The closure phase is an observable quantity in imaging astronomical interferometry, which allowed the use of interferometry with very long baselines. It forms the basis of the self-calibration approach to interferometric imaging. The observable which is usually used in most "closure phase" observations is actually the complex quantity called the triple product (or bispectrum). The closure phase is the phase (argument) of this complex quantity.
Roger Jennison developed this novel technique for obtaining information about visibility phases in an interferometer when delay errors are present. Although his initial laboratory measurements of closure phase had been done at optical wavelengths, he foresaw greater potential for his technique in radio interferometry. In 1958 he demonstrated its effectiveness with a radio interferometer, but it became widely used for long baseline radio interferometry only in 1974. A minimum of three antennas are required. This method was used for the first VLBI measurements, and a modified form of this approach ("Self-Calibration") is still used today. The "closure-phase" or "self-calibration" methods are also used to eliminate the effects of astronomical seeing in optical and infrared observations using astronomical interferometers.
A minimum of three antennas are required for closure phase measurements. In the simplest case, with three antennas in a line separated by the distances a1 and a2 shown in diagram at the right. The radio signals received are recorded onto magnetic tapes and sent to a laboratory such as the Very Long Baseline Array. The effective baselines for a source at an angle θ θ --> {\displaystyle \theta } will be x 1 = a 1 cos --> θ θ --> {\displaystyle x_{1}=a_{1}\cos \theta } , x 2 = a 2 cos --> θ θ --> {\displaystyle x_{2}=a_{2}\cos \theta } , and x 3 = ( a 1 + a 2 ) cos --> θ θ --> {\displaystyle x_{3}=(a_{1}+a_{2})\cos \theta } . When one mixes signals from two of antennas (compensating for a delay for the angle θ θ --> 0 {\displaystyle \theta _{0}} ) one observes interference signal with phase x ( θ θ --> ) − − --> x ( θ θ --> 0 ) . {\displaystyle x(\theta )-x(\theta _{0}).} Taking into account that signals may come from several sources, the complex interference signal is the Fourier transform P {\displaystyle P} of the power density of the sources.
The phases of the complex visibility of the radio source corresponding to baselines a1, a2 and a3 are denoted by ϕ ϕ --> 1 {\displaystyle \phi _{1}} , ϕ ϕ --> 2 {\displaystyle \phi _{2}} and ϕ ϕ --> 3 {\displaystyle \phi _{3}} respectively. These phases will contain errors resulting from εB and εC in the signal phases. The measured phases for baselines x1, x2 and x3, denoted ψ ψ --> 1 {\displaystyle \psi _{1}} , ψ ψ --> 2 {\displaystyle \psi _{2}} and ψ ψ --> 3 {\displaystyle \psi _{3}} , will be:
Jennison defined his observable O (now called the closure phase) for the three antennas as:
As the error terms cancel:
The closure phase is unaffected by phase errors at any of the antennas. Because of this property, it is widely used for aperture synthesis imaging in astronomical interferometry. For a point source, O {\displaystyle O} is 0; so O {\displaystyle O} carries information on the spatial distribution of the source. While | P ( x ) | {\displaystyle |P(x)|} may be measured directly, and the phase of P ( x ) {\displaystyle P(x)} cannot be found from 2-antennas VLBI, using 3 antennas one can find the phase of P ( x 1 ) P ( x 2 ) P ∗ ∗ --> ( x 1 + x 2 ) . {\displaystyle P(x_{1})P(x_{2})P^{*}(x_{1}+x_{2}).}
In most real observations, the complex visibilities are actually multiplied together to form the triple product instead of simply summing the visibility phases. The phase of the triple product is the closure phase.
In optical interferometry, the closure phase was first introduced by the bispectrum speckle interferometry,[citation needed] the principle of which is to compute the closure phase from the complex measurement instead of the phase itself:
The closure phase is then computed as the argument of this bispectrum:
This method of computation is robust to noise and allow to perform averaging even if the noise dominates the phase signal.
Example: even when power distribution of the source is symmetric, so P ( x ) {\displaystyle P(x)} is real, measuring | P ( x ) | {\displaystyle |P(x)|} still leaves the signs unknown. The closure phase allows finding the sign of P ( x 1 + x 2 ) {\displaystyle P(x_{1}+x_{2})} when signs of P ( x 1 ) {\displaystyle P(x_{1})} , P ( x 2 ) {\displaystyle P(x_{2})} are known. Since P ( x ) {\displaystyle P(x)} is positive for small x {\displaystyle x} , one can fully map how the sign changes, and calculate P ( x ) {\displaystyle P(x)} .
Aperture masks are often used on single telescopes to allow the extraction of closure phases from the images. Kernel-phases can be seen as a generalization of closure phase for redundant arrays in cases where the wavefront errors are low enough.
