- •Contents
- •General Introduction
- •Objectives
- •1 Geometric Optics
- •Rays, Refraction, and Reflection
- •Introduction
- •Point Sources, Pencils, and Beams of Light
- •Object Characteristics
- •Image Characteristics
- •Magnification
- •Image Location
- •Depth of Focus
- •Image Quality
- •Light Propagation
- •Optical Media and Refractive Index
- •Law of Rectilinear Propagation
- •Optical Interfaces
- •Law of Reflection (Specular Reflection)
- •Law of Refraction (Specular Transmission)
- •Normal Incidence
- •Total Internal Reflection
- •Dispersion
- •Reflection and Refraction at Curved Surfaces
- •The Fermat Principle
- •Pinhole Imaging
- •Locating the Image: The Lensmaker’s Equation
- •Ophthalmic Lenses
- •Vergence
- •Reduced Vergence
- •Thin-Lens Approximation
- •Lens Combinations
- •Virtual Images and Objects
- •Focal Points and Planes
- •Paraxial Ray Tracing Through Convex Spherical Lenses
- •Paraxial Ray Tracing Through Concave Spherical Lenses
- •Objects and Images at Infinity
- •Principal Planes and Points
- •Section Exercises
- •Focal Lengths
- •Gaussian Reduction
- •Knapp’s Law, the Badal Principle, and the Lensmeter
- •Afocal Systems
- •Section Exercises
- •Questions
- •Power of a Lens in a Medium
- •Spherical Interface and Thick Lenses
- •Thick Lens
- •Back Vertex Power Is Not True Power
- •Aberrations of Ophthalmic Lenses
- •Third-Order Seidel Aberrations
- •Chromatic Aberrations
- •Avoiding Aberrations
- •Mirrors
- •Reflection From a Plane Mirror
- •Spherically Curved Mirrors
- •Reversal of the Image Space
- •The Central Ray for Mirrors
- •Vergence Calculations for Mirrors
- •Spherocylindrical Lenses
- •Combination of Spherocylindrical Lenses
- •The Conoid of Sturm
- •The Jackson Cross Cylinder
- •Prisms
- •Prism Diopter
- •Prismatic Effect of Lenses and the Prentice Rule
- •Prism Aberrations
- •Fresnel Prisms
- •Chapter Exercises
- •Questions
- •Appendix 1.1
- •Quick Review of Angles, Trigonometry, and the Pythagorean Theorem
- •Appendix 1.2
- •Light Properties and First-Order Optics
- •2 Optics of the Human Eye
- •The Human Eye as an Optical System
- •Schematic Eyes
- •Important Axes of the Eye
- •Pupil Size and Its Effect on Visual Resolution
- •Visual Acuity
- •Contrast Sensitivity and the Contrast Sensitivity Function
- •Refractive States of the Eyes
- •Binocular States of the Eyes
- •Accommodation and Presbyopia
- •Epidemiology of Refractive Errors
- •Developmental Myopia
- •Developmental Hyperopia
- •Prevention of Refractive Errors
- •Chapter Exercises
- •Questions
- •3 Clinical Refraction
- •Objective Refraction Technique: Retinoscopy
- •Positioning and Alignment
- •Fixation and Fogging
- •The Retinal Reflex
- •The Correcting Lens
- •Finding Neutrality
- •Retinoscopy of Regular Astigmatism
- •Aberrations of the Retinoscopic Reflex
- •Subjective Refraction Techniques
- •Astigmatic Dial Technique
- •Stenopeic Slit Technique
- •Cross-Cylinder Technique
- •Refining the Sphere
- •Binocular Balance
- •Cycloplegic and Noncycloplegic Refraction
- •Overrefraction
- •Spectacle Correction of Ametropias
- •Spherical Correcting Lenses and the Far Point Concept
- •The Importance of Vertex Distance
- •Cylindrical Correcting Lenses and the Far Point Concept
- •Prescribing for Children
- •Myopia
- •Hyperopia
- •Anisometropia
- •Clinical Accommodative Problems
- •Presbyopia
- •Accommodative Insufficiency
- •Accommodative Excess
- •Accommodative Convergence/Accommodation Ratio
- •Effect of Spectacle and Contact Lens Correction on Accommodation and Convergence
- •Prescribing Multifocal Lenses
- •Determining the Add Power of a Bifocal Lens
- •Types of Bifocal Lenses
- •Trifocal Lenses
- •Progressive Addition Lenses
- •The Prentice Rule and Bifocal Lens Design
- •Occupation and Bifocal Segment
- •Prescribing Special Lenses
- •Aphakic Lenses
- •Absorptive Lenses
- •Special Lens Materials
- •Therapeutic Use of Prisms
- •Chapter Exercises
- •Questions
- •Appendix 3.1
- •Common Guidelines for Prescribing Cylinders for Spectacle Correction
- •4 Contact Lenses
- •Introduction
- •Contact Lens Glossary
- •Clinically Important Features of Contact Lens Optics
- •Field of Vision
- •Image Size
- •Accommodation
- •Convergence Demands
- •Tear Lens
- •Correcting Astigmatism
- •Correcting Presbyopia
- •Contact Lens Materials and Manufacturing
- •Materials
- •Manufacturing
- •Patient Examination and Contact Lens Selection
- •Patient Examination
