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- Herausgeber: Wiley-VCH
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
Optical Devices in Ophthalmology and Optometry
Medical technology is a fast growing field. Optical Devices in Ophthalmology and Optometry gives a comprehensive review of modern optical technologies in ophthalmology and optometry alongside their clinical deployment. It bridges the technology and clinical domains and will be suitable in both technical and clinical environments. The book introduces and develops basic physical methods (in optics, photonics, and metrology) and their applications in the design of optical systems for use in ophthalmic medical technology. Medical applications described in detail demonstrate the advantage of utilizing optical-photonic methods. Exercises and solutions for each chapter help understand and apply basic principles and methods.
From the contents:
- Structure and Function of the Human Eye
- Optics of the Human Eye
- Visual Disorders and Major Eye Diseases
- Introduction to Ophthalmic Diagnosis and Imaging
- Determination of the Refractive Status of the Eye
- Optical Visualization, Imaging, and Structural Analysis
- Optical Coherence Methods for Three-Dimensional Visualization and Structural Analysis
- Functional Diagnostics
- Laser???Tissue Interaction
- Laser Systems for Treatment of Eye Diseases and Refractive Errors
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Veröffentlichungsjahr: 2013
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Contents
Preface
Part One
1 Structure and Function
1.1 Anatomy of the Human Eye
1.2 Retina: The Optical Sensor
1.3 Recommended Reading
References
2 Optics of the Human Eye
2.1 Optical Imaging
2.2 Schematic Eye Models
2.3 Color Vision
2.4 Recommended Reading
References
3 Visual Disorders and Major Eye Diseases
3.1 Refractive Errors
3.2 Cataract
3.3 Glaucoma
3.4 Age-Related Macular Degeneration
3.5 Diabetic Retinopathy
3.6 Retinal Vein Occlusions
3.7 Infective Eye Diseases
3.8 Major Causes for Visual Impairment
3.9 Major Causes of Blindness
3.10 Socio-Economic Impact of Eye Diseases
3.11 Recommended Reading
Problems to Chapters 1–3
References
Part Two
4 Introduction to Ophthalmic Diagnosis and Imaging
4.1 Determination of the Eye’s Refractive Status
4.2 Visualization, Imaging, and Structural Analysis
4.3 Determination of the Eye’s Functional Status
4.4 Light Hazard Protection
References
5 Determination of the Refractive Status of the Eye
5.1 Retinoscopy
5.2 Automated Objective Refractometers (Autorefractors)
5.3 Aberrometers
5.4 Wavefront Reconstruction and Wavefront Analysis
5.5 Excursus: Refractive Correction with Eye Glasses and Contact Lenses
5.6 Recommended Reading
5.7 Problems
References
6 Optical Visualization, Imaging, and Structural Analysis
6.1 Medical Magnifying Systems
6.2 Surgical Microscopes
6.3 Reflection Methods for Topographic Measurements
6.4 Slit Lamp
6.5 Scanning-Slit Projection Devices
6.6 Ophthalmoscope
6.7 Fundus Camera
6.8 Scanning-Laser Devices
6.9 Recommended Reading
6.10 Problems
References
7 Optical Coherence Methods for Three-Dimensional Visualization and Structural Analysis
7.1 Introduction to Optical Coherence Tomography
7.2 Development of OCT and LCI as an Example of Modern Medical Technology Innovation
7.3 Principles of Low-Coherence Interferometry and Optical Coherence Tomography
7.4 Elements of OCT Theory
7.5 Device Design of OCTs
7.6 Ophthalmic Applications of OCT
7.7 Optical Biometry by Low-Coherence Interferometry
7.8 Prospects
7.9 Recommended Reading
7.10 Problems
References
8 Functional Diagnostics
8.1 Visual Field Examination
8.2 Metabolic Mapping
8.3 Recommended Reading
8.4 Problems
References
Part Three
9 Laser–Tissue Interaction
9.1 Absorption
9.2 Elastic Scattering
9.3 Optical Properties of Biological Tissue
9.4 Interaction of Irradiated Biological Tissue
9.5 Propagation of Femtosecond Pulses in Transparent Media
9.6 Ophthalmic Laser Safety
9.7 Recommended Reading
9.8 Problems
References
10 Laser Systems for Treatment of Eye Diseases and Refractive Errors
10.1 Laser Systems Based on Photochemical Interactions
10.2 Laser Systems Based on Photothermal Interactions
10.3 Laser Systems Based on Photoablation
10.4 Laser Systems Based on Photodisruption with Nanosecond Pulses
10.5 Laser Systems Based on Plasma-Induced Ablation with Femtosecond Pulses
10.6 Recommended Reading
10.7 Problems
References
A Basics of Optics
A.1 Geometric Optics and Optical Imaging
A.2 Wave Optics
A.3 Recommended Reading
A.4 Problems
References
B Basics of Laser Systems
B.1 Einstein’s Two-Level Model of Light–Atom Interaction
B.2 Light Amplification by Stimulated Emission
B.3 Laser Oscillator
B.4 The Gaussian Oscillator
B.5 Technical Realization of Laser Sources
B.6 Recommended Reading
B.7 Problems
References
C Summary of Used Variables and Abbreviations
C.1 Chapters 1–3
C.2 Chapters 4 and 5
C.3 Chapter 6
C.4 Chapter 7
C.5 Chapter 8
C.6 Chapters 9 and 10
C.7 Appendix A
C.8 Appendix B
Index
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Gross, H., Gross, H., Blechinger, F., Achtner, B.
Handbook of Optical Systems
Volume 4: Survey of Optical Instruments
2008ISBN: 978-3-527-40380-6
Authors
Dr. Michael KaschkeCarl Zeiss AGOberkochenGermany
Dr. Karl-Heinz DonnerhackeJenaGermany
Dr. Michael Stefan RillCarl Zeiss AGOberkochenGermany
CoverBackground illustration: © Hammerstudio/Fotolia
Other illustrations: authors.
