Table of Contents

Foreword

Preface

1 Optics of the Eye

1.1 The Foundations of Vision

      1.1.1 Our Understanding: The First Steps

1.2 Retinal Image Formation

      1.2.1 The Eye versus the Photo Camera

1.3 Image Perception and Encoding

1.4 Ocular Refraction

      1.4.1 Cardinal Points

      1.4.2 Optical Power of the Human Eye

1.5 Models of the Eye

      1.5.1 From the Simplest to the Most Complicated

      1.5.2 Schematic Eye Models

      1.5.3 Ray Tracing

1.6 Optics of the Eye Quiz

2 Refractive Elements of the Eye

2.1 Cornea

      2.1.1 Corneal Shape

      2.1.2 Corneal Structure and Physiology

      2.1.3 Corneal Optical Power

      2.1.4 Corneal Asphericity and Toricity

      2.1.5 Tear Film

2.2 Crystalline Lens

      2.2.1 Crystalline Lens: Shape & Optical Properties

      2.2.2 Refractive Indices in the Eye

2.3 Anterior Chamber Optics

      2.3.1 Purkinje Images

      2.3.2 Anterior Chamber

2.4 Optical Apertures and Axes in the Human Eye

      2.4.1 The Necessity of the Diaphragm

      2.4.2 Iris and Pupil

      2.4.3 Axes and Reference Points in the Human Eye

      2.4.4 Angles in the Human Eye

2.5 The Transit of Light in the Human Eye

      2.5.1 Losses due to Reflection

      2.5.2 The Complicated Nature of Reflection Coefficients

      2.5.3 Losses due to Absorption

      2.5.4 The UltraViolet Radiation and the Eye

      2.5.5 Losses due to Scattering

2.6 Refractive Elements of the Eye Quiz

2.7 Ocular Refraction & Eye Elements Summary

3 Visual Acuity

3.1 Angular Expressions

      3.1.1 Viewing Angle

      3.1.2 Resolution Limit and Resolving Power

3.2 Diffraction, a Limit to Vision

      3.2.1 The Rayleigh Criterion

      3.2.2 Aberrations and Visual Acuity

      3.2.3 Other Factors Affecting Visual Acuity

3.3 Visual Acuity Charts

      3.3.1 Historical Background

      3.3.2 The Snellen Optotype Geometry

      3.3.3 Snellen Chart Limitations

3.4 The Measurement of Visual Acuity

      3.4.1 Visual Acuity Notations

      3.4.2 Pinhole Visual Acuity

      3.4.3 Expressions of Visual Acuity

      3.4.4 Advanced Optotypes and Eye Charts

      3.4.5 The logMAR Metric and the ETDRS Charts

      3.4.6 The Visual Acuity Rating

      3.4.7 Other Vision Assessment Metrics

      3.4.8 Digital / Electronic Charts

3.5 Visual Acuity Quiz

3.6 Visual Acuity Summary

4 Optics of the Retina

4.1 Retinal Structure, Geometry, and Optics

      4.1.1 Retinal Shape

      4.1.2 Thickness and Layered Structure of the Retina

      4.1.3 Field of View / Visual Field Mapping

4.2 Photoreceptors

      4.2.1 Cones and Rods

      4.2.2 Photoreceptor Pathways

      4.2.3 Fovea: the Center of Vision

4.3 The Photonic Sensation

      4.3.1 Spectral Sensitivity

      4.3.2 Response to Luminance

      4.3.3 Light and Dark Adaptation

      4.3.4 The Purkinje Shift

      4.3.5 Receptive Fields

      4.3.6 Ganglion Cell Excitation and Inhibition

4.4 Photoreceptor Optics

      4.4.1 Optical Fiber Guidance

      4.4.2 Stiles–Crawford Effect

4.5 Digital Signal and Analysis

      4.5.1 The Retina Display

      4.5.2 Sampling and Digital Sensation

      4.5.3 Digital Resolution of the Human Eye? Is it 240 Mpixel?

4.6 Retina Quiz

4.7 Retina Summary

5 Color Perception

5.1 Color in Optics

      5.1.1 Primary Colors

      5.1.2 Color Properties

      5.1.3 Additive & Subtractive Colors

      5.1.4 Color Spaces

5.2 Perception of Colors in the Human Eye

      5.2.1 The Three Cone Types

      5.2.2 Process Theories

      5.2.3 Subjectivity of Color Perception

      5.2.4 Color Vision in Other Species

5.3 Color Vision Deficiency

      5.3.1 Classification of Color Vision Deficiencies

      5.3.2 Inheritance of Color Vision Deficiency

      5.3.3 Acquired Color Vision Deficiencies

5.4 Testing Color Vision Deficiency

      5.4.1 Lantern Tests

      5.4.2 Pseudoisochromatic Tests

      5.4.3 Arrangement Tests

      5.4.4 The Anomaloscope

      5.4.5 Computerized CVD tests

5.5 Color Perception Quiz

5.6 Color Perception Summary

6 Ametropias

6.1 Focusing in the Eye

      6.1.1 Vergence and Effective Power

      6.1.2 The Circle of Least Confusion

      6.1.3 The Near and Far Points

      6.1.4 Depth of Field and Depth of Focus

      6.1.5 Depth of Field and Range of Clear Vision

6.2 Emmetropia

