Uniform illumination of distant targets using a spherical light-emitting diode array

An array of light- emitting diodes (LEDs) assembled upon a spherical surface can produce a wider angle distribution of light than a typical array (i. e., an array assembled by mounting LEDs into a flat surface). Arranging each single LED into an optimal placement, the uniformity of the illumination of a target can be improved. We derive approximate formulas and equations for the optimum LED- to-LED angular spacing of several spherical arrangements for uniform far-field irradiance. These design conditions are compact and simple tools that incorporate an explicit dependence on the half-intensity viewing angle (half width half maximum angle) of LEDs. (C) 2007 Society of Photo-Optical Instrumentation Engineers.