- •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
Clinically Important Features of Contact Lens Optics
Contact lenses and conventional lenses have 4 parameters in common: posterior surface curvature (base curve), anterior surface curvature (power curve), diameter, and power (see Fig 4-1). However, unlike for spectacle lenses, the shape of contact lenses’ posterior surface is designed primarily to have certain fitting relationships with the anterior surface of the eye.
The refractive performance of contact lenses differs from that of spectacle lenses for 2 primary reasons: (1) contact lenses have a shorter vertex distance and (2) tears, rather than air, form the interface between the contact lens and the cornea. Unique optical considerations that are related to contact lenses include field of vision, image size, accommodation, convergence demand, the tear lens, correction of astigmatism, and correction of presbyopia. Each type of contact lens has unique optical considerations (Table 4-1).
Table 4-1
Field of Vision
Spectacle frames reduce the field of vision by approximately 20°. Owing to their proximity to the entrance pupils and lack of frames, contact lenses provide a larger field of corrected vision and avoid much of the peripheral distortion, such as spherical aberration, created by high-power spectacle lenses.
Image Size
Retinal image size is influenced by the vertex distance and power of corrective lenses. Contact lenses have shorter vertex distances than do spectacles, so image size changes less with contact lenses than
with spectacles.
Anisometropia and image size
Axial ametropia is predominant in eyes with higher (non–surgically induced) refractive errors. Theoretically, the anisometropic aniseikonia of such eyes is minimized when the corrective lens is placed in the eyes’ anterior focal plane (see discussion of Knapp’s law in Chapter 1), which is, on average, approximately 15.7 mm anterior to the corneal vertex. In axial myopia, moving the corrective lens posterior to the eye’s focal plane (closer to the cornea) increases the size of the retinal image compared with that of an emmetropic eye. The reverse is true in axial hyperopia. In practice, however, using contact lenses to correct the refractive error of the eyes is usually best for managing anisometropia because anisophoria generated by induced prism in off-axis viewing of spectacle lenses is eliminated. In addition, the greater separation between the elements in the stretched retinas of larger myopic eyes may explain the less-than-perceived magnification observed with contact lenses. Surgically induced anisometropia (resulting from, for example, cataract or refractive surgery) without an axial component is usually managed best through use of contact lenses or additional surgery; in either method, the images will be closer in size than if spectacles are used.
Monocular aphakia and aniseikonia
Minimizing aniseikonia in monocular aphakia improves the functional level of binocular vision. An optical model of surgical aphakia can be represented by inserting a neutralizing (minus-power) lens in the location of the crystalline lens and correcting the resulting ametropia with a forward-placed plus-power lens. Doing so effectively creates a Galilean telescope within the optical system of the eye. Accordingly, magnification is reduced as the effective plus-power corrective lens (corrected for vertex distance) is moved closer to the neutralizing minus-power lens (the former site of the crystalline lens). This model illustrates why contact lens correction of aphakia creates significantly less magnification than does a spectacle lens correction; a posterior chamber intraocular lens creates the least magnification of all.
Although the ametropia of an aphakic eye is predominantly refractive, it can also have a significant preexisting axial component. For example, the coexistence of axial myopia would further increase the magnification of a contact lens–corrected aphakic eye (compared with the image size of the spectacle-corrected fellow phakic myopic eye). Even if the image size of the fellow myopic eye were to be increased by fitting this eye with a contact lens, the residual aniseikonia might still exceed the limits of fusion and cause diplopia (Clinical Example 4-1). Divergent strabismus can develop in aphakic adult eyes (and esotropia may develop in children) if fusion is interrupted for a significant period. If diplopia does not resolve within several weeks, excessive aniseikonia should be suspected and confirmed by demonstration of the patient’s inability to fuse images superimposed with the aid of prisms. Such patients are usually aware that the retinal image in the aphakic eye is larger than that in the fellow phakic eye.
Clinical Example 4-1
Fitting a unilateral aphakic eye causes diplopia that persists in the presence of prisms that superimpose the 2 images. The refractive error of the fellow eye is –5.00 D, and the image of the aphakic eye is described as being larger than that of the fellow myopic eye.
How can the diplopia be resolved?
The goal is to reduce the aniseikonia of the 2 eyes by magnifying the image size of the phakic eye and/or reducing the image size of the contact lens–corrected aphakic eye. To achieve the former, correct the myopic phakic eye with a contact lens to increase its image size. If doing so is inadequate, overcorrect the contact lens by 5.00 D and prescribe a spectacle lens of – 5.00 D for that eye, thereby introducing a reverse Galilean telescope into the optical system of the eye. (If, however, the phakic eye were hyperopic, its image size would be increased by correcting its refractive error with a spectacle lens rather than a contact lens.)
