LED array: where does far-field begin?

Any cluster of light-emitting diodes (LEDs) can be modeled as a directional point source if the far-zone condition is met. A general condition is derived for the distance beyond which the far-zone approximation can be used in measuring or modeling propagation of light from an LED array. A simple equation gives the far-field condition in function of parameters of influence, such as LED radiation pattern, array geometry, and number of LEDs. We calculate the near-zone extension of clusters with LED radiation patterns of practical interest; for example Lambertian-type, batwing, and side emitting. The far-field condition is shown to be considerable shorter for high packaging density LED arrays. Moreover, the far-field dramatically changes in function of the beam divergence of the LED radiation pattern. For example, the near-zone of a square LED array with highly directional LEDs (small half-intensity viewing angle) can extend to more than 70 times the cluster size. This value is far from the classical rule of thumb (5 times the source size)