Charles E. Campbell

Model eyes for evaluation of intraocular lenses

In accordance with the present international standard for intraocular lenses (IOLs), their imaging performance should be measured in a model eye having an aberration-free cornea. This was an acceptable setup when IOLs had all surfaces spherical and hence the measured result reflected the spherical aberration of the IOL. With newer IOLs designed to compensate for the spherical aberration of the cornea there is a need for a model eye with a physiological level of spherical aberration in the cornea. A literature review of recent studies indicated a fairly high amount of spherical aberration in human corneas. Two model eyes are proposed. One is a modification of the present ISO standard, replacing the current achromat doublet with an aspheric singlet cut in poly(methyl methacrylate) (PMMA). The other also has an aspheric singlet cut in PMMA, but the dimensions of it and the entire model eye are close to the physiological dimensions of the eye. They give equivalent results when the object is at infinity, but for finite object distances only the latter is correct. The two models are analyzed by calculation assuming IOLs with different degrees of asphericity to elucidate their sensitivity to variation and propose tolerances. Measured results in a variant of the modified ISO model eye are presented.

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. An algorithm is given for creating the conversion matrix along with computer code to implement the algorithm.

Ray vector fields

The concept of treating lenses and other powered optical elements as operators acting on light-ray bundles, with these ray bundles being treated as vector fields, is introduced. A matrix method is developed with this vector field concept to analyze the behavior of optical systems. The method is especially useful for ophthalmic optics.

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. A plastic lens was ablated by the laser and then returned to the wave-front device, where it was measured and compared with the analytically defined wave-front surface. The two surfaces agreed up to 6th-order Zernike terms, validating the accuracy of the system.

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. Both the boundary and the magnitude of the wavefront change after the propagation. Taylor monomials were used to realize the propagation because of their simple form for this purpose. The method we developed to identify changes in low-order aberrations was verified with the classical vertex correction formula. The method we developed to identify changes in high-order aberrations was verified with ZEMAX ray-tracing software. Although the method may not be valid for highly irregular wavefronts and it was only proven for wavefronts with low-order or high-order aberrations, our analysis showed that changes in the propagating wavefront are significant and should, therefore, be included in calculating vision correction. This new approach could be of major significance in calculating wavefront-driven vision correction whether by refractive surgery, contact lenses, intraocular lenses, or spectacles.

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. The patients ablations appeared to be miniature versions of the intended ablation profiles, with small areas of emmetropic central cornea surrounded by annuli of rapidly increasing keratometric power; that is, systematic underablation. This may explain why some patients have visual aberrations with pupil diameters smaller than the programmed optical zones.

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. Am. A 28, 2148 (2011)] that only variable power optical effects that can be described by quadratic functions can be formed by laterally translating two-element variable power lenses. In the case of rotationally translating two-element variable power lenses, possible designs are found by mapping possible laterally translating designs from a Cartesian space to the polar coordinate space of the rotationally translating lens. Several designs that have been manufactured or suggested theoretically are examined in Part 2 to see which ones are true variable power lenses.

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. In the case of rotationally translating two-element variable power lenses, possible designs are found by mapping possible laterally translating designs from a Cartesian space to the polar coordinate space of the rotationally translating lens.

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. Calculations of model eyes are made that support this view. Four model eyes are examined, an emmetropic eye, a hyperopic eye, a myopic eye, and an emmetropic eye accommodating 2.5 D.

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.