The use of autorefractors using the image-size principle in determining on-axis and off-axis refraction. Part 2: Theoretical study of peripheral refraction with the Grand Seiko AutoRef/Keratometer WAM-5500.

Purpose: To determine, through simulations, the likely validity of Grand-Seiko autorefractors with annular targets in peripheral refraction.

Methods: Using a physical model eye, the distance inside the eye to which the Grand Seiko AutoRef/Keratometer WAM-5500 beam was converging and the effective size of its outer diameter at the cornea were determined. Grand-Seiko refraction was calculated from R  = (θ + α)/h , where θ is the angle of the ingoing radiation beam, h is the height of the beam at the anterior cornea and α is the angle of the beam emerging from the eye following reflection at the retina.

The use of autorefractors using the image-size principle in determining on-axis and off-axis refraction. Part 1: Analysis of optical principles of autorefractors.

Purpose: To study the optical principles and properties of autorefractors that use the image-size principle in which the size of the reimaged retinal image determines refraction.

Methods: The retinal illumination and reimaging of the retinal image were described, as were variations in the basic system. Imaging was determined for systems in which the light source is either diverging or converging as it passes into the eye.

A comparison of a traditional and wavefront autorefraction.

Purpose: To evaluate the agreement between the autorefraction function of the Canon RK-F2, an autorefractor/keratometer based on the ray deflection principle, and the Carl Zeiss Vision i.Profiler(Plus), an wavefront aberrometer, compared with each other and with a noncycloplegic subjective refraction.

Methods: Objective refraction results obtained using both instruments were compared with noncycloplegic subjective refractions for 174 eyes of 100 participants.

Conditions under which two-element variable power lenses can be created. Part 2. Application to specific designs.

It was found in Part 1 of this paper [J. Opt. Soc.

Conditions under which two-element variable power lenses can be created. Part 1. Theoretical analysis.

The conditions under which a two-element variable power lens can be created are examined. Such a lens is defined as one in which the functional form of the optical effect created does not change as the elements translate with respect to one another--only the magnitude of the effect changes. It is found that only variable power optical effects that can be described by quadratic functions can be formed by laterally translating two-element variable power lenses.

Nested shell optical model of the lens of the human eye.

A nested shell model of the human lens is developed based on the known anatomical construction of the lens, on the known way in which the lens grows throughout its life, on the measured characteristics of the lens surfaces as a function of the age of the lens, on the measured changes in the shape of the lens during accommodation, and on measured material characteristics of the lens materials, such as density and index of refraction throughout. The observed changes in central surface curvature and thickness force the shell thicknesses to vary in a predictable way and in turn force the shell surface asphericity to take certain values. Thus, in addition to giving the shape of each shell, the model predicts the change expected in the asphericity of the lens surfaces as the lens ages and adds cortical cell layers.

Relative importance of sources of chromatic refractive error in the human eye.

The relative importance of the various optical elements of the human eye are analyzed to determine which contribute most to the chromatic variance in total refractive power of the eye. The concept of differential dispersion, defined as the change in the difference in index of refraction across a refractive surface with change in wavelength, is used to provide a theoretical tool for this analysis. The theoretical treatment shows that almost all the chromatic effect will be caused by the air-tear interface.

Determining spherocylindrical correction using four different wavefront error analysis methods: comparison to manifest refraction.

Purpose: To evaluate methods that determine refractive correction from wavefront data that best matches the manifest refraction.

Methods: Wavefront data in the form of Zernike polynomial coefficients from several VISX US Investigational Device Exemption studies were used to calculate the spherocylindrical distance correction using four methods: full pupil second order, central curvature, reduced aperture, and 4-mm pupil. The data were analyzed in two groups, preoperative (3686 measurements, 882 eyes) and 6-month postoperative (2570 measurements, 797 eyes).

Spherical aberration of a hydrogel contact lens when measured in a wet cell.

A method is given for calculating the spherical aberration induced when the power of a hydrogel contact lense is measured in a wet cell. Application of the method to measurement of contact lenses with varying power over the entire optical zone is included.

The range of local wavefront curvatures measurable with Shack-Hartmann wavefront sensors.

Shack-Hartmann wavefront sensor systems are studied to assess the range of local wavefront curvatures that may be measured for a given choice of lenslet size and focal length and illumination beam characteristics, with special emphasis on systems design for use in wavefront eye refractors. Effects considered include blur effects on detected spot size,spot differential movement due to local wavefront curvature and source size effects.Examples are given, using a full diffractive treatment of the spot intensity patterns, to illustrate that the maximum range values found using the method of this paper result in neighbouring spot intensity patterns that are at the limit for resolution.

Wavefront propagation from one plane to another with the use of Zernike polynomials and Taylor monomials.

In wavefront-driven vision correction, ocular aberrations are often measured on the pupil plane and the correction is applied on a different plane. The problem with this practice is that any changes undergone by the wavefront as it propagates between planes are not currently included in devising customized vision correction. With some valid approximations, we have developed an analytical foundation based on geometric optics in which Zernike polynomials are used to characterize the propagation of the wavefront from one plane to another.

