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[[File:T antenna.svg|thumb|upright=1.8|Types of T antennas: ''(a)'' simple ''(b)'' multiwire. <font color="red">Red</font> parts are [[Electrical insulator|insulators]], <font color="grey">grey</font> are supporting towers.]]
{{Gravitational Lensing}}
'''Gravitational microlensing''' is an [[astronomy|astronomical]] phenomenon due to the [[gravitational lens]] effect. It can be used to detect objects ranging from the mass of a planet to the mass of a star, regardless of the light they emit. Typically, astronomers can only detect bright objects that emit lots of light ([[star]]s) or large objects that block background light (clouds of gas and dust). These objects make up only a tiny fraction of the mass of a galaxy. Microlensing allows the study of objects that emit little or no light.
When a distant star or [[quasar]] gets sufficiently aligned with a massive compact foreground object, the bending of light due to its gravitational field, as discussed by [[Einstein]] in 1915, leads to two distorted unresolved images resulting in an observable magnification. The time-scale of the transient brightening depends on the mass of the foreground object as well as on the relative proper motion between the background 'source' and the foreground 'lens' object.
A '''T-aerial''' or '''flat-top aerial''' is a simple wire radio aerial ([[antenna (radio)|antenna]])<ref name="Graf">{{cite book
| last = Graf
| first = Rudolf F.
| authorlink =
| coauthors =
| title = Modern dictionary of electronics, 7th Ed.
| isbn = 0-7506-9866-7}}</ref> used in the [[very low frequency|VLF]], [[low frequency|LF]], [[medium frequency|MF]] and [[shortwave]] bands.<ref name="Chatterjee" >{{cite book
| accessdate = 2012-02-23}}</ref> T-aerials are widely used as receiving aerials for [[shortwave listening]], and transmitting aerials for [[amateur radio]] stations<ref name="ARRL">{{cite book
| last = Straw
| first = R. Dean, Ed.
| authorlink =
| coauthors =
| title = The ARRL Antenna Book, 19th Ed.
| publisher = American Radio Relay League
| year = 2000
| location = USA
| pages = 6.36
| url =
| doi =
| id =
| isbn = 0-87259-817-9}}</ref> and [[long wave]] and [[medium wave]] broadcasting stations.
Since microlensing observations do not rely on radiation received from the lens object, this effect therefore allows astronomers to study massive objects no matter how faint. It is thus an ideal technique to study the galactic population of such faint or dark objects as [[brown dwarfs]], [[red dwarfs]], [[planets]], [[white dwarfs]], [[neutron stars]], [[black holes]], and
It consists of a horizontal wire suspended between two [[radio masts and towers|radio masts]] or buildings and insulated from them at the ends.<ref name="Graf" /><ref name="Edwards" /> A vertical wire is connected to the center of the horizontal wire and hangs down close to the ground, where it is connected to the [[transmitter]] or [[radio receiver|receiver]]. The two wires form a 'T' shape, hence the name. The transmitter power is applied, or the receiver is connected, between the bottom of the vertical wire and a [[ground (electricity)|ground]] connection. Sometimes multiple parallel horizontal wires are used, connected together at the center wire.
[[Massive compact halo object|Massive Compact Halo Objects]]. Moreover, the microlensing effect is wavelength-independent, allowing study of source objects that emit any kind of electromagnetic radiation.
Microlensing by an isolated object was first detected in 1989. Since then, microlensing has been used to constrain the nature of the [[dark matter]], detect [[extrasolar planets]], study [[limb darkening]] in distant stars, constrain the [[binary star]] population, and constrain the structure of the Milky Way's disk. Microlensing has also been proposed as a means to find dark objects like brown dwarfs and black holes, study [[sunspot|starspots]], measure stellar rotation, and probe [[quasars]]<ref name="W2006">{{Cite arxiv| year=2006|title=Gravitational Lensing: Strong, Weak and Micro|periodical=Saas-Fee Lectures, Springer-Verlag|eprint=astro-ph/0604278| author1=Joachim Wambsganss| class=astro-ph| doi=10.1007/978-3-540-30310-7_4| volume=33| pages=453–540| chapter=Gravitational Microlensing| series=Saas-Fee Advanced Courses| isbn=978-3-540-30309-1}}</ref><ref>{{Cite journal| last=Kochanek| year=2004|title=Quantitative Interpretation of Quasar Microlensing Light Curves|journal=The Astrophysical Journal|volume=605 |page=58|arxiv=astro-ph/03074223|doi=10.1086/382180|first1=C. S.|bibcode=2004ApJ...605...58K}}</ref> including their [[accretion disks]].<ref>{{Cite journal|last=Poindexter et al.| year=2008|title=The Spatial Structure of An Accretion Disk|first3=Christopher S.|last3=Kochanek|journal=The Astrophysical Journal,|first2=Nicholas|volume=673|issue= |last2=Morgan| page=34|arxiv=0707.0003|doi=10.1086/524190|first1=Shawn|bibcode=2008ApJ...673...34P}}</ref><ref>{{Cite journal|last=Eigenbrod et al.| year=2008|title=Microlensing variability in the gravitationally lensed quasar QSO 2237+0305 = the Einstein Cross. II. Energy profile of the accretion disk|journal= Astronomy & Astrophysics|volume=490|issue= 3| page=933|arxiv=0810.0011 |bibcode = 2008A&A...490..933E |doi = 10.1051/0004-6361:200810729|first1=A.|last2=Courbin|first2=F.|last3=Meylan|first3=G.|last4=Agol|first4=E.|last5=Anguita|first5=T.|last6=Schmidt|first6=R. W.|last7=Wambsganss|first7=J. }}</ref><ref>{{Cite journal| last=Mosquera et al.| year=2009|title=Detection of chromatic microlensing in Q 2237+0305 A|first3=E.|last3=Mediavilla|journal=The Astrophysical Journal,|first2=J. A.|volume=691|issue= 2| last2=Muñoz| page=1292|arxiv=0810.1626|doi=10.1088/0004-637X/691/2/1292|first1=A. M.|bibcode=2009ApJ...691.1292M}}</ref><ref>{{cite journal| last1=Floyd ''et al.''|year=2009|title=The accretion disc in the quasar SDSS J0924+0219| pages=233–239|volume=398|doi=10.1111/j.1365-2966.2009.15045.x| journal=Monthly Notices of the Royal Astronomical Society|arxiv=0905.2651|bibcode=2009MNRAS.398..233F| first1=David J. E.| last2=Bate| first2=N. F.| last3=Webster| first3=R. L.}}</ref>
The T-aerial functions as a [[monopole antenna]] with capacitive top-loading; other antennas in this category include the inverted-L, [[umbrella antenna|umbrella]], delta, and triatic antennas. It was invented during the first decades of radio, the [[wireless telegraphy]] era before 1920.
==How it works==
==How it works==
[[File:T antenna vs vertical antenna.svg|thumb|upright=1.5|RF current distributions <font color="red">''(red)''</font> in a vertical antenna ''(a)'' and the T antenna ''(b)'', showing how the horizontal wire serves to improve the efficiency of the vertical radiating wire.<ref name="Huang" /> The width of the red area perpendicular to the wire at any point is proportional to the current. At resonance the current is the tail part of a sinusoidal [[standing wave]]. In the vertical antenna, the current must go to zero at the top. In the T, the current flows into the horizontal wire, increasing the current in the top part of the vertical wire. The [[radiation resistance]] and thus the radiated power in each, is proportional to the square of the area of the vertical part of the current distribution.]]
