shadow4.physical_models.prerefl package

Submodules

shadow4.physical_models.prerefl.prerefl module

python version of the mirror reflectivity code and refractive index calculations in shadow.

class shadow4.physical_models.prerefl.prerefl.PreRefl[source]

Bases: object

get_attenuation_coefficient(energy1)[source]

Returns the attenuation coefficient.

Parameters:

energy1 (float or numpy array) – The photon energy or array of energies in eV.

Returns:

The attenuation coefficient in cm^-1.

Return type:

float or numpy array

classmethod get_attenuation_coefficient_external_dabax(photon_energy_ev=10000.0, material='SiC', density=3.217, dabax=None)[source]

Standalone method to return the attenuation coefficient.

Parameters:

  • photon_energy_ev (float or numpy array) – The photon energy or array of energies in eV.

  • material (str, optional) – The symbol/formula of the material.

  • density (float, optional) – The material density in g/cm3.

  • dabax (None or instance of DabaxXraylib) – A pointer to the dabax library. Use None for default.

Returns:

The array with attenuation coefficient in cm^-1.

Return type:

float or numpy array

classmethod get_attenuation_coefficient_external_xraylib(photon_energy_ev=10000.0, material='SiC', density=3.217)[source]
get_refraction_index(energy1)[source]

Returns the complex refraction index.

Parameters:

energy1 (float or numpy array) – The photon energy or array of energies in eV.

Returns:

The complex refraction index.

Return type:

complex or numpy array

classmethod get_refraction_index_external_dabax(photon_energy_ev=10000.0, material='SiC', density=3.217, dabax=None)[source]

Standalone method to return the complex refraction index using DABAX.

Parameters:

  • photon_energy_ev (float or numpy array) – The photon energy or array of energies in eV.

  • material (str, optional) – The symbol/formula of the material.

  • density (float, optional) – The material density in g/cm3.

  • dabax (None or DabaxXraylib, optional) – The pointer to the DabaxXraylib instance (default: None, it uses DabaxXraylib()).

Returns:

The array with complex refraction index.

Return type:

float or numpy array

classmethod get_refraction_index_external_xraylib(photon_energy_ev=10000.0, material='SiC', density=3.217)[source]

Standalone method to return the complex refraction index using xraylib.

Parameters:

  • photon_energy_ev (float or numpy array) – The photon energy or array of energies in eV.

  • material (str, optional) – The symbol/formula of the material.

  • density (float, optional) – The material density in g/cm3.

Returns:

The array with complex refraction index.

Return type:

float or numpy array

classmethod get_refraction_index_real_external_dabax(photon_energy_ev=10000.0, material='SiC', density=3.217, dabax=None)[source]

Standalone method to return the complex refraction index using DABAX.

Parameters:

  • photon_energy_ev (float or numpy array) – The photon energy or array of energies in eV.

  • material (str, optional) – The symbol/formula of the material.

  • density (float, oprional) – The material density in g/cm3.

  • dabax (None or DabaxXraylib, optional) – The pointer to the DabaxXraylib instance (default: None, it uses DabaxXraylib()).

Returns:

The array with the real part of the refraction index.

Return type:

float or numpy array

classmethod get_refraction_index_real_external_xraylib(photon_energy_ev=10000.0, material='SiC', density=3.217)[source]

Standalone method to return the real part of the refraction index using xraylib.

Parameters:

  • photon_energy_ev (float or numpy array) – The photon energy or array of energies in eV.

  • material (str, optional) – The symbol/formula of the material.

  • density (float, optional) – The material density in g/cm3.

Returns:

The array with the real part of refraction index.

Return type:

float or numpy array

info()[source]

Prints some information.

preprocessor_info()[source]

Prints some information.

classmethod prerefl(interactive=True, SYMBOL='SiC', DENSITY=3.217, FILE='prerefl.dat', E_MIN=100.0, E_MAX=20000.0, E_STEP=100.0, materials_library=None)[source]

Creates an instance of PreRefl with parameters initialized from the keyword parameters and the prerefl preprocessor file. It uses xraylib for accessing the optical constants.

Parameters:

  • interactive (bool, optional) – Set True for running interactively in the terminal and answer the questions (like in shadow2).

  • SYMBOL (str, optional) – The material symbol/formula.

  • DENSITY (float, optional) – The density of the material in g/cm3.

  • FILE (str, optional) – The file name (output) for the prerefl preprocessor file.

  • E_MIN (float, optional) – The minimum photon energy in eV (for creating the tabulated refraction index).

  • E_MAX (float, optional) – The maximum photon energy in eV (for creating the tabulated refraction index).

  • E_STEP (float optional) – The photon energy step in eV.

