DETPROJ - projects waveform onto antenna patern of detector
[h, fPlus, fCross] = detproj(htt, detId, nSrc);
htt TT gauge metric perturbation
detId detector identifier string
nSrc Position and orientation of source wrt Earth
Position is unit vector pointing from the Earth to the source
Orientation angle describes rotation between Earth-based e+,
ex and source-based e+ and ex (rotation angle from Earth to
source)
.x cos source co-declination
.phi source longitude
.psi orientation angle
h signal vector in strain
fPlus (optional) + polarization beam pattern function
fCross (optional) x polarization beam pattern function
$Id: detproj.m,v 1.18 2004/06/15 22:54:24 lsf Exp $
SEE ALSO: GRAVEN, GETIFO0001 function varargout = detproj(htt, detId, nSrc) 0002 % DETPROJ - projects waveform onto antenna patern of detector 0003 % 0004 % [h, fPlus, fCross] = detproj(htt, detId, nSrc); 0005 % 0006 % htt TT gauge metric perturbation 0007 % detId detector identifier string 0008 % nSrc Position and orientation of source wrt Earth 0009 % Position is unit vector pointing from the Earth to the source 0010 % Orientation angle describes rotation between Earth-based e+, 0011 % ex and source-based e+ and ex (rotation angle from Earth to 0012 % source) 0013 % .x cos source co-declination 0014 % .phi source longitude 0015 % .psi orientation angle 0016 % 0017 % h signal vector in strain 0018 % fPlus (optional) + polarization beam pattern function 0019 % fCross (optional) x polarization beam pattern function 0020 % 0021 % $Id: detproj.m,v 1.18 2004/06/15 22:54:24 lsf Exp $ 0022 % 0023 % SEE ALSO: GRAVEN, GETIFO 0024 0025 % $Id: detproj.m,v 1.18 2004/06/15 22:54:24 lsf Exp $ 0026 0027 % INITIALIZE output variable 0028 % CHECK inputs for errors 0029 % DEFINE nSrc angles from struct 0030 % DEFINE X and Y unit vectors in souce frame from sky location 0031 % DEFINE e+ and ex in source frame 0032 % DEFINE e+ and ex in detector frame 0033 % DEFINE F+ and Fx 0034 % DETERMNINE strain at the detector 0035 0036 if (nargout < 1 || nargout > 3) 0037 error('usage: [h, fPlus, fCross] = detproj(htt, detId, nSrc)'); 0038 end 0039 0040 % Check htt and nSrc for errors 0041 errorcheck(htt, nSrc); 0042 0043 % From the given cosine of the source's 0044 % co-dec sky location, define the sine 0045 cosTheta = nSrc.x; 0046 sinTheta = sqrt(1-cosTheta^2); 0047 % Define other nSrc angles 0048 phi = nSrc.phi; 0049 psi = nSrc.psi; 0050 0051 % Define X and Y unit vectors such that [X, Y, nSrc] is a right-handed 0052 % coordinate system 0053 % GOTCHA: the orientation of exEarth and eyEarth that span the polarization 0054 % plane must correspond to choices made in makett. 0055 exEarth = [cos(phi)*cosTheta, sin(phi)*cosTheta, -sinTheta]; 0056 eyEarth = [-sin(phi), cos(phi), 0]; 0057 0058 % Earth e+ and ex 0059 % e+ = ex'*ex - ey'*ey 0060 % ex = ex'*ey + ey'*ex 0061 ePlusEarth = (exEarth'*exEarth)-(eyEarth'*eyEarth); 0062 eCrossEarth = (exEarth'*eyEarth)+(eyEarth'*exEarth); 0063 0064 % Source e+ and ex: i.e., h = h+ e+Src + hx exSrc 0065 % e+Src = cos(2*psi)*e+ + sin(2*psi)*ex 0066 % exSrc = cos(2*psi)*ex - sin(2*psi)*ep 0067 ePlus = (cos(2*psi)*ePlusEarth) + (sin(2*psi)*eCrossEarth); 0068 eCross = (cos(2*psi)*eCrossEarth)- (sin(2*psi)*ePlusEarth); 0069 0070 % Define detector projection matrix 0071 % from unit vectors for the detectors arms 0072 Cordnt = getifo(detId); % Function that returns the IFO unit vectors 0073 0074 % Make sure that the unit vectors are in 1x3 form 0075 Cordnt.V = Cordnt.V(:)'; 0076 Cordnt.W = Cordnt.W(:)'; 0077 0078 % D = 0.5*(Xhat'*Xhat - Yhat'*Yhat) 0079 % where Xhat is the unit vector for the 'X' arm and Yhat is the unit vector 0080 % for the 'Y' arm 0081 D = 0.5*((Cordnt.V'*Cordnt.V)-(Cordnt.W'*Cordnt.W)); 0082 0083 % Define F+ and Fx 0084 % F+ = D^ij e+_ij 0085 fPlus = trace(D*ePlus); 0086 % Fx = D^ij ex_ij 0087 fCross = trace(D*eCross); 0088 0089 % Determine strain at the detector 0090 % h = F+*h+ + Fx*hx 0091 varargout{1} = (fPlus*htt(1,:))+(fCross*htt(2,:)); 0092 0093 if (nargout > 1) 0094 varargout{2} = fPlus; 0095 end 0096 if (nargout > 2) 0097 varargout{3} = fCross; 0098 end 0099 0100 return 0101 0102 % ~~~ END MAIN ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0103 0104 function errorcheck(htt, nSrc) 0105 0106 % ERRORCHECK - checks detproj's input data for errors and stops the code if 0107 % an error is found 0108 % 0109 % errorcheck(hij, nSrc) 0110 % 0111 % htt TT gauge metric perturbation 0112 % Source is assumed to be in the direction of the North Pole 0113 % detId detector identifier string 0114 % nSrc Position and orientation of source wrt Earth 0115 % Position is unit vector pointing from the Earth to the source 0116 % Orientation is angle of rotation about this axis from Earth 0117 % polarization angle to source polarization angle 0118 % .x cos source co-declination 0119 % .phi source longitude 0120 % .psi orientation angle 0121 0122 if (size(htt,1) ~= 2) 0123 % htt must be in 2 x nSamp format 0124 if (isempty(htt)) 0125 error('detproj: htt empty'); 0126 else 0127 dims = size(htt); 0128 errstr = sprintf('%d',dims(1)); 0129 if (length(dims) > 1) 0130 errstr = [errstr, sprintf(', %d',dims(2:end))]; 0131 end 0132 error('detproj: size(htt) = [%s] should be [2 nSamp]',errstr); 0133 end 0134 end 0135 0136 % nSrc must contain fields x, phi and psi; these must be in limits 0137 if ~(isfield(nSrc, 'x') && -1 <= nSrc.x && nSrc.x <= 1) 0138 error('detproj: scalar nSrc.x must satisfy -1 <= nSrc.x <= 1') 0139 end 0140 if ~(isfield(nSrc, 'phi') && -pi <= nSrc.phi && nSrc.phi <= pi) 0141 error('detproj: scalar nSrc.phi must satisfy -pi <= nSrc.phi <= pi'); 0142 end 0143 if ~(isfield(nSrc, 'psi') && 0 <= nSrc.psi && nSrc.psi < 2*pi) 0144 error('detproj: nSrc.psi must satisfy 0 <= nSrc.psi < 2*pi') 0145 end 0146 return