Microlensing is based on the [[gravitational lens]] effect. A massive object (the lens) will bend the light of a bright background object (the source). This can generate multiple distorted, magnified, and brightened images of the background source.<ref>{{cite journal|author1=Refsdal, S.|title=The gravitational lens effect|journal=Monthly Notices of the Royal Astronomical Society|volume=128|page=295|year=1964|bibcode=1964MNRAS.128..295R}}</ref>
When the length of the wire segments are shorter than a quarter [[wavelength]] (λ/4) of the radio waves, as is typical for use below 1 MHz, the antenna functions as a vertical [[electrical length|electrically short]] [[monopole antenna]] with capacitive top-loading.<ref name="Rudge" /> Because the two arms of the "T" have equal but oppositely-directed currents in them, which causes the radio waves from them to cancel far from the antenna, and because of similar cancelling ground currents, the horizontal wire radiates little radio power.<ref name="Rudge, 1983, p.554">[http://books.google.com/books?id=QjYtNJZmWLEC&pg=PA546 Rudge, 1983, p.554]</ref> Instead it serves to add [[capacitance]] to the top of the antenna.<ref name="Huang">{{cite book
| isbn = 0-470-51028-5}}</ref><ref name="Rudge, 1983, p.554"/> This increases the currents in the upper portion of the vertical wire ''(see drawing at right)'', increasing the [[radiation resistance]] and thus its efficiency,<ref name="Huang" /> allowing it to radiate more power, or in a receiving antenna be more sensitive to incoming radio signals. The top load wire can increase radiated power by 2 to 4 times (3 to 6 dB).
However, the antenna is still typically not as efficient as a full-height λ/4 vertical [[Monopole antenna|monopole]],<ref name="ARRL" /> and has a higher [[Q factor|Q]] and thus a narrower [[bandwidth (signal processing)|bandwidth]]. T antennas are typically used at low frequencies where it is not practical to build a quarter-wave vertical antenna because of its height,<ref name="Edwards" /><ref name="Griffith">{{cite book
| last = Griffith
| first = B. Whitfield
| authorlink =
| coauthors =
| title = Radio-Electronic Transmission Fundamentals, 2nd Ed.
| isbn = 1-884932-13-4}}</ref> and the vertical radiating wire is often very [[Electrical length|electrically short]], only a small fraction of a wavelength long, 0.1λ or less. Since the radiation resistance and efficiency increases with height, the antenna should be suspended as high as possible.
Microlensing is caused by the same physical effect as strong lensing and weak lensing, but it is studied using very different observational techniques. In strong and weak lensing, the mass of the lens is large enough (mass of a galaxy or a galaxy cluster) that the displacement of light by the lens can be resolved with a high resolution telescope such as the [[Hubble Space Telescope]]. With microlensing, the lens mass is too low (mass of a planet or a star) for the displacement of light to be observed easily, but the apparent brightening of the source may still be detected. In such a situation, the lens will pass by the source in a reasonable amount of time, seconds to years instead of millions of years. As the alignment changes, the source's apparent brightness changes, and this can be monitored to detect and study the event. Thus, unlike with strong and weak gravitational lenses, a microlensing event is a transient phenomenon from a human timescale perspective.<ref>{{cite journal|author1=Paczynski, B.|title=Gravitational microlensing by the galactic halo|journal=Astrophysical Journal|volume=304|page=1|year=1986|doi=10.1086/164140|bibcode=1986ApJ...304....1P}}</ref>
To increase the top-load capacitance, several parallel horizontal wires are often used, connected together at the center where the vertical wire attaches.<ref name="ARRL" /> This increases the radiation resistance, and thus efficiency and bandwidth. The capacitance does not increase proportionally with the number of wires, however, because each wire's electric field is partially shielded from the ground by proximity to the adjacent wires.<ref name="ARRL" />
Unlike with strong and weak lensing, no single observation can establish that microlensing is occurring. Instead the rise and fall of the source brightness must be monitored over time using [[photometry (astronomy)|photometry]]. This function of brightness versus time is known as a [[light curve]]. A typical microlensing light curve is shown below: [[Image:Gravitational.Microlensing.Light.Curve.OGLE-2005-BLG-006.png|700px|center|Typical light curve of gravitational microlensing event (OGLE-2005-BLG-006) with its model fitted (red)]]
==Radiation pattern==
Since the vertical wire is the actual radiating element, the antenna radiates [[vertical polarization|vertically polarized]] radio waves in an [[omnidirectional antenna|omnidirectional]] [[radiation pattern]], with equal power in all azimuthal directions.<ref name="Barclay">{{cite book
| isbn = 0-85296-102-2}}</ref> The axis of the horizontal wire makes little difference. The power is maximum in a horizontal direction or at a shallow elevation angle, decreasing to zero at the zenith. This makes it a good antenna at LF or MF frequencies, which propagate as [[ground wave]]s with vertical polarization, but it also radiates enough power at higher elevation angles to be useful for [[sky wave]] ("skip") communication. The effect of poor ground conductivity is generally to tilt the pattern up, with the maximum signal strength at a higher elevation angle.
A typical microlensing event like this one has a very simple shape, and only one physical parameter can be extracted: the time scale, which is related to the lens mass, distance, and velocity. There are several effects, however, that contribute to the shape of more atypical lensing events:
==Transmitting antennas==
[[Image:Titanic antenne T 01.JPG|thumb|upright=2.0|One of the first uses of T-aerials in the early 20th century was on ships, since they could be strung between masts. This is the antenna of the RMS Titanic, which broadcast the rescue call during her sinking in 1912. It was a multiwire T with a 50 m vertical wire and four 120 m horizontal wires. ]]
* Lens mass distribution. If the lens mass is not concentrated in a single point, the light curve can be dramatically different, particularly with [[Caustic (optics)|caustic]]-crossing events, which may exhibit strong spikes in the light curve. In microlensing, this can be seen when the lens is a [[binary star]] or a [[Extrasolar planet|planetary system]].
Since it is shorter than λ/4 the T antenna has a high [[capacitive reactance]]. In transmitting antennas, to make the antenna [[resonant]] so it can be driven efficiently, this capacitance must be canceled out by adding an [[inductor]], a [[loading coil]], in series with the bottom of the antenna. Particularly at lower frequencies, the high inductance and capacitance compared to its low radiation resistance makes the loaded antenna behave like a high [[Q factor|Q]] [[tuned circuit]], with a narrow bandwidth over which it will remain [[impedance matching|impedance matched]] to the transmission line, compared to a λ/4 monopole. To operate over a large frequency range the loading coil often must be adjustable, and adjusted when the frequency is changed to keep the [[standing wave ratio|SWR]] low. The high Q also causes high voltages and currents on the antenna, roughly Q times the driving-point voltage and current. The insulators at the ends must be designed to withstand these voltages. In high power transmitters the output power is often limited by the onset of [[corona discharge]] on the wires.<ref name="AntennaReactance" >{{cite web
* Finite source size. In extremely bright or quickly-changing microlensing events, like caustic-crossing events, the source star cannot be treated as an infinitesimally small point of light: the size of the star's disk and even [[limb darkening]] can modify extreme features.
| last = LaPorte
* [[Parallax]]. For events lasting for months, the motion of the Earth around the Sun can cause the alignment to change slightly, affecting the light curve.
