### Beam divergence

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

• The wavelength follows a log-normal distribution around the mean value of $1$ $\unicode{x212B}$ 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 $\sigma_{\alpha_i} = \sigma_{\varphi_i} = 0.1^{\circ}$.

The DWBA simulation 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.
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64  #!/usr/bin/env python3 """ Cylinder form factor in DWBA with beam divergence """ import bornagain as ba from bornagain import deg, nm def get_sample(): """ Returns a sample with uncorrelated cylinders on a substrate. """ # Define materials material_Particle = ba.HomogeneousMaterial("Particle", 0.0006, 2e-08) material_Substrate = ba.HomogeneousMaterial("Substrate", 6e-06, 2e-08) material_Vacuum = ba.HomogeneousMaterial("Vacuum", 0.0, 0.0) # Define form factors ff = ba.FormFactorCylinder(5.0*nm, 5.0*nm) # Define particles particle = ba.Particle(material_Particle, ff) # Define particle layouts layout = ba.ParticleLayout() layout.addParticle(particle, 1.0) layout.setWeight(1) layout.setTotalParticleSurfaceDensity(0.01) # Define layers layer_1 = ba.Layer(material_Vacuum) layer_1.addLayout(layout) layer_2 = ba.Layer(material_Substrate) # Define sample sample = ba.MultiLayer() sample.addLayer(layer_1) sample.addLayer(layer_2) return sample def get_simulation(sample): beam = ba.Beam(1.0, 0.1*nm, ba.Direction(0.2*deg, 0*deg)) detector = ba.SphericalDetector(100, 2*deg, 1*deg, 1*deg) simulation = ba.GISASSimulation(beam, sample, detector) distr_1 = ba.DistributionLogNormal(0.1*nm, 0.1) simulation.addParameterDistribution("*/Beam/Wavelength", distr_1, 5, 0.0) distr_2 = ba.DistributionGaussian(0.2*deg, 0.1*deg) simulation.addParameterDistribution("*/Beam/InclinationAngle", distr_2, 5, 0.0) distr_3 = ba.DistributionGaussian(0*deg, 0.1*deg) simulation.addParameterDistribution("*/Beam/AzimuthalAngle", distr_3, 5, 0.0) return simulation if __name__ == '__main__': import ba_plot sample = get_sample() simulation = get_simulation(sample) ba_plot.run_and_plot(simulation) 
BeamDivergence.py