Reflective and refractive surfaces configured to project desired caustic pattern

摘要

Techniques are described for designing and manufacturing a surface that produces a desired image when illuminated by a light source. As described, the desired image may be decomposed into a collection of Gaussian kernels (referred to as Gaussians). A shape of a micropatch lens corresponding to each Gaussian may be determined, and the resulting micropatch lenses may be assembled to form a highly continuous surface that will cast an approximation of the desired image formed form the sum of a plurality of Gaussian caustics. The disclosed techniques may be used to create a design for a light-redirecting surface amenable to milling (or other manufacturing process).

主权项

1. A method for designing a light-redirecting surface, comprising:
decomposing, using a computer, an input image into a plurality of Gaussian kernel functions, wherein the decomposing comprises:
generating a dense point sampling representation of the input image,tessellating the input image to create an initial estimate of the plurality of Gaussian kernel functions, wherein the initial estimate provides a plurality of isotropic Gaussian functions, andevolving the initial estimate of the plurality of the Gaussian kernel functions using Expectation Maximization to derive a plurality of anisotropic Gaussian kernel functions representing the approximation of the input image; for each of a plurality of micropatch lenses on the light-redirecting surface being designed:
determining a mapping between a plurality of points on a micropatch domain and corresponding points on a projection surface such that an intensity of light energy distributed by the mapping corresponds to one of the Gaussian kernel functions, anddetermining, from the mapping, a surface topology for a micropatch lens that will cast a Gaussian caustic corresponding to one of the Gaussian kernel functions; anddetermining an arrangement of the micropatch lenses on the light-redirecting surface, wherein the Gaussian caustics cast by the plurality of arranged micropatch lenses sum to form an approximation of the input image.