Abstract.
Consider a point source of light O radiating with intensity I(m) in direction m. Let R be a perfectly reflecting smooth surface. Suppose that a light ray emitted by the source O in direction m hits the surface R and reflects off it in direction y. Denote by γ:my the corresponding map defined by the surface R which transforms the set of rays incident on R into a set of reflected directions. If J(γ(·)) is the Jacobian of this map then the light intensity in direction y=γ(m) is given by I(m)/|J(γ(m))|. The problem consists of constructing a reflecting surface R such that for given sets of input and output directions (input and output apertures, respectively) and given input and output light intensities I and L, the surface R maps the input aperture into the output aperture and relates the input and output intensities via the energy conservation law of geometrical optics, that is, I(γ-1(y))|J(γ-1(y))|=L(y). This equation can be re-written as a second order equation of Monge–Ampère type. Theoretical results regarding its solvability have been established in [2] and a numerical method for calculating its solutions was proposed in [1]. In this paper we investigate a numerical procedure which in combination with the method in [1] provides a faster computational scheme for numerical solution of this problem.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 1 July 1999 / Accepted: 6 December 2000 / Published online: 5 May 2003
RID="*"
ID="*"The research of V.I. Oliker was partially supported by a grant from Emory University Research Committee.
Communicated by W. Jäger
Rights and permissions
About this article
Cite this article
Kochengin, S., Oliker, V. Computational algorithms for constructing reflectors. Comput Visual Sci 6, 15–21 (2003). https://doi.org/10.1007/s00791-003-0103-2
Issue Date:
DOI: https://doi.org/10.1007/s00791-003-0103-2