def coherent_transmission_matrix(self, frequency, eps_1, eps_2, mu1, npol):
"""compute the transmission coefficients for the azimuthal mode m
and for an array of incidence angles (given by their cosine)
in medium 1. Medium 2 is where the beam is transmitted.
:param eps_1: permittivity of the medium where the incident beam is propagating.
:param eps_2: permittivity of the other medium.
:param mu1: array of cosine of incident angles.
:param npol: number of polarization.
:return: the transmission matrix
"""
R01_v, R01_h, R1t_v, R1t_h, exp_kd, exp_2kd, mu_t = self._prepare_computation(frequency, eps_1, eps_2, mu1)
T_v = (1 + R01_v) * (1 + R1t_v) * exp_kd / (1 + R01_v * R1t_v * exp_2kd) # see TsnagI 5.2.10-12
T_h = (1 + R01_h) * (1 + R1t_h) * exp_kd / (1 + R01_h * R1t_h * exp_2kd)
transmission_coefficients = smrt_matrix.ones((npol, len(mu1)))
nt = np.sqrt(eps_2 / eps_1).real
transmission_coefficients[0] = abs2(T_v) * mu_t / mu1 / nt # for the coef see TsangIII 2.1.140b
transmission_coefficients[1] = abs2(T_h) * mu_t / mu1 * nt # for the coef see TsangIII 2.1.140a
if npol >= 3:
# this part is to be confirmed.
R_v = (R01_v + R1t_v * exp_2kd) / (1 + R01_v * R1t_v * exp_2kd)
R_h = (R01_h + R1t_h * exp_2kd) / (1 + R01_h * R1t_h * exp_2kd)
transmission_coefficients[2] = mu_t / mu1 * ((1 + R_v) * np.conj(1 + R_h)).real # TsangI Eq 7.2.95
return transmission_coefficients
def specular_reflection_matrix(self, frequency, eps_1, eps_2, mu1, npol):
"""compute the reflection coefficients for an array of incidence angles (given by their cosine)
in medium 1. Medium 2 is where the beam is transmitted.
:param eps_1: permittivity of the medium where the incident beam is propagating.
:param eps_2: permittivity of the other medium.
:param mu1: array of cosine of incident angles.
:param npol: number of polarization.
:return: the reflection matrix
"""
R01_v, R01_h, R1t_v, R1t_h, exp_kd, exp_2kd, mu_t = self._prepare_computation(frequency, eps_1, eps_2, mu1)
R_v = (R01_v + R1t_v * exp_2kd) / (1 + R01_v * R1t_v * exp_2kd)
R_h = (R01_h + R1t_h * exp_2kd) / (1 + R01_h * R1t_h * exp_2kd)
reflection_coefficients = smrt_matrix.ones((npol, len(mu1)))
reflection_coefficients[0] = abs2(R_v)
reflection_coefficients[1] = abs2(R_h)
if npol >= 3:
reflection_coefficients[2] = (R_v * np.conj(R_h)).real # TsangI Eq 7.2.93
return reflection_coefficients
def fresnel_reflection_matrix(eps_1, eps_2, mu1, npol):
"""compute the fresnel reflection matrix for/in medium 1 laying above medium 2.
:param npol: number of polarizations to return.
:param eps_1: permittivity of medium 1.
:param eps_2: permittivity of medium 2.
:param mu1: cosine zenith angle in medium 1.
:returns: a matrix or the diagional depending on `return_as_diagonal`
"""
mu1 = np.atleast_1d(mu1)
assert len(mu1.shape) == 1 # 1D array
reflection_coefficients = smrt_matrix.ones((npol, len(mu1)))
rv, rh, _ = fresnel_coefficients(eps_1, eps_2, mu1)
reflection_coefficients[0] = abs2(rv)
reflection_coefficients[1] = abs2(rh)
if npol >= 3:
reflection_coefficients[2] = (rv *
np.conj(rh)).real # TsangI Eq 7.2.93
return reflection_coefficients
def coherent_transmission_matrix(self, frequency, eps_1, eps_2, mu1, npol):
"""compute the transmission coefficients for the azimuthal mode m
and for an array of incidence angles (given by their cosine)
in medium 1. Medium 2 is where the beam is transmitted.
:param eps_1: permittivity of the medium where the incident beam is propagating.
:param eps_2: permittivity of the other medium
:param mu1: array of cosine of incident angles
:param npol: number of polarization
:return: the transmission matrix
"""
return smrt_matrix.ones((npol, len(mu1)))