      6.2.1 Axial Length and Focal Length

      6.2.2 Retinal Image Size in the Emmetropic Eye

6.3 Ametropia ≠ Emmetropia

      6.3.1 Chromatic Aberration and Vision

      6.3.2 Monochromatic Aberrations

6.4 Myopia and Hyperopia

      6.4.1 Myopia

      6.4.2 Hyperopia

      6.4.3 Defocus, Axial Length, and Corneal Curvature

6.5 Effects of Ametropia

      6.5.1 Cardinal Points in Ametropia

      6.5.2 Retinal Image Size and Blur in Uncorrected Ametropia

      6.5.3 Effect of Ametropias on Visual Acuity

      6.5.4 Effect of Ametropias on Depth of Focus

6.6 Spectacle Correction of Myopia and Hyperopia

      6.6.1 Correction of Myopia: Optical Principles

      6.6.2 Correction of Hyperopia: Principles

      6.6.3 The Challenge of Hyperopia Correction

      6.6.4 The Correction of Aphakia

      6.6.5 Knapp's Rule

6.5 Ametropia Quiz

6.6 Ametropia Summary

7 Accommodation and Presbyopia

7.1 The Nature of Accommodation

      7.1.1 The Need to Adapt for Shorter Distances

      7.1.2 Accommodation Theories

      7.1.3 Variable Lenticular Power

7.2 Magnitude and Measurement of Accommodation

      7.2.1 Magnitude of Accommodation

      7.2.2 Amplitude of Accommodation

      7.2.3 Measurement of the Amplitude of Accommodation

7.3 Classification of Accommodation

      7.3.1 Classification on the Basis of Measurement

      7.3.2 Classification of Involuntary Accommodation

      7.3.3 Pseudoaccommodation

7.4 Anomalies of Accommodation

7.5 Convergence and Accommodation Effects

      7.5.1 Influence of Refractive Error

      7.5.2 Accommodation in the Corrected Hyperope

      7.5.3 Accommodation in the Corrected Myope

7.6 Convergence and Accommodation Effects

      7.6.1 Convergence and Spectacle Wear

7.7 Presbyopia

      7.7.1 Understanding the Problem

      7.7.2 Physiological Etiology

      7.7.3 The Add Power

      7.7.4 Presbyopia Classification

7.8 The Management of Presbyopia

      7.7.1 Spectacle Correction for Presbyopia

      7.7.2 Physiological Etiology

      7.7.3 The Add Power

      7.7.4 Presbyopia Classification

7.9 Low Vision

      7.9.1 Low-Vision Definitions

      7.9.2 Traditional Semi-Quantitative Tests for Low Vision

      7.9.3 Handheld Low-Vision Card Tests

      7.9.4 Vision Testing with Gratings

7.10 Near Vision Testing

      7.10.1 Standardized Reading Chart Tests

7.11 Accommodation and Presbyopia Quiz

7.12 Accommodation and Presbyopia Summary

8 Astigmatism

8.1 Geometry and Classification of Astigmatism

      8.1.1 Meridians

      8.1.2 Classification of Astigmatism

8.2 Magnitude and Axis of Astigmatism

      8.2.1 Astigmatic Prescriptions

      8.2.2 Spherical Equivalent

8.3 The Seat of Astigmatism

8.4 Effect of Astigmatism on Vision

      8.4.1 The Astigmatic (Clock) Dial

      8.4.2 Effect of Astigmatism on Letter Legibility

8.5 Correction of Astigmatism: Principles

      8.5.1 Toric Lens Correction

      8.5.2 Correction with Spherical Equivalent

      8.5.3 Distortion in the Corrected Retinal Astigmatic Image

8.6 Stokes Lens and Jackson Cross-Cylinder

8.7 Astigmatism Quiz

8.8 Astigmatism Summary

9 Ophthalmic Lens Optics

9.1 Some Historical Facts

9.2 Lens Power and Vergence

      9.2.1 Surface Power and the Nominal Power

      9.2.2 Equivalent Power and Gullstrand's Relationship

      9.2.3 Vergence Distance and Upstream and Downstream Power

      9.2.4 Effective (Downstream) Power & Vertex Distance

      9.2.5 Front and Back Vertex Lens Power

9.3 Corrected Image and Spectacle Magnification

      9.3.1 Corrected Retinal Image in Ametropia

      9.3.2 Apparent Eye Size

      9.3.3 Lens Effect on Field of View

9.4 Ophthalmic Lens Geometry

      9.4.1 Optical Center

      9.4.2 Sagitta

      9.4.3 Surface Power Curves

      9.4.4 Lens Thickness

9.5 Cylinder and Toric Lens

      9.5.1 The Cylinder Lens

      9.5.2 The Toric Lens

      9.5.3 Toric Power Cartesian Vector Representation

      9.5.4 Combination of Oblique Cross Cylinders

      9.5.5 Toric Formulas

9.6 Light Transmission in Ophthalmic Lenses

      9.6.1 Transmissivity and Reflectivity

      9.6.2 Spectacles of Higher Refractive Index

9.7 Hand Neutralization and Lensometry

      9.7.1 Hand Neutralization in Spherical Lenses

      9.7.2 Hand Neutralization in Astigmatic and Cylinder Lenses

