Thinned-array curse: Difference between revisions

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{{Short description|Theorem in electromagnetic theory of antennas}}

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 (typically, the [[main lobe]] has a [[solid angle]] that is smaller by an amount proportional to the ratio of the area of the synthesized array to 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.

{{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 (typically, the [[main lobe]] has a [[solid angle]] that is smaller by an amount proportional to the ratio of the area of the synthesized array to 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.<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 "thinned array curse" 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>

The origin of the term "thinned array curse" 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>

==Example==

Consider a number of small sub-apertures that are mutually adjacent to one another, so that they form a [[filled aperture array]]. Suppose that they are in orbit, beaming [[microwave]]s at a spot on the ground. Now, suppose you hold constant the number of sub-apertures and the power emitted by each, but separate thesethe sub-apertures (butwhile keepkeeping them mutually phased) so as to [[aperture synthesis|synthesize a larger aperture (such as a [[radio telescope]] 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.

Thus:

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==Consequences==

The thinned array curse means that while synthesized apertures are useful for receivers with high angular resolution, they are not useful for power transmitters. It also means that if a filled array transmitter has gaps between individual elements, the main lobe of the beam will lose an amount of power proportional to the area of the gaps. Likewise, if a transmitter comprises multiple individual transmitters, some of which fail, the power lost from the main lobe will exceed the power of the lost transmitter, because power will be also be diverted into the side lobes.

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. Forward,| "title=Roundtrip Interstellarinterstellar Traveltravel Usingusing Laserlaser-pushed Pushedlightsails Lightsails,"| ''J.journal=Journal of Spacecraft and Rockets, Vol.| publisher=American Institute of Aeronautics and Astronautics (AIAA) | volume=21,'' No.| issue=2, Mar-Apr| year=1984, pp| issn=0022-4650 | doi=10.2514/3.8632 190| pages=187–195 | bibcode=1984JSpRo..21..187F | citeseerx=10.1.1.1079.9524 }}</ref>

==See also==

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{{Refbegin}}

*The general theory of phased array antennas, from which the thinned array curse can be derived, can be found in [http://www.ece.rutgers.edu/~orfanidi/ewa/ch19.pdf Chapter 19] of Sophocles J. Orfanidis, ''Electromagnetic Waves and Antennas'' (electronic version accessed July 20, 2009).

*See also Constantine A. Balanis: “Antenna Theory, Analysis and Design”, John Wiley & Sons, Inc., 2nd ed. 1982 {{ISBN |0-471-59268-4}}

{{Refend}}

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[[Category:Interferometry]]

[[Category:Electromagnetic radiation]]

[[Category:Abstract curses]]