import numpy as np 
import matplotlib.pyplot as plt 

N = 4096 # points 
ht = Hankel_qDHT(N) 
r_axis = ht.r   # the generated ratial axis, r is almost equally spaced, 
                # corresponding to the positive-zeros of 0-order Bessel 
                # function J_0(x) 
# field before 0-order Hankel Transform: 
field =  np.exp(-np.pi * r_axis**2 / (1.0 + 1.0J * 0.2)) 
# field after the transform, lives still on ht.r axis: 
field_H0 = ht.transform(field) # 

plt.plot(r_axis, np.abs(field), "b-") 
plt.plot(r_axis, np.abs(field_H0), "r--") 
plt.xlabel("r") 
plt.ylabel("abs. field") 
plt.show()