SMRT

smrt.interface package

Submodules

smrt.interface.coherent_flat module

Implement the coherent flat pseudo-interface, as in MEMLS. This interface is obtained by collapsing one layer and two interfaces into a single interface. Scattering in the layer is neglected.

process_coherent_layers(snowpack, emmodel_list, sensor)
class CoherentFlat(interfaces, layer, permittivity)

Bases: object

A flat surface. The reflection is in the specular direction and the coefficient is calculated with the Fresnel coefficients

args = []
optional_args = {}
specular_reflection_matrix(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.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium.
  • mu1 – array of cosine of incident angles.
  • npol – number of polarization.
Returns:

the reflection matrix
diffuse_reflection_matrix(frequency, eps_1, eps_2, mu_s, mu_i, dphi, npol)
coherent_transmission_matrix(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.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium.
  • mu1 – array of cosine of incident angles.
  • npol – number of polarization.
Returns:

the transmission matrix
diffuse_transmission_matrix(frequency, eps_1, eps_2, mu_s, mu_i, dphi, npol)

smrt.interface.flat module

Implement the flat interface boundary condition between layers charcterized by their effective permittivities. The reflection and transmission are computed using the Fresnel coefficient.

class Flat(**kwargs)

Bases: smrt.core.interface.Interface

A flat surface. The reflection is in the specular direction and the coefficient is calculated with the Fresnel coefficients

args = []
optional_args = {}
specular_reflection_matrix(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.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium.
  • mu1 – array of cosine of incident angles.
  • npol – number of polarization.
Returns:

the reflection matrix
diffuse_reflection_matrix(frequency, eps_1, eps_2, mu_s, mu_i, dphi, npol)
coherent_transmission_matrix(frequency, eps_1, eps_2, mu1, npol)
compute the transmission coefficients for an array of incidence angles (given by their cosine)
in medium 1. Medium 2 is where the beam is transmitted.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium.
  • mu1 – array of cosine of incident angles.
  • npol – number of polarization.
Returns:

the transmission matrix
diffuse_transmission_matrix(frequency, eps_1, eps_2, mu_s, mu_i, dphi, npol)

smrt.interface.geometrical_optics module

Implement the interface boundary condition under the Geometrical Approximation between layers charcterized by their effective permittivities. This approximation is suitable for surface with roughness much larger than the roughness scales, typically k*s >> 1 and k*l >> 1, where s the rms heigth and l the correlation length. The precise validity range must be investigated by the user, this code does not raise any warning. An important charcateristic of this approximation is that the scattering do not directly depend on frequency, the only (probably weak) dependence is through the permittivities of the media.

The model is parameterized by the mean_square_slope which can be calculated as mean_square_slope = 2*s**2/l**2 for surface with a Gaussian autocorrelation function. Other equations may exist for other autocorrelation function.

This implementation is largely based on Tsang and Kong, Scattering of Electromagnetic Waves: Advanced Topics, 2001 (Tsang_tomeIII in the following)

class GeometricalOptics(**kwargs)

Bases: smrt.core.interface.Interface

A very rough surface.

args = ['mean_square_slope']
optional_args = {'shadow_correction': True}
clip_mu(mu)
specular_reflection_matrix(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.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium
  • mu1 – array of cosine of incident angles
  • npol – number of polarization
Returns:

the reflection matrix
diffuse_reflection_matrix(frequency, eps_1, eps_2, mu_s, mu_i, dphi, npol)
compute the reflection coefficients for an array of incident, scattered and azimuth angles
in medium 1. Medium 2 is where the beam is transmitted.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium
  • mu1 – array of cosine of incident angles
  • npol – number of polarization
Returns:

the reflection matrix
ft_even_diffuse_reflection_matrix(frequency, eps_1, eps_2, mu_s, mu_i, m_max, npol)
ft_even_diffuse_transmission_matrix(frequency, eps_1, eps_2, mu_s, mu_i, m_max, npol)
coherent_transmission_matrix(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.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium
  • mu1 – array of cosine of incident angles
  • npol – number of polarization
Returns:

the transmission matrix
diffuse_transmission_matrix(frequency, eps_1, eps_2, mu_t, mu_i, dphi, npol)
compute the transmission coefficients for an array of incident, scattered and azimuth angles
in medium 1. Medium 2 is where the beam is transmitted.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium
  • mu_i – array of cosine of incident angles
  • mu_t – array of cosine of transmitted wave angles
  • npol – number of polarization
Returns:

the transmission matrix
reflection_integrand_for_energy_conservation_test(frequency, eps_1, eps_2, mu_s, mu_i, dphi)

function relevant to compute energy conservation. See p87 in Tsang_tomeIII.

