%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% TeX definitions of mathematical symbols and names used for the %%%%%% %%% Measuerement Equation of Generic Interferometer (MEGI) %%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\thisfile{~/aips++/nfra/megi-symbols.tex} % The following list is available as a LaTeX list of definitions. It % could be the start of an official AIPS++ list of symbol names, to % encourage (enforce?) consistency in all AIPS++ documents and code. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Some user-defined TeX commands: \newcommand{\tbt}[4] {\left(\begin{array}{cc}#1 & #2\\ #3 & #4 \end{array}\right)} \newcommand{\ddp}[2]{\frac {\partial #1}{\partial #2}} \newcommand{\ddpn}[3]{\frac {\partial^{#3}{#1}}{\partial{#2}^{#3}}} \newcommand{\dirprod}[2]{{#1}\otimes{#2}^\ast} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Naming system (method in the madness): % \mmName % Matrix % \mjName % Jones matrix (2x2) % \vvName % Vector % \ssName % subscript or superscript (e.g. \ssI: \Feed I) % \ccName % Coordinate (e.g. \ccL: Sky L-coordinate) % \aaName % Projected angle (e.g. \aaXY: from X-axis to Y-axis) % \ppName % Parameter % I,J % \Feed labels (e.g. \FeedI) % X,Y,R,L % Polarisation labels % A,B % \Receptor labels (e.g. \RcpB) % P,Q % \IFout labels (e.g. \IFP) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % \gloshead{Names of things for which there is a precise definition} % NB: Use a closing backslash (e.g. `\Receptot\ ') for interword space! \def\Receptor{{\sl receptor}} % Converts field to voltage (e.g. dipole) \def\Receptors{{{\Receptor}s}} % plural \def\Feed{{\sl feed}} % Logical e.m.-to-signal converter \def\Feeds{{{\Feed}s}} % plural \def\Antenna{{\sl antenna}} % Physical grouping of Feeds \def\Antennas{{{\Antenna}s}} % plural \def\IFchannel{{\sl IF-channel}} % Signal outputs from an \Feed \def\IFchannels{{{\IFchannel}s}} % plural \def\IFout{{\IFchannel}} % Old symbol (still supported) \def\IFouts{{\IFchannels}} % plural \def\Telescope{{\sl telescope}} % Entire instrument (e.g. WSRT, GBT) \def\Telescopes{{\Telescope}s} % plural \def\Interferometer{{\sl interferometer}} % Two \IFout's or two \Feed's \def\Interferometers{{{\Interferometer}s}} % plural \def\Visibility{{\sl visibility}} % 1-4 complex spectra, \def\Visibilities{{\sl visibilities}} % plural % output of an \Interferometer. \def\Projected{{\sl projected}} % Projected on sky plane (or on the % plane perpendicular to propagation) % \gloshead{Labels:} \def\FeedI{{\sf i}} % The `first' \Feed in an interferometer \def\FeedJ{{\sf j}} % The `second' \Feed in an interferometer \def\AntI{{\FeedI}} % old symbol, still supported \def\AntJ{{\FeedJ}} % old symbol, still supported \def\RcpA{{\sf a}} % The `first' dipole in a \Feed \def\RcpB{{\sf b}} % The `second' dipole in a \Feed \def\IFP{{\sf p}} % The `first' IF-channel