- •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
Power Calculation Methods for the Post–Keratorefractive Procedure Eye
In 2002, Aramberri developed the double-K method, which uses the pre-LASIK corneal power (or, if unknown, 43.50 D) to calculate the ELP, and the post-LASIK (much flatter) corneal power to calculate the IOL power. These calculations can be performed automatically with computer programs.
Aramberri’s method is only one of more than 20 methods proposed over the years to either calculate the true corneal power or adjust the calculated IOL power to account for the errors discussed in the preceding sections. Some methods require knowledge of pre-refractive surgery values such as refractive error and K reading. Many of these methods have come in and out of favor on the basis of studies investigating their accuracy. It is up to the surgeon to keep abreast of the most accurate available methods.
It is not possible to describe all these methods in this chapter, but all of them are included in the Hoffer/Savini LASIK IOL Power Tool, which can be downloaded free of charge (see reference below). The tool requests the data needed to calculate each method, and the results are automatically calculated for every method for which complete data have been entered. The ultimate choice is left to the surgeon. The entire results can be printed on a single page and entered in the patient’s chart. Calculations can also be performed through the American Society of Cataract and Refractive Surgery website, but it lacks the Hoffer Q formula in all calculations, especially needed in short eyes.
Perhaps in the future there will be a more satisfactory method of measuring true corneal power by use of topography and advanced measuring techniques. At present, the ideal method for use with post–refractive surgery patients has yet to be determined.
Hoffer KJ. The Hoffer/Savini LASIK IOL Power Tool. Available at www.iolpowerclub.org/post-surgical-iol-calc. Accessed June 3, 2013.
Koch DD, Liu JF, Hyde LL, Rock RL, Emery JM. Refractive complications of cataract surgery after radial keratotomy. Am J Ophthalmol. 1989;108(6):676–682.
Intraocular Lens Power in Corneal Transplant Eyes
It is very difficult to predict the ultimate power of the cornea after the eye has undergone penetrating keratoplasty. Thus, in 1987 Hoffer recommended that the surgeon wait for the corneal transplant to heal completely before implanting an IOL. The current safety of intraocular surgery allows for such a double-procedure approach in all but the rarest cases. Geggel has proven the validity of this approach by showing that posttransplant eyes have better uncorrected visual acuity (68% with 20/40 or better) and that the range of IOL power error decreases from 10 D to 5 D (95% within ±2.00 D).
If simultaneous IOL implantation and corneal transplant are necessary, surgeons may use either the K reading of the fellow eye or the average postoperative K value of a previous series of transplants, but these approaches are fraught with error. When there is corneal scarring in an eye but no need for a corneal graft, it might be best to use the corneal power of the other eye or even a power that is commensurate with the eye’s AL and refractive error.
Geggel HS. Intraocular lens implantation after penetrating keratoplasty. Improved unaided visual acuity, astigmatism, and safety in patients with combined corneal disease and cataract. Ophthalmology. 1990;97(11):1460–1467.
Hoffer KJ. Triple procedure for intraocular lens exchange. Arch Ophthalmol. 1987;105(5):609–610.
Silicone Oil Eyes
Ophthalmologists considering IOL implantation in eyes filled with silicone oil encounter 2 major problems. The first is obtaining an accurate AL measurement with the ultrasonic biometer. Recall that this instrument measures the transit time of the ultrasound pulse and, using estimated ultrasound velocities through the various ocular media, calculates the distance. This concept must be taken into consideration when velocities differ from the norm, for example, when silicone oil fills the posterior segment (980 m/s for silicone oil vs 1532 m/s for vitreous). Use of the IOLMaster to measure AL solves this problem somewhat. It is recommended that retinal surgeons perform an optical or immersion AL measurement before silicone oil placement, but doing so is not common practice. The second problem is that the oil filling the vitreous cavity acts like a negative lens power in the eye when a biconvex IOL is implanted. This problem must be counteracted by an increase in IOL power of 3–5 D.
Pediatric Eyes
Several issues make IOL power selection for children much more complex than that for adults. The first challenge is obtaining accurate AL and corneal measurements, which is usually performed when the child is under general anesthesia. The second is that, because shorter AL causes greater IOL power errors, the small size of a child’s eye compounds power calculation errors, particularly if the child is very young. The third problem is selecting an appropriate target IOL power, one that will not only provide adequate visual acuity to prevent amblyopia but also allow adequate vision due to the large myopic shift that occurs after maturity.
A possible solution to the third problem is to implant 2 (or more) IOLs simultaneously: one IOL with the predicted adult emmetropic power placed posteriorly and the other (or others) with the power that provides childhood emmetropia placed anterior to the first lens. When the patient reaches adulthood, the obsolete IOL(s) can be removed (sequentially). Alternatively, corneal refractive surgery may be used to treat myopia that develops in adulthood. Most recent studies have shown that the best modern formulas do not perform as accurately for children’s eyes as they do for adults.
Hoffer KJ, Aramberri J, Haigis W, Norrby S, Olsen T, Shammas HJ; IOL Power Club Executive Committee. The final frontier: pediatric intraocular lens power. Am J Ophthalmol. 2012;154(1):1–2.e1.
Image Magnification
Image magnification of as much as 20%–35% is the major disadvantage of aphakic spectacles. Contact lenses magnify images by only 7%–12%, whereas IOLs magnify images by 4% or less. An IOL implanted in the posterior chamber produces less image magnification than does an IOL in the anterior chamber. The issue of magnification is further complicated by the correction of residual postsurgical refractive errors. A Galilean telescope effect is created when spectacles are worn over pseudophakic eyes. Clinically, each diopter of spectacle overcorrection at a vertex of 12 mm causes a 2% magnification or minification (for plus or minus lenses, respectively). Thus, a pseudophakic patient with a posterior chamber IOL and a residual refractive error of –1 D would have 2% magnification from the IOL and 2% minification from the spectacle lens, resulting in little change in image size.
Aniseikonia is defined as a difference in image size between the 2 eyes and can cause disturbances in stereopsis. Generally, a person can tolerate spherical aniseikonia of 5%–8%. In
clinical practice, aniseikonia is rarely a significant problem; however, it should be considered in patients with unexplained vision symptoms.
Lens-Related Vision Disturbances
The presence of IOLs may cause numerous optical phenomena. Various light-related visual phenomena encountered by pseudophakic (and phakic) patients are termed dysphotopsias. These phenomena are divided into positive and negative dysphotopsias. Positive dysphotopsias are characterized by brightness, streaks, and rays emanating from a central point source of light, sometimes with a diffuse, hazy glare. Negative dysphotopsias are characterized by subjective darkness or shadowing. Such optical phenomena may be related to light reflection and refraction along the edges of the IOL. High-index acrylic lenses with square or truncated edges produce a more intense edge glare (Fig 5-11A). These phenomena may also be due to internal re-reflection within the IOL itself; such re-reflection is more likely to occur with materials that have a higher IR, such as acrylic (Fig 5-11B). With a less steeply curved anterior surface, the lens may be more likely to have internal reflections that are directed toward the fovea and are therefore more distracting (Fig 5-11C, D).