| first = Edmund A.
| authorlink =
| coauthors =
| title = Antenna Reactance
| work = Radio Antenna Engineering
| publisher = [http://vias.org Virtual Institute of Applied Science]
Most focus is currently on the more unusual microlensing events, especially those that might lead to the discovery of extrasolar planets. Although it has not yet been observed, another way to get more information from microlensing events that may soon be feasible involves measuring the [[Astrometry|astrometric]] shifts in the source position during the course of the event<ref>{{cite journal|author1=Boden, A. F.|author2=Shao, M.|author3=van Buren, D.|title=Astrometric Observation of MACHO Gravitational Microlensing|journal=Astrophysical Journal|volume=502|issue=2|page=538|year=1998|doi=10.1086/305913|bibcode=1998ApJ...502..538B|arxiv = astro-ph/9802179 }}</ref> and even resolving the separate images with [[Interferometry#astro|interferometry]].<ref>{{cite journal|bibcode=2001A&A...375..701D|arxiv = astro-ph/0108178 |doi = 10.1051/0004-6361:20010783|title=Resolving gravitational microlensing events with long-baseline optical interferometry|year=2001|last1=Delplancke|first1=F.|last2=Górski|first2=K. M.|last3=Richichi|first3=A.|journal=Astronomy and Astrophysics|volume=375|issue=2|pages=701–710 }}</ref>
At low frequencies the radiation resistance is very low; often less than an ohm,<ref name="ARRL" /><ref name="Balanis">{{cite book
| isbn = 1-118-20975-3}}</ref> so the efficiency is limited by other resistances in the antenna. The input power is divided between the radiation resistance and the ohmic resistances of the antenna-ground circuit, chiefly the coil and the ground. The resistance in the coil and particularly the ground system must be kept very low to minimize the power dissipated in them.
==Observing microlensing==
It can be seen that at low frequencies the design of the loading coil can be challenging:<ref name="ARRL" /> it must have high inductance but very low losses at the transmitting frequency (high [[Q]]), must carry high currents, withstand high voltages at its ungrounded end, and be adjustable.<ref name="Griffith" /> It is often made of [[litz wire]].<ref name="Griffith" />
In practice, because the alignment needed is so precise and difficult to predict, microlensing is very rare. Events, therefore, are generally found with surveys, which photometrically monitor tens of millions of potential source stars, every few days for several years. Dense background fields suitable for such surveys are nearby galaxies, such as the Magellanic Clouds and the Andromeda galaxy, and the Milky Way bulge. In each case, the lens population studied comprises the objects between Earth and the source field: for the bulge, the lens population is the Milky Way disk stars, and for external galaxies, the lens population is the Milky Way halo, as well as objects in the other galaxy itself. The density, mass, and location of the objects in these lens populations determines the frequency of microlensing along that line of sight, which is characterized by a value known as the optical depth due to microlensing. (This is not to be confused with the more common meaning of [[optical depth]], although it shares some properties.) The optical depth is, roughly speaking, the average fraction of source stars undergoing microlensing at a given time, or equivalently the probability that a given source star is undergoing lensing at a given time. The MACHO project found the optical depth toward the LMC to be 1.2×10<sup>−7</sup> or about 1 in 8,000,000,<ref>{{cite journal |author1=The MACHO collaboration |author2=Alcock |author3=Allsman |author4=Alves |author5=Axelrod |author6=Becker |author7=Bennett |author8=Cook |author9=Dalal |displayauthors=9 |title=The MACHO Project: Microlensing Results from 5.7 Years of LMC Observations |year=2000 |pages=281–307 |volume=542 |doi=10.1086/309512 |journal=Astrophys.J. |arxiv=astro-ph/0001272 |bibcode=2000ApJ...542..281A}}</ref> and the optical depth toward the bulge to be 2.43×10<sup>−6</sup> or about 1 in 400,000.<ref>{{cite journal |author1=Alcock |author2=Allsman |author3=Alves |author4=Axelrod |author5=Becker |author6=Bennett |author7=Cook |author8=Drake |author9=Freeman |displayauthors=9 |title=The MACHO project: Microlensing Optical Depth towards the Galactic Bulge from Difference Image Analysis |year=2000 |doi=10.1086/309484 |journal=Astrophysical Journal |bibcode=2000ApJ...541..734A |arxiv=astro-ph/0002510 |volume=541 |issue=2 |pages=734–766}}</ref>
At low frequencies the antenna requires a good low resistance [[ground (electricity)|ground]] to be efficient. The RF ground is typically constructed of a "star" of many radial copper cables buried about 1 ft. in the earth, extending out from the base of the vertical wire, and connected together at the center. The radials should ideally be long enough to extend beyond the [[displacement current]] region near the antenna. At VLF frequencies the resistance of the soil becomes a problem, and the radial ground system is sometimes raised and mounted a few feet above ground, insulated from it, to form a [[counterpoise]].
Complicating the search is the fact that for every star undergoing microlensing, there are thousands of stars changing in brightness for other reasons (about 2% of the stars in a typical source field are naturally [[variable stars]]) and other transient events (such as [[nova]]e and [[supernovae]]), and these must be weeded out to find true microlensing events. After a microlensing event in progress has been identified, the monitoring program that detects it often alerts the community to its discovery, so that other specialized programs may follow the event more intensively, hoping to find interesting deviations from the typical light curve. This is because these deviations – particularly ones due to exoplanets – require hourly monitoring to be identified, which the survey programs are unable to provide while still searching for new events. The question of how to prioritize events in progress for detailed followup with limited observing resources is very important for microlensing researchers today.
==Equivalent circuit==
The power radiated (or received) by an electrically short vertical antenna like the T is proportional to the square of the "effective height" of the antenna,<ref name="ARRL" /> so the antenna should be made as high as possible. Without the horizontal wire, the RF current distribution in the vertical wire would decrease linearly to zero at the top (see drawing ''a'' above), giving an effective height of half the physical height of the antenna. With an ideal "infinite capacitance" top load wire, the current in the vertical would be constant along its length, giving an effective height equal to the physical height, therefore increasing the power radiated fourfold. So the power radiated (or received) by a T antenna is up to four times that of a vertical monopole of the same height.
==History==
The [[radiation resistance]] of an ideal T antenna with very large top load capacitance is<ref name="Huang" />
where '''''h''''' is the height of the antenna, '''''λ''''' is the wavelength, and '''''I<sub>0</sub>''''' is the RMS input current in amperes.
