Vol. 53, Issue 3, pp. 377-391

Vol. 53 Issue 3 pp. 377-391

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

Huazhong Xiang, Peng Wang, Zexi Zheng, Gang Zheng, Jiabi Chen, Cheng Wang, Dawei Zhang, Songlin Zhuang


toric, astigmatism, spherocylinder, aspheric, ellipsoidal surface


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.

Vol. 53
Issue 3
pp. 377-391

1.54 MB
OPTICA APPLICATA - a quarterly of the Wrocław University of Science and Technology, Faculty of Fundamental Problems of Technology