Numerical implementation of generalized Coddington equations for ophthalmic lens design

A method for general implementation in any software platform of the generalized Coddington equations is presented, developed, and validated within a Matlab environment. The ophthalmic lens design strategy is presented thoroughly, and the basic concepts of generalized ray tracing are introduced. The methodology for ray tracing is shown to include two inter-related processes. Firstly, finite ray tracing is used to provide the main direction of propagation of the considered ray at the incidence point of interest. Afterwards, generalized ray tracing provides the principal curvatures of the local wavefront at that point, and its orientation after being refracted by the lens. The curvature values of the local wavefront are interpreted as the sagital and tangential powers of the lens at the point of interest. The proposed approach is validated using a double-check of the calculated lens performance in the spherical lens case: while finite ray tracing is validated using a commercial ray tracing software, generalized ray tracing is validated using a software application for ophthalmic lens design based on the classical version of Coddington equations. Equations of the complete tracing process are developed in detail for the case of generic astigmatic ophthalmic lenses as an example. Three-dimensional representation of the sagital and tangential powers of the ophthalmic lens at all directions of gaze then becomes possible, and results are presented for lenses with different geometries.

[1]  M P Keating,et al.  Oblique Central Refraction in Spherocylindrical Lenses Tilted Around an Off-Axis Meridian , 1993, Optometry and vision science : official publication of the American Academy of Optometry.

[2]  Orestes N. Stavroudis,et al.  Caustic surfaces and the structure of the geometrical image , 1976 .

[3]  Theodore Grosvenor.  Optometría de atención primaria , 2004 .

[4]  D. Burkhard,et al.  Simplified formula for the illuminance in an optical system. , 1981, Applied optics.

[5]  D. Atchison.  Spectacle Lens Design – Development and Present State , 1984 .

[6]  J. Simon,et al.  Alternative uses of coddington's equations in optical design , 2001 .

[7]  Orestes N. Stavroudis.  The Optics of Rays, Wavefronts, and Caustics , 2012 .

[8]  W. T. Welford,et al.  Aberrations of optical systems , 1986 .

[9]  J. E. A. Landgrave,et al.  Generalized Coddington equations in ophthalmic lens design , 1996 .

[10]  C. Campbell,et al.  Generalized Coddington equations found via an operator method. , 2006, Journal of the Optical Society of America. A, Optics, image science, and vision.

[11]  Orestes N. Stavroudis.  Simpler derivation of the formulas for generalized ray tracing , 1976 .

[12]  D. Uttenweiler,et al.  Derivation of the refraction equations for higher-order aberrations of local wavefronts at oblique incidence. , 2010, Journal of the Optical Society of America. A, Optics, image science, and vision.

[13]  D A Atchison.  Spectacle lens design: a review. , 1992, Applied optics.

[14]  Rudolf Kingslake,et al.  WHO? DISCOVERED CODDINGTON'S Equations? , 1994 .

[15]  David A. Atchison,et al.  Performance of aspheric spectacle lenses , 1992 .

[16]  John A. Kneisly.  Local Curvature of Wavefronts in an Optical System , 1964 .