In 1704 [[Isaac Newton]] suggested that a light ray could be deflected by gravity. In 1801 [[Johann Georg von Soldner]] calculated the amount of deflection of a light ray from a star under Newtonian gravity. In 1915 [[Einstein]] correctly predicted the amount of deflection under [[General Relativity]], which was twice the amount predicted by von Soldner. Einstein's prediction was validated by a 1919 expedition led by [[Arthur Stanley Eddington|Arthur Eddington]], which was a great early success for General Relativity.<ref>Schneider, Ehlers, and Falco. ''Gravitational Lenses''. 1992.</ref> In 1924 [[Orest Chwolson]] found that lensing could produce multiple images of the star. A correct prediction of the concomitant brightening of the source, the basis for microlensing, was published in 1936 by Einstein.<ref>{{cite journal|last1=Einstein|first1=A.|title=Lens-Like Action of a Star by the Deviation of Light in the Gravitational Field|journal=Science|volume=84|issue=2188|year=1936|pmid=17769014|doi=10.1126/science.84.2188.506|bibcode = 1936Sci....84..506E|pages=506–7 }}</ref> Because of the unlikely alignment required, he concluded that "there is no great chance of observing this phenomenon". Gravitational lensing's modern theoretical framework was established with works by Yu Klimov (1963), Sidney Liebes (1964), and [[Sjur Refsdal]] (1964).<ref name="W2006"/>
The equivalent circuit of the antenna (including loading coil) is the series combination of the capacitive reactance of the antenna, the inductive reactance of the loading coil, and the radiation resistance and the other resistances of the antenna-ground circuit. So the input impedance is
Gravitational lensing was first observed in 1979, in the form of a quasar lensed by a foreground galaxy. That same year Kyongae Chang and Sjur Refsdal showed that individual stars in the lens galaxy could act as smaller lenses within the main lens, causing the source quasar's images to fluctuate on a timescale of months.<ref>{{cite journal|last1=Chang|first1=K.|last2=Refsdal|first2=S.|title=Flux variations of QSO 0957 + 561 A, B and image splitting by stars near the light path|journal=Nature|volume=282|issue=5739|page=561|year=1979|doi=10.1038/282561a0|bibcode = 1979Natur.282..561C }}</ref> [[Bohdan Paczyński]] first used the term "microlensing" to describe this phenomenon. This type of microlensing is difficult to identify because of the intrinsic variability of quasars, but in 1989 Mike Irwin et al. published detection of microlensing in [[Huchra's Lens]].
In 1986, Paczyński proposed using microlensing to look for [[dark matter]] in the form of massive compact halo objects (MACHOs) in the [[dark matter halo|Galactic halo]], by observing background stars in a nearby galaxy. Two groups of particle physicists working on dark matter heard his talks and joined with astronomers to form the Anglo-Australian MACHO collaboration<ref>[http://wwwmacho.mcmaster.ca mcmaster.ca]</ref> and the French EROS<ref>[http://eros.in2p3.fr/ eros.in2p3.fr]</ref> collaboration.
At resonance the capacitive reactance of the antenna is cancelled by the loading coil so the input impedance at resonance '''''z<sub>0</sub>''''' is just the sum of the resistances in the antenna circuit<ref name="RadiationEfficiency" >{{cite web
| last = LaPorte
| first = Edmund A.
| authorlink =
| coauthors =
| title = Radiation Efficiency
| work = Radio Antenna Engineering
| publisher = [http://vias.org Virtual Institute of Applied Science]
In 1986, [[Robert J. Nemiroff]] predicted the likelihood of microlensing<ref>{{cite journal |last=Nemiroff |first=Robert J. |title=Random gravitational lensing |journal=Astrophysics and Space Science |date=June 1986 |volume=123 |issue=2 |pages=381-387 |doi=10.1007/BF00653957 |url=http://articles.adsabs.harvard.edu/full/1986Ap%26SS.123..381N |accessdate=27 January 2014}}</ref> and calculated basic microlensing induced light curves for several possible lens-source configurations in his 1987 thesis.<ref>{{cite journal|last=Nemiroff|first=Robert J.|title=Prediction and analysis of basic gravitational microlensing phenomena|date=December 1987 |url=http://adsabs.harvard.edu/abs/1987PhDT........12N|accessdate=27 January 2014}}</ref>
In 1991 Mao and Paczyński suggested that microlensing might be used to find binary companions to stars, and in 1992 Gould and Loeb demonstrated that microlensing can be used to detect exoplanets. In 1992, Paczyński founded the OGLE microlensing experiment,<ref>[http://ogle.astrouw.edu.pl/ OGLE homepage at ogle.astrouw.edu.pl]</ref> which began searching for events in the direction of the [[Galactic center|Galactic bulge]].
So the efficiency ''η'' of the antenna, the ratio of radiated power to input power from the feedline, is
The first two microlensing events in the direction of the [[Large Magellanic Cloud]] that might be caused by dark matter were reported in back to back [[Nature (journal)|Nature]] papers by MACHO<ref>{{cite journal|doi=10.1038/365621a0|title=Possible gravitational microlensing of a star in the Large Magellanic Cloud|year=1993|last1=Alcock|first1=C.|last2=Akerlof|first2=C. W.|last3=Allsman|first3=R. A.|last4=Axelrod|first4=T. S.|last5=Bennett|first5=D. P.|last6=Chan|first6=S.|last7=Cook|first7=K. H.|last8=Freeman|first8=K. C.|last9=Griest|first9=K. |displayauthors=9 |journal=Nature|volume=365|issue=6447|pages=621–623|arxiv = astro-ph/9309052 |bibcode = 1993Natur.365..621A }}</ref> and EROS<ref>{{cite journal|doi=10.1038/365623a0|title=Evidence for gravitational microlensing by dark objects in the Galactic halo|year=1993|last1=Aubourg|first1=E.|last2=Bareyre|first2=P.|last3=Bréhin|first3=S.|last4=Gros|first4=M.|last5=Lachièze-Rey |first5=M. |last6=Laurent |first6=B. |last7=Lesquoy |first7=E. |last8=Magneville |first8=C. |last9=Milsztajn |first9=A. |displayauthors=9 |journal=Nature|volume=365|issue=6447|pages=623–625|bibcode = 1993Natur.365..623A }}</ref> in 1993, and in the following years, events continued to be detected. The MACHO collaboration ended in 1999. Their data refuted the hypothesis that 100% of the dark halo comprises MACHOs, but they found a significant unexplained excess of roughly 20% of the halo mass, which might be due to MACHOs or to lenses within the Large Magellanic Cloud itself.<ref>{{cite journal |author1=Alcock, C. |author2=Allsman, R. A. |author3=Alves, D. R. |author4=Axelrod, T. S. |author5=Becker, A. C. |author6=Bennett, D. P. |author7=Cook, K. H. |author8=Dalal, N. |author9=Drake, A. J. |displayauthors=9 |title=The MACHO Project: Microlensing Results from 5.7 Years of Large Magellanic Cloud Observations |journal=The Astrophysical Journal |volume=542 |page=281 |year=2000 |doi=10.1086/309512 |bibcode=2000ApJ...542..281A |arxiv=astro-ph/0001272}}</ref>
EROS subsequently published even stronger upper limits on MACHOs,<ref>{{cite journal |bibcode=2007A&A...469..387T |arxiv=astro-ph/0607207 |doi=10.1051/0004-6361:20066017 |title=Limits on the Macho content of the Galactic Halo from the EROS-2 Survey of the Magellanic Clouds |year=2007 |last1=Tisserand |first1=P. |last2=Le Guillou |first2=L. |last3=Afonso |first3=C. |last4=Albert |first4=J. N. |last5=Andersen |first5=J. |last6=Ansari |first6=R. |last7=Aubourg |first7=É. |last8=Bareyre |first8=P. |last9=Beaulieu |first9=J. P. |displayauthors=9 |journal=Astronomy and Astrophysics|volume=469|issue=2|pages=387–404}}</ref> and it is currently uncertain as to whether there is any halo microlensing excess that could be due to dark matter at all. The SuperMACHO project<ref>[http://www.ctio.noao.edu/supermacho/ An NOAO Long Term Survey with the MOSAIC Imager on the Blanco 4 meter telescope]. Ctio.noao.edu (2005-01-03). Retrieved 2011-05-22.</ref> currently underway seeks to locate the lenses responsible for MACHO's results.
