Biomedical subjects

Jochen Wahl

Publications and source records attributed to Jochen Wahl.

3 recordsLinked to original sources

PubMed2003

Simplified mathematics for customized refractive surgery.

PURPOSE: To describe a simple mathematical approach to customized corneal refractive surgery or customized intraocular lens (IOL) design that allows "hypervision" and to investigate the accuracy limits. SETTING: University eye hospital, Mainz, Germany. METHODS: Corneal shape and at least 1 IOL surface are approximated by the well-known Cartesian conic section curves (ellipsoid, paraboloid, or hyperboloid). They are characterized by only 2 parameters, the vertex radius and the numerical eccentricity. Residual refraction errors for this approximation are calculated by numerical ray tracing. These errors can be displayed as a 2-dimensional refraction map across the pupil or by blurring the image of a Landolt ring superimposed on the retinal receptor grid, giving an overall impression of the visual outcome. RESULTS: If the eye is made emmetropic for paraxial rays and if the numerical eccentricities of the cornea and lens are appropriately fitted to each other, the residual refractive errors are small enough to allow hypervision. Visual acuity of at least 2.0 (20/10) appears to be possible, particularly for mesopic pupil diameters. However, customized optics may have limited application due to their sensitivity to misalignment errors such as decentrations or rotations. CONCLUSIONS: The mathematical approach described by Descartes 350 years ago is adequate to calculate hypervision optics for the human eye. The availability of suitable mathematical tools should, however, not be viewed with too much optimism as long as the accuracy of the implementation in surgical procedures is limited.

Cornea↗

PubMed2003

Corneal model.

PURPOSE: To describe the optical region of the cornea with as few parameters as possible and to compare this approach to commonly used mathematical models for the cornea. SETTING: University eye hospital, Mainz, Germany. METHODS: Corneal surface is approximated by a simple model (SM) that is defined by 2 perpendicular vertex radii, their angle to the horizontal, and a unique numerical eccentricity. These parameters, together with a parameter quantifying the decentration of the recording, are obtained in a consistent fit of corneal topographic data. The SM is compared to Zernike polynomial approximations of the 4th (Z4 model) and 8th (Z8 model) radial orders. Residual refraction errors for these approximations are calculated by numerical ray tracing, allowing a comparison of the different approaches. The statistical evaluation was carried out in 100 healthy eyes. RESULTS: The model approximation accuracy for the SM was at least as high as the reproducibility of the topographic measurements. For small optical zones up to 4.0 mm in diameter, the SM was on average more accurate than the Z4 model. CONCLUSIONS: The parameters of the SM, which are closely related to conventional parameters of the cornea, provided a highly accurate basis for following refractive interventions (customized corneal or cataract surgery). Zernike polynomials tend to improve peripheral optical quality at the expense of the central quality. Except in cases of technical optics, this is an unwanted effect in the human eye.

Adolescent↗

PubMed2002

Ray tracing for intraocular lens calculation.

PURPOSE: To improve accuracy in intraocular lens (IOL) calculations and clarify the effect of various errors. SETTING: University eye hospitals, Mainz, Germany, and Vienna, Austria. METHODS: A numerical ray-tracing calculation has been developed for the pseudophakic eye. Individual rays are calculated and then undergo refractions on all surfaces of the IOL and cornea. The calculations do not use approximations; ie, the refractions are calculated exactly using Snell's law. Rays can be calculated for any distance from the optical axis and for other parameter variations. The effects of aspheric surfaces can also be investigated. Instead of IOL powers, manufacturers' IOL data (radii, refractive index, thickness) are used in the calculations for different IOL types. The resulting optical quality is visualized by using Landolt rings superimposed on the grid of retinal receptors. RESULTS: Intraocular lens design, corneal asphericity, and specific spherical aberration influence the visual quality of the pseudophakic eye significantly. The IOL refractive power is an ambiguous parameter that cannot characterize the visual outcome sufficiently accurately for an IOL implanted at a given position. The effects can be calculated only in numerical ray tracing, not in Gaussian optics. The accuracy of numerical ray tracing is independent of axial length. Therefore, very long or very short eyes gain the most from the higher accuracy of this approach. For average-size eyes, however, the results are the same as with SRK calculations. CONCLUSION: Calculations in Gaussian optics should be replaced by state-of-the-art numerical methods, which can be run on any standard personal computer.

Humans↗