- •Contact Lens Selection
- •Contact Lens Fitting
- •Soft Contact Lenses
- •Rigid Gas-Permeable Contact Lenses
- •Toric Soft Contact Lenses
- •Contact Lenses for Presbyopia
- •Keratoconus and the Abnormal Cornea
- •Contact Lens Overrefraction
- •Gas-Permeable Scleral Contact Lenses
- •Therapeutic Lens Usage
- •Orthokeratology and Corneal Reshaping
- •Custom Contact Lenses and Wavefront Technology
- •Contact Lens Care and Solutions
- •Contact Lens–Related Problems and Complications
- •Infections
- •Hypoxic/Metabolic Problems
- •Toxicity
- •Mechanical Problems
- •Inflammation
- •Chapter Exercises
- •Questions
- •Appendix 4.1
- •Transmission of Human Immunodeficiency Virus in Contact Lens Care
- •Appendix 4.2
- •Federal Law and Contact Lenses
- •5 Intraocular Lenses
- •Intraocular Lens Designs
- •Classification
- •Background
- •Optical Considerations for Intraocular Lenses
- •Intraocular Lens Power Calculation
- •Piggyback and Supplemental Intraocular Lenses
- •Intraocular Lens Power Calculation After Corneal Refractive Surgery
- •Instrument Error
- •Index of Refraction Error
- •Formula Error
- •Power Calculation Methods for the Post–Keratorefractive Procedure Eye
- •Intraocular Lens Power in Corneal Transplant Eyes
- •Silicone Oil Eyes
- •Pediatric Eyes
- •Image Magnification
- •Lens-Related Vision Disturbances
- •Nonspherical Optics
- •Multifocal Intraocular Lenses
- •Types of Multifocal Intraocular Lenses
- •Clinical Results of Multifocal Intraocular Lenses
- •Accommodating Intraocular Lenses
- •Intraocular Lens Standards
- •Chapter Exercises
- •Questions
- •Appendix 5.1
- •History of Intraocular Lens Design
- •6 Optical Considerations in Keratorefractive Surgery
- •Corneal Shape
- •Angle Kappa
- •Pupil Size
- •Irregular Astigmatism
- •Application of Wavefront Analysis in Irregular Astigmatism
- •Causes of Irregular Astigmatism
- •Conclusion
- •Chapter Exercises
- •Questions
- •7 Optical Instruments and Low Vision Aids
- •Magnification
- •Telescopes
- •Galilean Telescope
- •Astronomical Telescope
- •Accommodation Through a Telescope
- •Surgical Loupe
- •General Principles of Optical Engineering
- •Terminology
- •Measurements of Performance of Optical Systems
- •Optical Instruments and Techniques Used in Ophthalmic Practice
- •Direct Ophthalmoscope
- •Indirect Ophthalmoscope
- •Fundus Camera
- •Slit-Lamp Biomicroscope
- •Gonioscopy
- •Surgical Microscope
- •Geneva Lens Clock
- •Lensmeter
- •Knapp’s Rule
- •Optical Pachymeter
- •Applanation Tonometry
- •Specular Microscopy
- •Keratometer
- •Topography
- •Ultrasonography of the Eye and Orbit
- •Macular Function Tests
- •Scanning Laser Ophthalmoscopes
- •Scheimpflug Camera
- •Autorefractors
- •Optical Coherence Tomography
- •Optical Aids
- •Magnifiers
- •Telescopes
- •Prisms
- •High-Add Spectacles
- •Nonoptical Aids
- •Electronic Devices
- •Lighting, Glare Control, and Contrast Enhancement
- •Nonvisual Assistance
- •Eccentric Viewing or Fixation Training
- •Instruction and Training
- •Chapter Exercises
- •Questions
- •Appendix 7.1
- •Approach to the Patient With Low Vision
- •8 Physical Optics
- •The Corpuscular Theory of Light
- •Diffraction
- •The Speed of Light
- •The Superposition of Waves
- •Coherence
- •Electromagnetic Waves
- •Polarization
- •Refractive Index and Dispersion
- •Reflection, Transmission, and Absorption
- •The Electromagnetic Spectrum
- •Frequency and Color
- •Energy in an Electromagnetic Wave
- •Quantum Theory
- •Light Sources
- •Thermal Sources
- •Luminescent Sources
- •Fluorescence
- •Phosphorescence
- •Lasers
- •Light–Tissue Interactions
- •Photocoagulation
- •Photoablation
- •Photodisruption
- •Photoactivation
- •Light Scattering
- •Rayleigh Scattering
- •Mie Scattering
- •The Tyndall Effect
- •Radiometry and Photometry
- •Light Hazards
- •Clinical Applications
- •Polarization
- •Interference
- •Diffraction
- •Imaging and the Point Spread Function
- •Image Quality—Modulation Transfer Function
- •Chapter Exercises
- •Questions
- •Appendix 8.1
- •Radiometric and Photometric Units
- •Basic Texts
- •Related Academy Materials
- •Requesting Continuing Medical Education Credit
shapes that approximate various types of irregular astigmatism more closely than the simple “football” model. These aberrations include such shapes as spherical aberration, coma, and trefoil. See Chapter 6 of this book and BCSC Section 13, Refractive Surgery, for further discussion.