All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.
Library of Congress Card No.:applied for
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Bibliographic information published by the Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.d-nb.de.
© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany
All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.
Cover Design Simone Benjamin, Bluesea Design, McLeese Lake, CanadaTypesetting le-tex publishing services GmbH, Leipzig
ISBN 978-3-527-41068-2ePDF ISBN 978-3-527-64899-3ePub ISBN 978-3-527-64898-6Mobi ISBN 978-3-527-64897-9obook ISBN 978-3-527-64896-2
To Sylvia without her support nothing would have been possible.
Michael Kaschke
To Christel for her abundance of understanding all the time.
Karl-Heinz Donnerhacke
To my family and friends for their steady support.
Michael Stefan Rill
Preface
This book is based on lectures “Optical Systems in Medical/Ophthalmic Technology” held by two of the authors since 2007 at the Karlsruhe Institute of Technology (Germany) and since 2003 at the Ernst Abbe University of Applied Sciences in Jena (Germany). The idea behind these lectures was to create a link between fundamental physical methods in optics, photonics, and measurement technology on the one hand, and to communicate their applications in medical sciences, in particular ophthalmology and optometry, to graduate students in physics and in electrical and mechanical engineering on the other. As this book is essentially based on these lectures, the structure, motivation, and target group of readers for this is quite similar. However, this book is intended as a textbook and compendium for the engineer and physicist in academic and industrial research and development. It will also be useful for the teaching and practicing ophthalmologist and optometrist with an interest in optical technology. To cover the broad spectrum of readers, we have not only described the application of optical methods to the design of ophthalmic diagnostic and laser treatment systems, but have also discussed clinical applications in such a way that the advantage of using a particular optical system and design becomes evident.
A large number of excellent reference books and textbooks exist on ophthalmology and optometry. The same applies to applied and technical optics. However, most of these books focus on a certain aspect (e.g., disease diagnosis, treatment procedures, etc.) or distinct optical and photonics techniques (e.g., OCT, aberrometry, etc.). Consequently, they often address experts with a certain scientific background. Students looking for a systematic and relatively complete introduction to the topic of optical methods and systems in ophthalmology and optometry are thus confronted with a number of books from which the necessary information has to be extracted with considerable effort. The situation is actually very similar for engineers and scientists of academic and research institutions, who often look for a compendium or reference book which gives them a general overview of available solutions in medical technology associated with their area of expertise. To close this gap, we provide an interdisciplinary overview of the currently most relevant (and most often used) techniques and technologies in ophthalmology and optometry, their underlying optical principles, as well as their corresponding diagnostic and therapeutic application.
The eye is our most important sensory organ and any reduction or loss of vision is a major impairment of our quality of life. Although the eye is quite accessible for optical examination methods, the diagnostic options available to the ophthalmologist were very limited until the middle and end of the nineteenth century. It was not until 1850 that Herrmann von Helmholtz invented the ophthalmoscope affording a view of the inside of the living eye for the very first time. This can be considered as the advent of modern ophthalmology and the birth of ophthalmic equipment making. Over the years, it has been demonstrated that no other organ necessitates the use of as many different optical-medical devices as the eye. It is also no surprise that ophthalmology has become by far the most successful application area of lasers in medicine since the invention of the laser in the 1960s. Ophthalmic and optometric methods and technologies have rapidly grown and matured during the last couple of decades and have actually seen an acceleration, but this is still a very active field of research today. Presenting an in-depth coverage of all the ongoing activities is certainly beyond the scope of this book. Consequently, we will try to walk the line between covering the more general and principal approaches in design, development and application of ophthalmic systems, and providing detailed background information on exciting current research topics.
As this book is intended to bridge technology and clinical domains, we will discuss modern optical technologies alongside their clinical deployment. In this way, it addresses graduate and postgraduate students in physics, electrical, mechanical, and biomedical engineering who want to gain a general insight into the principles and concepts of ophthalmic systems. We have also added some topic-related application-oriented “Problems” at the end of each chapter. The problems are presented with fully elaborated solutions, which can be downloaded from the reserved website of Wiley (http://www.wiley.com). These problems demonstrate how basic design parameters of an ophthalmic device are calculated.
Ophthalmologists and optometrists who want to gain a profound understanding of how the diagnostic and therapy systems work will also greatly benefit from the application oriented approach used in our book. We also give references to the most current and relevant literature throughout the chapters and in corresponding “Recommended Reading” sections. These references might be particularly useful for specialists or students who want to acquire further expertise in a special subject.
The book has a modular structure so that it can be used by readers with different backgrounds and interests. In the first part, a basic introduction to key aspects of ophthalmology and optometry is given, including a brief introduction to anatomy, optical properties, as well as refractive errors and diseases of the human eye. The second part is dedicated to ophthalmic diagnosis and imaging devices and techniques. Within this part, Chapter 4 gives as an overview of the link-up between common eye diseases and clinical conditions as well as relevant ophthalmic devices and methods. In the third part of this book, we focus on the therapeutic aspects of ophthalmology in which the use of laser systems is of particular importance. The appendix of this book provides the basics of optics and lasers, which are relevant to understanding the physical concepts of the presented ophthalmic and optometric systems. Here, the intention was not to present the entire content of textbooks on optics and lasers, but rather to focus on the topics relevant to ophthalmic devices and to provide a consistent reference base and notation.
Table 1 Examples of structured courses.
The chapters of this book may be combined in various ways for use in semester courses. Representative examples of such structured courses are shown in Table 1 in which we also suggest a potentially beneficial sequence for reading the chapters of this book. Topics which should have already been treated during a previous course or are considered to be already known are marked with an “R”, standing for “revision”.