Frantz Martinache 2010 ApJ 724 464 doi:10.1088/0004-637X/724/1/464
2001 studio album by Aphex TwindrukQsStudio album by Aphex TwinReleased22 October 2001 (2001-10-22)Genre Drill 'n' bass[1][2] classical[3][4] DnB[5][3] electroacoustic[2] acid[2] techno[3] IDM[4] ambient[6] Length100:37LabelWarpProducerAphex TwinRichard D. James chronology 2 Remixes by AFX(2001) drukQs(2001) 26 Mixes for Cash(2003) Aphex Twin album chronology Richard D. James Album(1996…
Charity Shield FA 1908TurnamenCharity Shield FA Manchester United Queens Park Rangers Final Manchester United Queens Park Rangers 1 1 Tanggal27 April 1908StadionStamford Bridge, LondonPenonton6.000Ulangan Queens Park Rangers Manchester United 4 0 Tanggal29 Agustus 1908StadionStamford Bridge, LondonPenonton50.0001909 → Charity Shield FA 1908 adalah pertandingan sepak bola antara Manchester United dan Queens Park Rangers yang diselenggarakan pada 27 April 1908 di Stamford Bridge, London. Per…
El MVP de las Finales de la Conferencia Oeste de la NBA o el Trofeo Earvin Magic Johnson (The Earvin Magic Johnson Trophy) es un premio anual otorgado por la NBA al jugador más destacado de las Finales de la Conferencia Oeste. Entregado desde 2022, habitualmente se concede al jugador más destacado del equipo vencedor y lleva el nombre de la leyenda de los Lakers: Magic Johnson.[1] El trofeo levanta una bola de plata de ley, similar a los trofeos de los campeones de conferencia. El prime…
У Вікіпедії є статті про інших людей із прізвищем Сіссе. Карамоко Сіссе Особисті дані Народження 14 листопада 1988(1988-11-14) (35 років) Кубія, Гвінея Зріст 186 см Вага 78 кг Громадянство Гвінея Позиція нападник Інформація про клуб Поточний клуб «Юве Стабія» Професіональні
Cúmulo abierto Messier 36. Messier 36 (también conocido como M36 o NGC 1960) es un cúmulo abierto en la constelación de Auriga. Fue descubierto por Giovanni Batista Hodierna antes de 1654. El M36 está a una distancia de unos 4.100 años luz desde la Tierra y abarca unos 14 años luz de amplitud. Hay al menos sesenta miembros en el cúmulo. El cúmulo es muy similar a al cúmulo (M45) de Pléyades, y si estuviera a la misma distancia de la Tierra serían de magnitud similar. Sus estrellas, m…
الجرح المزمن معلومات عامة من أنواع جرح تعديل مصدري - تعديل الجرح المزمن هو الجرح الذي لا يكتمل برئه في مجموعة مراحل منتظمة وفي فترة زمنية يتوقع خلالها الشفاء منه كما هو الحال في معظم الجروح الأخرى؛ وبوجه عام فإن الجروح التي لا تلتئم في غضون ثلاثة أشهر غالبا ما تعتبر مز
هذه المقالة يتيمة إذ تصل إليها مقالات أخرى قليلة جدًا. فضلًا، ساعد بإضافة وصلة إليها في مقالات متعلقة بها. (يونيو 2013) آيريس (بالإنجليزية: Interferometric Reflectance Imaging Sensor -IRIS) هو مستشعر تصوير الانعكاسية بقياس التداخل (آيريس) هو جهاز كان يُعرف سابقًا باسم المستشعر البيولوجي لتصوير الان…
مايكل كودليتز (بالإنجليزية: Michael Cudlitz) معلومات شخصية الميلاد 29 ديسمبر 1964 (العمر 58 سنة)لونغ آيلند، نيويورك، الولايات المتحدة مواطنة الولايات المتحدة عدد الأولاد 2 الحياة العملية المدرسة الأم معهد كاليفورنيا للفنون المهنة ممثل اللغة الأم الإنجليزية اللغات الإن
غول خان (بالإنجليزية: Gul Khan) معلومات شخصية الميلاد 5 مارس 1973 (50 سنة) دلهي مواطنة الهند الحياة العملية المدرسة الأم الجامعة الملية الإسلامية المهنة منتجة أفلام، وكاتبة سيناريو، ومنتجة تلفزيونية المواقع الموقع الموقع الرسمي IMDB صفحتها على IMDB…
Buildings by Ludwig Mies van der Rohe Lange and Esters HousesHaus Lange Haus EstersHouse Lange and House Ester viewed from the streetGeneral informationTypeVillaArchitectural styleModernistLocationKrefeld, GermanyCoordinates51°20′49.26″N 6°34′57.29″E / 51.3470167°N 6.5825806°E / 51.3470167; 6.5825806Current tenantsKunstmuseen KrefeldConstruction started1928 (1928)Completed1930 (1930)Design and constructionArchitect(s)Ludwig Mies van der RoheReference…
رتينول رتينول رتينول رتينول الاسم النظامي (IUPAC) (2E,4E,6E,8E)-3,7-dimethyl-9-(2,6,6-trimethylcyclohex-1-enyl)nona-2,4,6,8-tetraen-1-ol المعرفات رقم CAS 68-26-8 Y بوب كيم (PubChem) 1071 مواصفات الإدخال النصي المبسط للجزيئات OC/C=C(/C=C/C=C(/C=C/C1=C(/CCCC1(C)C)C)C)C المعرف الكيميائي الدولي 1S/C20H30O/c1-16(8-6-9-17(2)13-15-21)11-12-19-18(3)10-7-14-20(19,4)5/h6,8-9,11-13,21H,7,10,14-15…
