Central lobe energy in the far-field irradiance pattern of a 2-D array of coherent Gaussian sources

The far-field irradiance of a phase-locked M x N array of Gaussian emitters is investigated theoretically. Combining the changing shape of the far-field pattern from a single element with the grating lobe structure from an array leads to a trade-off curve which represents the fraction of energy or power which can be located in the central lobe. A significant factor in this trade-off is the fact that any of the energy which is lost due to truncation is made unavailable in the far field. The theoretical limit to power in the central lobe occurs when the fill factor is 100 percent and the output of each diode is uniform (not Gaussian).