Far-field condition for light-emitting diode arrays

In practice, any cluster of light-emitting diodes (LEDs) can be modeled or measured as a directional point source if the detector is far enough away from the cluster. We propose a far-zone condition for measuring or modeling propagation of light from an LED array. An equation gives the far-field distance as a function of the LED radiation pattern, array geometry, and number of LEDs. The far field is shorter for high packaging density clusters, and the far field considerably increases with increasing beam directionality of LEDs. In contrast with the classical rule of thumb (5 times the source size), the near zone of an array with highly directional LEDs can extend to more than 60 times the array size. We also analyze the effect of introducing random variations of light flux among LEDs of the array, which shows that far-field variability is low in high packaging density arrays.