Abstract
A basic problem in lighting technology is to design an optical system that illuminates a certain object in a prescribed manner. If this optical system consists of a fixed light source and a reflector that is to be chosen, then this problem is called a reflector design problem. This paper discusses mathematical methods which help to solve the reflector design problem.
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References
F. Brickell, L. Marder and B.S. Westcott, The geometrical optics design of reflectors using complex coordinates, J. Phys. A: Math. Gen. 10, No. 2, 1977, pp. 245 - 260.
F. Brickell and B.S. Westcott, Reflector design for two-variable beam shaping in the hyperbolic case, J. Phys. A: Math. Gen. 9, No. 1, 1976, pp. 113 - 128.
F. Brickell and B.S. Westcott, Phase and power density distributions on plane apertures of reflector antennas, J. Phys. A: Math. Gen. 11, No. 4, 1978, pp. 777 - 789.
A.J.E.M. Janssen and M.J.J.J.B. Maes, An optimization problem in reflector design, Philips Journal of Research, 47, 1992, pp. 99 - 143.
H.A.E. Keitz, Light Calculations and Measurements, MacMillan and Co. Ltd., London, 1971.
J.B. Keller, The inverse scattering problem in geometrical optics and the design of reflectors, IRE Trans. Antenn. Propag., 1958, pp. 146 - 149.
M.J.J.J.B. Maes and A.J.E.M. Janssen, A note on cylindrical reflector design, Optik 88, No. 4, 1991, pp. 177 - 181.
L. Marder, Uniqueness in reflector mappings and the Monge-Ampère equation, Proc. R. Soc. Loud. A 378, 1981, pp. 529 - 537.
A.P. Norris and B.S. Westcott, Computation of reflector surfaces for bivariate beamshaping in the elliptic case, J. Phys. A: Math. Gen. 9, No. 12, 1976, pp. 2159 - 2169.
V.I. Oliker, Near radially symmetric solutions of an inverse problem in geometric optics, Inverse Problems 3, 1987, pp. 743 - 756.
V.I. Oliker, On reconstructing a reflecting surface from the scattering data in the geometric optics approximation, Inverse Problems 5, 1989, pp. 51 - 65.
J.S. Schruben, Formulation of a reflector-design problem for a lighting fixture, J. Opt. Soc. 62, No. 12, 1972, pp. 1498 - 1501.
V.V. Trembac: Luminaires. Soviet Union Publishing Institute for Energy Technology, Moscow, Leningrad 1958.
B.S. Westcott and F. Brickell, Computation of reflector surfaces for two-variable beam shaping in the hyperbolic case, J. Phys. A: Math. Gen. 9, No. 4, 1976, pp. 611 - 625.
B.S. Westcott and A.P. Norris, Reflector synthesis for generalized far-fields, J. Phys. A: Math. Gen. 8, No. 4, 1975, pp. 521 - 532.
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© 1994 Springer Fachmedien Wiesbaden
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Maes, M. (1994). Mathematical Methods for 2D Reflector Design. In: Engl, H.W., McLaughlin, J. (eds) Proceedings of the Conference Inverse Problems and Optimal Design in Industry. European Consortium for Mathematics in Industry. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-96658-2_7
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DOI: https://doi.org/10.1007/978-3-322-96658-2_7
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-322-96659-9
Online ISBN: 978-3-322-96658-2
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