Commonly accepted notation and symbols have been used whenever possible. However, as this book covers a number of different topics, a number of symbols exist that have multiple meanings. To avoid confusion, we have added an overview of abbreviations and symbols to the Appendix C.
Acknowledgments
We would like to acknowledge all the inspiration and motivation we received from many people while writing this book. We would like to thank Herbert Gross and Rudolf von Bünau in particular for their useful hints, support and extensive discussions. We are also indebted to Michael Vincent Patella for valuable help and clarifications on the topic of functional imaging in Chapter 8 and Michael Kempe for detailed discussions on OCT in Chapter 7 and the laser Sections 9 and 10. We also greatly acknowledge further help by (in alphabetical order) Peter Andrews, Detlef Biernat, Mark Bischoff, Tobias Bühren, Tobias Damm, Manfred Dick, Matt Everett, Gerald Kunath-Fandrei, Werner Nahm, and Clive Poole. Our thanks go to all the people who supported us by providing relevant data and pictures, in particular Thomas Behling, Jens Dawczynski, Peter Esser, Herbert Gross, and all the organizations and companies who consented to the inclusion of their graphic material throughout this book. We also would like to thank the students and academic staff at the Karlsruhe Institute of Technology (Germany) and the Ernst Abbe University of Applied Sciences in Jena (Germany).
We are grateful to our editors Valérie Molière and Anja Tschörtner at WILEY-VCH Verlag GmbH (Germany).
The book would not have been possible without the encouragement, support and interest of our families and friends. We therefore also see it as their book.
Part One
1
Structure and Function
In the following chapters of this book, we will deal with the examination and treatment of the human eye. As the majority of readers are expected to have an engineering or scientific background, we would like to provide a background in human ocular anatomy. This chapter shall also serve as an introduction and general reference for the more technical chapters. Of course, these chapters cannot claim to cover the entire anatomy and physiology of the eye, but they should be sufficient to gain an understanding of the interaction between the eye and the ophthalmic devices under consideration.
The human eye is a sophisticated sensory organ through which 80% of the sensory information we receive is processed. It is indeed our most important connection to the outside world. Any reduction or loss of vision means a major impairment of our quality of life.
In principle, the eye works like an artificial optical imaging system. To create an image, optical components focus light rays onto a photosensitive detector. But vision is more than just a projection of the surroundings onto a passive screen. The optical data is “preprocessed” by the photosensitive and neuronal tissue before it is sent to the brain for final “image analysis”. Even with efficient preprocessing, the eye sends 10 × more data to the brain than all other sensory organs altogether. To analyze this huge amount of information flow with almost no latency1), 30 different parts of the brain are involved simultaneously. During image processing, relevant information is filtered by recognition of known patterns.
The brain’s important role for vision is illustrated in Figure 1.1. In Figure 1.1a, an animated image is shown as it would be directly projected onto photosensitive tissue. Here, a sharp image exists only in the center of the visual field. The eye now automatically changes the viewing direction in a fast manner and, for a moment, the margins of the image are sharply imaged as well. All the image segments are then merged by the brain so that the perceived field of sharp vision extends to the margins (Figure 1.1b).
Figure 1.1 Image processing by the brain. (a) Simulated “raw” image as it would be detected by photosensitive tissue. (b) Due to fast changes of the viewing direction and preprocessing of the “detected data”, the perceived field of clear vision is considerably extended. Taken with permission from [1].
We can trick the brain’s hard-wired processing algorithms by looking at visual illusions (Figure 1.2). It is an interesting and currently not fully answered question how much visual illusions are based purely on innate factors, or to what extent they are also based on experience and adaption.
Figure 1.2 Visual illusions which trick the image processing capability of the brain. (a) The checkerboard field A seems to be darker than B although the gray scales are equal in both cases. (b) The big dark dot at the top appears larger than the lower one, even though both dots are exactly the same size. (c) The circles seem to rotate. (d) Does the image show spirals? A closer look reveals that the structures are closed rings. (e) Fixate the pattern in the center. When moving your head, the circle seems to move independently from the background. When bringing your head closer, the pattern inside the circle seems to approach. (f) The lines appear to be bent although they are perfectly straight. See also [2].
1.1 Anatomy of the Human Eye
The human eye can be divided into the anterior and posterior segments (Figure 1.3b and c, respectively). The anterior segment (Figure 1.4) is the optical window to the environment. It mainly consists of optical components, such as the cornea, eye lens, and iris. The posterior segment of the eye (Figure 1.5) is referred to as the fundus. It is connected to the visual cortex of the brain via the optic nerve (Figure 1.6).
Figure 1.3 Anatomy of the human eye. (a) Oblique view of the human eye ball. (b) Side view of the eye with highlighted anterior segment. (c) Side view of the eye with highlighted posterior segment.
Figure 1.4 Scheme of the eye’s anterior segment (see also Figure 1.3b). The depicted eye components are not to scale.
Figure 1.5 Scheme of the eye’s posterior segment (see also Figure 1.3c). The depicted eye components are not to scale.
Figure 1.6 Transverse cross-section of the visual pathway including the primary visual cortex. The left and right areas of the retina are connected to different parts of the visual cortex. Hence, if one side of the visual cortex is impaired, the visual information of both eyes can still be used.
Sclera and cornea The spherical outer shell of the human eye consists of the white, opaque sclera. It serves as a mechanical support and protects the eye from injuries caused by mechanical force. The collagen fibers in the sclera are randomly distributed. Consequently, the incident light is strongly scattered (Section 9.2) so that the tissue appears white and opaque, which is why this part is also called “the whites of the eyes”.
