Case study: A simple optical inverse problem from a geometrical optics point of view

Abstract

In this paper, we revisit the simple problem of reflection from a dielectric sphere for light rays and define a form of optical inverse problem in the sense of geometrical optics (GO). A general analytic formula is derived to obtain the refraction index of the sphere for any incidence light to emerge in a deflected angle. Numerical wave simulation and ray tracing are performed to verify the inverse formulae derived.

Creation of One- and Two-Dimensional Copper and Zinc Oxides Semiconductor Structures

“…Once the values of (x2, y2) were obtained and related to (x1, y1), free-form surfac optimization was carried out [129]. As an example of an inverse optical problem, one can consider the situation when is required to focus a beam into a specific region, for example, into a specific figure or lin in the focal plane [130,131]. To fulfil such a problem, it is possible to create an optica component that has the desired surface shape since only the intensity distribution is de fined in the focal region.…”

“…It is assumed that the following parameters are specified: The illu minance distribution I(x), x ∈ G, formed in the plane z = 0 by an incident beam with a plan wavefront, the desired illuminance distribution L(y), y ∈ D, formed in the output plane = f, and the desired eikonal Ψ(y) distribution in the same plane (Figure 9). It is necessar As an example of an inverse optical problem, one can consider the situation when it is required to focus a beam into a specific region, for example, into a specific figure or line in the focal plane [130,131]. To fulfil such a problem, it is possible to create an optical component that has the desired surface shape since only the intensity distribution is defined in the focal region.…”