Finding Intensity Peaks

To find the intensity peaks from a GISAXS simulation, the result must be casted in the form of a histogram2d. This must then be passed to the method FindPeaks to get the (x,y) coordinates of each peak:

    result = run_simulation().histogram2d()
    peaks = ba.FindPeaks(result, 2, "nomarkov", 0.001)
    peaks_x = [peak[0] for peak in peaks]
    ypeak_y = [peak[1] for peak in peaks]

Intensity images

The following script offers a complete example in which the peaks are found after carrying on a GISAXS simulation. This particular example uses as a sample a grating of long boxes distributed along a 1D lattice.

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"""
Simulation of grating using very long boxes and 1D lattice.
Monte-carlo integration is used to get rid of
large-particle form factor oscillations.
"""
import bornagain as ba
from bornagain import deg, angstrom, nm, micrometer
from matplotlib import pyplot as plt


def get_sample(lattice_rotation_angle=0.0*deg):
    """
    Returns a sample with a grating on a substrate.
    lattice_rotation_angle = 0 - beam parallel to grating lines
    lattice_rotation_angle = 90*deg - beam perpendicular to grating lines
    """
    # defining materials
    m_ambience = ba.HomogeneousMaterial("Air", 0.0, 0.0)
    m_si = ba.HomogeneousMaterial("Si", 5.78164736e-6, 1.02294578e-7)

    box_length, box_width, box_height = 50*micrometer, 70*nm, 50*nm
    lattice_length = 150*nm

    # collection of particles
    interference = ba.InterferenceFunction1DLattice(
        lattice_length, 90.0*deg - lattice_rotation_angle)

    pdf = ba.ba.FTDecayFunction1DGauss(450.0)
    interference.setDecayFunction(pdf)

    box_ff = ba.FormFactorLongBoxLorentz(box_length, box_width, box_height)
    box = ba.Particle(m_si, box_ff)

    particle_layout = ba.ParticleLayout()
    particle_layout.addParticle(
        box, 1.0, ba.kvector_t(0.0, 0.0, 0.0), ba.RotationZ(lattice_rotation_angle))
    particle_layout.setInterferenceFunction(interference)

    # assembling the sample
    air_layer = ba.Layer(m_ambience)
    air_layer.addLayout(particle_layout)
    substrate_layer = ba.Layer(m_si)

    roughness = ba.LayerRoughness()
    roughness.setSigma(5.0 * nm)
    roughness.setHurstParameter(0.5)
    roughness.setLatteralCorrLength(10.0 * nm)

    multi_layer = ba.MultiLayer()
    multi_layer.addLayer(air_layer)
    multi_layer.addLayerWithTopRoughness(substrate_layer, roughness)
    return multi_layer


def get_simulation():
    """
    Create and return GISAXS simulation with beam and detector defined
    """
    simulation = ba.GISASSimulation()
    simulation.setDetectorParameters(200, -0.5*deg, 0.5*deg,
                                     200, 0.0*deg, 0.6*deg)
    simulation.setBeamParameters(1.34*angstrom, 0.4*deg, 0.0*deg)
    simulation.setBeamIntensity(1e+08)
    simulation.getOptions().setMonteCarloIntegration(True, 100)
    return simulation


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


if __name__ == '__main__':
    result = run_simulation().histogram2d()
    ba.plot_histogram(result, cmap='jet', aspect='auto')

    peaks = ba.FindPeaks(result, 2, "nomarkov", 0.001)
    xpeaks = [peak[0] for peak in peaks]
    ypeaks = [peak[1] for peak in peaks]
    print(peaks)
    plt.plot(xpeaks, ypeaks, linestyle='None', marker='x', color='white',
             markersize=10)
    plt.show()

FindPeaks.py