      9.7.3 Hand Neutralization in Prisms

      9.7.4 Lensometry

9.8 Ophthalmic Optics Quiz

9.9 Ophthalmic Optics Summary

10 Prismatic Effects

10.1 Thin Prism Optics and Geometry

      10.1.1 Prism Deviation Angle

      10.1.2 Prism Power

      10.1.3 Prism Thickness

10.2 Effective Prism Power

10.3 Fresnel and Risley Prisms

10.4 The Lens as a Prism

      10.4.1 Prentice's Rule

      10.4.2 Prism Ground on a Lens

      10.4.3 Prismatic Effects in Cylinder Decentration

10.5 Prisms in Vision Correction

      10.5.1 Specifying the Prism Base

      10.5.2 Prisms in Front of Both Eyes

      10.5.3 Prisms for Binocular Vision Dysfunction

10.6 Combinations of Thin Prisms

10.7 Lens Tilt and Shift Effects

      10.7.1 Wrap Tilt and Pantoscopic Tilt

      10.7.2 Compensation: Martin's Rule of Tilt

10.8 Prismatic Effects Quiz

10.9 Prismatic Effects Summary

Appendix

Conventions and Notations

Answers to Quiz Questions

Index

Preface

Visual optics is, in essence, an application of optics for a very important sensory organ: the eye. While rather complicated, the process of vision can be divided into two parts, the optical and the neural. This book extensively and comprehensively covers the the optical part, while providing a simple description of the neural part, which is restricted to those aspects that are critical to understanding visual function.

The topic of visual optics can be quite challenging and fascinating. This topic bridges knowledge acquired from more science-oriented, geometrical and wave optics material with the application of this knowledge to the eye, and extends in clinical relevance to optometry and ophthalmology. Optics is the foundation of how the eye works, how we image the eye for diagnosis, and, more recently, how we use many laser-based therapeutic and cosmetic applications. A good understanding of the simple yet powerful relationships that describe the interaction between light and the eye helps to pave the way to a comfortable approach to understanding the operation of traditional examination techniques such as retinoscopy as well as modern ocular diagnostics such as topography and optical coherence tomography. Thus, the first three books in this series provide the scientific foundation for the explorations and applications discussed in this book. The applications of ocular imaging are extensively presented in the final volume of this series, Ocular Imaging.

Combining optical science with clinical relevance, this Visual Optics volume is written specifically for adult learners in the optometry and ophthalmology professions. It is referenced with the most recent research findings that have been published in peer-reviewed journals—almost 1000 external references are included.

The text follows the didactic principles adopted throughout the series, with adherence to a deductive approach, lots of practical examples, ample illustrations, and clear, concise language. Often my students tell me that the words from the lectures are also the words in my texts. While I see this as an exaggeration, it is true that, despite endeavoring to explain complex concepts and the need to adhere to strict and rigorous definitions, simple language is always sought, with the goal of being thoroughly understood in a clinically meaningful way.

The book is organized based on two broad concepts. The first concept, spanning Chapters 1 to 5, pertains to the well-functioning eye, or the eye that produces retinal images of sufficient quality; let's call this emmetropic visual optics. The second concept spans Chapters 6 to 10 and is called ametropic visual optics. This covers the science of spherocylindrical ametropias, i.e., myopia, hyperopia (Chapter 6), and astigmatism (Chapter 8) for distance- and near-vision accommodation (Chapter 7) and extends to aspects of the aging eye, which include presbyopia and low vision (Chapter 7), optical correction and its considerations (Chapter 9 on ophthalmic lens optics), and prismatic effects (Chapter 10).

Every chapter is followed by an extensive, multiple-choice quiz and a short summary. The quiz questions are in the format followed by the National Board of Examiners in Optometry (NBEO) and aim to be an element of self-evaluation and assessment for the reader.

George Asimellis
Boston, Massachusetts
October 2021