[Visual image in high ametropia. Computer-assisted simulation with optic ray calculation]

Calculating Intraocular Lens Geometry by Real Ray Tracing

PURPOSE

An implementation of real ray tracing based on Snell's law is tested by predicting the refraction of pseudophakic eyes and calculating the geometry of intraocular lenses (IOLs).

METHODS

The refraction of 30 pseudophakic eyes was predicted with the measured corneal topography, axial length, and the known IOL geometry and compared to the manifest refraction. Intraocular lens calculation was performed for 30 normal eyes and 12 eyes that had previous refractive surgery for myopia correction and compared to state-of-the-art IOL calculation formulae.

RESULTS

Mean difference between predicted and manifest refraction for a 2.5-mm pupil were sphere 0.11 +/- 0.43 diopters (D), cylinder -0.18 +/- 0.52 D, and axis 5.13 degrees +/- 30.19 degrees. Pearson's correlation coefficient was sphere r = 0.92, P < .01; cylinder r = 0.79, P < .01; and axis r = 0.91, P < .01. Intraocular lens calculation for the normal group showed that the mean absolute error regarding refractive outcome is largest for SRK II (0.49 D); all other formulae including ray tracing result in similar values ranging from 0.36 to 0.40 D. Intraocular lens calculation for the refractive group showed that depending on pupil size (3.5 to 2.5 mm), ray tracing delivers values 0.95 to 1.90 D higher compared to the average of Holladay 1, SRK/T, Haigis, and Hoffer Q formulae.

CONCLUSIONS

It has been shown that ray tracing can compete with state-of-the-art IOL calculation formulae for normal eyes. For eyes with previous refractive surgery, IOL powers obtained by ray tracing are significantly higher than those from the other formulae. Thus, a hyperopic shift may be avoided using ray tracing even without clinical history.

simEye: Computer-based simulation of visual perception under various eye defects using Zernike polynomials

We describe a computer eye model that allows for aspheric surfaces and a three-dimensional computer-based ray-tracing technique to simulate optical properties of the human eye and visual perception under various eye defects. Eye surfaces, such as the cornea, eye lens, and retina, are modeled or approximated by a set of Zernike polynomials that are fitted to input data for the respective surfaces. A ray-tracing procedure propagates light rays using Snell's law of refraction from an input object (e.g., digital image) through the eye under investigation (i.e., eye with defects to be modeled) to form a retinal image that is upside down and left-right inverted. To obtain a first-order realistic visual perception without having to model or simulate the retina and the visual cortex, this retinal image is then back-propagated through an emmetropic eye (e.g., Gullstrand exact schematic eye model with no additional eye defects) to an output screen of the same dimensions and at the same distance from the eye as the input object. Visual perception under instances of emmetropia, regular astigmatism, irregular astigmatism, and (central symmetric) keratoconus is simulated and depicted. In addition to still images, the computer ray-tracing tool presented here (simEye) permits the production of animated movies. These developments may have scientific and educational value. This tool may facilitate the education and training of both the public, for example, patients before undergoing eye surgery, and those in the medical field, such as students and professionals. Moreover, simEye may be used as a scientific research tool to investigate optical lens systems in general and the visual perception under a variety of eye conditions and surgical procedures such as cataract surgery and laser assisted in situ keratomileusis (LASIK) in particular.

Refractive correction method for digital charge-coupled device-recorded Scheimpflug photographs by means of ray tracing

Our purpose is to correct digital CCD-recorded Scheimpflug photographs, imaging both the anterior and posterior corneal surface, the anterior chamber, and the anterior eye lens surface for optical distortions. In a ray-tracing algorithm the imaging of the posterior corneal surface in a given Scheimpflug photograph is corrected by applying Snell's law on parallel incident rays entering through the anterior corneal surface. Once the posterior corneal surface is corrected, the procedure is repeated, again with parallel incident rays entering through both the anterior and now corrected posterior corneal surface, to correct the imaging of the anterior eye lens surface. The refractive indices necessary for Snell's law are taken from Gullstrand's exact schematic eye model. Due to the optical/refractive correction, the digital Scheimpflug photograph decreases in size perpendicular to the direction of the optical axis. As a consequence the curvature radii of both the posterior corneal surface and the anterior lens surface are reduced significantly, as compared to the original digital Scheimpflug photograph. Furthermore, the corneal thickness and the anterior chamber depth are increased. The presented refractive correction method enables us to extract from Scheimpflug photographs the following quantities rather realistically: structure coordinates and curvature radii of both the posterior corneal surface and the anterior lens surface, corneal thickness, and anterior chamber depth. This method can readily be applied to other imaged quantities, such as the posterior eye lens surface, the lens thickness, and the pupillary opening.

Beam-deflection method of diagnosing impaired vision

We describe a simple method to assign a diagnosis of cataract to patients with obscurely impaired vision as well as to those with mild lens opacities. When the narrowest slit is used in a slitlamp examination, a small beam of light appears on the macula. Routine fundoscopy with the 78.0 diopter lens or a 3-mirror glass is appropriate. If a cataract is present, the beam of light is scattered into several straight lines, distorted lines, or both. This has proved a useful diagnostic tool when the lens appears clear but the patient's vision is impaired, and extensive examinations such as computer tomography or nuclear magnetic resonance tomography for impaired vision may be avoided. The beam-deflection method uses devices that are generally available and can detect cataract in the early stages of development.