Charles Campbell

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 spherocylindrical 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. Formulas are given to convert standard Zernike coefficients to the magnitude and axis values.

The refractive group.

Spherocylindrical optical elements can be decomposed into a sphere-equivalent component and two cross-cylinder components, oriented at 45° to one another. These components in turn can be represented with a simple matrix formalism. This matrix formalism allows it to be seen that the components also form members of an eight element group, designated the refractive group. The structure of this group is developed including its algebra and its representation with Cayley diagrams. The group is identified as the eight element dihedral group, D4, and is compared to another well-known eight element group, the quaternion group. An example is given using the group formal algebra to develop the transfer equations for spherocylindrical wavefronts. Certain properties of propagating spherocylindrical wavefronts, such as nonrotation of cylinder axes, are seen to come directly as consequences of the group properties.

The Effect of Spherical Aberration of Contact Lens to the Wearer

Abstract To determine the influence of the spherical aberration of a contact lens on the total spherical aberration of the eye‐contact lens system, appropriate formulas are derived. By comparing the total spherical aberration of the eye without a contact lens with that found when a contact lens is in place, it is shown that the spherical aberration of the eye is determined, almost entirely, by the first refracting surface (either cornea or contact lens). The amount of aberration when converted to a dioptric value shows the relative effects clearly.

Corneal aberrations, monocular diplopia, and ghost images : Analysis using Corneal topographical data

Corneal irregularities can create conditions in which monocular diplopia, “ghost images,” and multiple images of various types occur, thus degrading vision. For these secondary images to occur, corneal irregularities must create areas which form: (1) images which are displaced from the primary image; (2) sufficiently focused images; and (3) images which have sufficient contrast to be noticed in the presence of the primary image. Criteria necessary to satisfy these three conditions using measurable data are developed. The concept of a differential deflection field is introduced, and a method to create this field using corneal topography data is developed. It is shown how to use differential deflection field data to assess if conditions necessary for creating secondary images will occur in cases of corneal distortion.

Reconstruction of the corneal shape with the MasterVue Corneal Topography System

This paper explains how the Humphrey MasterVue Corneal Topography System measures the corneal shape and explains what is meant by the various values presented. Covered are the geometrical concepts underlying the method, the necessary reconstruction steps, a description of the arc step reconstruction method used, a description of the cone of focus concept, and definitions of the presented power values.

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.ProfilerPlus, 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. Analysis of sphere, cylinder, and axis using spherical equivalent difference and a new measurement, cross-cylinder difference, was performed. The spherical equivalent refraction and cross-cylinder difference for the manifest refraction were compared using Bland-Altman limits of agreement and 95th percentile analysis. Results The 100 participants represent 52 women and 48 men with a mean (±SD) age of 51.7 (±13.8) years, an average (±SD) spherical power of −0.67 (±2.53) diopters (D), and an average (±SD) cylinder power of −0.94 (±0.87) D. The spherical equivalent difference is 0.03 D (Canon) and −0.11 D (Zeiss). The 95% limits of agreement for the spherical equivalent are −0.69 to 0.75 D (Canon) and −0.75 to 0.75 D (Zeiss). The mean cross-cylinder power difference is −0.08 D (Canon) and 0.02 D (Zeiss). The 95% limits of agreement for the cross-cylinder power difference are 0.63 to 0.50 D (Canon) and 0.49 to 0.75 D (Zeiss). The mean axis power difference is −0.04 D (Canon) and 0.05 D (Zeiss). The 95% limits of agreement for axis power difference are −0.71 to 0.63 D (Canon) and −0.78 to 0.78 D (Zeiss). The double-angle astigmatic plot center of distribution for the RK-F2 is 0.035 D at 70 degrees, and that for the i.ProfilerPlus is 0.053 D at 32 degrees. Conclusions Both instruments provided clinically useful spherical equivalent refractive data compared with a subjective refraction, whereas the Canon RK-F2 was slightly more accurate in determining the cylinder power compared with a subjective refraction.

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.

An optical device with variable astigmatic power.

A new variable power cross-cylinder lens set is described. It differs from the well known Stokes variable power cross-cylinder lens set, which is made of cylinder lenses of equal but opposite power, in that in the new variable power cross-cylinder lens set both lens elements are identical. These elements can be sphero cylindrical of any type and can be designed to give the same effect as a Stokes lens set or create a spherical bias or offset of a desired amount. The action of this lens set is analyzed using 3-dimensional refractive space.