When the fellow phakic eye is significantly myopic, correcting it with a contact lens increases its image size and often reduces the aniseikonia sufficiently to resolve the diplopia. If excessive aniseikonia persists, the clinician should aim to further reduce the image size of the contact lens– corrected aphakic eye. Overcorrecting the aphakic contact lens and neutralizing the resulting induced myopia with a forward-placed spectacle lens of appropriate minus power can achieve the additional reduction in image size. In effect, this process introduces a reverse Galilean telescope into the optical system of that eye. Empirically, increasing the power of the distance aphakic contact lens by +3 D and prescribing a –3 D spectacle lens for that eye usually suffice. Alternatively, if it is impractical to fit the fellow myopic eye with a contact lens, the clinician may elect to add plus power to the aphakic contact lens by an amount equal to the spherical equivalent of the refractive error of the fellow eye, in effect equalizing the myopia of the 2 eyes. The resulting decrease in the residual aniseikonia usually improves fusional potential and facilitates the recovery of fusion even of significant aniseikonic exotropia over several weeks. However, the resolution of aphakic esotropia or cyclotropia is less certain.
In contrast with axial myopia, coexisting axial hyperopia reduces the magnification of a contact lens–corrected aphakic eye. Residual aniseikonia can be further mitigated by correction of the fellow hyperopic eye with a spectacle lens (rather than a contact lens) to maximize image size.
Infantile aphakia
Management of aphakia in infants and young children represents a challenge because of the possibility of amblyopia and permanent vision loss. Contact lens wear may be ineffective in children because of poor patient adherence; therefore, intraocular lens implants may be a better option. Aphakia may be corrected in infants with contact lenses or lens implants. The optimal method in this group of patients is not yet known. The rapid change in axial length and corneal power during infancy (see Chapter 2) may make the selection of implant power difficult. Aggressive management of both optical correction and amblyopia treatment is necessary to achieve an optimal outcome in such young patients.
Autrata R, Rehurek J, Vodicková K. Visual results after primary intraocular lens implantation or contact lens correction for aphakia in the first year of age. Ophthalmologica. 2005;219(2):72–79.
Infant Aphakia Treatment Group; Lambert SR, Buckley EG, et al. The infant aphakia treatment study: design and clinical measures at enrollment. Arch Ophthalmol. 2010;128(1):21–27.
Accommodation
Accommodation is defined as the difference in vergence at the first principal point of the eye (1.35 mm behind the cornea) between rays originating at infinity and those originating at a near point.
This disparity creates different accommodative demands for spectacle and contact lenses. Compared with spectacles, contact lenses increase the accommodative requirements of myopic eyes and decrease those of hyperopic eyes in proportion to the size of the refractive error. The difference between the accommodative efficiency of spectacle lenses and that of contact lenses results from the effect of these 2 modalities on the vergence of light rays as they pass through the respective lenses. Contact lens correction requires an accommodative effort equal to that of emmetropic eyes. In other words, contact lenses eliminate the accommodative advantage enjoyed by those with spectaclecorrected myopia and the disadvantage experienced by those with spectacle-corrected hyperopia. The accommodative advantage observed in patients with spectacle-corrected myopia is consistent with the clinical observation that patients with spectacle-corrected high myopia can read through their distance correction at older ages than can patients with emmetropia. The opposite is true of patients with spectacle-corrected hyperopia (Clinical Example 4-2).
Clinical Example 4-2
What is the accommodative demand of a –7 D myopic eye corrected with a spectacle lens compared with a contact lens? A 7 D hyperopic eye? Assume a vertex distance of 15 mm and a near-object distance of 33.3 cm.
The myopic refractive error of the first eye is –7 D at a vertex distance of 15 mm, and the object distance is 33.3 cm. The vergence of rays originating at infinity and exiting the spectacle lens is –7 D. Due to the vertex distance, the vergence of these rays at the front surface of the cornea (which is approximately the location of the first principal point) is – 6.3 D. Use the focal point of the –7 D spectacle lens, 1/7 = 0.143 m, plus the vertex distance of 0.015 m (0.158 m) to find the vergence at the corneal surface: 1/0.158 m = –6.3 D (Fig 4- 2A).
