Corrected sign of iota to correspond to findchirp paper

Included effects of arrival time delay in the formulae for the waveforms (assuming a round earth)

Expressed output X sin(phi) + Y cos(phi) in the alternative form r sin(phi+offset)

Currently offset is printed in degrees.  Printing code assumes UTF-8 on the terminal. This may be fragile, I'm not sure.

src/antenna.c

@@ -9,6 +9,11 @@
 // For converting degrees to radians
 const double deg_to_rad = M_PI/180.0;
 
+// For computing arrival time delays, need mean radius of the earth in
+// seconds. Get this by dividing radius in km by speed of light in
+// km/s.
+const double radius_earth = 6371.0/299792.458;
+
 // Event time
 // GPS 1187008882
 // UTC:	Thu 2017 Aug 17	12:41:04
@@ -235,21 +240,41 @@ void print_source() {
 }
 
 // This dots the mass quadrupole with the antenna functions
-void get_UV_combinations(int det, double *alpha, double *beta) {
+void get_UV_combinations(int det, double *alpha, double *beta, double *rdotn) {
   
-   double a=0,b=0;
+   double a=0,b=0,dot=0;
    int i, j;
    
    double *su=source.u;
    double *sv=source.v;
+   double *n=source.vec;
+   
    double *dx=detectors[det].lx;
    double *dy=detectors[det].ly;
+   double *r=detectors[det].vec;
+   
+   for (i=0; i<3; i++)
+      for (j=0; j<3; j++)
+	 a += (su[i]*su[j] - sv[i]*sv[j]) * (dx[i]*dx[j] - dy[i]*dy[j]);
    
-   for (i=0;i<3;i++) for (j=0;j<3;j++) a+=(su[i]*su[j]-sv[i]*sv[j])*(dx[i]*dx[j]-dy[i]*dy[j]);
-   for (i=0;i<3;i++) for (j=0;j<3;j++) b+=(su[i]*sv[j]+sv[i]*su[j])*(dx[i]*dx[j]-dy[i]*dy[j]);
+   for (i=0; i<3; i++)
+      for (j=0; j<3; j++)
+	 b += (su[i]*sv[j] + sv[i]*su[j]) * (dx[i]*dx[j] - dy[i]*dy[j]);
+
+   // The quantity dot is positive if the vector from the earth center
+   // to a detector has the SAME direction as the vector from the
+   // earth center to the source.  This means that the signal arrives
+   // EARLIER at that detector.  Hence the signal waveform seen at the
+   // detector is of the form h(t) = wave(t + R*dot) where R is the
+   // (positive) earth radius in units of time and wave(t) is the
+   // emitted source waveform.
+   
+   for (i=0; i<3; i++)
+      dot += n[i]*r[i];
    
    *alpha = a;
    *beta = b;
+   *rdotn = dot;
 }
 
 // This function requires two floating point arguments on the command
@@ -263,7 +288,7 @@ int main(int argc, char *argv[]) {
    if (argc != 3) {
       fprintf(stderr,
 	      "Wrong argument count! Correct usage:\n"
-	      "%s float_iota float_psi\n",
+	      "%s float_iota_in_degrees float_psi_in_degrees\n",
 	      argv[0]);
       exit(1);
    }
@@ -283,25 +308,48 @@ int main(int argc, char *argv[]) {
    iota *= deg_to_rad;
    psi *= deg_to_rad;
 
-   // get angles needed to calculate antenna response
-   double ci = cos(iota);
-   double si = sin(iota);
+   // get angles needed to calculate antenna response. The minus sign
+   // in the definition of cos(iota) is because my calculational notes
+   // assume that iota=0 corresponds to orbital motion CCW in the
+   // (right-handed) UV coordinate system.  That corresponds to having
+   // the orbital angular momentum pointing radially AWAY from earth.
+   // But the standard convention is that iota=0 is face-on, meaning
+   // orbital angular momentum pointing TO the earth.  So I change the
+   // sign of cos(iota) below to correct for this.
+   
+   double ci = -cos(iota);
    double c2p = cos(2*psi);
    double s2p = sin(2*psi);
 
    // Now find waveforms.  At each site, waveform is w^2 [X sin(2wt) + Y cos(2wt) ]
    // loop over detectors
    for (i=0; i<3; i++) {
-      double alpha, beta, X, Y;
+      double alpha, beta, X, Y, dt;
 
       // get antenna pattern overlap with source plane
-      get_UV_combinations(i, &alpha, &beta);
+      get_UV_combinations(i, &alpha, &beta, &dt);
 
       // form combinations as functions of inclination and polarization angles
       X =         2.0*ci*(alpha*s2p - beta*c2p);
       Y = -(ci*ci + 1.0)*(alpha*c2p + beta*s2p);
+
+      // compute time delay
+      dt *= radius_earth;
+      
+      printf("For detector %s the waveform is w^2 [ %.3f sin(2w(t%+.3f s))%+.3f cos(2w(t%+.3f s)) ]\n", detectors[i].name, X, dt, Y, dt);
+
+      // compute alternative form of output
+      // X sin(phi) + Y cos(phi) = sqrt(X^2+Y^2) sin(phi + ang) where ang=atan2(Y,X)
+      
+      double amp = sqrt(X*X + Y*Y);
+      double ang = atan2(Y, X);
+      
+      // degree character in UTF-8 character set (most likely terminal type!)
+      int deg1=0xC2, deg2=0xB0;
+
+      printf("                              =  %.3f w^2 cos[2w(t%+.3f s) %+.1f%c%c]\n", amp, dt, ang, deg1, deg2);
+
       
-      printf("For detector %s the waveform is w^2 [ %f sin(2wt) + %f cos(2wt) ] \n", detectors[i].name, X, Y);
    }
    return 0;
 }

src/conventions.txt

@@ -8,16 +8,19 @@ x,y,z coordinate system for Earth is as follows:
 
 (a) The equator lies in the XY plane
 (b) The north pole lies on the positive Z axis
-(c) The line of longitude 0 lies in the XZ plane and passes through
+(c) The line of longitude 0 lies in the XZ plane, and passes through
     the positive X axis
 
-#THE FOLLOWING STATEMENT MAY NEED A SIGN CHANGE
-The orbital inclination angle iota (from 0 to 180 degrees) is the angle
-between the orbital angular momentum vector (defined with the
-right-hand rule) and the vector from earth to source.
+According to the findchirp paper, the orbital inclination angle iota
+(from 0 to 180 degrees) is the angle between the orbital angular
+momentum vector (defined with the right-hand rule) and the vector from
+source to earth.
 
-Face-on is iota=0 and face-off is iota=180.
+Face-on is iota=0 (orbital angular momentum pointing to earth) and
+face-off is iota=180 (orbital angular momentum pointing away from
+earth).
 
+## CHECK THIS!
 The orientation angle psi is the angle (from 0 to 180 degrees,
 measured counterclockwise from North) between the long angle of the
 ellipse (projected into the plane of the sky) and the northerly