Beam Angular Spread in Specular Simulations

This example demonstrates beam angular spread effects in reflectivity computations. It also offers a comparison with data generated using another well known code: GenX. Further information about reflectometry simulations can be found in the Reflectometry Simulation Tutorial.

The observed reflectometry signal can be affected either by a spread in the beam wavelength or in the incident angle.

Intensity image

In this example, a Gaussian distribution is used to spread the incident angle, with a standard deviation of $\sigma_{\alpha} = 0.01^{\circ}$.

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#!/usr/bin/env python3
"""
An example of taking into account beam angular divergence
and beam footprint correction in reflectometry calculations.
"""
import numpy as np, os, sys
from matplotlib import pyplot as plt
import bornagain as ba
from bornagain import angstrom, ba_plot as bp, deg, std_samples

# input parameters
wavelength = 1.54*angstrom
alpha_i_min = 0  # min incident angle, deg
alpha_i_max = 2*deg  # max incident angle, rad
beam_sample_ratio = 0.01  # beam-to-sample size ratio

# convolution parameters
d_ang = 0.01*deg  # spread width for incident angle
n_sig = 3  # number of sigmas to convolve over
n_points = 25  # number of points to convolve over


def reference_data(filename):
    """
    Loads and returns reference data from GenX simulation
    """
    ax_values, real_data = np.loadtxt(filename,
                                      usecols=(0, 1),
                                      skiprows=3,
                                      unpack=True)

    # translating axis values from double incident angle # to incident angle
    ax_values *= 0.5

    return ax_values, real_data


def get_sample():
    return std_samples.alternating_layers()


def get_simulation(sample, **kwargs):
    """
    Returns a specular simulation with beam and detector defined.
    """
    n = bp.simargs['n']
    footprint = ba.FootprintSquare(beam_sample_ratio)
    alpha_distr = ba.RangedDistributionGaussian(n_points, n_sig)

    scan = ba.AlphaScan(wavelength, n, alpha_i_min, alpha_i_max)
    scan.setFootprintFactor(footprint)
    scan.setAbsoluteAngularResolution(alpha_distr, d_ang)

    return ba.SpecularSimulation(scan, sample)


if __name__ == '__main__':
    bp.parse_args(sim_n=500)

    datadir = os.getenv('BA_EXAMPLE_DATA_DIR', '')
    data_fname = os.path.join(datadir, "genx_angular_divergence.dat.gz")
    print(f"DIR={datadir} NAM={data_fname}")

    sample = get_sample()
    simulation = get_simulation(sample)
    result = simulation.simulate()
    bp.plot_simulation_result(result)
    genx_axis, genx_values = reference_data(data_fname)
    plt.yscale('log')
    plt.plot(genx_axis, genx_values, 'ko', markevery=300)
    plt.legend(['BornAgain', 'GenX'], loc='upper right')
    if bp.do_show:
        plt.show()
Examples/specular/BeamAngularDivergence.py

Reference data: Examples/data/genx_angular_divergence.dat.gz