from a \Feed \def\IFQ{{\sf q}} % The `second' IF-channel from a \Feed \def\RPol{{\sf r}} % r-pol \def\LPol{{\sf l}} % l-pol \def\XPol{{\ccX}} % x-pol \def\YPol{{\ccY}} % y-pol % \gloshead{Coordinate frames:} \def\ccT{{\sf t}} % time-coord \def\ccF{{\sf f}} % frequency-coord % Polarisation-frame (for electric polarisation vector): \def\ccX{{\sf x}} % x-coord \def\ccY{{\sf y}} % y-coord \def\ccZ{{\sf z}} % y-coord \def\ccXPol{{\XPol}} % x-pol-coord \def\ccYPol{{\YPol}} % y-pol-coord \def\ccRPol{{\RPol}} % r-pol-coord \def\ccLPol{{\LPol}} % l-pol-coord % Array-frame (for baseline vector): \def\ccU{{\sf u}} % u-coord \def\ccV{{\sf v}} % v-coord \def\ccW{{\sf w}} % w-coord \def\vvUVW{{\vec{u}}} % Projected baseline vector \def\ccGX{{\sf x}} % antenna position coord \def\ccGY{{\sf y}} % antenna position coord \def\ccGZ{{\sf z}} % antenna position coord \def\vvAntPos{{\vec{r}}} % Projected `Antenna' position vector % (Receptor phase centre?) \def\vvAntPosEl{{\sf r}} % element % Sky coord. frame (source positions) w.r.t. Delay Centre: \def\ccL{{\sf l}} % l-coord \def\ccM{{\sf m}} % m-coord \def\ccN{{\sf n}} % n-coord (=sqrt[1-l^2-m^2]) \def\vvLMN{{\vec{\rho}}} % Vector (l,m) in Sky frame \def\vvFTC{{\vvLMN_{ftc}}} % Fringe Tracking Centre (l,m,f) \def\vvMC{{\vvLMN_{mc}}} % Map centre (l,m) % Antenna coord. frame (l',m'), projected on the Sky: \def\ccLI{{\ccL^{'}_{\FeedI}}} % l'-coord of \Feed-frame \def\ccMI{{\ccM^{'}_{\FeedI}}} % m'-coord \def\ccLIO{{\ccL_{\FeedI{0}}}} % l-coord of origin of \Feed-frame i \def\ccMIO{{\ccM_{\FeedI{0}}}} % m-coord % Receptor coord. frames (l'',m''), projected on the Sky: \def\ccLIA{{\ccL^{''}_{{\FeedI\RcpA}}}} % l''-coord for \RcpA-frame \def\ccMIA{{\ccM^{''}_{{\FeedI\RcpA}}}} % m''-coord \def\ccLIAO{{\ccLI_{\RcpA{0}}}} % l'-coord of origin of \RcpA-frame \def\ccMIAO{{\ccMI_{\RcpA{0}}}} % m'-coord \def\ccLIB{{\ccL^{''}_{{\FeedI\RcpB}}}} % l''-coord for \RcpB-frame \def\ccMIB{{\ccM^{''}_{{\FeedI\RcpB}}}} % m''-coord \def\ccLIBO{{\ccLI_{\RcpB{0}}}} % l'-coord of origin of \RcpB-frame \def\ccMIBO{{\ccMI_{\RcpB{0}}}} % m'-coord % Projected angles between the various coord frames: \def\aaProj{{\gamma}} % Projected angle \def\aaXY{{\aaProj_{\ccX\ccY}}} % from Pol x-axis to Pol y-axis \def\aaLM{{\aaProj_{\ccL\ccM}}} % from Sky l-axis to Sky m-axis \def\aaLX{{\aaProj_{\ccL\ccX}}} % from Sky l-axis to Pol x-axis \def\aaLI{{\aaProj_{\ccL\FeedI}}} % from Sky l-axis to \Feed l'-axis \def\aaIA{{\aaProj_{\FeedI\RcpA}}} % from \Feed l'-axis to \RcpA l''-axis \def\aaIB{{\aaProj_{\FeedI\RcpB}}} % from \Feed l'-axis to \RcpB l''-axis \def\aaXI{{\aaProj_{\ccX\FeedI}}} % from x-axis to \Feed l'-axis \def\aaXA{{\aaProj_{\ccX\RcpA}}} % from x-axis to \RcpA l''-axis \def\aaYB{{\aaProj_{\ccY\RcpB}}} % from y-axis (!) to \RcpB l''-axis \def\aaXYexp{{\pi/2}} % from x-axis to y-axis \def\aaLMexp{{\pi/2}} % from