In the anterior segment of the eye, the sclera passes into the transparent cornea. The cornea is composed of multiple functional layers (Figure 1.7) and is covered by the 4–7 μm thick tear film. The tear film consists of a viscous, aqueous fluid that smooths the surface roughness of the corneal surface. A smooth surface reduces light scattering (Section 9.2), and thus improves the clarity of vision. The corneal epithelium is a 50 μm thick chemical barrier of the outer cornea which protects the eye against water, large molecules, and toxic substances. This is followed by Bowman’s membrane which is a thin layer (8–14 μm) above the 500 μm thick stroma. The stroma is composed of approximately 250 stacked collagen layers termed lamellae. Each lamella has a thickness of about 2 μm and contains ordered, cylindrical shaped collagen fibrils with diameters of 25–35 nm and a spacing of 20–50 nm [3]. Underneath the stroma we have the Descemet’s membrane (approximately 10 μm thick) which forms the basement layer of endothelial cells. The innermost corneal layer is the 5 μm thick endothelium. It is composed of hexagonal cells arranged in a honeycomb lattice and allows leakage of nutrients to the upper layers of the cornea. At the same time, the endothelium actively pumps water out of the cornea to keep it clear and transparent.
Figure 1.7 Detailed view of the corneal layer structure. The layer thicknesses are not to scale. Corresponding mean values are shown in parentheses. For reference, the cross-section of the whole eye is also shown. Adapted from [4].
Uvea, choroid, iris, and ciliary body The uvea forms the middle shell of the eye. In the posterior part of the eye (Figure 1.5), the uvea forms the so-called choroid, that is, a blood-rich tissue supplying nutrients to the retina (Section 1.2). The choroid has a total thickness of 350–450 μm. In the anterior segment (Figure 1.4), the uvea has evolved into the iris. In optical terms, the iris is an adjustable aperture stop whose diameter can be modified by two antagonistic muscles (sphincter and dilator pupillae). The hole of the iris is called the pupil. Note that the “anatomic pupil” does not correspond to the optical entrance or exit pupils (Sections 2.1.1 and A.1.4). The color of the iris depends on the amount of pigmentation in the anterior limiting layer of iris and stroma.
Between iris and choroid, the uvea has formed into the ciliary body which has two important functions. On the one hand, it produces the aqueous humor. On the other hand, it comprises the ciliary muscle which may relax the tension on the eye lens so that near vision is possible (Section 2.1.4).
Eye lens Similar to the cornea, the eye lens is a transparent tissue which contains no nerve fibers or blood vessels. The required nutrients are supplied by the aqueous humor, which is a clear fluid. The eye lens is embedded into an elastic capsule which is again attached to the ciliary body via zonular fibers. The capsule is composed of collagen and varies from 2–28 μm in thickness. The lens itself consists of an epithelial layer, which is only located in the anterior part of lens, and the lens fibers. The cells of the epithelium are located between the lens capsule and the outermost layer of lens fibers. Lens fibers form the bulk of the interior of the lens. They are long (up to 12 mm), thin, and transparent cells whose diameter ranges between 4 and 7 μm. The eye lens consists of two kinds of fiber. The inner core, the so-called nucleus, is formed by primary lens fibers. The nucleus is surrounded by the cortex which is formed by secondary lens fibers. The major purpose of the lens is the refractive change (i.e. accommodation; Section 2.1.4) to focus nearby objects.
Eye chambers The interior of the eye is divided into three chambers. The space between cornea and iris is called the anterior chamber, and between iris and eye lens we have the posterior chamber. The remaining space between lens and retina is referred to as the vitreous. The anterior and posterior chambers are filled with aqueous humor which contains nutrients for the eye lens and inner cornea. The aqueous humor is produced by the epithelial cells of the ciliary body in an amount of approximately 2.4 mm3/min and dispensed to the posterior chamber. It then flows continuously through the pupil to the trabecular meshwork, where it is eventually drained through Schlemm’s canal (Figure 1.4). The relationship between production and discharge of aqueous humor determines the intraocular pressure, which is slightly higher than atmospheric pressure and approximately matches the intercranial pressure. The vitreous is filled with a transparent, colorless, gelatinous mass. In contrast to the aqueous humor, the vitreous does not flow through the eye.
Retina The inner layer of the human eye is referred to as the retina. The retina is an upstream part of the brain which “detects” light and converts the stimulus to neuronal signal, which are then transmitted by the optic nerve to the visual centers of the brain, where the image is eventually “formed”. The retina will be highlighted in detail in the following section because of its high structural and functional complexity as well as its importance for vision.
Most parts of the eye are optically not accessible. When looking at the eye, we can only see the colored iris with the pupil and the white sclera. For optical imaging and structural analysis of the other parts, special optical techniques are required which we will discuss in Part Two of this book.
1.2 Retina: The Optical Sensor
The retina has evolved from the central nervous system and is actually part of the brain. It consists of approximately 127 million photoreceptors which convert incident light to electrical signals by a light-induced chemical reaction. These signals are than to some extent preprocessed by the retinal neural network and the ganglion cells. The nerve fibers of the approximately 1.2 million ganglion cells (called axons) merge on the optic nerve head (also called optic disk) into the optic nerve (Figure 1.5). From there, the neuronal signals are transmitted to the primary visual cortex of the brain (Figure 1.6).
1.2.1 Retinal Structure
The human retina is a multilayered tissue with a total thickness of about 180 μm in the fovea and between 200 and 400 μm elsewhere. The retinal structure is schematically shown in Figure 1.8. The retina contains two types of photoreceptors which are named after their shape: rods and cones (Figure 1.9). The photoreceptors are separated into three subregions, that is, outer segment, inner segment, and synaptic terminal. The outer segment is built up of a densely-packed stack of membranes which include the chromophores rhodopsin (rods) or iodopsin (cones)2). This part of the receptor is amazingly sensitive to incident light. If the eye is totally adapted to a dark environment, five to eight photons can be perceived when they hit the membrane within 20 ms3). The inner segment of a photoreceptor consists of the cell nucleus, mitochondria, and the endoplasmic reticulum. The synaptic terminal is a fiber-like extension of the nerve cell which conducts electric nerve impulses to the horizontal and bipolar cells of the retinal neural network. After some preprocessing there, these electrical signals are then conducted via the axons of the ganglion cells to the brain.
