The Parallel Refractor
نویسندگان
چکیده
The problem considered in this paper is the following. Suppose we have a domain Ω ⊂ Rn−1 and a domain Σ contained in an n − 1 dimensional surface in Rn; Σ is referred to as the target domain or screen to be illuminated (for the practical application, one can think that n = 3). Let n1 and n2 be the indexes of refraction of two homogeneous and isotropic media I and II, respectively, and suppose that from the region Ω surrounded by medium I, radiation emanates in the direction en with intensity f (x) for x ∈ Ω, and Σ is surrounded by media II. That is, all emanating rays from Ω are collimated. We seek an optical surface R interface between media I and II, such that all rays refracted by R into medium II are received at the surface Σ, and the prescribed radiation intensity received at each point p ∈ Σ is g(p). Of course some conditions on the relative position of Σ and and Ω are needed so rays can be refracted to Σ, see conditions (A) and (B) below. Assuming no loss of energy in this process, we have the conservation of energy equation ∫
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