l-axis to m-axis \def\aaLXexp{{\pi/2}} % from l-axis to x-axis \def\aaXIexp{{-\aaLX+\aaLI}} % x to l' \def\aaXAexp{{-\aaLX+\aaLI+\aaIA}} % x to l''(A) \def\aaYBexp{{-\aaXY-\aaLX+\aaLI+\aaIB}} % x to l''(B) % \gloshead{Miscellaneous parameters:} \def\ppHA{{HA}} % Hour Angle \def\ppDEC{{DEC}} % Declination \def\ppRA{{RA}} % Right Ascension \def\ppLAT{{LAT}} % Latitude (on the Earth) \def\ppParall{{\beta}} % parallactic angle (between great % circles through North Pole and Zenith) \def\ppFarad{{\chi}} % Faraday rotation angle (rad) \def\ppAmpl{{a}} % Amplitude \def\ppPhase{{\psi}} % Phase \def\ppPhaseZero{{\zeta}} % Phase-zero \def\ppRcpPosDev{{\phi}} % \Receptor pos. angle deviation \def\ppRcpEllDev{{\theta}} % \Receptor ellipticity deviation \def\ppDiposErr{{\ppRcpPosDev}} % old symbol, still supported \def\ppEllipt{{\ppRcpEllDev}} % old symbol, still supported \def\ppBellipt{{\epsilon}} % beam ellipticity (shape) factor \def\ppBsigma{{\sigma}} % sigma of gaussian beam % \gloshead{Jones Matrices (2x2):} \def\mjJones{{\sf J}} % Jones instrumental response matrix \def\mjJonesEl{{\sf j}} % matrix element \def\mjFrot{{\sf F}} % Faraday rotation matrix \def\mjFrotEl{{\sf f}} % matrix element of \mjFrot \def\mjTrop{{\sf T}} % Atmospheric gain matrix \def\mjTropEl{{\sf t}} % matrix element of \mjGatm \def\mjGatm{{\mjTrop}} % Old symbol, still supported \def\mjGatmEl{{\mjTropEl}} % Old symbol, still supported \def\mjKern{{\sf K}} % Fourier Transform kernel matrix \def\mjKernEl{{\sf k}} % matrix element \def\mjKref{{\mjKern^0}} % FT kernel for field centre \def\mjKrefEl{{\mjKernEl^0}} % matrix element \def\mjKoff{{\mjKern^{'}}} % For source, relative to field centre \def\mjKoffEl{{\mjKernEl^{'}}} % matrix element \def\mjWarr{{\mjKern}} % Old symbol (used to be \sf W) \def\mjWarrEl{{\mjKernEl}} % Old symbol (used to be \sf w) \def\mjProj{{\sf P}} % Receptor projection angle w.r.t. Sky \def\mjProjEl{{\sf p}} % matrix element \def\mjPrcp{{\mjProj}} % Old symbol, still supported \def\mjPrcpEl{{\mjProjEl}} % Old symbol, still supported \def\mjBtot{{\sf B}} % Total Voltage Pattern (=DPE) \def\mjBtotEl{{\sf b}} % matrix element of \mjBtot \def\mjBeam{{\sf E}} % Antenna Voltage Beam matrix \def\mjBeamEl{{\sf e}} % matrix element of \mjBeam % \def\mjBatt{{\sf B}} % Attenuation beam matrix (obsolete) % \def\mjBattEl{{\sf b}} % matrix element of \mjBatt % \def\mjObst{{\sf O}} % Beam obstruction effect matrix (obsolete) % \def\mjObstEl{{\sf o}} % matrix element of \mjObst \def\mjConf{{\sf C}} % configuration matrix \def\mjConfEl{{\sf c}} % matrix element \def\mjDrcp{{\sf D}} % \Receptor cross-`leakage' matrix \def\mjDrcpEl{{\sf d}} % matrix element of \mjDrcp \def\mjLeak{{\mjDrcp}} % Old symbol, still supported \def\mjLeakEl{{\mjDrcpEl}} % Old symbol, still supported \def\mjHybr{{\sf H}} % Hybrid network matrix (linear to