Figure 1.8 Cross-section of the functional retinal layers. At the top, the cross-section of the whole eye is added as a reference. The layer thicknesses and the relative distance (and density) of the photoreceptors are not to scale. Measured (mean) thickness values [5] of some retinal layers are shown in parentheses. The different colors of the cones refer to their distinct spectral absorption of light (Section 2.3). S, M, and L cones are shown in blue, green, and red, respectively. Adapted from [4].
Figure 1.9 Segmentation and structure of retinal photoreceptors.
The spatial distribution of the photoreceptors across the retina is highly nonuniform (Figure 1.10b). The density of the about 6–7 million cones is highest in the fovea. The peak density of the about 120 million rods is located at about 15° from the eye’s optical axis. In the fovea, no rods are present. Cones are only used under sufficient ambient light conditions, that is, daylight or photopic vision (Section 2.1.6). In this case, three types of cones are used with different spectral absorptions so that we are able to perceive colors (Section 2.3). S, M, and L cones (color coding in Figure 1.8) contain pigments which absorb in the blue, green, and red spectral range, respectively. The human eye is thus trichromatic in daylight. The nervous system combines the signals of all types of cones and assigns a respective color.
Figure 1.10 (a) Image of the eye fundus as a reference for the diagram in (b). The penetration point of the optical axis as well as the locations of fovea and optic nerve head are highlighted. (b) Distribution of photoreceptors and nerve fibers in the retina relative to the optical axis (0°). The logarithm of the number of photoreceptors N per degree of field angle is taken as the vertical axis. Datataken from [1].
In contrast to cones, rods are needed when the ambient light conditions are poor, that is, night or scotopic vision (Section 2.1.6). All rods contain the same chromophore so that the color impression decreases progressively with the light level. To achieve sufficient light sensitivity, the output signal of about 100 rods is combined on the way to the brain. As a consequence of this sampling the spatial resolution (Section 2.1.5) for scotopic vision is much lower compared to photopic vision, as in the fovea the density of cones is highest (Figure 1.10b), and each cone is connected to one nerve fiber.
1.2.2 Functional Areas
The macula (anatomic fovea centralis) is located in the center of the retina and is about 1.5 mm in diameter (Figures 1.5 and 1.10a). The most central part of the macula, called fovea (anatomic foveola), has a depression with a diameter of about 0.35 mm located at a field angle of approximately 5° from the eye’s optical axis (Section 2.1.3). In this region we find the highest density of cone photoreceptors (Figure 1.10b). As a consequence, visual acuity and resolution for photopic vision (Section 2.1.5, Figure 2.8) have their maximum values in this region.
In the fovea, the cone nerve fibers are spread radially from the center and nearly parallel to the surface of the retina and form the so-called Henle fiber layer (Info Box 6.5). The first connection between the cone fibers and the bipolar cells of the neuronal network occurs outside the fovea. Consequently, there are no tissue layers such as inner plexiform, ganglion cell, and nerve fiber layers (Figure 1.8) above the foveal cones, which could result in an impaired image quality due to scattering of light (see Section 9.2) by these layers. For the same reason, the central part of the macula (500 μm in diameter) contains no retinal capillaries (so-called foveal avascular zone). Since rods are not present in the fovea, this area is basically nightblind. The sharpest vision in the case of scotopic vision is achieved at about 15° from the eye’s optical axis because there we find the highest of the rod density (Figure 1.10b).
It is worth noting that the human retina is an inverted detector (Figure 1.8). Incident light is converted to an electric signal by photoreceptors which form the lowest layer. After being preprocessed, the electric signal is transmitted by nerve fibers of the ganglion cell layer that form the top layer (towards the vitreous). This kind of structure has the advantage that photoreceptors can be directly supplied with nutrients by the choroid. At one common exit point, the nerve fibers are connected to the brain and, thus, have to penetrate all other layers (not shown in Figure 1.8). Here, at the optic nerve head, the retina is 600 μm thick, but does not comprise any photoreceptors (Figure 1.10b). The optic nerve head is located about 10° nasally relative to the optical axis and 1.5° upwards relative to the fovea (Figure 1.10a).
1.3 Recommended Reading
Further details about the anatomy, structure, and function of the human eye are presented in [1, 4, 6–10]. Further examples of visual illusions can be found in [11].
References
1 Gross, H., Blechinger, F., and Achtner, B. (2008) Handbook of Optical Systems – Survey of Optical Instruments, vol. 4, Wiley-VCH Verlag GmbH, Weinheim.
2 Ditzinger, T. (2006) Illusion des Sehens, Spektrum, Heidelberg.
3 Komai, Y. and Ushiki, T. (1991) The three-dimensional organization of collagen fibrils in the human cornea and sclera. Invest. Ophthalmol. Vis. Sci., 32, 2244–2258.
4 Grehn, F. (2008) Augenheilkunde, Springer.
5 Bagci, A.M., Shahidi, M., Ansari, R., Blair, M., Blair, N.P., and Zelkha, R. (2008) Thickness profiles of retinal layers by optical coherence tomography image segmentation. Am. J. Ophthalmol., 146, 679–687.
