Journal of the European Optical Society - Rapid publications, Vol 9 (2014)

Computation of dioptric and magnification matrices in ophthalmic lenses

S. Barbero


The diopter power and magnification matrices characterize the first-order properties of ophthalmic lenses for different gaze directions. Therefore an efficient method to compute them is highly valuable in ophthalmic lens design and optical performance simulations. I present a novel method to numerically compute these matrices in ophthalmic lenses comprising any set of arbitrary surfaces. The method is based on computing one base ray, along the gaze direction, and two rays close to it. These two rays are obtained varying a small parameter that indicates their separation from the base ray. The method was validated comparing the results with a single refractive surface where exact solutions are directly obtained.

© The Authors. All rights reserved. [DOI: 10.2971/jeos.2014.14023]

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D. J. Meister, and S. W. Fisher, ”Progress in the spectacle correction of presbyopia. Part 1: Design and development of progressive lenses,” Clin. Exp. Optom. 91, 240–250 (2008).

S. Barbero, ”The Alvarez and Lohmann refractive lenses revisited,” Opt. Express. 17, 9376–9390 (2009).

O. N. Stavroudis, The mathematics of geometrical and physical optics : the k-function and its ramifications (Wiley-VCH, Weinheim, 2006).

A. Walther, The ray and wave theory of lenses (Cambridge University Press, Cambridge, 1995).

B. Bourdoncle, J. P. Chauveau, and J. L. Mercier, ”Traps in displaying optical performances of a progressive addition lens,” Appl. Opt. 31, 3586–3593 (1992).

S. Barbero, and J. Rubinstein, ”Adjustable-focus lenses based on the Alvarez principle,” J. Opt. 13, 125705 (2011).

S. Barbero, and J. Rubinstein, ”Power-adjustable sphero-cylindrical refractor comprising two lenses,” Opt. Eng. 52, 063002–063002 (2013).

W. F. Harris, ”Image size magnification and power and dilation factors for optical instruments in general,” Ophth. Phy. Opt. 23, 251–261 (2003).

A. Malet, ”Kepler and the telescope,” Ann. Sci. 60, 107–136 (2003).

J. Rubinstein, and G. Wolansky, ”Differential relations for the imaging coefficients of asymmetric systems,” JOSA-A 20, 2365–2369 (2003).

W. F. Harris, ”Dioptric power: Its nature and its representation in three- and fourdimensional space,” Opt. Vis. Sci. 74, 349–366 (1997).

J. M. Howard, and B. D. Stone, ”Imaging a point to a line with a single spherical mirror,” Appl. Opt. 37, 1826–1834 (1998).

R. Legras, N. Chateau, and W. N. Charman, ”Assessment of justnoticeable differences for refractive errors and spherical aberration using visual simulation,” Opt. Vis. Sci. 81, 718–728 (2004).