transmission_integrand_for_energy_conservation_test(frequency, eps_1, eps_2, mu_t, mu_i, dphi)

function relevant to compute energy conservation. See p87 in Tsang_tomeIII.

reflection_coefficients(frequency, eps_1, eps_2, mu_i)
transmission_coefficients(frequency, eps_1, eps_2, mu_i)
shadow_function(mean_square_slope, cotan)

smrt.interface.geometrical_optics_backscatter module

Implement the interface boundary condition under the Geometrical Approximation between layers charcterized by their effective permittivities. This code is for backscatter only, that is, to use as a substrate and at low frequency when the backscatter is the main mecahnism, and conversely when mulitple scattering and double bounce between snow and substrate are negligible. In any other case, it is recommended to use GeometricalOptics.

The transmitted energy is also computed in an approximate way suitable for 1st order scattering. We use energy conservation to compute the total transmitted energy and consider that all this energy is transmitted in the refraction (specular) direction.

class GeometricalOpticsBackscatter(**kwargs)

Bases: smrt.core.interface.Interface

A very rough surface.

args = ['mean_square_slope']
optional_args = {'shadow_correction': True}
specular_reflection_matrix(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.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium
  • mu1 – array of cosine of incident angles
  • npol – number of polarization
Returns:

the reflection matrix
diffuse_reflection_matrix(frequency, eps_1, eps_2, mu_s, mu_i, dphi, npol)
compute the reflection coefficients for an array of incident, scattered and azimuth angles
in medium 1. Medium 2 is where the beam is transmitted.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium
  • mu1 – array of cosine of incident angles
  • npol – number of polarization
Returns:

the reflection matrix
ft_even_diffuse_reflection_matrix(frequency, eps_1, eps_2, mu_s, mu_i, m_max, npol)
coherent_transmission_matrix(frequency, eps_1, eps_2, mu1, npol)
compute the transmission coefficients for an array of incidence angles (given by their cosine)
in medium 1. Medium 2 is where the beam is transmitted. While Geometrical Optics, we here consider that power not reflected is scattered in the specular transmitted direction. This is an approximation which is reasonable in the context of a “1st order” geometrical optics.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium
  • mu1 – array of cosine of incident angles
  • npol – number of polarization
Returns:

the transmission matrix

smrt.interface.iem_fung92 module

Implement the interface boundary condition under IEM formulation provided by Fung et al. 1992. in IEEE TGRS. Use of this code requires special attention because of two issues:

1) it only computes the backscatter diffuse reflection as described in Fung et al. 1992, the specular reflection and the coherent transmission. It does not compute the full bi-static diffuse reflection and transmission. As a consequence it is only suitable when single scattering is dominant, usually at low frequency when the medium is weakly scattering. This happends when the main mechanism is the backscatter from the interface attenuated by the medium. Another case is when the rough surface is relatively smooth, the specular reflection is relatively strong and the energy can be scattered back by the medium (double bounce). For other situations, this code is not recommended.

2) Additionaly, IEM is known to work for a limited range of roughness. Usually it is considered valid for ks < 3 and ks*kw < sqrt(eps) where k is the wavenumber, s the rms height and l the correlation length. The code print a warning when out of this range. There is also limitation for smooth surfaces but no warning is printed.