6 Remington, L. (2011) Clinical Anatomy and Physiology of the Visual System, Butterworth–Heinemann.
7 Snell, R.S. and Lemp, M.A. (1997) Clinical Anatomy of the Eye, Wiley–Blackwell.
8 Lemp, M.A. (1998) Clinical Anatomy of the Eye, Blackwell Publishers.
9 Tasman, W. (ed.) (1992) Duane’s Foundations of Clinical Ophthalmology, vol. 2, Lippincott Williams & Wilkins.
10 Atchison, D.A. and Smith, G. (2006) Optics of the Human Eye, Butterworth–Heinemann.
11 Seckel, A. (2009) Optical Illusions, Firefly Books.
1) The average period of latency to transmit a light stimulus from the retina to the visual cortex takes about 95–115 ms, and it takes about 300 ms to perceive the signal. However, the brain “simulates” a real-time perception.
2) Each pigment molecule consists of two components, a large protein molecule (opsin) and a small molecule derived from vitamin A (retinal). The latter is responsible for light absorption.
3) Light perception (also referred to as transduction) takes place in less than 1 ms. During this short period, the retinal molecule changes its shape and dissociates from its binding site on the opsin. This process, known as bleaching, is the only step in vision which depends on light. Then, an electrically conductive sodium ion (Na+) channel is closed. As long as the channel is open in the dark, the excitatory neurotransmitter glutamate is steadily released.
2
Optics of the Human Eye
In all ophthalmic and optometric devices to be presented, the eye is an essential part of the entire optical system. Because of this, the functional principles of these devices cannot be fully understood without an understanding of basic optics of the human eye. In this chapter, we will see that the eye can be described in a similar way as other optical systems. This finding is very important for further discussions in this book, so that this chapter serves as a basic reference.
The anatomy of the human eye is readily comparable to the design of a photo camera (Figure 2.1). We can thus identify the iris as an aperture stop (Section 2.1.1), that the cornea and eye lens form the objective lens (Section 2.1.4), that the retina is a photo sensor, and that the brain acts as a very sophisticated image processing computer with intelligent algorithms. In contrast to a photo camera, the eye is not a centered optical system as its refractive components and aperture stop are not centered at a common optical axis (Section 2.1.3). The performance of the “light sensors” are also different for the photo camera and the human eye. The resolution of the photo camera’s detector is equal for the whole area, whereas the retinal resolution is inhomogeneous (Section 2.1.5). In the central part of the retina, the resolution is high and decreases at the margins.
Figure 2.1 Comparison of human eye and photo camera. The optical system of the photo camera is reduced to the most necessary components. Usually, the arrangement is much more complicated since optical aberrations (Section A.1.7) have to be corrected.
2.1 Optical Imaging
When light is incident to the eye, first of all it enters the cornea. As our eyes are usually surrounded by air, the refractive power (Section A.1.2.1) at the air–cornea interface1) is as high as 42 diopters (D). According to the Fresnel2) equation (A5), the transmittance of the air–cornea interface is 98%. However, this value does not take scattering (Section 9.2) and absorption (Section 9.1) of the ocular media into account. Nevertheless, healthy corneal tissue is remarkably transparent. This is due to the ordered collagen fibrils3) which are weak scatterers, as their radius is much smaller than the wavelength of visible light (fibril diameter: 25–35 nm; wavelength of visible light: 380–780 nm). In addition, the spatial distribution of fibrils reduces scattering because of destructive interference (Section A.2.3).
After the incident light rays have been refracted (Section A.1.1) by the cornea, they travel through the anterior chamber and cross the iris. For the eye as an optical system, the iris forms an aperture stop with a variable inner diameter (Figure 2.1). It limits the maximum acceptance angle, that is, the so-called visual field, for incident light rays to about 105°. On the nasal side, this angle is further reduced to 60° by the nose. For an iris diameter of 8 mm (scotopic vision), the eye has a maximum numerical aperture (Section A.1.4) of about 0.23 [1]. For an iris diameter of 3 mm, the numerical aperture reduces to 0.1.
When the light rays have passed the iris, they travel through the posterior chamber and enter the eye lens. The shape of the eye lens and thus its refractive power can be adjusted depending on the distance of the object being fixated. The lens consists of multiple shells which are stacked layer-by-layer. Each shell has a different refractive index, where a maximum refractive index of 1.42 is found in the core.
Behind the lens, light passes through the vitreous and is eventually “detected” by the retina. The image formed on the retina is inverted, that is, upside down, which is analogous to the imaging of a single lens (Figure A.6). Another inversion process happens in the brain, which results in the correct visual perception of our environment.
2.1.1 Entrance and Exit Pupils
In ophthalmology and optometry, the term “pupil” is often referred to as the hole of the iris (iris aperture). But technically, the iris is actually an aperture stop (Section A.1.4).4) The cornea forms an image of this aperture stop which is in optical terms the entrance pupil of the eye. The exit pupil of the eye is the image of the same aperture stop formed by the eye lens.
As shown in Figure 2.2, we follow the paths of a marginal ray and the chief ray to determine the location and diameter of the entrance and exit pupils. The optical design of the eye has been simplified in this scheme, because we assume that the iris is centered on an optical axis. The chief ray emanates from the outermost off-axis point O1 of the focused object. It is then refracted by the cornea, crosses the center of the iris, and is again refracted by the eye lens. Eventually, the chief ray hits the retina at point . As explained in Section A.1.4, the extensions of the chief ray define the positions of the pupil centers on the optical axis. The detailed view in Figure 2.2b shows the resulting pupil centers, E (entrance pupil) and E′ (exit pupil), relative to the ocular parts. The optical design in this figure is not to scale, but reveals correctly that the entrance pupil is larger and in front of the iris.
Figure 2.2 Location of entrance and exit pupils of the human eye. The indication of parameters is comparable to Figure A.13. (a) Path of the chief ray which starts at the outermost point O1 of the object and passes through the center of the iris. The extensions of the chief ray on the object and image side define the centers of the entrance and exit pupils, respectively. E is the center of the entrance pupil and E′ the center of the exit pupil. φ and φ′ denote the included angles between optical axis and chief ray on the object and image side, respectively. The corresponding angles between marginal ray and optical axis are α and α′. (b) Detailed view (dashed box of (a)) of the optical design in the anterior segment. Adapted from [2].