Wavefront measurements of diffractive and refractive multifocal intraocular lenses in an artificial eye.

Purpose: To investigate whether wavefront measurements taken in eyes that have implanted multifocal intraocular lenses (IOLs) are reliable when creating laser refractive surgical treatments to remove residual refractive error from these eyes.

Methods: A specially designed fluid-filled model eye holding a multifocal IOL was refracted using a commercial wavefront eye refractor. The wavefront findings were then compared to the expected refractive error.

Generalized Coddington equations found via an operator method.

Generalized Coddington equations allow the optical properties of an arbitrarily oriented incoming astigmatic ray bundle to be found following refraction by an arbitrary surface. Generalized Coddington equations are developed using the abstract concept of vergence and refraction operators. After suitable incoming vergence and refraction operators have been formed, these operators are re-expressed in a common coordinate system via similarity transformations created from the series of space rotations necessary to align the coordinate systems.

Analysis of wavefront-guided corrections to see if they fully correct ocular aberrations.

In a recent paper [J. Opt. Soc.

Variable power phase lenses.

A method is given to construct a phase lens capable of creating an optical aberration of variable power that is described by a single Zernike polynomial function whose meridional index is 1 or greater. The phase lens is created from two identical phase elements, each creating a single Zernike aberration, that can be rotated with respect to each other, thereby increasing the aberration effect from zero to twice the value of either. This is possible because these aberrations are vectorlike.

A test eye for wavefront eye refractors.

Purpose: A multi-site study was conducted to test feasibility of a modified automatic refractor style test eye as a test device for wavefront refractors of various types and to determine whether a) they could be measured and b) when measurements could be made, to see if they were similar. This study did not attempt to assess which instrument most accurately measures the aberrations of the test eye or human eye.

Methods: Three automatic refractor style test eyes were modified for use as test devices for wavefront refractors.

Improving visual function diagnostic metrics with the use of higher-order aberration information from the eye.

Purpose: This paper reviews the currently used visual function diagnostic metrics, acuity, refractive error, and contrast sensitivity, and suggests ways to create new metrics using the information that has recently become available due to advances in measuring the higher-order aberrations of the eye. Particularly, emphasis is placed on finding metrics that address certain aspects of vision rather than on general metrics.

Methods: Two metrics based on the modulation transfer function are introduced, the Visual Quality Factor (VQF), which is a value based on the modulation transfer function between the spatial frequencies of 3 and 12 cycles per degree (c/deg) giving a measure of the overall degradation of visual quality due to aberrations, and the Subjective Sharpness Factor (SSF), which is a value based on the modulation transfer function between the spatial frequencies of 15 and 40 c/deg, giving a measure of the decrease in perceived image "sharpness" due to aberrations.

System for the design, manufacture, and testing of custom lenses with known amounts of high-order aberrations.

Now that excimer laser systems can be programmed to correct complex aberrations of the eye on the basis of wave-front measurements, a method is needed to test the accuracy of the system from measurement through treatment. A closed-loop test method was developed to ensure that treatment plans generated by a wavefront measuring system were accurately transferred to and executed by the excimer laser. A surface was analytically defined, and a Shack-Hartmann-based wave-front system was used to formulate a treatment plan, which was downloaded to an excimer laser system.

Systematic underablation in laser in situ keratomileusis: ablation pattern identified by advanced topographical analysis.

Topographical analysis based on the differential geometry of surfaces-curvature topography-was developed and applied to a patient after laser in situ keratomileusis. The patient had a minimal residual refractive error and normal best corrected visual acuity but had multiple visual aberrations, including ghosting and glare, unless the pupils were maximally constricted. The corneal loci responsible for the aberrations were difficult or impossible to identify on axial topographies but were readily identified with curvature topography.

Matrix method to find a new set of Zernike coefficients from an original set when the aperture radius is changed.

A matrix method is developed that allows a new set of Zernike coefficients that describe a surface or wave front appropriate for a new aperture size to be found from an original set of Zernike coefficients that describe the same surface or wave front but use a different aperture size. The new set of coefficients, arranged as elements of a vector, is formed by multiplying the original set of coefficients, also arranged as elements of a vector, by a conversion matrix formed from powers of the ratio of the new to the original aperture and elements of a matrix that forms the weighting coefficients of the radial Zernike polynomial functions. In developing the method, a new matrix method for expressing Zernike polynomial functions is introduced and used.

A new method for describing the aberrations of the eye using Zernike polynomials.

The standard Zernike polynomial functions are reformulated in a way so that the number of functions (or terms) needed to describe an arbitrary wavefront surface to a given Zernike radial order is reduced by a factor of approximately two, and the terms are described in a fashion quite similar to that used to describe common sphero-cylindrical errors of the eye. A wavefront is represented using these terms by assigning a pair of values, a magnitude and an axis, to all terms that are radially symmetric so that the individual aberrations are presented in a way similar to the way common astigmatism is currently given in terms of cylinder power and axis. The root mean square of these magnitudes gives the root mean square wavefront error just as does the root mean square of the standard Zernike coefficients.