Cylinders in Born Approximation

Scattering from a monodisperse distribution of cylinders using the Born approximation.

  • The cylinders are all identical with radii and heights equal to 5 nanometers.
  • The wavelength is equal to 1 Å.
  • The incident angles are equal to αi = 0.2° and Φi=0°.
  • There is no substrate (particles are embedded in the air layer), hence no refraction, hence no distorted waves, hence DWBA boils down to regular Born approximation.
  • Scattering is not affected by inter-particle correlations (dilute-particles approximation).
Real-space model: 
Intensity Image: 
Python Script: 
Cylinder formfactor in Born approximation
import numpy
import bornagain as ba
from bornagain import deg, angstrom, nm

phi_min, phi_max = -2.0, 2.0
alpha_min, alpha_max = 0.0, 2.0

def get_sample():
    Returns a sample with cylinders in a homogeneous environment ("air"),
    implying a simulation in plain Born approximation.
    # defining materials
    m_ambience = ba.HomogeneousMaterial("Air", 0.0, 0.0)
    m_particle = ba.HomogeneousMaterial("Particle", 6e-4, 2e-8)

    # collection of particles
    cylinder_ff = ba.FormFactorCylinder(5*nm, 5*nm)
    cylinder = ba.Particle(m_particle, cylinder_ff)
    particle_layout = ba.ParticleLayout()
    particle_layout.addParticle(cylinder, 1.0)

    air_layer = ba.Layer(m_ambience)

    multi_layer = ba.MultiLayer()
    return multi_layer

def get_simulation():
    Returns a GISAXS simulation with beam and detector defined
    simulation = ba.GISASSimulation()
    simulation.setDetectorParameters(200, phi_min*deg, phi_max*deg,
                                     200, alpha_min*deg, alpha_max*deg)
    simulation.setBeamParameters(1.0*angstrom, 0.2*deg, 0.0*deg)
    return simulation

def run_simulation():
    Runs simulation and returns intensity map.
    sample = get_sample()
    simulation = get_simulation()
    return simulation.getIntensityData()

if __name__ == '__main__':
    result = run_simulation()