The marginal ray emanates from an on-axis object point O0 and grazes the inner edge of the iris. When we extend the object- and image-side parts of the marginal ray to the pupil planes, we obtain the inner diameters of the entrance and exit pupils, respectively.
We can now use the chief ray to determine the image size on the retina. In paraxial approximation (Section A.1.2), the absolute value of the image size follows as5) (Figure 2.2):
(2.1)
(2.2)
2.1.2 Cardinal Points
For human eyes, the description of optical imaging can be simplified by introducing three types of cardinal points.8) In centered optical systems, these points represent special locations on the optical axis which determine the basic imaging properties like image size, image location, and orientation. As the eye is not a centered optical system, we still use the concept of cardinal points but should understand that these points can merely be used as an approximate reference.
Focal points When incident light rays cross the object-side focal point F (Section A.1.2.1) and pass into the eye, they propagate parallel after refraction at cornea and lens. For an emmetropic eye (i.e., without refractive errors; Section 3.1), the image is formed at an infinite distance on the image side. If the incident light rays are parallel, they will be focused on the retina (at point F′) after refraction at cornea and (unaccommodated) eye lens.
Principal points The two principal points P and P′ are defined by the intersections of the principal planes (see, e.g., planes K and K′ in Figure A.8 of Section A.1.2.2) with the optical axis. These points are of interest if the combination of cornea and lens is considered to be one “thick” lens. In this case, the optical design may be simplified by assuming that incident rays are effectively refracted at the two principal planes.
Nodal points We consider a light ray emanated from the off-axis object point O1 in Figure 2.3 which travels towards nodal point N. After refraction by cornea and lens, the same ray seems to originate from image-side nodal point N′. The special feature of this ray is that its angle to the optical axis is equal for the ray’s incident (between O and the corneal front surface) and refracted part (between rear surface of lens and retina). As this ray passes through both nodal points, it is referred to as the nodal ray. It also defines the visual axis (Section 2.1.3) of the eye if marks the center of the fovea. In centered optical systems, the nodal and chief rays coincide so that the nodal points are actually located in the pupil centers.
Figure 2.3 Axes and cardinal points of the eye with corresponding inclination angles. V is the point of intersection of the optical axis with the cornea (corneal vertex). E and E′ represent the centers of the entrance and exit pupils. N and N′ denote the nodal points of the eye, and C is the rotation center of the eye. P and P′ are the principal points of the eye. n and n′ represent the refractive indices outside and inside the eye, and k is the angle between visual axis and optical axis. Adapted from [2].
Relation between cardinal points From geometrical considerations (Figure 2.3), we may derive some useful relations between the cardinal points [2]. We have
(2.3)
(2.4)
(2.5)
(2.6)
denotes the total refractive power of the human eye, n is the refractive index of the object space (usually air), and n′ the refractive index of the image space (i.e., the refractive index of the vitreous). Values for and n′ will be specified in Section 2.2.
2.1.3 Eye Axes
In centered optical systems, the optical axis is usually determined by the line which intersects with the centers of curvature of all refracting and reflecting surfaces. Since the ocular parts are decentered, it is useful to “redefine” the optical axis of an eye as the best-fit line between the centers of curvature of all refracting surfaces (black line in Figure 2.3). In addition, we introduce some other axes that help us to describe the eye’s optical geometry (see also [2]).
Visual axis The line between the fixated point O1 and fovea by way of nodal points N and N′ is referred to as the visual axis. The visual axis thus consists of the two line segments (red line in Figure 2.3) and forms the actual imaging axis of the eye. On average, the optical axis and the visual axis enclose an angle of k ≈ 5° on the object side.
With the visual axis, we can once again determine the retinal image size (compare with Section 2.1.1). In the case of paraxial optics, the absolute value of the retinal image size is given by
(2.7)
(2.8)
where .
Line of sight The line of sight is given by the line between a fixated object point O1 and the center of entrance pupil E (green line in Figure 2.3). On average, the angle between the line of sight and the pupillary axis is approximately 2.5°. The position at which the line of sight crosses the cornea is referred to as the corneal sight center.
Pupillary axis The pupillary axis passes through the center of entrance pupil E and is perpendicular to the corneal surface (orange line in Figure 2.3). It is used as an objective measure to judge the amount of eccentric fixation. As the eye is not a centered optical system, the entrance pupil is often not concentric to the cornea. The cornea may also have an irregular shape. Both factors cause the pupillary axis to be different from the optical axis. However, for the following discussions, we assume the center of the entrance pupil to lie on the optical axis.
Fixation axis The fixation axis is the reference axis for eye movements. It is determined by the line between object point O1 and center of eye rotation C (blue line in Figure 2.3).
2.1.4 Accommodation
In healthy eyes, the refractive power of the eye lens is at maximum and thus contributes only ≤ 30% to the total eye refraction.9) However, within a certain limit, the lens is able to change the refractive power so that nearby as well as distant objects can be sharply imaged on the retina. This process is referred to as accommodation. The range over which the refractive power can be changed depends on age.
Mechanism of accommodation If the eye focuses on nearby objects, the ciliary muscle is contracted and the zonular fibers are relaxed (accommodated eye). When the tension on the lens is decreased, the elasticity of the lens capsule keeps it in a more spherical shape (upper part of Figure 2.4). As the lens becomes more strongly curved in this case,10) the eye’s total refractive power increases (near vision). To focus objects which are located far away from the eye (far vision), the deformable, elastic lens is brought to a more elliptical shape by pulling on the lens capsule. The pulling force acting on the zonular fibers is generated by a relaxed ciliary muscle (relaxed eye). This situation is illustrated in the lower part of Figure 2.4.
