DETPROJ - projects waveform onto antenna patern of detector
[h, fPlus, fCross] = detproj(htt, detId, External);
htt TT gauge metric perturbation
Source is assumed to be in the direction of the North Pole
detId detector identifier string
External struct describing position and orientation of source wrt Earth
in the direction pointing from the Earth to the source
.x cos source co-declination
.phi source longitude
.psi source's polarization angle (angle between the projection the
the Earth's Z axis and the source's Z axis on the transverse
plane)
h signal vector in strain
fPlus (optional) + polarization beam pattern function
fCross (optional) x polarization beam pattern function
SEE ALSO: GRAVEN, GETIFO0001 function [h, fPlus, fCross] = detproj(htt, detId, External) 0002 0003 % DETPROJ - projects waveform onto antenna patern of detector 0004 % 0005 % [h, fPlus, fCross] = detproj(htt, detId, External); 0006 % 0007 % htt TT gauge metric perturbation 0008 % Source is assumed to be in the direction of the North Pole 0009 % detId detector identifier string 0010 % External struct describing position and orientation of source wrt Earth 0011 % in the direction pointing from the Earth to the source 0012 % .x cos source co-declination 0013 % .phi source longitude 0014 % .psi source's polarization angle (angle between the projection the 0015 % the Earth's Z axis and the source's Z axis on the transverse 0016 % plane) 0017 % 0018 % h signal vector in strain 0019 % fPlus (optional) + polarization beam pattern function 0020 % fCross (optional) x polarization beam pattern function 0021 % 0022 % SEE ALSO: GRAVEN, GETIFO 0023 0024 % $Id: detproj.m,v 1.15 2004/05/17 19:04:04 stuver Exp $ 0025 0026 % INITIALIZE output variable 0027 % CHECK inputs for errors 0028 % DEFINE external angles from struct 0029 % DEFINE X and Y unit vectors in souce frame from sky location 0030 % DEFINE e+ and ex in source frame 0031 % DEFINE e+ and ex in detector frame 0032 % DEFINE F+ and Fx 0033 % DETERMNINE strain at the detector 0034 0035 % Initialize output variable 0036 h = []; 0037 0038 % Check htt and External for errors 0039 errorcheck(htt, External); 0040 0041 % From the given cosine of the source's co-dec sky location, define the sine 0042 cosTheta = External.x; 0043 sinTheta = sqrt(1-External.x^2); 0044 % Define other external angles 0045 phi = External.phi; 0046 psi = External.psi; 0047 0048 % Define X and Y unit vectors in source frame from sky location 0049 % (This is found from rotating about z counterclockwise angle phi and then 0050 % rotating counterclockwise about y angle theta) 0051 exEarth = [cos(phi)*cosTheta, sin(phi)*cosTheta, -sinTheta]; 0052 eyEarth = [-sin(phi), cos(phi), 0]; 0053 % The Z unit vector now points from the Earth to the source on the 0054 % line-of-sight 0055 0056 % Define e+ and ex in source frame 0057 % e+ = ex'*ex - ey'*ey 0058 ePlusEarth = (exEarth'*exEarth)-(eyEarth'*eyEarth); 0059 % ex = ex'*ey + ey'*ex 0060 eCrossEarth = (exEarth'*eyEarth)+(eyEarth'*exEarth); 0061 0062 % Define e+ and ex in detector frame 0063 % e+@IFO = cos(2*psi)*e+ + sin(2*psi)*ex 0064 ePlus = (cos(2*psi)*ePlusEarth)+(sin(2*psi)*eCrossEarth); 0065 % ex@IFO = cos(2*psi)*ex - sin(2*psi)*ep 0066 eCross = (cos(2*psi)*eCrossEarth)-(sin(2*psi)*ePlusEarth); 0067 0068 % Define detector projection matrix from unit vectors for the detectors arms 0069 Cordnt = getifo(detId); % Function that returns the IFO unit vectors 0070 0071 % Make sure that the unit vectors are in 1x3 form 0072 Cordnt.V = Cordnt.V(:)'; 0073 Cordnt.W = Cordnt.W(:)'; 0074 0075 % D = 0.5*(Xhat'*Xhat - Yhat'*Yhat) 0076 % where Xhat is the unit vector for the 'X' arm and Yhat is the unit vector 0077 % for the 'Y' arm 0078 D = 0.5*((Cordnt.V'*Cordnt.V)-(Cordnt.W'*Cordnt.W)); 0079 0080 % Define F+ and Fx 0081 % F+ = D^ij e+_ij 0082 fPlus = trace(D*ePlus); 0083 % Fx = D^ij ex_ij 0084 fCross = trace(D*eCross); 0085 0086 % Determine strain at the detector 0087 % h = F+*h+ + Fx*hx 0088 h = (fPlus*htt(1,:))+(fCross*htt(2,:)); 0089 0090 return 0091 0092 % ~~~ END MAIN ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0093 0094 function errorcheck(htt, External) 0095 0096 % ERRORCHECK - checks detproj's input data for errors and stops the code if 0097 % an error is found 0098 % 0099 % errorcheck(hij, External) 0100 % 0101 % htt TT gauge metric perturbation 0102 % Source is assumed to be in the direction of the North Pole 0103 % detId detector identifier string 0104 % External struct describing position and orientation of source wrt Earth 0105 % in the direction pointing from the Earth to the source 0106 % .x cos source co-declination 0107 % .phi source longitude 0108 % .psi source's polarization angle measured clockwise along Earth's 0109 % longitide from the Prime Meridian 0110 0111 if size(htt,1) ~= 2 0112 % htt must be in 2xtime format 0113 sizeHtt = size(htt) 0114 error('detproj: htt must be in 2xtime format') 0115 end 0116 0117 % External must be a structure 0118 if ~strcmp(class(External), 'struct') 0119 External 0120 error('detproj: External must be a structure') 0121 end 0122 0123 % External must contain fields x, phi and psi 0124 if ~isfield(External, 'x') 0125 External 0126 error('detproj: The External struct must contain the field x') 0127 elseif abs(External.x) > 1 | ~isreal(External.x) 0128 % If External.x exists, it must be real and have a value between 0129 % -1 and 1 0130 External.x 0131 error('detproj: External.x must be real and between -1 and 1') 0132 end 0133 if ~isfield(External, 'phi') 0134 External 0135 error('detproj: The External struct must contain the field phi') 0136 elseif External.phi < -pi | External.phi > pi | ~isreal(External.phi) 0137 % If External.phi exits, it must be real and have a value between 0138 % -pi and pi 0139 External.phi 0140 error(['detproj: External.phi must be real and betweeen -pi '... 0141 'and pi']) 0142 end 0143 if ~isfield(External, 'psi') 0144 External 0145 error('detproj: The External struct must contain field psi') 0146 elseif External.psi < 0 | External.psi > (2*pi) | ... 0147 ~isreal(External.psi) 0148 % If External.psi exists, it must be real and have a value 0149 % between 0 and 2*pi 0150 External.psi 0151 error('detproj: External.psi must be real and between 0 and 2*pi') 0152 end