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Purpose. To describe a paraxial computing scheme for tracing an axial pencil of rays through the ‘optical system eye’ containing astigmatic surfaces with their axes at random.
Methods. Two rays (−10 prism diopters from vertical and horizontal) are traced through the uncorrected and corrected eye. In the uncorrected eye one specific ray is selected from the pencil of rays, which passes through the pupil center. In the corrected eye any ray can be traced through the eye. From the slope angle, the intersection of the ray with the refractive surface and the refraction the slope angle of the exiting ray is determined and the ray is traced to the subsequent surface. From both rays traced through the eye an ellipse is fitted to the image to characterize the image distortion of an circular object.
Example. Assumptions: target refraction −0.5–1.0D/A = 90° at 14 mm, corneal refraction 42.5 + 3.5D/A = 15°, axial length 23.6 mm, IOL position 4.6 mm, central lens thickness 0.8 mm, refractive index 1.42, front/back surface of the toric IOL 10.0 D/7.14 + 6.47D/A = 101.8°. The vertical incident ray was imaged to (x, y) = (0.0055 mm, −1.6470 mm)/(0.0067 mm, −1.6531 mm) in the uncorrected/corrected eye. The horizontal incident ray was imaged to (x, y) = (1.6266 mm, −0.0055 mm)/(1.6001 mm, −0.0067 mm) in the uncorrected/corrected eye. The ellipse (semi‐major/semi‐minor meridian) fitted to the conjugate image of a circle sized 1.648 mm/1.625 mm in an orientation 14.2° in the uncorrected and 1.654 mm/1.599 mm in an orientation 7.1° in the corrected eye.
Conclusion. This concept may be relevant for the assessment of aniseikonia after implantation of toric intraocular lenses for correction of high corneal astigmatism.
Globe rupture is one of the most severe open globe injuries, permanently impairing visual acuity or leading to blindness. The risk of globe rupture is increased after previous intraocular surgery (27-fold), in myopia, older age, females, and after sudden falls. The differentiation between an occult globe rupture and severe ocular contusion may be complicated by pronounced subconjunctival hemorrhage with conjunctival swelling. In case of doubt, a rupture of the eyeball should be ruled out after a severe blunt ocular trauma. Limbal and scleral exploration after 360 degrees peritomy leads to the correct diagnosis. Immediate and watertight wound closure is essential to avoid expulsive choroidal hemorrhage, persisting ocular hypotony or epithelial ingrowth. Delayed wound closure raises the risk of posttraumatic endophthalmitis. Early vitrectomy may prevent tractional retinal detachment in case of retinal injury with vitreal bleeding. Silicone oil instillation stabilizes the central retina after open globe injury; scleral buckling is controversial.
Ray tracing is used in ophthalmology for evaluation of the optical properties of the eye. We demonstrate an algebraic method for tracing a bundle of rays through the optical system of an eye containing aspheric surfaces. Restricting to second-order surfaces (quadric surfaces) such as ellipsoids, paraboloids or hyperboloids, a surface is described by a 4 x 4 matrix. In this case, the normal vector can be derived analytically and the ray-surface intersection is calculated by solving a quadratic equation. We applied this straightforward matrix-based strategy to the spherical 4-surface Le Grand schematic eye, and the Le Grand eye modified by Kooijman containing four aspheric surfaces. We calculated the spot diagram for the focal plane as well as a pre- and post-focal plane for both model eyes, and found that the optical quality of the aspheric model characterized by the ray scatter in the spot diagram at the focal plane is much better than that of the spherical model. This calculation strategy may be helpful for evaluating the image distortion of decentred or tilted spherical or aspheric artificial intra-ocular lenses.
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