名古屋高速道路 名古屋高速3号大高線 地図 路線延長 12.1 km 開通年 1979年 - 2003年 接続する主な道路(記法) 都心環状線E87 知多半島道路E1A 伊勢湾岸自動車道C2 名古屋第二環状自動車道 ■テンプレート(■ノート ■使い方) ■PJ道路 名古屋高速3号大高線(なごやこうそく3ごうおおだかせん)は、愛知県名古屋市中区の鶴舞南JCTから、愛知県名古屋市緑区の名古屋南JCTへ至
List of flags associated with the Federated States of Micronesia This is a list of flags associated with the Federated States of Micronesia. National flags Flag Duration Use Description 1978–present Flag of the Federated States of Micronesia A flag in a 10:19 featuring four stars, arranged in a circle, on a blue field.[1][2][3][4] Flags of the States of Micronesia Flag Duration Use Description 1997–present Flag of Chuuk State 1981–present Flag of Kosrae 1992…
Dutch actor (1842–1925) Louis BouwmeesterBornLouis Frederik Johannes Bouwmeester(1842-09-05)5 September 1842Middelharnis, NetherlandsDiedApril 28, 1925(1925-04-28) (aged 82)Amsterdam, NetherlandsOccupationActor Louis Frederik Johannes Bouwmeester (5 September 1842 – 28 April 1925) was a Dutch actor best known for his Shakespeare interpretations.[1][2] He is also known as Louis Bouwmeester Sr. for distinction from his son. He performed several times in Vienna, London and …
King's College London was granted a royal charter in 1829 by its patron, King George IV. Portrait by Sir Thomas Lawrence The history of King's College London, on its own, spans over 190 years since it was founded as a 'university college' by royal charter in 1829.[1] However, its formation as a full 'university' would have to wait until 1836 as a part of the University of London. The full history, however, includes the medical schools that now constitute GKT School of Medical Education. …
London Underground station Bounds Green Station entranceBounds GreenLocation of Bounds Green in Greater LondonLocationBounds GreenLocal authorityLondon Borough of HaringeyManaged byLondon UndergroundNumber of platforms2Fare zone3 and 4OSIBowes Park[1]London Underground annual entry and exit2018 5.87 million[2]2019 5.99 million[3]2020 2.95 million[4]2021 2.51 million[5]2022 4.15 million[6]Railway companiesOriginal companyLondon Electric RailwayKey d…
Battle of LubiszewoPart of the War of the Gdańsk RebellionCommonwealth HussarDateApril 17, 1577LocationLubiszewo Tczewskie (near Gdańsk)Result Royal victoryBelligerents Polish–Lithuanian Commonwealth Principality of Transylvania City of DanzigCommanders and leaders Jan Zborowski Hans WinkelbruchStrength 1,450 cavalry1,050 infantry and artillery 10,000–12,000 of which 800 were cavalryCasualties and losses 88 killed100 wounded 4,420 killed5,000 capturedvteDanzig rebellion Lubieszów Elbing D…
Concordia-class cruise ship Costa Serena in 2008 History NameCosta Serena OwnerCarnival Corporation & plc OperatorCosta Crociere Port of registry Italy, Genoa Ordered1 October 2004 Cost€450 million (£372 million, US$570 million) Yard number6130 Laid down1 February 2005 Launched4 August 2006 Completed9 March 2007 In service2007 Identification Call sign: ICAZ IMO number: 9343132 MMSI number: 247187600 StatusIn service Notes[1][2] General characteristics Class and t…
Fictional character from Election Fictional character Tracy FlickElection characterReese Witherspoon as Tracy FlickFirst appearanceElection (1998)Created byTom PerrottaPortrayed byReese WitherspoonLucy Liu (voice)In-universe informationGenderFemaleOccupationHigh School StudentRelativesJudith Flick (mother, portrayed by Colleen Camp) Tracy Enid Flick is a fictional character who is the subject of the 1998 novel Election by Tom Perrotta and portrayed by Reese Witherspoon in the 1999 film adaptatio…
This article is about the district. For the town, see Kanpur. This article possibly contains original research. Please improve it by verifying the claims made and adding inline citations. Statements consisting only of original research should be removed. (April 2018) (Learn how and when to remove this template message) District of Uttar Pradesh in IndiaKanpur Nagar districtDistrict of Uttar PradeshClockwise from top-left: Kanpur Central Rail Station, IIT Kanpur Central Library, Nana Sahib statue…
Lokasi Pengunjung: 18.116.24.20