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Beam divergence

By default, the incident beam is perfectly monochromatic and collimated. Here we show how to set finite distributions of wavelengths and of grazing angles.

  • The wavelength follows a log-normal distribution around the mean value of 0.1 nm with a scale parameter equal to $0.1$.
  • Both incident angles follow a Gaussian distribution around the average values $\alpha_i = 0.2 ^{\circ}$ and $\varphi_i = 0^{\circ}$, respectively and $\sigma_{\alpha_i} = \sigma_{\varphi_i} = 0.1^{\circ}$.

First, the distributions should be defined:

distr_lambda = ba.DistributionLogNormal(0.1*nm, 0.1, 5, 2)
distr_alpha = ba.DistributionGaussian(0.2*deg, 0.1*deg, 5, 2)
distr_phi = ba.DistributionGaussian(0, 0.1*deg, 5, 2)

Then the distributions are to be applied to the simulation object in the following way:

simulation = ba.ScatteringSimulation(...)
simulation.addParameterDistribution(role, distribution)

The role is a special object itself, indicating which parameter is distributed. There are three roles:

role_wavelength = ba.ParameterDistribution.BeamWavelength
role_grazing_angle = ba.ParameterDistribution.BeamGrazingAngle
role_azimuthal_angle = ba.ParameterDistribution.BeamAzimuthalAngle

Distributions are passed to the simulation together with their role:

simulation.addParameterDistribution(role_wavelength, distr_lambda)
simulation.addParameterDistribution(role_grazing_angle, distr_alpha)
simulation.addParameterDistribution(role_azimuthal_angle, distr_phi)

Example

The DWBA simulation example is shown for a standard sample model:

  • The sample is composed of monodisperse cylinders deposited on a substrate.
  • The cylinders are dilute and distributed at random, hence there is no interference between scattered waves.

Real-space model

Intensity image

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#!/usr/bin/env python3
"""
Cylinder form factor in DWBA with beam divergence
"""
import bornagain as ba
from bornagain import ba_plot as bp, deg, nm


def get_sample():
    from bornagain import std_samples
    return std_samples.cylinders()


def get_simulation(sample):
    beam = ba.Beam(1e9, 0.1*nm, 0.2*deg)
    n = 100
    detector = ba.SphericalDetector(n, 0., 2*deg, n, 0., 2*deg)
    simulation = ba.ScatteringSimulation(beam, sample, detector)
    distr_1 = ba.DistributionLogNormal(0.1*nm, 0.1, 5, 2)
    simulation.addParameterDistribution(
        ba.ParameterDistribution.BeamWavelength, distr_1)
    distr_2 = ba.DistributionGaussian(0.2*deg, 0.1*deg, 5, 2)
    simulation.addParameterDistribution(
        ba.ParameterDistribution.BeamGrazingAngle, distr_2)
    distr_3 = ba.DistributionGaussian(0, 0.1*deg, 5, 2)
    simulation.addParameterDistribution(
        ba.ParameterDistribution.BeamAzimuthalAngle, distr_3)
    return simulation


if __name__ == '__main__':
    sample = get_sample()
    simulation = get_simulation(sample)
    result = simulation.simulate()
    bp.plot_datafield(result)
    bp.plt.show()
auto/Examples/scatter2d/BeamDivergence.py