Reflective/refractive surfaces projecting caustic pattern (optical illusion).
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).
BACKGROUND(1) Field of the Invention(2) The present invention generally relates to a translucent surface (such as a milled acrylic plate) that projects a desired image when light passes through it, as well as to techniques for designing such a surface. More specifically, the present invention relates to techniques for determining a surface pattern that will cast caustics which generate a recognizable image on a projection surface.(3) Description of the Related Art(4) In optics, a caustic refers to an envelope of light rays reflected or refracted by a curved surface, as well as to the projection of such light rays onto another surface. More specially, a caustic is the curve or surface tangent to each light ray, defining a boundary of an envelope of rays as a curve of concentrated light. For example, light passing through the curved surface of a wine glass creates a cusp-like pattern on a table which the wine glass is resting. Note, caustics are different from projecting light through a slide, as light is redirected (whether reflected or refracted) rather than absorbed, maintaining higher light levels and contrast.(5) One known application of reflective caustic design is luminaire design—the creation of lamp reflectors that create a desired radiance distribution for a given light source position. Other applications include e.g., in architecture (pattern glass that casts attractive caustics into a room) or designing security features which create hard-to-forge artifacts that can
1. A light-redirecting surface, comprising: a plurality of micropatch lenses, wherein each of the plurality of micropatch lenses has a respective surface topology that is configured to cast a respective one of a plurality of Gaussian caustics on a projection surface, the respective Gaussian caustic corresponding to a respective one of a plurality of Gaussian kernel functions; wherein the plurality of Gaussian kernel functions is decomposed from a selected image by tessellating the selected image in order to create an initial estimate of the plurality of Gaussian kernel functions, wherein the initial estimate provides a plurality of isotropic Gaussian functions and is evolved using Expectation Maximization in order to derive a plurality of anisotropic Gaussian kernel functions, wherein the plurality of micropatch lenses is arranged such that the plurality of Gaussian caustics sum to form an approximation of the selected image; wherein a topology of the light-redirecting surface is determined by, for at least a first one of the plurality of micropatch lenses, determining a mapping between a plurality of points on a micropatch domain and corresponding points on the projection surface such that an intensity of light energy distributed by the mapping corresponds to a first one of the plurality of Gaussian kernel functions, wherein the surface topology of the first micropatch lens is determined based on the mapping. |
8. A computer-implemented method for designing a light-redirecting surface, the computer-implemented method comprising: decomposing a selected image into a plurality of Gaussian kernel functions and by operation of one or more computer processors, wherein the decomposing comprises tessellating the selected image in order to create an initial estimate of the plurality of Gaussian kernel functions, wherein the initial estimate provides a plurality of isotropic Gaussian functions and is evolved using Expectation Maximization in order to derive a plurality of anisotropic Gaussian kernel functions; and for at least a first one 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 a first one of the plurality of Gaussian kernel functions and determining a surface topology that will cast a respective one, of a plurality of Gaussian caustics, that corresponds to a respective one of the plurality of Gaussian kernel functions; and determining an arrangement of the micropatch lenses on the light-redirecting surface such that the plurality of Gaussian caustics sum to form an approximation of the selected image. |
15. A non-transitory computer-readable medium storing one or more applications executable to perform an operation for designing a light-redirecting surface, the operation comprising: decomposing a selected image into a plurality of Gaussian kernel functions and by operation of one or more computer processors when executing the one or more applications, wherein the decomposing comprises tessellating the selected image in order to create an initial estimate of the plurality of Gaussian kernel functions, wherein the initial estimate provides a plurality of isotropic Gaussian functions and is evolved using Expectation Maximization in order to derive a plurality of anisotropic Gaussian kernel functions; for at least a first one of a plurality of micropatch lenses on the light-redirecting surface being designed, determining (i) 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 plurality of Gaussian kernel functions and (ii) a surface topology that will cast a respective one, of the plurality of Gaussian caustics, that corresponds to a respective one of the plurality of Gaussian kernel functions; and determining an arrangement of the micropatch lenses on the light-redirecting surface such that the plurality of Gaussian caustics sum to form an approximation of the selected image.