- •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
Corboy JM. The Retinoscopy Book: An Introductory Manual for Eye Care Professionals. 4th ed. Thorofare, NJ: Slack; 1995. Wirtschafter JD, Schwartz GS. Retinoscopy. In: Tasman W, Jaeger EA, eds. Duane’s Clinical Ophthalmology [CD-ROM]. Vol 1.
Philadelphia: Lippincott Williams & Wilkins; 2006:chap 37.
Subjective Refraction Techniques
In subjective refraction techniques, the examiner relies on the patient’s responses to determine the refractive correction. If all refractive errors were spherical, subjective refraction would be easy. However, determining the astigmatic portion of the correction is more complex, and various subjective refraction techniques may be used. The Jackson cross cylinder is the most common instrument used in determining the astigmatic correction. However, we begin by discussing the astigmatic dial technique because it is easier to understand.
Astigmatic Dial Technique
An astigmatic dial is a test chart with radially arranged lines that may be used to determine the axes of astigmatism. A pencil of light from a point source is imaged by an astigmatic eye as a conoid of Sturm. The spokes of the astigmatic dial that are parallel to the principal meridians of the eye’s astigmatism are imaged as sharp lines, which correspond to the focal lines of the conoid of Sturm.
Figure 3-15A shows an eye with compound hyperopic astigmatism and how it sees an astigmatic dial. The vertical line of the astigmatic dial is the blackest and sharpest because the vertical focal line of each conoid of Sturm is closer to the retina than the horizontal focal line is. By accommodating, however, the patient might pull both focal lines forward, far enough to make even the horizontal line of the astigmatic dial clear. To avoid accommodation, fogging is used. Sufficient plus sphere is placed before the eye to pull both focal lines into the vitreous, creating compound myopic astigmatism (Fig 3-15B).
Figure 3-15 Astigmatic dial technique. A, Conoid of Sturm and retinal image of an astigmatic dial as viewed by an eye with compound hyperopic astigmatism. B, Fogging to produce compound myopic astigmatism. C, The conoid of Sturm is collapsed to a single point. D, Minus sphere is added (or plus sphere subtracted) to produce a sharp image, and a visual
acuity chart is used for viewing.
Because accommodating with the eye fogged causes increased blurring of the lines, the patient relaxes accommodation. The focal line closest to the retina can then be identified with certainty as the horizontal line because it is now the blackest and sharpest line of the astigmatic dial. Note that the terms blackest and sharpest are more easily understood by patients and should be used in place of the word clearest.
After the examiner locates 1 of the principal meridians of the astigmatism, the conoid of Sturm can be collapsed by moving the anterior focal line back toward the posterior focal line. This task can be accomplished by adding a minus cylinder with an axis parallel to the anterior focal line. In Figure 3-15C the vertical focal line has been moved back to the position of the horizontal focal line and collapsed to a point by the addition of a minus cylinder with an axis at 90°. Notice that the minus cylinder is placed with its axis perpendicular to the blackest meridian on the astigmatic dial. Also note that as the conoid of Sturm is collapsed, the focal lines disappear into a point focus.
All of the lines of the astigmatic dial now appear equally black but still are not in perfect focus, because the eye remains slightly fogged to control accommodation. At this point, a visual acuity chart is used; plus sphere is removed until the best visual acuity is obtained (Fig 3-15D).
In summary, the following steps are used in astigmatic dial refraction:
1.Obtain the best visual acuity using spheres only.
2.Fog the eye to approximately 20/50 by adding plus sphere.
3.Ask the patient to identify the blackest and sharpest line of the astigmatic dial.
4.Add minus cylinder with the axis perpendicular to the blackest and sharpest line until all lines appear equal. (If using a positive cylinder phoropter, add plus cylinder with the axis parallel to the blackest and sharpest line until all lines appear equal.)
5.Reduce plus sphere (or add minus) until the best visual acuity is obtained with the visual acuity chart.
Astigmatic dial refraction can also be performed with plus cylinder equipment, but this technique must be used in a way that simulates minus cylinder effect. All of the above steps remain the same except for step 4, which becomes “Add plus cylinder with the axis parallel to the blackest and sharpest line.” As each 0.25 D of plus cylinder power is added, change the sphere simultaneously by 0.25 D in the minus direction. Doing so simulates minus cylinder effect exactly by moving the anterior focal line posteriorly without changing the position of the posterior focal line.
Michaels DD. Visual Optics and Refraction: A Clinical Approach. 3rd ed. St Louis: Mosby; 1985:319–322.
Stenopeic Slit Technique
The stenopeic slit is an opaque trial lens with an oblong slit whose width forms a pinhole with respect to vergence perpendicular to the slit (Fig 3-16). If an examiner is unable to decipher the astigmatism by performing the usual retinoscopy because of the subject eye’s irregular astigmatism or unclear media, he or she may neutralize the refractive error with spherical lenses and the slit at various meridians to find a spherocylindrical correction. This correction can then be refined subjectively. This process is especially useful for patients with small pupils and lenticular or corneal opacities. If the subject can accommodate, fog and unfog using plus sphere to find the most plus power accepted. Then turn the slit until the subject says the image is sharpest. If, for example, –3.00
D sphere is best there, when the slit is oriented vertically, this finding indicates –3.00 D at 90° in a power cross. If the best sphere with the slit oriented horizontally is –5.00 D, then the result is –3.00 – 2.00 × 90.
