# 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 bornagain as ba
from bornagain import deg, angstrom, nm

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()

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, -2.0*deg, 2.0*deg,
200, 0.0*deg, 2.0*deg)
simulation.setBeamParameters(1.0*angstrom, 0.2*deg, 0.0*deg)
return simulation

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

if __name__ == '__main__':
result = run_simulation()
ba.plot_intensity_data(result)
```