Abstract
In the framework of geometrical optics, we consider the following inverse problem: given a two-parameter family of curves (congruence) (i.e., ), construct the refractive-index distribution function of a 3D continuous transparent inhomogeneous isotropic medium, allowing for the creation of the given congruence as a family of monochromatic light rays. We solve this problem by following two different procedures: 1. By applying Fermat’s principle, we establish a system of two first-order linear nonhomogeneous PDEs in the unique unknown function relating the assigned congruence of rays with all possible refractive-index profiles compatible with this family. Moreover, we furnish analytical proof that the family of rays must be a normal congruence. 2. By applying the eikonal equation, we establish a second system of two first-order linear homogeneous PDEs whose solutions give the equation of the geometric wavefronts and, consequently, all pertinent refractive-index distribution functions . Finally, we make a comparison between the two procedures described above, discussing appropriate examples having exact solutions.
© 2016 Optical Society of America
Full Article | PDF ArticleMore Like This
Francesco Borghero and George Bozis
J. Opt. Soc. Am. A 23(12) 3133-3138 (2006)
Francesco Borghero and Thomas Kotoulas
J. Opt. Soc. Am. A 28(2) 278-283 (2011)
Wenda Shen, Jufang Zhang, Shitao Wang, and Shitong Zhu
J. Opt. Soc. Am. A 14(10) 2850-2854 (1997)