Figure 3-16 Stenopeic slit. The image on the right demonstrates the placement of a spherical lens in front of the stenopeic slit in order to determine the best visual acuity. (Courtesy of Tommy Korn, MD.)
Cross-Cylinder Technique
The Jackson cross cylinder, in Edward Jackson’s words, is probably “far more useful, and far more used” than any other lens in clinical refraction. Every ophthalmologist should be familiar with the principles involved in its use. Although the cross cylinder is usually used to refine the cylinder axis and power of a refraction that has already been obtained, it can also be used for the entire astigmatic refraction.
The first step in cross-cylinder refraction is adjusting the sphere to yield the best visual acuity with accommodation relaxed. Begin by placing the prescription the patient is wearing into a trial frame or phoropter. Fog the eye to be examined with plus sphere while the patient views a visual acuity chart; then decrease the fog until the best visual acuity is obtained. If astigmatism is present, decreasing the fog places the circle of least confusion on the retina, creating a mixed astigmatism. Then use test figures that are 1–2 lines larger than the patient’s best visual acuity. At this point, introduce the cross cylinder, first for refinement of cylinder axis and then for refinement of cylinder power.
If no cylindrical correction is present initially, the cross cylinder may still be used, placed at 90° and 180°, to check for the presence of astigmatism. If a preferred flip position is found, cylinder is added with the axis parallel to the respective plus or minus axis of the cross cylinder until the 2 flip choices are equal. If no preference is found with the cross-cylinder axes at 90° and 180°, then check the axes at 45° and 135° before assuming that no astigmatism is present. Once any cylinder power is found, axis and power should be refined in the usual manner.
Another method of determining the presence of astigmatism is to dial 0.50 D of cylinder into the
phoropter (while preserving the spherical equivalent with a compensatory 0.25 D change in the sphere). Ask the patient to slowly rotate the cylinder axis once around using the knob on the phoropter. If doing so has no effect, there is no clinically significant astigmatism. If the patient finds a preferred position, it becomes the starting point for the cross-cylinder refinement.
Always refine cylinder axis before refining cylinder power. This sequence is necessary because the correct axis may be found in the presence of an incorrect power, but the full cylinder power is found only in the presence of the correct axis.
Refinement of cylinder axis involves the combination of cylinders at oblique axes. When the axis of the correcting cylinder is not aligned with that of the astigmatic eye’s cylinder, the combined cylinders produce residual astigmatism with a meridian roughly 45° away from the principal meridians of the 2 cylinders. To refine the axis, position the principal meridians of the cross cylinder 45° away from those of the correcting cylinder (if using a handheld Jackson cross cylinder, the stem of the lens handle will be parallel to the axis of the correcting cylinder). Present the patient with alternative flip choices, and select the choice that is the blackest and sharpest to the patient. Then rotate the axis of the correcting cylinder toward the corresponding plus or minus axis of the cross cylinder (plus cylinder axis is rotated toward the plus cylinder axis of the cross cylinder, and minus cylinder axis is rotated toward the minus cylinder axis of the cross cylinder). Low-power cylinders are rotated in increments of 15°; high-power cylinders are rotated by smaller amounts, usually 5°. Repeat this procedure until the flip choices appear equal.
To refine cylinder power, align the cross-cylinder axes with the principal meridians of the correcting lens (Fig 3-17). The examiner should change cylinder power according to the patient’s responses; the spherical equivalent of the refractive correction should remain constant to keep the circle of least confusion on the retina. Ensure that the correction remains constant by changing the sphere half as much and in the opposite direction as the cylinder power is changed. In other words, for every 0.50 D of cylinder power change, change the sphere by 0.25 D in the opposite direction. Periodically, the sphere power should be adjusted for the best visual acuity.
Figure 3-17 Jackson cross cylinder. (Courtesy of Tommy Korn, MD.)
Continue to refine cylinder power until the patient reports that both flip choices appear equal. At that point, the 2 flip choices produce equal and opposite mixed astigmatism, blurring the visual acuity chart equally.
Remember to use the proper-power cross cylinder for the patient’s visual acuity level. For example, a ±0.25 D cross cylinder is commonly used with visual acuity levels of 20/30 and better. A high-power cross cylinder (±0.50 D or ±1.00 D) allows a patient with poorer vision to recognize differences in the flip choices.
The patient may be confused with prior choices during cross-cylinder refinement. Giving different numbers to subsequent choices avoids this problem: “Which is better, 1 or 2, 3 or 4?” and so forth. If the patient persists in choosing either the first or second number, reverse the order of presentation to check for consistency.
Table 3-2 summarizes the cross-cylinder refraction technique.
Table 3-2