Binocular States of the Eyes
The spherical equivalent of a refractive state is defined as the algebraic sum of the spherical component and half of the astigmatic component. Anisometropia refers to any difference in the spherical equivalents between the 2 eyes. Uncorrected anisometropia in children may lead to amblyopia, especially if 1 eye is hyperopic. Although adults may be annoyed by uncorrected anisometropia, they may be intolerant of initial spectacle correction. Unequal image size, or aniseikonia, may occur, and the prismatic effect of the glasses will vary in different directions of gaze, inducing anisophoria. Anisophoria may be more bothersome than aniseikonia for patients with spectacle-corrected anisometropias.
Aniseikonia can also be due to a difference in the shape of the images formed in the 2 eyes. The most common cause is the differential magnification inherent in the spectacle correction of anisometropia. Even though aniseikonia is difficult to measure, anisometropic spectacle correction can be prescribed in such a manner as to reduce aniseikonia. Making the front surface power of a lens less positive can reduce magnification. Decreasing center thickness also reduces magnification. Decreasing vertex distance diminishes the magnifying effect of plus lenses as well as the minifying effect of minus lenses. These effects become increasingly noticeable as lens power increases. Contact lenses may provide a better solution than spectacles for most patients with anisometropia, particularly children, in whom fusion may be possible.
Unilateral aphakia is an extreme example of hyperopic anisometropia arising from refractive ametropia. In the adult patient, spectacle correction produces an intolerable aniseikonia of about 25%; contact lens correction produces aniseikonia of about 7%, which is usually tolerated. If necessary, the clinician may reduce aniseikonia still further by adjusting the powers of contact lenses and simultaneously worn spectacle lenses to provide the appropriate minifying or magnifying effect via the Galilean telescope principle. For further information on correcting aphakia, see Chapters 3, 4, and 5.
Accommodation and Presbyopia
Accommodation is the mechanism by which the eye changes refractive power by altering the shape of its crystalline lens. The mechanisms that achieve this alteration have been described by Helmholtz. The posterior focal point is moved forward in the eye during accommodation (Fig 2-13A). Correspondingly, the far point moves closer to the eye (Fig 2-13B). Accommodative effort occurs when the ciliary muscle contracts in response to parasympathetic stimulation, thus allowing the zonular fibers to relax. The outward-directed tension on the lens capsule is decreased, and the lens becomes more convex. Accommodative response results from the increase in lens convexity (primarily the anterior surface). It may be expressed as the amplitude of accommodation (in diopters) or as the range of accommodation, the distance between the far point of the eye and the nearest point at which the eye can maintain focus (near point). It is evident that as the lens loses elasticity from the aging process, the accommodative response wanes (a condition called
presbyopia), even though the amount of ciliary muscle contraction (or accommodative effort) is virtually unchanged. For an eye with presbyopia, the amplitude is a more useful measurement for calculating the power requirement of the additional spectacle lens. For appraising an individual’s ability to perform a specific visual task, the range is more informative.
Figure 2-13 Emmetropia with accommodation stimulated. A, Parallel light rays now come to a point locus in front of the retina, forming a blurred image on the retina. B, Light rays emanating from a point on the retina focus to a near point in front of the eye, between optical infinity and the cornea. (Illustration b y C. H. Wooley.)
Glasser A, Kaufman PL. The mechanism of accommodation in primates. Ophthalmology. 1999;106(5):863–872.
Epidemiology of Refractive Errors
An interplay among corneal power, lens power, anterior chamber depth, and axial length determines an individual’s refractive status. All 4 elements change continuously as the eye grows. On average, babies are born with about 3.00 D of hyperopia. In the first few months of life, this hyperopia may increase slightly, but it then declines to an average of about 1.00 D of hyperopia by the end of the first year because of marked changes in corneal and lenticular powers, as well as axial length growth. By the end of the second year, the anterior segment attains adult proportions; however, the curvatures of the refracting surfaces continue to change measurably. One study found that average corneal power decreased 0.10–0.20 D and lens power decreased about 1.80 D between ages 3 years and 14 years.