Return type:

instance of PreRefl

classmethod prerefl_cxro(input_file='https://henke.lbl.gov/tmp/xray8378.dat', output_file='prerefl.dat', E_MIN=None, E_MAX=None, NPOINTS=1000)[source]

Creates an instance of PreRefl with parameters initialized from the keyword parameters and a file with energy, alpha and beta created by the CXRO web site https://henke.lbl.gov/optical_constants/getdb2.html

When running the cxro site, request a “text file” and copy the link below “If your file does not appear, click here.”

Parameters:

  • input_file (str, optional) – The URL from where the data is downloaded.

  • output_file (str, optional) – The file name (output) for the prerefl preprocessor file.

  • E_MIN (float, optional) – The minimum photon energy in eV (for creating the tabulated refraction index).

  • E_MAX (float, optional) – The maximum photon energy in eV (for creating the tabulated refraction index).

  • NPOINTS (int optional) – The number of points for the photon energy array.

Return type:

instance of PreRefl

classmethod prerefl_refractiveindexinfo(shelf='main', book='SiO2', page='Franta', output_file='prerefl.dat', WAVELENGTH_MIN=1e-07, WAVELENGTH_MAX=5e-07, NPOINTS=1000, density=2.2, use_absorption=1, invert_refraction_index=0)[source]

Creates an instance of PreRefl with parameters initialized from the keyword parameters and data from https://refractiveindex.info/ .

Parameters:

  • shelf (str) – The shelf name (see [1]_ and [2]_).

  • book (str) – The book name (see [1]_ and [2]_).

  • page (str) – The page name (see [1]_ and [2]_).

  • output_file (str, optional) – The file name (output) for the prerefl preprocessor file.

  • WAVELENGTH_MIN (float, optional) – The minimum value for the wavelength in m.

  • WAVELENGTH_MAX (float, optional) – The maximum value for the wavelength in m.

  • NPOINTS (int, optional) – The number of points.

  • density (float, optional) – The density in g/cm^3.

  • use_absorption (int, optional) – Set to zero for using zero absorption (zero imaginary part of refraction index).

  • invert_refraction_index (int, optional) – Set to 1 to invert the refraction index (to be used for example, for total internal reflection)

Return type:

instance of PreRefl

References

read_preprocessor_file(filename)[source]

Reads a preprocessor (prerefl) file. The same as in shadow3.

Parameters:

filename (str) – The name of the filename.

reflectivity_amplitudes_fresnel(photon_energy_ev=10000.0, grazing_angle_mrad=3.0, roughness_rms_A=0.0, method=0)[source]

Calculates the reflectivity (amplitude) of an interface using Fresnel formulas.

Parameters:

  • photon_energy_ev (float or numpy array) – The photon energy in eV.

  • grazing_angle_mrad (float or numpy array) – The grazing incident angle in mrad.

  • roughness_rms_A (float or numpy array) – The rouughness RMS in Angstroms,

  • method (int, optional) – 0=Born&Wolf, 1=Parratt, 2=shadow3 (avoid using 0 or 1, experimental!!)

Returns:

(rs, rp, runp) the s-polarized, p-pol and unpolarized reflectivities

Return type:

tuple

classmethod reflectivity_amplitudes_fresnel_external(photon_energy_ev=10000.0, refraction_index_1=1.0, refraction_index_2=1.0, grazing_angle_mrad=3.0, roughness_rms_A=0.0, method=0)[source]
Standalone method to calculate the complex Fresnel reflectivity amplitudes

(r_s, r_p) of a single interface using different formulations.

This routine supports three different implementations that correspond to different physical approximations and historical usages.

Exact solution of Maxwell boundary conditions at a planar interface.

Uses Snell’s law:

n1 sin(theta1) = n2 sin(theta2)

Fresnel amplitudes:

r_s = (n1 cos(theta1) - n2 cos(theta2)) /

(n1 cos(theta1) + n2 cos(theta2))

r_p = (n2 cos(theta1) - n1 cos(theta2)) /

(n2 cos(theta1) + n1 cos(theta2))

Characteristics:

  • Fully complex

  • Correct magnitude and phase

  • Correct Brewster angle behavior

  • Correct total internal reflection (TIR)

  • Correct total external reflection (X-rays)

  • Correct sigma–pi phase difference

Valid for:

  • Visible optics

  • Infrared

  • X-rays

  • Polarization studies

  • Phase-sensitive problems

  • Interference simulations

Recommended when phase or polarization matters.

Based on the grazing-angle X-ray approximation:

n = 1 - delta + i beta f = sqrt(phi^2 - 2 delta - 2 i beta) r = (f1 - f2) / (f1 + f2)

where phi is the grazing angle (rad).

This corresponds to the small-angle X-ray limit of the s-polarized Fresnel coefficient.

IMPORTANT:

In the present implementation, r_p is set equal to r_s. Therefore polarization effects are not properly described.

