Robert L. Forward cites use of the term in unpublished Hughes Research Laboratories reports dating from 1976.
[2][3] Consider a number of small sub-apertures that are mutually adjacent to one another, so that they form a filled aperture array.
The spot size on the ground is reduced in size proportionally to the diameter of the synthesized array (and hence the area is reduced proportionally to the diameter of the synthesized array squared), but the power density at the ground is unchanged.
The thinned array curse means that while synthesized apertures are useful for receivers with high angular resolution, they are not useful for power transmitters.
A short derivation of the thinned array curse, focusing on the implications for use of lasers to provide impulse for an interstellar probe (an application of beam-powered propulsion), can be found in Robert Forward's paper "Roundtrip Interstellar Travel Using Laser Pushed Lightsails.