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Structure equation as novel strategy for optimum reflector design

Ou Chung-Jen

Optica Applicata

2020

Vol. 50, nr 1

95--110

The optimal use of energy resources is the central dogma for green technology and bio-optics. Reflectors provide a simple and fundamental structure for energy transport from a light emitting diode (LED) chip, and an appropriately designed reflector can reduce the fabrication cost of secondary optics for the LED. This paper demonstrates the role of three proposed reflector geometric factors in the two performance metrics – uniformity and collected energy (power), for designing LED reflectors. Through canonical factor analysis, a linear structure equation for LED reflector is suggested, and the methodology for designing the optimal shape is discussed. In addition, a generalized factor and a synthesis response are proposed for a more comprehensive investigation of optical performance. Results indicate a key parameter for balancing the optical performance, and the effects of various parameters and the trade-offs are revealed.

Delaunay surfaces expressed in terms of a Cartan moving frame

Bracken Paul

Journal of Applied Analysis

2020

Vol. 26, nr 1

153--160

Delaunay surfaces are investigated by using a moving frame approach. These surfaces correspond to surfaces of revolution in the Euclidean three-space. A set of basic one-forms is defined. Moving frame equations can be formulated and studied. Related differential equations which depend on variables relevant to the surface are obtained. For the case of minimal and constant mean curvature surfaces, the coordinate functions can be calculated in closed form. In the case in which the mean curvature is constant, these functions can be expressed in terms of Jacobi elliptic functions.