Characteristics:

  • Valid for grazing-incidence X-rays

  • Assumes delta, beta << 1

  • Assumes small angles (mrad)

  • Good for reflectivity curves

  • Suitable for multilayer recursion (Parratt method)

Limitations:

  • No Brewster angle

  • No proper p-polarization behavior

  • Not valid for visible optics

  • Not valid for moderate angles

  • Not suitable for polarization phase studies

Derived from grazing-incidence X-ray reflectivity formulas.

Computes reflectivity (intensity) first:

R = |r|^2

Then reconstructs amplitude as:

r ≈ sqrt(R)

This approach was historically sufficient for ray tracing, where only intensities were required.

Characteristics:

  • Good reflectivity magnitude for X-ray mirrors

  • Designed for ray-tracing simulations

  • Phase is not physically correct

  • Sigma–pi phase difference not reliable

Limitations:

  • Phase information lost

  • Not suitable for interference

  • Not suitable for polarization studies

  • Not valid for visible optics

  • Use method=0 (Born & Wolf) whenever phase or polarization matters.

  • Use method=1 for grazing-incidence X-ray reflectivity curves.

  • Use method=2 only for intensity-based ray-tracing applications.

photon_energy_evfloat or numpy array

Photon energy in eV (used only for Debye-Waller factor).

grazing_angle_mradfloat or numpy array

Grazing incident angle in mrad (angle from surface).

roughness_rms_Afloat

Surface roughness RMS in Angstrom.

methodint

0 = Born & Wolf [1]_ (full Fresnel, recommended) 1 = Parratt grazing approximation [2]_ (X-rays) 2 = Shadow3 reflectivity approximation [3] (intensity-based)

refraction_index_1complex

Refractive index of medium 1 (incident medium).

refraction_index_2complex

Refractive index of medium 2 (transmitted medium).

tuple

(r_s, r_p) complex amplitude reflectivities including optional Debye-Waller roughness factor.

classmethod reflectivity_amplitudes_fresnel_external_dabax(photon_energy_ev=10000.0, coating_material='SiC', coating_density=3.217, grazing_angle_mrad=3.0, roughness_rms_A=0.0, method=0, dabax=None)[source]

Standalone method to calculate the reflectivity (amplitude) of an interface using Fresnel formulas using dabax.

Parameters:

  • photon_energy_ev (float or numpy array) – The photon energy in eV.

  • grazing_angle_mrad (float or numpy array) – The grazing incident angle in mrad.

  • roughness_rms_A (float or numpy array) – The rouughness RMS in Angstroms,

  • method (int, optional) – 0=Born&Wolf, 1=Parratt, 2=shadow3 (avoid using 0 or 1, experimental!!)

  • dabax (None or instance of DabaxXraylib) – A pointer to the dabax library. Use None for default.

  • coating_material (int, optional) – The symbol/formula of the coating material.

  • coating_density (int, optional) – The density in g/cm3 of the coating material.

Returns:

(rs, rp, runp) the s-polarized, p-pol and unpolarized reflectivities

Return type:

tuple

classmethod reflectivity_amplitudes_fresnel_external_xraylib(photon_energy_ev=10000.0, coating_material='SiC', coating_density=3.217, grazing_angle_mrad=3.0, roughness_rms_A=0.0, method=0)[source]

Standalone method to calculate the reflectivity (amplitude) of an interface using Fresnel formulas using xraylib.

Parameters:

  • photon_energy_ev (float or numpy array) – The photon energy in eV.

  • grazing_angle_mrad (float or numpy array) – The grazing incident angle in mrad.

  • roughness_rms_A (float or numpy array) – The rouughness RMS in Angstroms,

  • method (int, optional) – 0=Born&Wolf, 1=Parratt, 2=shadow3 (avoid using 0 or 1, experimental!!)

  • coating_material (int, optional) – The symbol/formula of the coating material.

  • coating_density (int, optional) – The density in g/cm3 of the coating material.

Returns:

(rs, rp, runp) the s-polarized, p-pol and unpolarized reflectivities

Return type:

tuple

reflectivity_fresnel(photon_energy_ev=10000.0, grazing_angle_mrad=3.0, roughness_rms_A=0.0, method=2)[source]

Calculates the reflectivity (intensity) of an interface using Fresnel formulas.

Parameters:

  • photon_energy_ev (float or numpy array) – The photon energy in eV.

  • grazing_angle_mrad (float or numpy array) – The grazing incident angle in mrad.

  • roughness_rms_A (float or numpy array) – The rouughness RMS in Angstroms,

  • method (int, optional) – 0=Born&Wolf, 1=Parratt, 2=shadow3 (avoid using 0 or 1, experimental!!)

Returns:

(rs, rp, runp) the s-polarized, p-pol and unpolarized reflectivities

Return type:

tuple

Module contents