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{{Short description|Theorem in electromagnetic theory of antennas}}
{{Infobox theorem|name=Thinned-array Curse|type=electromagnetic theory of antennas|field=electromagnetic|first stated date=1976|first stated by=[[Robert L. Forward]]|statement=A transmitting antenna which is synthesized from a coherent phased array of smaller antenna apertures that are spaced apart will have a smaller minimum beam spot size.}}
The '''thinned-array curse''' (sometimes, '''sparse-array curse''') is a theorem in [[electromagnetic radiation|electromagnetic]] theory of [[antenna (radio)|antenna]]s. It states that a transmitting antenna which is [[Aperture synthesis|synthesized]] from a coherent [[phased array]] of smaller antenna apertures that are spaced apart will have a smaller minimum beam spot size, 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.<ref>{{Cite journal|last1=Glennon|first1=Eamonn P|last2=Dempster|first2=Andrew G|last3=Aboutanios|first3=Elias|date=2018-07-07|title=Distributed Beamforming Architectures: Taxonomy, Requirements & Synergies|url=https://www.ignss2018.unsw.edu.au/sites/ignss2018/files/u80/Papers/IGNSS2018_paper_29.pdf|journal=International Global Navigation Satellite Systems Association|volume=IGNSS Conference 2018|pages=11}}</ref>
The origin of the term is not clear. [[Robert L. Forward]] cites use of the term in unpublished [[Hughes Research Laboratories]] reports dating from 1976.<ref>T. R. O'Meara, ''The Thinned Array Curse Theorems,'' Hughes Research Laboratories, unpublished internal report, Malibu CA Dec. 1976</ref><ref>W. B. Bridges, ''Looking at the Thinned Array Curse from a Slightly Different View,'' Hughes Research Laboratories, unpublished internal report, Malibu CA April 1976</ref>
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The thinned array curse has consequences for [[microwave power transmission]] and [[wireless energy transfer]] concepts such as [[solar power satellite]]s; it suggests that it is not possible to make a smaller beam and hence reduce the size of a receiver (called a ''[[rectenna]]'' for microwave power beaming) by phasing together beams from many small satellites.
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."<ref name="Forward 1984 pp. 187–195">{{cite journal | last=Forward | first=Robert L. | title=Roundtrip interstellar travel using laser-pushed lightsails | journal=Journal of Spacecraft and Rockets | publisher=American Institute of Aeronautics and Astronautics (AIAA) | volume=21 | issue=2 | year=1984 | issn=0022-4650 | doi=10.2514/3.8632 | pages=187–195 |
==See also==
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