10 February 2006 Simple mathematical representation of toroidal surfaces
Author Affiliations +
Proceedings Volume 6046, Fifth Symposium Optics in Industry; 604601 (2006) https://doi.org/10.1117/12.674372
Event: Fifth Symposium Optics in Industry, 2005, Santiago De Queretaro, Mexico
Toroidal surfaces are surfaces of revolution generated by revolving a plane curve about an axis in the plane of the curve. To avoid the generation of self-intersecting surfaces, the extent of the curve is restricted, so that the curve does not intersect the axis. Unlike aspherical surfaces, there is no standard mathematical representation for toroidal surfaces. In the present work we propose equations for the sagitta, the unit normal vector and the principal curvatures of a toroidal surface which are appropriate for ray tracing purposes, and also for the propagation of thin pencils of rays. In addition, we derive the equations corresponding to a revolving curve with the shape of a conic section, from which one can readily deduce the equations corresponding to a toric surface. All these equations are of considerable importance in ophthalmic lens design, where the refraction of thin pencils of rays is required, and it is commonly performed with the aid of Coddington equations.
© (2006) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
J. E. A. Landgrave, J. E. A. Landgrave, Antonio Villalobos, Antonio Villalobos, Criseida González, Criseida González, "Simple mathematical representation of toroidal surfaces", Proc. SPIE 6046, Fifth Symposium Optics in Industry, 604601 (10 February 2006); doi: 10.1117/12.674372; https://doi.org/10.1117/12.674372


The point spread function in paraxial optics
Proceedings of SPIE (September 02 2015)
A new method to treat a spherical lens as a...
Proceedings of SPIE (November 02 2003)
Aberrations of a transparent sphere
Proceedings of SPIE (September 20 2010)
Exact sine condition in the presence of spherical aberration
Proceedings of SPIE (December 31 1990)
Third Order Distortion And Spectacle Lens Design
Proceedings of SPIE (May 08 1986)

Back to Top