Usage example:

::

# rms height and corr_length values work at 10 GHz substrate = make_soil(“iem_fung92”, “dobson85”, temperature=260,

roughness_rms=1e-3, corr_length=5e-2, autocorrelation_function=”exponential”, moisture=moisture, clay=clay, sand=sand, drymatter=drymatter)
class IEM_Fung92(**kwargs)

Bases: smrt.core.interface.Interface

A moderate rough surface model with backscatter, specular reflection and transmission only. Use with care!

args = ['roughness_rms', 'corr_length']
optional_args = {'autocorrelation_function': 'exponential', 'series_truncation': 10, 'warning_handling': 'print'}
specular_reflection_matrix(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.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium
  • mu1 – array of cosine of incident angles
  • npol – number of polarization
Returns:

the reflection matrix
check_validity(ks, kl, eps_r)
fresnel_coefficients(eps_1, eps_2, mu_i, ks, kl)

calculate the fresnel coefficients at the angle mu_i whatever is ks and kl according to the original formulation of Fung 1992

diffuse_reflection_matrix(frequency, eps_1, eps_2, mu_s, mu_i, dphi, npol, debug=False)
compute the reflection coefficients for an array of incident, scattered and azimuth angles
in medium 1. Medium 2 is where the beam is transmitted.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium
  • mu1 – array of cosine of incident angles
  • npol – number of polarization
Returns:

the reflection matrix
W_n(n, k)
ft_even_diffuse_reflection_matrix(frequency, eps_1, eps_2, mu_s, mu_i, m_max, npol)
coherent_transmission_matrix(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.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium
  • mu1 – array of cosine of incident angles
  • npol – number of polarization
Returns:

the transmission matrix

smrt.interface.iem_fung92_brogioni10 module

Implement the interface boundary condition under IEM formulation provided by Fung et al. 1992. in IEEE TGRS with an extended domain of validity (for large roughness or correlation length) by switching the Fresnel coefficients according to Brogioni et al. 2010, IJRS (doi: 10.1080/01431160903232808). A better but more complex approach is given by Wu et al. 2003 (to be implemented).

Use of this code requires special attention.

class IEM_Fung92_Briogoni10(**kwargs)

Bases: smrt.interface.iem_fung92.IEM_Fung92

A moderate rough surface model with backscatter, specular reflection and transmission only. Use with care!

check_validity(ks, kl, eps_r)
fresnel_coefficients(eps_1, eps_2, mu_i, ks, kl)

calculate the fresnel coefficients at the angle mu_i or 0° depending on ks*kl. The transition is abrupt.

smrt.interface.radar_calibration_sphere module

Surface with a backscatter of 4pi.

class RadarCalibrationSphere(**kwargs)

Bases: smrt.core.interface.Interface

args = []
optional_args = {}
specular_reflection_matrix(frequency, eps_1, eps_2, mu1, npol)
diffuse_reflection_matrix(frequency, eps_1, eps_2, mu_s, mu_i, dphi, npol)
ft_even_diffuse_reflection_matrix(frequency, eps_1, eps_2, mu_s, mu_i, m_max, npol)
coherent_transmission_matrix(frequency, eps_1, eps_2, mu1, npol)

smrt.interface.test_geometrical_optics module

test_compare_geometrical_optics()
test_reflectance_reciprocity()
test_transmission_reciprocity()

smrt.interface.test_iem_fung92 module

test_iem_fung92()

smrt.interface.test_iem_fung92_brogioni10 module

test_iem_fung92_biogoni10_continuty()
test_iem_fung92_brogioni10()

smrt.interface.transparent module

A transparent interface (no reflection). Useful for the unit-test mainly.

class Transparent

Bases: object

args = []
optional_args = {}
specular_reflection_matrix(frequency, eps_1, eps_2, mu1, npol)
compute the reflection 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.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium
  • mhu1 – array of cosine of incident angles
  • npol – number of polarization
diffuse_reflection_matrix(frequency, eps_1, eps_2, mu_s, mu_i, dphi, npol)
coherent_transmission_matrix(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.
Parameters:
  • eps_1 – permittivity of the medium where the incident beam is propagating.
  • eps_2 – permittivity of the other medium
  • mu1 – array of cosine of incident angles
  • npol – number of polarization
Returns:

the transmission matrix
diffuse_transmission_matrix(frequency, eps_1, eps_2, mu_s, mu_i, dphi, npol)

smrt.interface.vector3 module

class vector3

Bases: object

static from_xyz(x, y, z)
static from_angles(norm, mu, phi)
cross(other)
dot(other)

Module contents

This module contains different type of boundary conditions between the layers. Currently only flat interfaces are implemented.

For developers

All the different type of interface must defined the methods: specular_reflection_matrix and coherent_transmission_matrix.

It is currently not possible to implement rough interface, a (small) change is needed in DORT. Please contact the authors.