Figure 2.4 Physiology of accommodation. Upper half of figure: If the ciliary muscle is contracted, the zonular fibers are relaxed and the elasticity of the lens capsule keeps the lens in a more spherical shape. In this case, the refractive power of the lens is higher so that nearby objects can be imaged (near vision). Lower half of figure: To fixate objects which are located far away from the eye (far vision), the deformable eye lens is brought to an elliptical shape by pulling on the lens capsule. The pulling force which acts on the zonular fibers is generated by a relaxed ciliary muscle. For reference, the near point Qnear, far point Qfar, principal point P, and the corresponding distances (snear and sfar) are shown.
Accommodation is an unconscious process that is not yet fully understood. But it is a common belief that chromatic aberrations (Section A.1.9) may deliver the required optical stimulus [3, 4].
The difference between far and near point refraction is referred to as the amplitude of accommodation
(2.9)
Figure 2.5 Age-dependence of the amplitude of accommodation ΔAmax. The typical range of deviation from the mean values (black curve) is shown in gray. Data taken from [6].
2.1.5 Resolution
2.1.5.1 Visual Performance
The values we have calculated for MAR can only be achieved with healthy eyes under ideal ambient light conditions. Normal vision may be impaired by refractive errors (Section 3.1), higher-order aberrations (Section 5.4), eye diseases (Sections 3.2–3.7), and/or problems with the processing of visual signals.
To quantify the visual performance of a patient, we could directly determine the minimum angle of resolution (MAR). In practice, however, this quantity could be a bit confusing, since a large angle means low vision and vice versa. Thus, the visual performance is usually expressed by the inverse of the minimum angle of resolution
(2.10)
Another common measure for the visual performance is specified by the common logarithm of the minimum angle of resolution (log10 MAR). This so-called logMAR scale is particularly used in scientific publications. The visual acuity scale is related to the logMAR scale via
(2.11)
2.1.5.2 Determination of the Visual Performance
Visual acuity is measured by subjective methods. The smallest feature size which can be clearly resolved by the patient determines the visual acuity. For this purpose, a wall chart with Landolt rings13) (Figure 2.6a) is used as a test target. The symbols are displayed in different sizes and orientations at a defined distance from the patient. The patient is now asked to state in which direction the corresponding feature of interest shows. The smallest feature which can be clearly recognized by the patient determines the visual acuity. For example, if a patient is able to recognize the orientation of Landolt ring gaps (top, right, bottom, left) with a gap size of 1.75 mm at a distance of 6 m, he or she has a visual acuity of 1. Patients with a lower visual acuity see a blurred image (e.g., the Landolt ring is perceived as a closed ring or dot) and thus cannot find the right feature orientation.
Figure 2.6 Two typical symbols which are used to determine the visual acuity. For subjective measurements, the symbols are displayed in different sizes and in various states of rotation. The patient then has to state in which direction the respective feature of interest shows. This type of chart can thus also be used for patients who are illiterate or too young to read. (a) Landolt ring. The feature of interest is the gap of the “C”-shaped symbol. (b) Snellen E. The feature of interest is the limb.
In clinical practice, the so-called Snellen chart is used as an alternative measure for the visual acuity. It consist of letters of the alphabet (see e.g. the “Snellen E” in Figure 2.6b) which are arranged in rows. In each row, the size of the letters is different so that each row can be used to test a different level of acuity. The rating of the acuity relates to the distance at which an emmetropic test person (“normal” visual acuity) is able to recognize the letters in that line. The (Snellen) visual acuity is defined by
(2.12)
The 6/6 acuity line represents the “normal” line and contains letters that subtend an angle of 5′ (with a minimum feature size of 1′) at a distance of 6 m.
Subjective methods do not only check the performance of the pure optical system, but also determine the image processing capability of the sensory organ on the whole (i.e., the combined eye–brain imaging system).
2.1.5.3 Influence Factors on the Visual Performance
As already mentioned, refractive errors and insufficient ambient light conditions decrease the visual acuity of human eyes. In addition, a number of other factors may influence vision, such as the diameter of the eye’s entrance pupil (Figure 2.7). For photopic vision (Section 2.1.6), the best resolution is given for a pupil diameter of about dpupil ≈ 2.5 mm. A smaller pupil diameter deteriorates the resolution as diffraction (Section A.2.1.6) comes into play. If the pupil diameter is larger, optical aberrations (Section A.1.6) reduce the resolution so that the visual acuity eventually “saturates”.
Figure 2.7 Diameter of the eye’s entrance pupil versus visual acuity. A maximum visual acuity is attained for a pupil diameter of about 2.5 mm. Below 2.5 mm (gray area), the optical performance is limited by diffraction. Above 2.5 mm, aberrations deteriorate the optical resolution of the eye. Data points are taken from [7]. The dashed line is a best-fit curve through the data points and meant as a guidance.
As the density of cones and ganglion cells rapidly decreases outside the fovea, the visual performance for photopic vision also depends on the field angle at which the image is projected on the retina (Figure 2.8). At the optic nerve head, no photoreceptors exist at all so that the visual acuity equals to zero in this area (the so-called blind spot). Other influence factors for the visual performance are the shape, brightness, and color of considered objects as well as the degree of attention (psychological influence factors).
Figure 2.8 Dependence of the visual acuity on the field angle for photopic vision. The density of cones is maximal at the fovea (0°), but rapidly decreases outside this retinal region. As a consequence, the resolution is gradually reduced for increasing field angles. Adapted from [6].
2.1.6 Adaption
The eye is able to maintain a high sensitivity to small changes in light intensity across a broad range of ambient light levels. Full operation of human vision is possible for a luminance between 10–6 and 108 cd/m2 [8]. For this purpose, the eye uses the following mechanisms to adapt to the given ambient light conditions:
