The '''thinned array curse''' (sometimes, ''sparse array curse'') is a theorem in electromagnetic theory of transmitters. thatsaysIt states that a transmitting aperture which is synthesized by a coherent array of smaller apertures will have a smaller minimum beam spot size (typically, a main lobe of a solid angle that is smaller by an amount proportional to the ratio of the area of the synthesized array divided by the total area of the individual apertures), but the amount of power that is beamed into this main lobe is reduced by an exactly proportional amount, so that the total power density in the beam is constant.
Consider the case that you haveof a number of small apertures that are mutually adjacent to one another, so that they form a filled aperture array. Now, supose you separate these (but keep the mutually phased) so as to synthesize a larger aperture (that is, like a [[radiotelescope]] array). The spot size on the ground is reduced in size proportionally the diameter of the synthesized array (and hence the area reduced proportionate to the diameter of the synthesized array squared), *but the power density at the ground is unchanged.*
Thus:
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1. It is radiating the same amount of power (since the individual sub-apertures making the array don't care whether they're adjacent too the next aperture or not).
2. It hasthehas the same power per unit area at the center of the receiving spot on the ground.
