Computational algorithms for constructing reflectors

Computing and Visualization in Science

Volumn 6, Issue 1, 2003, Pages 15-21

  Kochengin, Sergey A ^a   Oliker, Vladimir I ^a  

^a EMORY UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LIGHT SOURCES;

COMPUTATIONAL ALGORITHM; COMPUTATIONAL SCHEMES; ENERGY CONSERVATION LAW; INPUT AND OUTPUTS; NUMERICAL PROCEDURES; NUMERICAL SOLUTION; REFLECTING SURFACE; SECOND-ORDER EQUATION;

GEOMETRICAL OPTICS;

EID: 31844435016     PISSN: 14329360     EISSN: 14330369     Source Type: Journal    
DOI: 10.1007/s00791-003-0103-2     Document Type: Article

References (13)

1. Caffarelli, L., Kochengin, S., Oliker, V.: On the numerical solution of the problem of reflector design with given far-field scattering data. Contemp. Math. 226, 13-32 (1999)
2. Caffarelli, L., Oliker, V.: Weak solutions of one inverse problem in geometric optics. Preprint, 1994
3. Galindo-Israel, V., Imbriale,W.A., Mittra, R.: On the theory of the synthesis of single and dual offset shaped reflector antennas. IEEE Trans. on Antennas and Propagation 35(8), 755-887 (1987)
4. Guan, P., Wang, X.J.: On a Monge-Ampére equation arising in geometrical optics. J. Diff. Geometry 48, 205-223 (1998)
5. Kinber, B.E.: Inverse Problems of the Reflector Antennas Theory - geometric optics approximation. Preprint No. 38, Academy of Sc., USSR, 1984
6. Marder, L.: Uniqueness in reflector mappings and the Monge-Ampère equation. Proc. R. Soc. London A 378, 529-537 (1981)
7. Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7, 308-313 (1965)
8. Neubauer, A.: Design of 3D-reflectors for near field and far field problems. Preprint
9. Oliker, V.I.: Near radially symmetric solutions of an inverse problem in geometric optics. Inverse Probl. 3, 743-756 (1987)
10. Oliker, V.I., Waltman, P.: Radially symmetric solutions of a Monge- Ampère equation arising in a reflector mapping problem. Lecture Notes in Math., Vol. 1285, pp. 361-374. Berlin, Heidelberg: Springer 1987
11. Wang, X.-J.: On design of reflector antenna. Inverse Probl. 12, 351-375 (1996)
12. Westcott, B.S.: Shaped Reflector Antenna Design. Letchworth, UK: Research Studies Press 1983
13. Westcott, B.S., Norris, A.P.: Reflector synthesis for generalized far fields. J. Phys. A: Math. Gen., 3(4), 521-532 (1975)