论文信息 - On the design of reflectors with prespecified distribution of virtual sources and intensities

On the design of reflectors with prespecified distribution of virtual sources and intensities

We consider the problem of determining a reflecting convex surface transforming the energy flow from a given point source of light into an energy flow from a prescribed-in-advance set of virtual sources. This set may consist of a finite set of point sources or of distributed sources. The problem is studied in the geometrical optics approximation. The analytic formulation of the problem leads to a complicated nonlinear partial differential equation of Monge-Ampere type. Here, we formulate the problem in terms of certain associated measures and prove the existence of weak solutions.

Vladimir Oliker | S. A. Kochengin | V. Oliker | Sergey A. Kochengin | Oliver von Tempski

[1] Vladimir Oliker,et al. Determination of reflector surfaces from near-field scattering data II. Numerical solution , 1998 .

[2] D. Gilbarg,et al. Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[3] David L. Shealy,et al. A Different Approach to Lighting and Imaging: Formulas for Flux Density, Exact Lens and Mirror Equations and Caustic Surfaces in Terms of the Differential Geometry of Surfaces , 1987, Optics & Photonics.

[4] Xu-jia Wang. On the design of a reflector antenna , 1996 .

[5] S. A. Kochengin,et al. Determination of reflector surfaces from near-field scattering data , 1997 .

[6] David L. Shealy,et al. Design of reflectors which will distribute sunlight in a specified manner , 1975 .

[7] V. Oliker,et al. Determining the intensities produced by reflected and refracted wave fronts in geometrical optics , 1995 .

[8] Donald G. Burkhard,et al. Specular aspheric surface to obtain a specified irradiance from discrete or continuous line source radiation: design. , 1975, Applied optics.

[9] Raj Mittra,et al. On the theory of the synthesis of single and dual offset shaped reflector antennas , 1987 .

[10] R. Schneider. Convex Bodies: The Brunn–Minkowski Theory: Minkowski addition , 1993 .

[11] T. E. Horton,et al. Design of a Specular Aspheric Surface to Uniformly Radiate a Flat Surface using a Nonuniform Collimated Radiation Source , 1972 .