Despite not solving the dark matter problem, microlensing has been shown to be a useful tool for many applications. Hundreds of microlensing events are detected per year toward the [[Galactic bulge]], where the microlensing optical depth (due to stars in the Galactic disk) is about 20 times greater than through the Galactic halo. In 2007, the OGLE project identified 611 event candidates, and the MOA project (a Japan-New Zealand collaboration)<ref>[http://www.phys.canterbury.ac.nz/moa/index.html Microlensing Observations in Astrophysics]</ref> identified 488 (although not all candidates turn out to be microlensing events, and there is a significant overlap between the two projects). In addition to these surveys, follow-up projects are underway to study in detail potentially interesting events in progress, primarily with the aim of detecting extrasolar planets. These include MiNDSTEp,<ref>[http://www.mindstep-science.org/]</ref> RoboNet,<ref>[http://robonet.lcogt.net/ RoboNet-II]</ref> MicroFUN <ref>[http://www.astronomy.ohio-state.edu/~microfun/ Microlensing Follow-up Network]</ref> and PLANET.<ref>[http://planet.iap.fr/ μFUN-PLANET collaboration]</ref>
where
:'''''R<sub>C</sub>''''' is the ohmic resistance of the antenna conductors (copper losses)
:'''''R<sub>D</sub>''''' is the equivalent series dielectric losses
:'''''R<sub>L</sub>''''' is the equivalent series resistance of the loading coil
:'''''R<sub>G</sub>''''' is the resistance of the ground system
:'''''R<sub>R</sub>''''' is the radiation resistance
:'''''C''''' is the capacitance of the antenna at the input terminals
:'''''L''''' is the inductance of the loading coil
==Mathematics==
It can be seen that, since the radiation resistance is usually very low, the major design problem is to keep the other resistances in the antenna-ground system low to obtain the highest efficiency.<ref name="RadiationEfficiency" />
The mathematics of microlensing, along with modern notation, are described by Gould<ref>{{cite journal|last1=Gould|first1=Andrew|title=A Natural Formalism for Microlensing|journal=The Astrophysical Journal|volume=542|issue=2|page=785|year=2000|doi=10.1086/317037|bibcode=2000ApJ...542..785G|arxiv = astro-ph/0001421 }}</ref> and we use his notation in this section, though other authors have used other notation. The [[Einstein radius]], also called the Einstein angle, is the [[Angular diameter|angular radius]] of the [[Einstein ring]] in the event of perfect alignment. It depends on the lens mass M, the distance of the lens d<sub>L</sub>, and the distance of the source d<sub>S</sub>:
==Multiple-tuned antenna==
The "multiple-tuned antenna" is a variant of the T antenna used in high power low frequency transmitters to reduce ground power losses.<ref name="Griffith" /> It consists of a long capacitive top-load consisting of multiple parallel wires supported by a line of transmission towers, sometimes several miles long. Several vertical radiator wires hang down from the top-load, each attached to its own ground through a loading coil. The antenna is driven either at one of the radiator wires, or more often at one end of the top-load, by bringing the wires of the top-load diagonally down to the transmitter. Although the vertical wires are separated, the distance between them is small compared to the length of the LF waves, so the currents in them are in phase and they can be considered as one radiator. Since the antenna current flows into the ground through N parallel grounds rather than one, the equivalent ground resistance, and therefore the power dissipated in the ground, is reduced to 1/N that of a simple T antenna.<ref name="Griffith" />
<math>\theta_E = \sqrt{\frac{4GM}{c^2} \frac{d_S - d_L}{d_S d_L}}</math> (in radians)
==See also==
*[[Dipole antenna]]
For M equal to the mass of the Sun, d<sub>L</sub> = 4000 parsecs, and d<sub>S</sub> = 8000 parsecs (typical for a Bulge microlensing event), the Einstein radius is 0.001 [[arcsecond]]s (1 milliarcsecond). By comparison, ideal Earth-based observations have [[Astronomical seeing|angular resolution]] around 0.4 arcseconds, 400 times greater. Since <math>\theta_E</math> is so small, it is not generally observed for a typical microlensing event, but it can be observed in some extreme events as described below.
*[[Longwave]]
*[[Mast radiator]]
Although there is no clear beginning or end of a microlensing event, by convention the event is said to last while the angular separation between the source and lens is less than <math>\theta_E</math>. Thus the event duration is determined by the time it takes the apparent motion of the lens in the sky to cover an angular distance <math>\theta_E</math>. The Einstein radius is also the same order of magnitude as the angular separation between the two lensed images, and the astrometric shift of the image positions throughout the course of the microlensing event.
During a microlensing event, the brightness of the source is amplified by an amplification factor A. This factor depends only on the closeness of the alignment between observer, lens, and source. The unitless number u is defined as the angular separation of the lens and the source, divided by <math>\theta_E</math>. The amplification factor is given in terms of this value:
This function has several important properties. A(u) is always greater than 1, so microlensing can only increase the brightness of the source star, not decrease it. A(u) always decreases as u increases, so the closer the alignment, the brighter the source becomes. As u approaches infinity, A(u) approaches 1, so that at wide separations, microlensing has no effect. Finally, as u approaches 0, A(u) approaches infinity as the images approach an Einstein ring. For perfect alignment (u = 0), A(u) is theoretically infinite. In practice, finite source size effects will set a limit to how large an amplification can occur for very close alignment, but some microlensing events can cause a brightening by a factor of hundreds.
Unlike gravitational macrolensing where the lens is a galaxy or cluster of galaxies, in microlensing u changes significantly in a short period of time. The relevant time scale is called the Einstein time <math>t_E</math>, and it's given by the time it takes the lens to traverse an angular distance <math>\theta_E</math> relative to the source in the sky. For typical microlensing events, <math>t_E</math> is on the order of a few days to a few months. The function u(t) is simply determined by the Pythagorean theorem:
The minimum value of u, called u<sub>min</sub>, determines the peak brightness of the event.
In a typical microlensing event, the light curve is well fit by assuming that the source is a point, the lens is a single point mass, and the lens is moving in a straight line: the ''point source-point lens'' approximation. In these events, the only physically significant parameter that can be measured is the Einstein timescale <math>t_E</math>. Since this observable is a [[Degeneracy (mathematics)|degenerate]] function of the lens mass, distance, and velocity, we cannot determine these physical parameters from a single event.
However, in some extreme events, <math>\theta_E</math> may be measurable while other extreme events can probe an additional parameter: the size of the Einstein ring in the plane of the observer, known as the ''Projected Einstein radius'': <math>\tilde{r}_E</math>. This parameter describes how the event will appear to be different from two observers at different locations, such as a satellite observer. The projected Einstein radius is related to the physical parameters of the lens and source by
It is mathematically convenient to use the inverses of some of these quantities. These are the Einstein [[proper motion]]
<math>\vec{\mu}_E = {t_E}^{-1}</math>
and the Einstein [[parallax]]
<math>\vec{\pi}_E = {\tilde{r}_E}^{-1}</math>.
