radio-lecture-wxp-pdf.pdf

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1、BasicofRadioInterferometryandImagingSynthesis武向平RadioInterferometry相位差平行光Lcos2t2cLLcosLVtik()tVtjk()RadioInterferometryVVcos[(tt)]VVcos(t)12XVV[cos(t)cos(2tt)]/212[VVcos(t)]/212AntennaResponseThesignalreceivedbyi-thantennaattimet,usu

2、allydenotedbytheresponsevoltageVoftheantenna,canbegenerallywrittenas2Vt()Gt()BsEstds()(,)iii感应电压增益响应函数入射电场Let’snowconsiderthek-thFouriercomponentofE,namely,itkEst(,)Esek()kThesignalobservedattimetandfrequencyisthusv/22Vtv(,)Gtv(,)BvsEsds(,)()ikikikk平面波感

3、应电压相距基线为L的天线接收到的信号Forthej-thantennaseparatedbyabaselineofLfromthei-thantenna,thesignalfromthesamecosmicsourceswillbedelayedbyatimeof∆twithrespecttothosereceivedbyi-thantennaduetogeometricconfigurationitk2Vtv(,)Gt(tv,)BvsEse(,)()dsjkjkjkk时延时延Visibility(可视度函数

4、)Thevisibilityisdefinedasthetime-averagedproductofthetwovoltages,i.e.,thecross-correlationof,inwhichtheraisedasteriskindicatesthecomplex*VVijconjugate:*VVij*2*2itkVGGBsEsds()()BsEsdse(')(')'ijijikjk2**2itkVGGBsEsds()()BsEsdse(')(')'ijijikj

5、kWeapproximatetheintegralsbythesumsofseriessuchthat***itkVijGGijBkEkBkEkei()1k()1j()2k()2kk122**itkGGijBkBkEki()j()k()ekwherewehaveusedthecoherenceconditionofastronomicalradiation.2*EkEk()()Ek()(kk)121122**itk2VGGBsBsEs()()()edsijijijkor2*2itkVG

6、GBsEs()()edsijijijk*2itkGGBsIse()()dsijij*Bs()BsBs()()ijijRadioInterferometryLsLtsccsLcos2t2cLLcosLLVtik()tVtjk()PhaseDifferenceWenowintroduceacoordinatesystemsuchthatthephaseinvisibilityfunctioncanbewrittenasLsLLt2vs2

7、(s)kkcc2(,,)(,,)uvwlmn2(ulvmwn)相位差在直角坐标系的表示方向余弦wTheunitdirectionvectorsisdefinedbyitsprojectionssonthe(u,v,w)axes.ThesecomponentsarecalledthenDirectionCosines.gbavmlcos()alLmcos()b22ncos()g1lmuThebaselinevectorLisspecifiedbyitscoordinates(u,v,w)(

8、measuredinwavelengths).b(uvw,,)referencepositionZwNorthPolecelestialequatorarrayplaneobserver’shorizonuvplane望远镜基线和uvw的坐标转换usinHcosH0LX1