Simple mathematical representation of toroidal surfaces

Landgrave, J. E. A.; Villalobos, A.; González, C. A.

doi:10.1117/12.674372

Cited by 2 publications

(1 citation statement)

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“…LANDGRAVE et al proposed equations for the sagitta, the unit normal vector, and the principal curvatures of a toroidal surface appropriate for all tracing purposes. He also derived equations corresponding to a revolving curve shaped like a conic section, based on which the equations corresponding to a toric surface can be readily deduced [11]. Further, it has been observed that (i) an ellipsoid is a better than spherical, toric, or parabolic lenses in approximation of the corneal surface in the human eye, and (ii) contact lenses with inner elliptical surfaces exhibit marked improvements in terms of comfort of the wearer and durability [12].…”

Section: Introductionmentioning

confidence: 99%

Aspherical, sphero-cylindrical, toroidal, and ellipsoidal surfaces for designing astigmatic spectacle lenses with axis orientation

Huazhong Xiang,

Peng Wang,

Zexi Zheng

et al. 2023

Optica Applicata

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In this paper, formulas for aspherical, sphero-cylindrical, toroidal, and ellipsoidal surfaces with astigmatic axes are derived. Based on this, four types of curved surfaces were designed to correct astigmatism with axis, and, subsequently, the lenses were simulated, fabricated, and measured. A total of ten spectacle lenses in two groups were designed. Those in the first group used identical optical parameters. The spherical and cylindrical powers and maximum and minimum edge thicknesses of aspherical, sphero-cylindrical, and ellipsoidal surfaces were compared. The results indicated that the power of the lens constructed using the toroidal surface was more accurate than those of the other three lenses. Moreover, the minimum edge thickness of the toroidal surface was 1.2%, 4.98%, and 4.87% lower than those of the aspherical, sphero-cylindrical, and ellipsoidal surfaces, respectively. The powers and edge thicknesses of toroidal surfaces with different diopters were compared in the second group. The minimum and maximum edge thicknesses were observed to be reduced by 8.97% and 6.05%, respectively, corresponding to the conic constants obtained via ray tracing. The conclusion will be significant for clinical ophthalmology and optical design for the patients with astigmatism.

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Section: Introductionmentioning

confidence: 99%