circular) \def\mjHybrEl{{\sf h}} % matrix element \def\mjComm{{\sf Y}} % signal-channel commutation matrix \def\mjCommEl{{\sf y}} % matrix element \def\mjZpzd{{\sf Z}} % Phase Zero Difference matrix \def\mjZpzdEl{{\sf z}} % matrix element \def\mjGrec{{\sf G}} % Receiver Gain matrix (electronics) \def\mjGrecEl{{\sf g}} % matrix element \def\mjQsum{{\sf Q}} % Receiver gain of sum-output of tied array \def\mjQsumEl{{\sf q}} % matrix element \def\mjGsum{{\mjQsum}} % Old symbol, still supported \def\mjGsumEl{{\mjQsumEl}} % Old symbol, still supported % \gloshead{Other ME matrices and vectors:} \def\mmZero{{\sf Zero}} % Zero matrix \def\mmUnit{{\cal U}} % Unit matrix \def\mmDiag{{\sf Diag}} % Diagonal matrix \def\mmMult{{\sf Mult}} % Multiplication/magnification matrix \def\mjZero{{\mmZero}} % 2x2 Zero matrix \def\mjUnit{{\mmUnit}} % 2x2 Unit matrix \def\mjDiag{{\mmDiag}} % 2x2 Diagonal matrix D(a,b) \def\mjMult{{\mmMult}} % 2x2 Multiplication matrix M(a)=D(a,a)=a.U \def\mjRot{{\sf Rot}} % 2x2 rotation matrix R(alpha[,beta]) \def\mjEll{{\sf Ell}} % 2x2 Ellipticity matrix E(alpha[,beta]) \def\mjLtoC{{\cal H}} % 2x2 Conversion from Linear to Circular pol \def\mjCtoL{{\mjLtoC^{-1}}} % 2x2 Conversion from Circular to Linear pol \def\vvZero{{\vec{0}}} % Zero vector \def\vvIQUV{{\vec{I}}} % Stokes vector (I,Q,U,V) \def\vvCoh{{\vec{V}}} % Visibility (`coherency') vector (2-4) \def\vvCohEl{{\sf v}} % element of \vvCoh \def\vvElec{{\vec{E}}} % Electric field vector (2-4) \def\vvElecEl{{\sf e}} % element of \vvElec \def\vvAifr{{\vec{A}}} % Additive ifr-based vector (4) \def\vvAifrEl{{\sf a}} % element of \vvAifr \def\mmStokes{{\sf S}} % Stokes conversion matrix (4x4) to Coherence \def\mmMueller{{\cal M}} % Mueller matrix (Stokes to Stokes) \def\mmXifr{{\sf X}} % Correlator matrix (ifr-based) \def\mmXifrEl{{\sf x}} % element of matrix \mmXAifr \def\mmMifr{{\sf M}} % Multiplicative ifr-based gain \def\mmMifrEl{{\sf m}} % element of matrix \mmMAifr %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Secondary symbols (much-used combinations of the basic symbols above) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \def\ssI{_{\FeedI}} % subscript \Feed I \def\ssJ{_{\FeedJ}} % subscript \Feed J \def\ssIn{_{\FeedI n}} % subscript \def\ssJm{_{\FeedJ m}} % subscript \def\ssIk{_{\FeedI k}} % subscript \def\ssJk{_{\FeedJ k}} % subscript \def\ssInk{_{\FeedI nk}} % subscript \def\ssJmk{_{\FeedJ mk}} % subscript \def\ssP{_{\IFP}} % subscript \IFout P \def\ssQ{_{\IFQ}} % subscript \IFout Q \def\ssA{_{\RcpA}} % subscript \Receptor A \def\ssB{_{\RcpB}} % subscript \Receptor B \def\ssX{_{\XPol}} % subscript \def\ssY{_{\YPol}} % subscript \def\ssR{_{\RPol}} % subscript \def\ssL{_{\LPol}} % subscript \def\ssLin{^{+}} % superscript for linear pol \def\ssLI{^{+}_{\FeedI}} % sub/super \def\ssLJ{^{+}_{\FeedJ}} % sub/super \def\ssLIJ{^{+}_{\FeedI\FeedJ}} % sub/super \def\ssLIA{^{+}_{\FeedI\RcpA}} % sub/super \def\ssLIB{^{+}_{\FeedI\RcpB}} % sub/super \def\ssCir{^{\odot}} % superscript for circular pol \def\ssCI{^{\odot}_{\FeedI}} % sub/super \def\ssCJ{^{\odot}_{\FeedJ}} % sub/super \def\ssCIJ{^{\odot}_{\FeedI\FeedJ}} % sub/super \def\ssCIA{^{\odot}_{\FeedI\RcpA}} % sub/super \def\ssCIB{^{\odot}_{\FeedI\RcpB}} % sub/super \def\ssVI{^{vis}_{\FeedI}} % sub/super \def\ssSI{^{sky}_{\FeedI}} % sub/super \def\ssVIn{^{vis}_{\FeedI n}} % sub/super \def\ssSIn{^{sky}_{\FeedI n}} % sub/super \def\ssSInk{^{sky}_{\FeedI nk}} % sub/super \def\ssVJ{^{vis}_{\FeedJ}} % sub/super \def\ssSJ{^{sky}_{\FeedJ}} % sub/super \def\ssVJm{^{vis}_{\FeedJ m}} % sub/super \def\ssSJm{^{sky}_{\FeedJ m}} % sub/super \def\ssSJmk{^{sky}_{\FeedJ mk}} % sub/super \def\ssIX{_{\FeedI\XPol}} % subscript \def\ssIY{_{\FeedI\YPol}} % subscript \def\ssIR{_{\FeedI\RPol}} % subscript \def\ssIL{_{\FeedI\LPol}} % subscript \def\ssIA{_{\FeedI\RcpA}} % subscript \def\ssIB{_{\FeedI\RcpB}} % subscript \def\ssIP{_{\FeedI\IFP}} % subscript \def\ssIQ{_{\FeedI\IFQ}} % subscript \def\ssIJ{_{\FeedI\FeedJ}} % subscript \def\ssXY{_{\XPol\YPol}} % subscript \def\ssRL{_{\RPol\LPol}} % subscript \def\ssAB{_{\RcpA\RcpB}} % subscript \def\ssPQ{_{\IFP\IFQ}} % subscript \def\ssIXX{_{\FeedI\XPol\XPol}} % subscript \def\ssIYX{_{\FeedI\YPol\XPol}} % subscript \def\ssIXY{_{\FeedI\XPol\YPol}} % subscript \def\ssIYY{_{\FeedI\YPol\YPol}} % subscript \def\ssIRR{_{\FeedI\RPol\RPol}} % subscript \def\ssILR{_{\FeedI\LPol\RPol}} % subscript \def\ssIRL{_{\FeedI\RPol\LPol}} % subscript \def\ssILL{_{\FeedI\LPol\LPol}} % subscript \def\ssIXA{_{\FeedI\XPol\RcpA}} % subscript \def\ssIYA{_{\FeedI\YPol\RcpA}} % subscript \def\ssIXB{_{\FeedI\XPol\RcpB}} % subscript \def\ssIYB{_{\FeedI\YPol\RcpB}} % subscript \def\ssIRA{_{\FeedI\RPol\RcpA}} % subscript \def\ssILA{_{\FeedI\LPol\RcpA}} % subscript \def\ssIRB{_{\FeedI\RPol\RcpB}} % subscript \def\ssILB{_{\FeedI\LPol\RcpB}} % subscript \def\ssIAA{_{\FeedI\RcpA\RcpA}} % subscript \def\ssIBA{_{\FeedI\RcpB\RcpA}} % subscript \def\ssIAB{_{\FeedI\RcpA\RcpB}} % subscript \def\ssIBB{_{\FeedI\RcpB\RcpB}} % subscript \def\ssIAP{_{\FeedI\RcpA\IFP}} % subscript \def\ssIBP{_{\FeedI\RcpB\IFP}} % subscript \def\ssIAQ{_{\FeedI\RcpA\IFQ}} % subscript \def\ssIBQ{_{\FeedI\RcpB\IFQ}} % subscript \def\ssIPP{_{\FeedI\IFP\IFP}} % subscript \def\ssIQP{_{\FeedI\IFQ\IFP}} % subscript \def\ssIPQ{_{\FeedI\IFP\IFQ}} % subscript \def\ssIQQ{_{\FeedI\IFQ\IFQ}} % subscript \def\ssIPJP{_{\FeedI\IFP\,\FeedJ\IFP}} % subscript \def\ssIPJQ{_{\FeedI\IFP\,\FeedJ\IFQ}} % subscript \def\ssIQJP{_{\FeedI\IFQ\,\FeedJ\IFP}} % subscript \def\ssIQJQ{_{\FeedI\IFQ\,\FeedJ\IFQ}} % subscript %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% End of MEGI symbols definition file megi-symbols.tex %%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%