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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. [ABSTRACT FROM AUTHOR]