These vector quantities point in the direction of the relative motion of the lens with respect to the source. Some extreme microlensing events can only constrain one component of these vector quantities. Should these additional parameters be fully measured, the physical parameters of the lens can be solved yielding the lens mass, parallax, and proper motion as
<math>M=\frac{c^2}{4G}\theta_E \tilde{r}_E</math>
<math>\pi_L=\pi_E\theta_E + \pi_S</math>
<math>\mu_L=\mu_E\theta_E + \mu_S</math>
==Extreme microlensing events==
In a typical microlensing event, the light curve is well fit by assuming that the source is a point, the lens is a single point mass, and the lens is moving in a straight line: the ''point source-point lens'' approximation. In these events, the only physically significant parameter that can be measured is the Einstein timescale <math>t_E</math>. However, in some cases, events can be analyzed to yield the additional parameters of the Einstein angle and parallax: <math>\theta_E</math> and <math>\pi_E</math>. These include very high magnification events, binary lenses, parallax, and xallarap events, and events where the lens is visible.
===Events yielding the Einstein angle===
Although the Einstein angle is too small to be directly visible from a ground-based telescope, several techniques have been proposed to observe it.
If the lens passes directly in front of the source star, then the finite size of the source star becomes an important parameter. The source star must be treated as a disk on the sky, not a point, breaking the point-source approximation, and causing a deviation from the traditional microlensing curve that lasts as long as the time for the lens to cross the source, known as a ''finite source light curve''. The length of this deviation can be used to determine the time needed for the lens to cross the disk of the source star <math>t_S</math>. If the angular size of the source <math>\theta_S</math> is known, the Einstein angle can be determined as
These measurements are rare, since they require an extreme alignment between source and lens. They are more likely when <math>\theta_S/\theta_E</math> is (relatively) large, i.e., for nearby giant sources with slow-moving low-mass lenses close to the source.
In finite source events, different parts of the source star are magnified at different rates at different times during the event. These events can thus be used to study the [[limb darkening|limb-darkening]] of the source star.
===Binary lenses===
If the lens is a binary star with separation of roughly the Einstein radius, the magnification pattern is more complex than in the single star lenses. In this case, there are typically three images when the lens is distant from the source, but there is a range of alignments where two additional images are created. These alignments are known as ''caustics''. At these alignments, the magnification of the source is formally infinite under the point-source approximation.
Caustic crossings in binary lenses can happen with a wider range of lens geometries than in a single lens. Like a single lens source caustic, it takes a finite time for the source to cross the caustic. If this caustic-crossing time <math>t_S</math> can be measured, and if the angular radius of the source is known, then again the Einstein angle can be determined.
As in the single lens case when the source magnification is formally infinite, caustic crossing binary lenses will magnify different portions of the source star at different times. They can thus probe the structure of the source and its limb darkening.
An animation of a binary lens event can be found at [http://www.youtube.com/watch?v=_0u7DVbw4o4 this YouTube video].
===Events yielding the Einstein parallax===
In principle, the Einstein parallax can be measured by having two observers simultaneously observe the event from different locations, e.g., from the earth and from a distant spacecraft.<ref>{{cite journal |last1=Gould |first1=Andrew |title=MACHO velocities from satellite-based parallaxes |journal=The Astrophysical Journal |volume=421 |pages=L75 |year=1994 |doi=10.1086/187191 |bibcode=1994ApJ...421L..75G}}</ref> The difference in amplification observed by the two observers yields the component of <math>\vec{\pi}_E</math> perpendicular to the motion of the lens while the difference in the time of peak amplification yields the component parallel to the motion of the lens. This direct measurement was recently reported<ref>{{cite journal |last1=Dong |first1=Subo |last2=Udalski |first2=A. |last3=Gould |first3=A. |last4=Reach |first4=W. T. |last5=Christie |first5=G. W. |last6=Boden |first6=A. F. |last7=Bennett |first7=D. P. |last8=Fazio |first8=G. |last9=Griest |first9=K. |displayauthors=9 |title=First Space‐Based Microlens Parallax Measurement:SpitzerObservations of OGLE‐2005‐SMC‐001 |journal=The Astrophysical Journal |volume=664 |issue=2 |page=862 |year=2007 |doi=10.1086/518536 |bibcode=2007ApJ...664..862D |arxiv = astro-ph/0702240}}</ref> using the [[Spitzer Space Telescope]]. In extreme cases, the differences may even be measurable from small differences seen from telescopes at different locations on the earth.<ref>{{cite journal |author1=Hardy, S. J. |author2=Walker, M. A. |title=Parallax effects in binary microlensing events|journal=Monthly Notices of the Royal Astronomical Society |volume=276 |pages=L79 |year=1995 |bibcode=1995MNRAS.276L..79H}}</ref>
More typically, the Einstein parallax is measured from the non-linear motion of the observer caused by the rotation of the earth about the sun. It was first reported in 1995 <ref>{{cite journal |last1=Alcock |first1=C. |last2=Allsman |first2=R. A. |last3=Alves |first3=D. |last4=Axelrod |first4=T. S. |last5=Bennett |first5=D. P. |last6=Cook |first6=K. H. |last7=Freeman |first7=K. C. |last8=Griest |first8=K. |last9=Guern |first9=J. |displayauthors=9 |title=First Observation of Parallax in a Gravitational Microlensing Event|journal=The Astrophysical Journal |volume=454 |issue=2 |year=1995 |doi=10.1086/309783 |bibcode=1995ApJ...454L.125A |arxiv=astro-ph/9506114}}</ref> and has been reported in a handful of events since. Parallax in point-lens events can best be measured in long-timescale events with a large <math>\pi_E</math>—from slow-moving, low mass lenses which are close to the observer.
If the source star is a [[binary star]], then it too will have a non-linear motion which can also cause slight, but detectable changes in the light curve. This effect is known as [[Xallarap]] (parallax spelled backwards).
==Detection of extrasolar planets==
{{see also|Methods of detecting extrasolar planets#Gravitational microlensing}}
[[Image:Gravitational micro rev.svg|thumb|right|250px|Gravitational microlensing of an extrasolar planet]]
If the lensing object is a star with a planet orbiting it, this is an extreme example of a binary lens event. If the source crosses a caustic, the deviations from a standard event can be large even for low mass planets. These deviations allow us to infer the existence and determine the mass and separation of the planet around the lens. Deviations typically last a few hours or a few days. Because the signal is strongest when the event itself is strongest, high-magnification events are the most promising candidates for detailed study. Typically, a survey team notifies the community when they discover a high-magnification event in progress. Follow-up groups then intensively monitor the ongoing event, hoping to get good coverage of the deviation if it occurs. When the event is over, the light curve is compared to theoretical models to find the physical parameters of the system. The parameters that can be determined directly from this comparison are the mass ratio of the planet to the star, and the ratio of the star-planet angular separation to the Einstein angle. From these ratios, along with assumptions about the lens star, the mass of the planet and its orbital distance can be estimated.
[[File:Exoplanet Discovery Method Bar ML.png|thumb|250px|Exoplanets discovered using microlensing, by year, through 2010-01-13.]]
