import numpy as np
from polsartools.utils.plot_utils import pol_sign, pol_sign2d, poincare_plot,poincare_sphere
def prepare_data(S2):
A0 = (1/4)*np.abs(S2[0,0]+S2[1,1])**2
B0 = (1/4)*np.abs(S2[0,0]-S2[1,1])**2 + np.abs(S2[0,1])**2
B_psi = (1/4)*np.abs(S2[0,0]-S2[1,1])**2 - np.abs(S2[0,1])**2
# C_psi = (1/2)*np.abs(S2[0,0]-S2[1,1])**2
# di-hedral fix convert real part of vv to positive
C_psi = (1/2) * np.abs(S2[0,0] - (np.real(S2[1,1]) * (1 if np.real(S2[1,1]) >= 0 else -1) + 1j * np.imag(S2[1,1])))**2
D_psi = np.imag(S2[0,0]*np.conjugate(S2[1,1]))
E_psi = np.real(np.conjugate(S2[0,1])*(S2[0,0]-S2[1,1]))
F_psi = np.imag(np.conjugate(S2[0,1])*(S2[0,0]-S2[1,1]))
G_psi = np.imag(np.conjugate(S2[0,1])*(S2[0,0]+S2[1,1]))
H_psi = np.real(np.conjugate(S2[0,1])*(S2[0,0]+S2[1,1]))
K_mat = np.array([
[A0+B0,C_psi,H_psi,F_psi],
[C_psi,A0+B_psi,E_psi,G_psi],
[H_psi,E_psi,A0-B_psi,D_psi],
[F_psi,G_psi,D_psi,-A0+B0]
])
XX_POL = []
cp_sign = np.zeros((181,91))
xp_sign = np.zeros((181,91))
x, y = np.mgrid[-90: 91 : 1, -45 : 46 : 1]
xx = 0
for tilt in np.arange(-90,91,1):
yy=0
for elep in np.arange(-45,46,1):
psi = tilt*np.pi/180
tau = elep*np.pi/180
S_co = np.array([1,
np.cos(2*psi)*np.cos(2*tau),
np.sin(2*psi)*np.cos(2*tau),
np.sin(2*tau)
])
stc = np.conjugate(S_co.T)
temp_pow_c = np.matmul(stc,np.matmul(K_mat,S_co))
S_cross = np.array([1,
-np.cos(2*psi)*np.cos(2*tau),
-np.sin(2*psi)*np.cos(2*tau),
-np.sin(2*tau)
])
stx = np.conjugate(S_cross.T)
temp_pow_x = np.matmul(stx,np.matmul(K_mat,S_co))
XX_POL.append([tilt,elep,temp_pow_c,temp_pow_x])
cp_sign[xx,yy] = temp_pow_c
xp_sign[xx,yy] = temp_pow_x
yy=yy+1
# print(xx,yy)
xx=xx+1
# cp_sign[cp_sign==0]=np.nan
# xp_sign[xp_sign==0]=np.nan
cp_sign = cp_sign/np.nanmax(cp_sign)
xp_sign = xp_sign/np.nanmax(xp_sign)
return cp_sign, xp_sign
[docs]
def fp_sign(S2=None, title='',pname='',cmap='jet',plotType = 1):
"""
Generates and visualizes polarimetric signatures from a given 2x2 scattering matrix (S2).
Examples
--------
>>> S2 = np.array([[1, 0], [0, 1]]) # Trihedral
>>> fp_sign(S2, title='Trihedral', plotType=1)
Parameters
----------
S2 : np.2darray (2x2) or None
Complex 2x2 scattering matrix representing polarimetric data.
Is None, for theoretical plot that don't require S2 will be generated.
title : str, optional
Title of the plot. Default is an empty string.
pname : str, optional
Name of the output file (*.png). Default is an empty string.
cmap : str, optional
Colormap used for visualizing the data. Default is 'jet'.
plotType : int, optional
Determines the type of plot to generate:
- 1: Standard polarimetric signature via `pol_sign`.
- 2: 2D polarimetric signature via `pol_sign2d`.
- 3: Poincaré sphere mapping via `poincare_plot`.
- 4: Render empty or canonical Poincaré sphere via `poincare_sphere` (S2 not required).
"""
if S2 is not None:
cp_sign, xp_sign = prepare_data(S2)
if plotType==4:
poincare_sphere(pname=pname)
elif S2 is not None and plotType==3:
poincare_plot(cp_sign, xp_sign, title=title, pname=pname,cmap=cmap)
elif S2 is not None and plotType==2:
pol_sign2d(cp_sign, xp_sign, title=title, pname=pname,cmap=cmap)
else:
pol_sign(cp_sign, xp_sign, title=title, pname=pname,cmap=cmap)
# S2 = np.array([[1,0],
# [0,1]])
# # fix this oriented dihedral
# S2 = np.array([[1, 0],
# [0,-1]])
# S2 = np.array([[0,1],
# [1,0]])
# S2 = np.array([[0,0],
# [0,1]])
# S2 = np.array([[1,-1],
# [-1,1]])
# array([[2248.6506 -5218.124j , -4.0451455 -46.991398j],
# [ -11.6204195 -27.771238j, 800.1831 -5830.6836j ]],
# dtype=complex64)
# fp_sign(S2, plotType = 3)
