diff --git a/src/init.c b/src/init.c
index 5514ce3..83bf260 100644
--- a/src/init.c
+++ b/src/init.c
@@ -63,15 +63,16 @@ static inline double find_root_5ord(double u1, double u2, double v1, double v2,
        pow(u2,2))*v1*v2);
 }
 
-// \chi(b) is the totol deflection angle with parameter b
-double chi(double b){
+// \chi(cotpsi) is the totol deflection angle with parameter cotpsi=-dr/(r √f dphi)
+double chi(double cotpsi){
   gsl_odeiv2_system sys = {func, jac, 2, NULL};
   gsl_odeiv2_driver *d = gsl_odeiv2_driver_alloc_y_new(&sys, gsl_odeiv2_step_rk8pd, 1e-3, 1e-12, 1e-10);
   
   double u0 = 1.0/R0;
   double y[2] = {
     u0,
-    sqrt(1.0/(b*b) - u0*u0 + 2.0*M*u0*u0*u0)
+    //sqrt(1.0/(b*b) - u0*u0 + 2.0*M*u0*u0*u0)
+    u0*sqrt(f(R0))*cotpsi
   };
   double phi = 0;
   double phi_max = 8*PI;
@@ -133,7 +134,7 @@ static void refine_interval(double xl, double xr, double yl, double yr, double r
   return ;
 }
 
-int init(double bmax, double rela_err_limit, int *size, double **x, double **y){
+int init(double rmax, double rela_err_limit, int *size, double **x, double **y){
   if (*x) free(*x);
   if (*y) free(*y);
   SampleData sample;
@@ -141,13 +142,15 @@ int init(double bmax, double rela_err_limit, int *size, double **x, double **y){
   sample.size=1;
   sample.x = malloc(sizeof(double) * 1);
   sample.y = malloc(sizeof(double) * 1);
-  sample.x[0] = bmin;
-  sample.y[0] = chi(bmin);
-  double chi_bmax = chi(bmax);
+  double cotpsi_min = 1/rmax;
+  sample.x[0] = cotpsi_min;
+  sample.y[0] = chi(cotpsi_min);
+  double cotpsi_max = sqrt(R0*R0/(bmin*bmin*f(R0)) - 1);
+  double chi_cotpsimax = chi(cotpsi_max);
 
-  refine_interval(bmin, bmax, sample.y[0], chi_bmax, rela_err_limit, &sample, 1);
+  refine_interval(cotpsi_min, cotpsi_max, sample.y[0], chi_cotpsimax, rela_err_limit, &sample, 1);
 
-  sample_push(&sample, bmax, chi_bmax);
+  sample_push(&sample, cotpsi_max, chi_cotpsimax);
 
   //sort
 
diff --git a/src/init.h b/src/init.h
index e6ee675..ae4a1dd 100644
--- a/src/init.h
+++ b/src/init.h
@@ -1,2 +1,2 @@
-double chi(double b);
-int init(double bmax, double rela_err_limit, int *size, double **x, double **y);
+double chi(double cotpsi);
+int init(double rmax, double rela_err_limit, int *size, double **x, double **y);