The first success of this technique was made in 2003 by both OGLE and MOA of the microlensing event [[OGLE-2003-BLG-235/MOA-2003-BLG-53|OGLE 2003–BLG–235 (or MOA 2003–BLG–53)]]. Combining their data, they found the most likely planet mass to be 1.5 times the mass of Jupiter.<ref>{{cite journal |author1=Bond |author2=Udalski |author3=Jaroszynski |author4=Rattenbury |author5=Paczynski |author6=Soszynski |author7=Wyrzykowski |author8=Szymanski |author9=Kubiak |displayauthors=9 |title=OGLE 2003-BLG-235/MOA 2003-BLG-53: A planetary microlensing event |year=2004 |pages=L155–L158 |issue=2 |volume=606 |doi=10.1086/420928 |journal=Astrophys.J. |arxiv=astro-ph/0404309 |bibcode=2004ApJ...606L.155B}}</ref> As of January 2011, eleven exoplanets have been detected by this method, including [[OGLE-2005-BLG-071Lb]],<ref>{{cite journal |author1=Udalski |author2=Jaroszynski |author3=Paczynski |author4=Kubiak |author5=Szymanski |author6=Soszynski |author7=Pietrzynski |author8=Ulaczyk |author9=Szewczyk |displayauthors=9 |title=A Jovian-mass Planet in Microlensing Event OGLE-2005-BLG-071 |year=2005 |doi=10.1086/432795 |journal=The Astrophysical Journal |volume=628 |issue=2 |pages=L109–L112 |arxiv=astro-ph/0505451 |bibcode=2005ApJ...628L.109U}}</ref> [[OGLE-2005-BLG-390Lb]],<ref>[http://ogle.astrouw.edu.pl/cont/4_main/epl/blg390/blg390.html OGLE website]</ref> [[OGLE-2005-BLG-169Lb]],<ref>{{cite journal |author1=Gould |author2=Udalski |author3=An |author4=Bennett |author5=Zhou |author6=Dong |author7=Rattenbury |author8=Gaudi |author9=Yock |displayauthors=9 |title=Microlens OGLE-2005-BLG-169 Implies Cool Neptune-Like Planets are Common |year=2006 |pages=L37–L40 |volume=644 |doi=10.1086/505421 |journal=Astrophys.J. |arxiv=astro-ph/0603276 |bibcode=2006ApJ...644L..37G}}</ref> two exoplanets around [[OGLE-2006-BLG-109L]],<ref>{{cite journal |author1=Gaudi |author2=Bennett |author3=Udalski |author4=Gould |author5=Christie |author6=Maoz |author7=Dong |author8=McCormick |author9=Szymanski |displayauthors=9 |title=Discovery of a Jupiter/Saturn Analog with Gravitational Microlensing |year=2008 |pages=927–930 |issue=5865 |volume=319 |doi=10.1126/science.1151947 |journal=Science |arxiv=0802.1920 |pmid=18276883 |bibcode=2008Sci...319..927G}}</ref> and [[MOA-2007-BLG-192Lb]].<ref>Paul Rincon, [http://news.bbc.co.uk/2/hi/science/nature/7432114.stm Tiniest extrasolar planet found], BBC, 2 June 2008</ref> Notably, at the time of its announcement in January 2006, the planet OGLE-2005-BLG-390Lb probably had the lowest mass of any known exoplanet orbiting a regular star, with a median at 5.5 times the mass of the Earth and roughly a factor two uncertainty. This record was contested in 2007 by [[Gliese 581 c]] with a minimal mass of 5 Earth masses, and since 2009 [[Gliese 581 e]] is the lightest known "regular" exoplanet, with minimum 1.9 Earth masses.
Comparing this method of detecting extrasolar planets with other techniques such as the [[Astronomical transit|transit]] method, one advantage is that the intensity of the planetary deviation does not depend on the planet mass as strongly as effects in other techniques do. This makes microlensing well suited to finding low-mass planets. It also allows to detect planets further away from the host star than most of the other methods. One disadvantage is that followup of the lens system is very difficult after the event has ended, because it takes a long time for the lens and the source to be sufficiently separated to resolve them separately.
==Microlensing experiments==
There are two basic types of microlensing experiments. "Search" groups use large-field images to find new microlensing events. "Follow-up" groups often coordinate telescopes around the world to provide intensive coverage of select events. The initial experiments all had somewhat risqué names until the formation of the PLANET group. There are current proposals to build new specialized microlensing satellites, or to use other satellites to study microlensing.
===Search collaborations===
* {{cite arxiv|eprint=astro-ph/9506101|author1=Alard|author2=Mao|author3=Guibert|title=Object DUO 2: A New Binary Lens Candidate|class=astro-ph|year=1995}} Photographic plate search of bulge. Remarkable for largely being the work of a single graduate student, Christophe Alard, for his Ph.D. Thesis.
* [http://eros.in2p3.fr/ Experience de Recherche des Objets Sombres (EROS)] (1993–2002) Largely French collaboration. EROS1: Photographic plate search of LMC: EROS2: CCD search of LMC, SMC, Bulge & spiral arms.
* [http://wwwmacho.mcmaster.ca/ MACHO] (1993–1999) Australia & US collaboration. CCD search of bulge and LMC.
* [[Optical Gravitational Lensing Experiment|Optical Gravitational Lensing Experiment (OGLE)]] ( 1992 – ), Polish collaboration established by Paczynski and Udalski. Dedicated 1.3m telescope in Chile run by the University of Warsaw. Targets on bulge and Magellanic Clouds.
* [[Microlensing Observations in Astrophysics|Microlensing Observations in Astrophysics (MOA)]] (1998 – ), Japanese-New Zealand collaboration. Dedicated 1.8m telescope in New Zealand. Targets on bulge and Magellanic Clouds.
* [http://www.ctio.noao.edu/supermacho/ SuperMACHO] (2001 – ), successor to the MACHO collaboration used 4 m CTIO telescope to study faint LMC microlenses.
* [http://planetquest.jpl.nasa.gov/Navigator/ao_support/gould.pdf SIM Microlensing Key Project] would have used the extremely high precision [[astrometry]] of the [[Space Interferometry Mission]] satellite to break the microlensing degeneracy and measure the mass, distance, and velocity of lenses. This satellite was postponed several times and finally cancelled in 2010.
* [http://wfirst.gsfc.nasa.gov/ Wide-Field Infrared Survey Telescope - Astrophysics Focused Telescope Assets (WFIRST - AFTA)] is to combine a microlensing survey with several other missions. The microlensing data will complement data from Kepler, with better sensitivity to planets like Earth that are not close in to their suns.
==References==
==References==
{{reflist|colwidth=30em}}
{{reflist}}
==External links==
{{Antenna Types}}
* [http://skyandtelescope.com/news/article_1667_1.asp Discovery of planet five times as massive as earth orbiting a star 20,000 light-years away]
{{Exoplanet}}
{{DEFAULTSORT:T-Aerial}}
[[Category:Power cables]]
[[Category:Radio frequency antenna types]]
{{DEFAULTSORT:Gravitational Microlensing}}
[[de:T-Antenne]]
[[Category:Effects of gravitation]]
[[fr:Antenne en T]]
[[Category:Gravitational lensing]]
Revision as of 06:05, 14 August 2014
Types of T antennas: (a) simple (b) multiwire. Red parts are insulators, grey are supporting towers.
It consists of a horizontal wire suspended between two radio masts or buildings and insulated from them at the ends.[1][4] A vertical wire is connected to the center of the horizontal wire and hangs down close to the ground, where it is connected to the transmitter or receiver. The two wires form a 'T' shape, hence the name. The transmitter power is applied, or the receiver is connected, between the bottom of the vertical wire and a ground connection. Sometimes multiple parallel horizontal wires are used, connected together at the center wire.
