Sage Journals: Discover world-class research

Abstract

Finding a reflector shape to provide a required light distribution is a major problem in the design of luminaires. Most methods for solving the problem assume the light source is a point. However, this assumption leads to great discrepancies between the required and calculated luminous intensity. In addition, it gives no answer to the question of whether it is possible to provide any arbitrary light distribution. A method for computing the shape of a specular reflector, with cylindrical or axial symmetry, operating with a finite size light source and providing a required light distribution, is presented in this study. The luminance distribution of the surface of the light source is specified very close to reality. The method is based on solving a system of first-order differential equations that describe a pro-file curve of a reflector under specified initial conditions (Cauchy problem). The study defines under what conditions a required light distribution of a reflector can be realized. The mechanism (image transformation function) for finding the optimum geometrical parameters of a reflector for a given light distribution and for given initial conditions is described.

Get full access to this article

View all access options for this article.

References

Tikhonov AN , Arsenin VYa . Methods of solving ill-posed problems. Moscow: Nauka, 1986 (Russian).

Boldyrev NG. Calculation of asymmetric specular reflectors. Svetotekhnika 1932; 7: 7-8 (in Russian).

Komissarov VD. Foundations of calculation of specular and prismatic fittings: Proceedings. Moscow. All-Union Electrotechnical Institute (VEI) 1941; 43: 6-61 (in Russian).

Schruben JS. Formulation of the reflection-design problem for a lighting fixture. J. Opt. Soc. Am. 1972; 62:1498-1501.

Schruben JS. Analysis of rotationally symmetric reflectors for illuminating systems. J. Opt. Soc. Am. 1974; 64: 55-58.

Cornbleet S. Microwave optics. New York; Academic Press, 1976.

Zakhidov RA. Mirror systems for the concentrating of radiant energy. Tashkent: Fan, 1986 (in Russian).

Kinber BB. The solution of inverse problem in geometrical acoustics. Acoustic Journal 1955; 1: 221-225 (in Russian).

Keller JB. The inverse scattering problem in geometrical optics and the design of reflectors. JRE Transactions of Antennas and Propagation 1959; Vol. AP-7, 2: 146-149.

10.

Weis B. Industriebeleuchtung. München: Pflaum, 2000.

11.

Zaremba K. A synthetic method of designing a rotationally symmetric reflector with reference to the lamp dimensions: Proceedings of the 24th Session of the CIE. Warsaw, Vol. 1, 1999.

12.

Korobko AA , Kush OK. Construction of the mirror surface of a luminaire with an extended source. Svetotekhnika 1982; 3: 3-6 (in Russian).

13.

Korobko AA , Kush OK. Calculating the profile of a cylindrical reflector from a specified illuminating-power curve. Light & Engineering 1997; 5: 37-47.

14.

Korobko AA , Kush OK. Equations of synthesis of specular axisymmetric reflector with a finite-size light source. Light & Engineering 2000; 8: 22-28.

15.

Sofronov NN. Luminance of themetal halide arc tube. Svetotekhnika 1988; 12: 4-7 (in Russian).

16.

Frieden BR ed. The computer in optical research. Berlin: Springer, 1980.

17.

Kush OK , Chepelevsky DY. Integrated concept of the computer-aided design of specular reflectors. Svetotekhnika 1995; 6: 25-28 (in Russian).

Synthesis of specular reflectors for a finite size light source

Abstract

Get full access to this article

References