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#!/usr/bin/env python3
# /// script
# requires-python = ">=3.10"
# dependencies = ["bornagain>=25,<26", "lmfit"]
# ///
"""
Fit example with data by M. Fitzsimmons et al,
https://doi.org/10.5281/zenodo.4072376.
Sample is a ~50 nm Pt film on a Si substrate.
Single event data from Spallation Neutron Source
Beamline-4A (MagRef) with 60 Hz pulses and a wavelength
band of roughly 4-7 Å in 100 steps of 2theta.
"""
import bornagain as ba
ba.require_versions("bornagain>=25,<26")
import os
import numpy as np
from bornagain import nm
import lmfit
####################################################################
# Sample and simulation model
####################################################################
# Use fixed values for the SLD of the substrate and Pt layer
sldPt = (6.3568e-06, 1.8967e-09)
sldSi = (2.0728e-06, 2.3747e-11)
def get_sample(P):
layer_color = (0.93, 0.72, 0.25)
layer_mat = ba.SLDMaterial("Pt", layer_color, *sldPt)
substrate_color = (0.30, 0.62, 0.86)
substrate_mat = ba.SLDMaterial("Si", substrate_color, *sldSi)
transient = ba.TanhTransient()
si_autocorr = ba.SelfAffineFractalModel(P["r_si"]*nm, 0.7, 25*nm)
pt_autocorr = ba.SelfAffineFractalModel(P["r_pt"]*nm, 0.7, 25*nm)
r_si = ba.Roughness(si_autocorr, transient)
r_pt = ba.Roughness(pt_autocorr, transient)
ambient_layer = ba.Layer(ba.Vacuum())
layer = ba.Layer(layer_mat, P["t_pt"]*nm, r_pt)
substrate_layer = ba.Layer(substrate_mat, r_si)
sample = ba.Sample()
sample.addLayer(ambient_layer)
sample.addLayer(layer)
sample.addLayer(substrate_layer)
return sample
def get_simulation(q_axis, P):
sample = get_sample(P)
scan = ba.QzScan(q_axis)
scan.setIntensity(P["intensity"])
scan.setOffset(P["q_offset"])
distr = ba.DistributionGaussian(0., 1., 25, 4.)
scan.setAbsoluteQResolution(distr, P["q_resolution"])
simulation = ba.SpecularSimulation(scan, sample)
return simulation
def load_data(filename):
"""
Reads q, reflectivity, and its uncertainty.
The unused fourth column is the width of a logarithmic q bin, not a
Gaussian instrument resolution.
"""
# By default, read data files from the script directory.
datadir = ba.data_dir(beside=__file__)
filepath = os.path.join(datadir, filename)
q_angstrom, intensity, sigma = ba.read_columns(
filepath, usecols=(0, 1, 2))
q = 10*q_angstrom
return q, intensity, sigma
####################################################################
# Main
####################################################################
if __name__ == '__main__':
P = lmfit.Parameters()
P.add("intensity", value=1, min=0.8, max=1.2) # (dimensionless)
P.add("q_offset", value=0.01, min=-0.02, max=0.02) # (1/nm)
P.add("q_resolution", value=0.01, min=0, max=0.02) # (1/nm)
P.add("t_pt", value=50, min=45, max=55) # (nm)
P.add("r_si", value=1.22, min=0, max=5) # (nm)
P.add("r_pt", value=0.25, min=0, max=5) # (nm)
initialP = P.valuesdict()
# Set q axis, load data:
qmin = 0.18
qmax = 2.4
qzs = np.linspace(qmin, qmax, 1500)
q_exp, exp_values, sigma = load_data("RvsQ_36563_36662.dat.gz")
exp_data = ba.Datafield(
ba.Frame(ba.ListScan("q_z (1/nm)", q_exp)),
exp_values.tolist(), sigma.tolist())
initial_result = get_simulation(qzs, initialP).simulate()
# Restrict data to given q range
in_range = (q_exp >= qmin) & (q_exp <= qmax)
q_fit = q_exp[in_range]
y_fit = exp_values[in_range]
# Fit:
def residuals(P):
sim_values = get_simulation(
q_fit, P.valuesdict()).simulate().intensities()
return y_fit - sim_values
result = lmfit.minimize(residuals, P, method="leastsq")
print(lmfit.fit_report(result))
finalP = result.params.valuesdict()
# Print and plot fit outcome:
print("Fit Result:")
print(finalP)
ba.showSample3D(get_sample(finalP), sample_size=120*nm, seed=0)
fitted_result = get_simulation(qzs, finalP).simulate()
figure, (initial_ax, fitted_ax) = ba.plt.subplots(
1, 2, figsize=(10, 4), layout="constrained")
ba.plot_specular_curves(
[("Experiment", exp_data, None)],
ax=initial_ax, ylabel="$R$", color="black")
ba.plot_specular_curves(
[("Initial model", None, initial_result)],
ax=initial_ax, ylabel="$R$")
initial_ax.set_title("Before fitting")
initial_ax.legend()
ba.plot_specular_curves(
[("Experiment", exp_data, None)],
ax=fitted_ax, ylabel="$R$", color="black")
ba.plot_specular_curves(
[("Fitted model", None, fitted_result)],
ax=fitted_ax, ylabel="$R$")
fitted_ax.set_title("After fitting")
fitted_ax.legend()
ba.plt.show()
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