The T-aerial functions as a monopole antenna with capacitive top-loading; other antennas in this category include the inverted-L, umbrella, delta, and triatic antennas. It was invented during the first decades of radio, the wireless telegraphy era before 1920.
RF current distributions (red) in a vertical antenna (a) and the T antenna (b), showing how the horizontal wire serves to improve the efficiency of the vertical radiating wire.[6] The width of the red area perpendicular to the wire at any point is proportional to the current. At resonance the current is the tail part of a sinusoidal standing wave. In the vertical antenna, the current must go to zero at the top. In the T, the current flows into the horizontal wire, increasing the current in the top part of the vertical wire. The radiation resistance and thus the radiated power in each, is proportional to the square of the area of the vertical part of the current distribution.
When the length of the wire segments are shorter than a quarter wavelength (λ/4) of the radio waves, as is typical for use below 1 MHz, the antenna functions as a vertical electrically shortmonopole antenna with capacitive top-loading.[3] Because the two arms of the "T" have equal but oppositely-directed currents in them, which causes the radio waves from them to cancel far from the antenna, and because of similar cancelling ground currents, the horizontal wire radiates little radio power.[7] Instead it serves to add capacitance to the top of the antenna.[6][7] This increases the currents in the upper portion of the vertical wire (see drawing at right), increasing the radiation resistance and thus its efficiency,[6] allowing it to radiate more power, or in a receiving antenna be more sensitive to incoming radio signals. The top load wire can increase radiated power by 2 to 4 times (3 to 6 dB).
However, the antenna is still typically not as efficient as a full-height λ/4 vertical monopole,[5] and has a higher Q and thus a narrower bandwidth. T antennas are typically used at low frequencies where it is not practical to build a quarter-wave vertical antenna because of its height,[4][8] and the vertical radiating wire is often very electrically short, only a small fraction of a wavelength long, 0.1λ or less. Since the radiation resistance and efficiency increases with height, the antenna should be suspended as high as possible.
To increase the top-load capacitance, several parallel horizontal wires are often used, connected together at the center where the vertical wire attaches.[5] This increases the radiation resistance, and thus efficiency and bandwidth. The capacitance does not increase proportionally with the number of wires, however, because each wire's electric field is partially shielded from the ground by proximity to the adjacent wires.[5]
Radiation pattern
Since the vertical wire is the actual radiating element, the antenna radiates vertically polarized radio waves in an omnidirectionalradiation pattern, with equal power in all azimuthal directions.[9] The axis of the horizontal wire makes little difference. The power is maximum in a horizontal direction or at a shallow elevation angle, decreasing to zero at the zenith. This makes it a good antenna at LF or MF frequencies, which propagate as ground waves with vertical polarization, but it also radiates enough power at higher elevation angles to be useful for sky wave ("skip") communication. The effect of poor ground conductivity is generally to tilt the pattern up, with the maximum signal strength at a higher elevation angle.
Transmitting antennas
One of the first uses of T-aerials in the early 20th century was on ships, since they could be strung between masts. This is the antenna of the RMS Titanic, which broadcast the rescue call during her sinking in 1912. It was a multiwire T with a 50 m vertical wire and four 120 m horizontal wires.
Since it is shorter than λ/4 the T antenna has a high capacitive reactance. In transmitting antennas, to make the antenna resonant so it can be driven efficiently, this capacitance must be canceled out by adding an inductor, a loading coil, in series with the bottom of the antenna. Particularly at lower frequencies, the high inductance and capacitance compared to its low radiation resistance makes the loaded antenna behave like a high Qtuned circuit, with a narrow bandwidth over which it will remain impedance matched to the transmission line, compared to a λ/4 monopole. To operate over a large frequency range the loading coil often must be adjustable, and adjusted when the frequency is changed to keep the SWR low. The high Q also causes high voltages and currents on the antenna, roughly Q times the driving-point voltage and current. The insulators at the ends must be designed to withstand these voltages. In high power transmitters the output power is often limited by the onset of corona discharge on the wires.[10]
At low frequencies the radiation resistance is very low; often less than an ohm,[5][11] so the efficiency is limited by other resistances in the antenna. The input power is divided between the radiation resistance and the ohmic resistances of the antenna-ground circuit, chiefly the coil and the ground. The resistance in the coil and particularly the ground system must be kept very low to minimize the power dissipated in them.
It can be seen that at low frequencies the design of the loading coil can be challenging:[5] it must have high inductance but very low losses at the transmitting frequency (high Q), must carry high currents, withstand high voltages at its ungrounded end, and be adjustable.[8] It is often made of litz wire.[8]
At low frequencies the antenna requires a good low resistance ground to be efficient. The RF ground is typically constructed of a "star" of many radial copper cables buried about 1 ft. in the earth, extending out from the base of the vertical wire, and connected together at the center. The radials should ideally be long enough to extend beyond the displacement current region near the antenna. At VLF frequencies the resistance of the soil becomes a problem, and the radial ground system is sometimes raised and mounted a few feet above ground, insulated from it, to form a counterpoise.
Equivalent circuit
The power radiated (or received) by an electrically short vertical antenna like the T is proportional to the square of the "effective height" of the antenna,[5] so the antenna should be made as high as possible. Without the horizontal wire, the RF current distribution in the vertical wire would decrease linearly to zero at the top (see drawing a above), giving an effective height of half the physical height of the antenna. With an ideal "infinite capacitance" top load wire, the current in the vertical would be constant along its length, giving an effective height equal to the physical height, therefore increasing the power radiated fourfold. So the power radiated (or received) by a T antenna is up to four times that of a vertical monopole of the same height.
where h is the height of the antenna, λ is the wavelength, and I0 is the RMS input current in amperes.
The equivalent circuit of the antenna (including loading coil) is the series combination of the capacitive reactance of the antenna, the inductive reactance of the loading coil, and the radiation resistance and the other resistances of the antenna-ground circuit. So the input impedance is
At resonance the capacitive reactance of the antenna is cancelled by the loading coil so the input impedance at resonance z0 is just the sum of the resistances in the antenna circuit[12]
So the efficiency η of the antenna, the ratio of radiated power to input power from the feedline, is
where
RC is the ohmic resistance of the antenna conductors (copper losses)
RD is the equivalent series dielectric losses
RL is the equivalent series resistance of the loading coil
RG is the resistance of the ground system
RR is the radiation resistance
C is the capacitance of the antenna at the input terminals
L is the inductance of the loading coil
It can be seen that, since the radiation resistance is usually very low, the major design problem is to keep the other resistances in the antenna-ground system low to obtain the highest efficiency.[12]
Multiple-tuned antenna
The "multiple-tuned antenna" is a variant of the T antenna used in high power low frequency transmitters to reduce ground power losses.[8] It consists of a long capacitive top-load consisting of multiple parallel wires supported by a line of transmission towers, sometimes several miles long. Several vertical radiator wires hang down from the top-load, each attached to its own ground through a loading coil. The antenna is driven either at one of the radiator wires, or more often at one end of the top-load, by bringing the wires of the top-load diagonally down to the transmitter. Although the vertical wires are separated, the distance between them is small compared to the length of the LF waves, so the currents in them are in phase and they can be considered as one radiator. Since the antenna current flows into the ground through N parallel grounds rather than one, the equivalent ground resistance, and therefore the power dissipated in the ground, is reduced to 1/N that of a simple T antenna.[8]
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↑20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
