

PSD Power spectral density

PSF Point spread function

PTFE Polytetrafluoroethylene

PV Peak to valley

PVA Polyvinyl alcohol

PVr Peak to valley (robust)

QMA Quad mirror anastigmat

QTH Quartz tungsten halogen (lamp)

QWP Quarter waveplate

RMS Root mean square

RSS Root sum square

SA Spherical aberration

SI Système Internationale

SLM Spatial light modulator

SNR Signal to noise ratio

TA Transverse aberration

TE Transverse electric (polarisation)

TGG Terbium gallium garnet

TM Transverse magnetic (polarisation)

TMA Three mirror anastigmat

TMT Thirty metre telescope

USAF United States Airforce

UV Ultraviolet

VCSEL Vertical cavity surface emitting laser

VPH Volume phase hologram

WDM Wavelength division multiplexing

WFE Wavefront error

YAG Yttrium aluminium garnet

YIG Yttrium iron garnet

YLF Yttrium lithium fluoride

About the Companion Website

This book is accompanied by a companion website:

www.wiley.com/go/Rolt/opt-eng-sci

The website includes:

● Problem Solutions
● Spreadsheet tools

Scan this QR code to visit the companion website.

1
Geometrical Optics

1.1 Geometrical Optics – Ray and Wave Optics

In describing optical systems, in the narrow definition of the term, we might only consider systems that manipulate visible light. However, for the optical engineer, the application of the science of optics extends well beyond the narrow boundaries of human vision. This is particularly true for modern instruments, where reliance on the human eye as the final detector is much diminished. In practice, the term optical might also be applied to radiation that is manipulated in the same way as visible light, using components such as lenses, mirrors, and prisms. Therefore, the word ‘optical’, in this context might describe electromagnetic radiation extending from the vacuum ultraviolet to the mid-infrared (wavelengths from ∼120 to ∼10 000 nm) and perhaps beyond these limits. It certainly need not be constrained to the narrow band of visible light between about 430 and 680 nm. Figure 1.1 illustrates the electromagnetic spectrum.

Geometrical optics is a framework for understanding the behaviour of light in terms of the propagation of light as highly directional, narrow bundles of energy, or rays, with ‘arrow like’ properties. Although this is an incomplete description from a theoretical perspective, the use of ray optics lies at the heart of much of practical optical design. It forms the basis of optical design software for designing complex optical instruments and geometrical optics and, therefore, underpins much of modern optical engineering.

Geometrical optics models light entirely in terms of infinitesimally narrow beams of light or rays. It would be useful, at this point, to provide a more complete conceptual description of a ray. Excluding, for the purposes of this discussion, quantum effects, light may be satisfactorily described as an electromagnetic wave. These waves propagate through free space (vacuum) or some optical medium such as water and glass and are described by a wave equation, as derived from Maxwell's equations:

(1.1)

E is a scalar representation of the local electric field; c is the velocity of light in free space, and n is the refractive index of the medium.

Of course, in reality, the local electric field is a vector quantity and the scalar theory presented here is a useful initial simplification. Breakdown of this approximation will be considered later when we consider polarisation effects in light propagation. If one imagines waves propagating from a central point, the wave equation offers solutions of the following form:

(1.2)

Equation (1.2) represents a spherical wave of angular frequency, ω, and spatial frequency, or wavevector, k. The velocity that the wave disturbance propagates with is ω/k or c/n. In free space, light propagates at the speed of light, c, a fundamental and defined constant in the SI system of units. Thus, the refractive index, n, is the ratio of the speed of light in free space to that in the specified medium. All points lying at the same distance, r, from the source, will oscillate at an angular frequency, ω, and in the same phase. Successive surfaces, where all points are oscillating entirely in phase are referred to as wavefronts and can be viewed at the crests of ripples emanating from a point disturbance. This is illustrated in Figure 1.2. This picture provides us with a more coherent definition of a ray. A ray is represented by the vector normal to the wavefront surface in the direction of propagation. Of course, Figure 1.2 represents a simple spherical wave, with waves spreading from a single point. However, in practice, wavefront surfaces may be much more complex than this. Nevertheless, the precise definition of a ray remains clear:

Figure 1.1 The electromagnetic spectrum.

Figure 1.2 Relationship between rays and wavefronts.

At any point in space in an optical field, a ray may be defined as the unit vector perpendicular to the surface of constant phase at that point with its sense lying in the same direction as that of the energy propagation.