Jim Schwiegerling

Representation of videokeratoscopic height data with Zernike polynomials

Videokeratoscopic data are generally displayed as a color-coded map of corneal refractive power, corneal curvature, or surface height. Although the merits of the refractive power and curvature methods have been extensively debated, the display of corneal surface height demands further investigation. A significant drawback to viewing corneal surface height is that the spherical and cylindrical components of the cornea obscure small variations in the surface. To overcome this drawback, a methodology for decomposing corneal height data into a unique set of Zernike polynomials is presented. Repeatedly removing the low-order Zernike terms reveals the hidden height variations. Examples of the decomposition-and-display technique are shown for cases of astigmatism, keratoconus, and radial keratotomy.

Scaling Zernike expansion coefficients to different pupil sizes

Recent developments in technologies to correct aberrations in the eye have fostered extensive research in wave-front sensing of the eye, resulting in many reports of Zernike expansions of wave-front errors of the eye. For different reports of Zernike expansions, to be compared, the same pupil diameter is required. Since no standard pupil size has been established for reporting these results, a technique for converting Zernike expansion coefficients from one pupil size to another is needed. This investigation derives relationships between the Zernike expansion coefficients for two different pupil sizes.

Corneal ablation patterns to correct for spherical aberration in photorefractive keratectomy

PURPOSE To determine the spherical aberration introduced by photorefractive keratectomy (PRK) and customize ablation patterns to compensate for this aberration and improve post-PRK visual performance. SETTING Department of Ophthalmology, University of Arizona, Tucson, Arizona, USA. METHODS Presurgical and postsurgical corneal topography of 16 patients who had PRK with the Summit OmniMed laser were obtained. The data were applied to a schematic eye model, and exact ray tracing was used to determine the introduction of spherical aberration from the procedure. Optimization routines were used to determine the ideal ablation pattern. RESULTS The magnitude of the spherical aberration introduced into the eyes after PRK increased with the level of attempted correction. The theoretical ideal ablation pattern requires additional flattening of the ablation periphery to avoid the introduction of spherical aberration. CONCLUSIONS Current PRK ablations introduce spherical aberration into the eye. Modifying the existing ablation algorithms to compensate for spherical aberration may boost postoperative visual performance.

Theoretical Limits to Visual Performance

Wavefront sensors and scanning laser technology are enabling the correction of the aberrations of the eye. The effects of aberrations on visual performance are reviewed, and the theoretical limit of visual performance is predicted to understand the ultimate endpoint of these new technologies. A schematic eye model that incorporates diffraction, chromatic aberration, photopic response, the Stiles-Crawford effect, and pupil size is ray-traced to determine its limiting optical properties. These properties are compared to the detection requirements of the retina and brain to determine the theoretical limit of foveal vision. The theoretical limits on foveal vision are found to be between 20/12 and 20/5, depending on pupil diameter. It is concluded that emerging refractive surgery technologies may provide substantial increases in visual performance.

Using corneal height maps and polynomial decomposition to determine corneal aberrations

Purpose. To review the use of corneal videokeratoscopic height data, elaborate on the advantages and disadvantages of such data, describe techniques for overcoming the limitations of height data, and demonstrate its use in quantifying the optical properties and aberrations of the cornea. Methods. The steep sag of the cornea hides fine variations in corneal height that arise naturally or due to disease or surgery. The dynamic range, or ratio of the overall sag to the feature height, is the primary limitation of videokeratoscopic height data. Techniques for removing single or multiple reference surfaces are described in detail, and applications of the methodology to wavefront and raytracing analysis of corneal aberrations arising from radial keratotomy (RK), photorefractive keratectomy (PRK), and keratoconus are described. Results. Removing a single reference surface from the raw corneal height data begins to reveal subtle variations in corneal height. However, expansion of surface height data into a complete set of basis functions provides a sophisticated method for extracting high-order corneal variations. Choosing an orthogonal basis set provides a robust least-squares fit and forms unique expansions of the surface. The resulting coefficients are uncorrelated and form a simple measure of the optical quality. Conclusion. Videokeratoscopic height data are useful for analyzing and quantifying corneal deformity arising from disease or refractive surgery and they provide a sophisticated alternative or complement to dioptric power maps.