From birth to age 6 years, the axial length of the eye grows by approximately 5 mm; thus, one might expect a high prevalence of myopia in infants. However, most children’s eyes are actually emmetropic, with only a 2% incidence of myopia at 6 years. This phenomenon is due to a stillundetermined mechanism called emmetropization. During this period of eye growth, a compensatory loss of 4.00 D of corneal power and 2.00 D of lens power keeps most eyes close to emmetropia. It appears that the immature human eye develops so as to reduce refractive errors.
American Academy of Ophthalmology. Refractive Management/Intervention Panel. Preferred Practice Pattern Guidelines. Refractive Errors. San Francisco: American Academy of Ophthalmology; 2002. Available at www.aao.org/ppp.
Lawrence MS, Azar DT. Myopia and models and mechanisms of refractive error control. Ophthalmol Clin North Am. 2002;15(1):127–133.
Prevent Blindness America; National Eye Institute. Vision Problems in the U.S.: Prevalence of Adult Vision Impairment and Age-Related Eye Disease in America. 5th ed. Chicago, IL: Prevent Blindness America; 2012.
Developmental Myopia
Myopia increases steadily with increasing age. In the United States, the prevalence of myopia has been estimated at 3% among children aged 5–7 years, 8% among those aged 8–10 years, 14% among those aged 11–12 years, and 25% among adolescents aged 12–17 years. In particular ethnic groups, a similar trend has been demonstrated, although the percentages in each age group may differ. Ethnic Chinese children have much higher rates of myopia at all ages. A national study in Taiwan found the prevalence was 12% among 6-year-olds and 84% among adolescents aged 16–18 years. Similar rates have been found in Singapore and Japan.
Different subsets of myopia have been characterized. Juvenile-onset myopia, defined as myopia with an onset between 7 years and 16 years of age, is due primarily to growth in axial length. Risk factors include esophoria, against-the-rule astigmatism, premature birth, family history, and intensive near work. In general, the earlier the onset of myopia is, the greater is the degree of progression. In the United States, the mean rate of childhood myopia progression is reported at about 0.50 D per year. In approximately 75% of teenagers, refractive errors stabilize at about age 15 or 16. In those whose errors do not stabilize, progression often continues into the 20s or 30s.
Adult-onset myopia begins at about 20 years of age, and extensive near work is a risk factor. A study of West Point cadets found myopia requiring corrective lenses in 46% at entrance, 54% after 1 year, and 65% after 2 years. The probability of myopic progression was related to the degree of initial refractive error. It is estimated that as many as 20%–40% of patients with low hyperopia or emmetropia who have extensive near-work requirements become myopic before age 25, compared with less than 10% of persons without such demands. Older Naval Academy recruits have a lower rate of myopia development than younger recruits over a 4-year curriculum (15% for 21-year-olds versus 77% for 18-year-olds). Some young adults are at risk for myopic progression even after a period of refractive stability. It has been theorized that persons who regularly perform considerable near work undergo a process similar to emmetropization for the customary close working distance, resulting in a myopic shift.
The etiologic factors concerning myopia are complex, involving both genetic and environmental factors. Regarding a genetic role, identical twins are more likely to have a similar degree of myopia than are fraternal twins, siblings, or parent and child. Identical twins separated at birth and having different work habits do not show significant differences in refractive error. Some forms of severe myopia suggest dominant, recessive, and even sex-linked inheritance patterns. However, studies of ethnic Chinese in Taiwan show an increase in the prevalence and severity of myopia over the span of 2 generations, a finding that implies that genetics alone are not entirely responsible for myopia. Some studies have reported that near work is not associated with a higher prevalence and progression of myopia, especially with respect to middle-distance activities such as tasks involving video displays. Higher educational achievement has been strongly associated with a higher prevalence of myopia. Poor nutrition has been implicated in the development of some refractive errors as well. Studies from Africa, for example, have found that children with malnutrition have an increased prevalence of high ametropia, astigmatism, and anisometropia.
Feldkämper M, Schaeffel F. Interactions of genes and environment in myopia. Dev Ophthalmol. 2003;37:34–49.
Fischer AJ, McGuire JJ, Schaeffel F, Stell WK. Lightand focus-dependent expression of the transcription factor ZENK in the chick retina. Nat Neurosci. 1999;2(8):706–712.
McCarty CA, Taylor HR. Myopia and vision 2020. Am J Ophthalmol. 2000;129(4):525–527.
Winawer J, Wallman J, Kee C. Differential responses of ocular length and choroidal thickness in chick eyes to brief periods of plus and minus lens-wear. Invest Ophthalmol Vis Sci Suppl. 1999;40:S963.