Visual acuity modeling using optical raytracing of schematic eyes

PURPOSE We developed a methodology to predict changes in visual performance that result from changes in the optical properties of the eye. METHODS Exact raytracing of schematic eyes was used to calculate the point spread function and the modulation transfer function of the visual system. The Stiles-Crawford effect, photopic response, diffraction, and the retinal contrast sensitivity are included in the model. Visual acuity was predicted by examining the modulation of the resultant retinal image of a bar target and by determining when the modulation falls below a threshold value. Visual acuity was predicted for refractive errors ranging from 0 to 5 diopters and for pupil diameters ranging from 0.5 to 8 mm. RESULTS Visual acuity predictions were compared to clinically found Snellen visual acuities and were found to be highly correlated (r2 = .909). CONCLUSIONS This modeling technique shows promise as a means of evaluating clinical and surgical procedures before undertaking clinical trails.

Keratoconus detection based on videokeratoscopic height data

Purpose. To develop a videokeratoscopic-based keratoconus detection scheme that avoids the ambiguity of dioptric power definitions and videokeratoscope design. Methods. Corneal height data obtained with a commercial videokeratoscope are decomposed into the set of orthogonal Zernike polynomials. Expansion coefficients of a “normal” group and a keratoconus group are compared to find significant differences. Elevated Zernike terms are used to detect the disease in these populations. The performance of this detection scheme is compared to other videokeratoscopic keratoconus indices. Results. Two low-order Zernike polynomial terms are identified as being elevated in keratoconus patients and combined to form a new detection index. This index performed at least as well as keratoconus detection schemes based on the inferior- superior (I-S) value, the steepest radial axes (SRAX), and the Surface Asymmetry Index (SAI) for the samples studied. Conclusion. The proposed Zernike scheme offers a potentially viable algorithm for detecting keratoconus that avoids the ambiguities of dioptric power definitions and is independent of videokeratoscope design.

Field guide to visual and ophthalmic optics

Visual optics requires an understanding of both biology and optical engineering. This Field Guide assembles the anatomy, physiology, and functioning of the eye, as well as the engineering and design of a wide assortment of tools for measuring, photographing, and characterizing properties of the surfaces and structures of the eye. Also covered are the diagnostic techniques, lenses, and surgical techniques used to correct and improve human vision.

Higher Order Aberrations in Normal, Dilated, Intraocular Lens, and Laser in situ Keratomileusis Corneas

PURPOSE To compare repeated measures of Zernike polynomial higher-order aberrations in 29 normal, 13 dilated normal, 11 intraocular lens (IOL), 11 laser in situ keratomileusis (LASIK), and one refractive keratectomy (RK)/IOL subject. METHODS At least three Shack-Hartmann images were obtained from each subject, and higher order (uncorrectable by spectacles) Zernike representation was determined. For each subject, confidence intervals for each Zernike coefficient were determined as a function of pupil size. Significant (P<.05) coefficients were averaged within groups, and group means were compared to normal subjects. RESULTS No differences were seen between the normal and dilated groups at P=.05. The patients with prior LASIK and IOL surgery showed statistically significant elevation of 4th order spherical aberration and total wavefront variance for pupil sizes greater than 5 mm, compared to normals. CONCLUSION Both IOL and LASIK surgery elevate spherical aberration and wavefront variance, with increasing magnitude of effect with increasing pupil size, although pupillary dilation alone did not produce statistically different changes, as compared to normal subjects. These findings demonstrate that IOL implantation can produce more net aberrations than LASIK, and demonstrate a new opportunity to optimize surgical results.

Tunable-focus flat liquid-crystal diffractive lens

We demonstrate an innovative variable-focus flat liquid-crystal diffractive lens (LCDL) with 95% diffraction efficiency and millisecond switching times using a +/-2.4 V ac input. This lens is based on the electrical modulation of a 3 mum layer of nematic liquid-crystal sandwiched between a Fresnel zone electrode structure and a reference substrate. Each zone is divided into 12 subzones to digitize the phase profiles and define the phase wrapping points. The focusing power can rapidly be switched by electrically changing the number of subzones and re-establishing the wrapping points. Potential applications include zooms with no moving parts and autofocus lenses for compact imaging devices.