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#!/usr/bin/env python3
"""
This example demonstrates how to fit a complex experimental setup using BornAgain.
It is based on real data published in https://doi.org/10.1002/advs.201700856
by A. Glavic et al.
In this example we utilize the scalar reflectometry engine to fit polarized
data without spin-flip for performance reasons.
"""
import os, sys
import numpy
import matplotlib.pyplot as plt
from scipy.optimize import differential_evolution
import bornagain as ba
from bornagain import angstrom, sample_tools as st
# number of points on which the computed result is plotted
scan_size = 1500
# restrict the Q-range of the data used for fitting
qmin = 0.08
qmax = 1.4
datadir = os.getenv('BA_EXAMPLE_DATA_DIR', '')
####################################################################
# Create Sample and Simulation #
####################################################################
def get_sample(parameters, sign, ms150=1):
m_Air = ba.MaterialBySLD("Air", 0, 0)
m_PyOx = ba.MaterialBySLD("PyOx",
(parameters["sld_PyOx_real"] + \
sign * ms150 * parameters["msld_PyOx"] )* 1e-6,
parameters["sld_PyOx_imag"] * 1e-6)
m_Py2 = ba.MaterialBySLD("Py2",
( parameters["sld_Py2_real"] + \
sign * ms150 * parameters["msld_Py2"] ) * 1e-6,
parameters["sld_Py2_imag"] * 1e-6)
m_Py1 = ba.MaterialBySLD("Py1",
( parameters["sld_Py1_real"] + \
sign * ms150 * parameters["msld_Py1"] ) * 1e-6,
parameters["sld_Py1_imag"] * 1e-6)
m_SiO2 = ba.MaterialBySLD("SiO2", parameters["sld_SiO2_real"]*1e-6,
parameters["sld_SiO2_imag"]*1e-6)
m_Si = ba.MaterialBySLD("Substrate", parameters["sld_Si_real"]*1e-6,
parameters["sld_Si_imag"]*1e-6)
l_Air = ba.Layer(m_Air)
l_PyOx = ba.Layer(m_PyOx, parameters["t_PyOx"]*angstrom)
l_Py2 = ba.Layer(m_Py2, parameters["t_Py2"]*angstrom)
l_Py1 = ba.Layer(m_Py1, parameters["t_Py1"]*angstrom)
l_SiO2 = ba.Layer(m_SiO2, parameters["t_SiO2"]*angstrom)
l_Si = ba.Layer(m_Si)
r_PyOx = ba.LayerRoughness(parameters["r_PyOx"]*angstrom)
r_Py2 = ba.LayerRoughness(parameters["r_Py2"]*angstrom)
r_Py1 = ba.LayerRoughness(parameters["r_Py1"]*angstrom)
r_SiO2 = ba.LayerRoughness(parameters["r_SiO2"]*angstrom)
r_Si = ba.LayerRoughness(parameters["r_Si"]*angstrom)
sample = ba.MultiLayer()
sample.addLayer(l_Air)
sample.addLayerWithTopRoughness(l_PyOx, r_PyOx)
sample.addLayerWithTopRoughness(l_Py2, r_Py2)
sample.addLayerWithTopRoughness(l_Py1, r_Py1)
sample.addLayerWithTopRoughness(l_SiO2, r_SiO2)
sample.addLayerWithTopRoughness(l_Si, r_Si)
sample.setRoughnessModel(ba.RoughnessModel.NEVOT_CROCE)
return sample
def get_simulation(q_axis, parameters, sign, ms150=False):
q_distr = ba.DistributionGaussian(0., 1., 25, 3.)
dq = parameters["dq"]*q_axis
scan = ba.QzScan(q_axis)
scan.setVectorResolution(q_distr, dq)
if ms150:
sample = get_sample(parameters=parameters,
sign=sign,
ms150=parameters["ms150"])
else:
sample = get_sample(parameters=parameters, sign=sign, ms150=1)
simulation = ba.SpecularSimulation(scan, sample)
simulation.setBackground(ba.ConstantBackground(5e-7))
return simulation
def run_simulation(q_axis, fitParams, *, sign, ms150=False):
parameters = dict(fitParams, **fixedParams)
simulation = get_simulation(q_axis, parameters, sign, ms150)
result = simulation.simulate()
result.data_field().scale(parameters["intensity"])
return result
def qr(result):
"""
Return q and reflectivity arrays from simulation result.
"""
q = numpy.array(result.convertedBinCenters(ba.Coords_QSPACE))
r = numpy.array(result.array(ba.Coords_QSPACE))
return q, r
####################################################################
# Plot Handling #
####################################################################
def plot(qs, rs, exps, shifts, labels, filename):
"""
Plot the simulated result together with the experimental data.
"""
fig = plt.figure()
ax = fig.add_subplot(111)
for q, r, exp, shift, l in zip(qs, rs, exps, shifts, labels):
ax.errorbar(exp[0],
exp[1]/shift,
yerr=exp[2]/shift,
fmt='.',
markersize=0.75,
linewidth=0.5)
ax.plot(q, r/shift, label=l)
ax.set_yscale('log')
plt.legend()
plt.xlabel("Q [nm${}^{-1}$]")
plt.ylabel("R")
plt.tight_layout()
plt.savefig(filename)
def plot_sld_profile(fitParams, filename):
plt.figure()
parameters = dict(fitParams, **fixedParams)
z_300_p, sld_300_p = st.materialProfile(get_sample(parameters, 1))
z_300_m, sld_300_m = st.materialProfile(get_sample(parameters, -1))
z_150_p, sld_150_p = st.materialProfile(
get_sample(parameters, 1, ms150=parameters["ms150"]))
z_150_m, sld_150_m = st.materialProfile(
get_sample(parameters, -1, ms150=parameters["ms150"]))
plt.figure()
plt.plot(z_300_p, numpy.real(sld_300_p)*1e6, label=r"300K $+$")
plt.plot(z_300_m, numpy.real(sld_300_m)*1e6, label=r"300K $-$")
plt.plot(z_150_p, numpy.real(sld_150_p)*1e6, label=r"150K $+$")
plt.plot(z_150_m, numpy.real(sld_150_m)*1e6, label=r"150K $-$")
plt.xlabel(r"$z$ [A]")
plt.ylabel(r"$\delta(z) \cdot 10^6$")
plt.legend()
plt.tight_layout()
plt.savefig(filename)
# plt.close()
####################################################################
# Data Handling #
####################################################################
def normalizeData(data):
"""
Removes duplicate q values from the input data,
normalizes it such that the maximum of the reflectivity is
unity and rescales the q-axis to inverse nm
"""
# delete repeated data
r0 = numpy.where(data[0] - numpy.roll(data[0], 1) == 0)
data = numpy.delete(data, r0, 1)
data[0] = data[0]/angstrom
norm = numpy.max(data[1])
data[1] = data[1]/norm
data[2] = data[2]/norm
# sort by q axis
so = numpy.argsort(data[0])
data = data[:, so]
return data
def get_Experimental_data(filename, qmin, qmax):
filepath = os.path.join(datadir, filename)
with open(filepath, 'r') as f:
input_Data = numpy.genfromtxt(f, unpack=True, usecols=(0, 2, 3))
data = normalizeData(input_Data)
minIndex = numpy.argmin(numpy.abs(data[0] - qmin))
maxIndex = numpy.argmin(numpy.abs(data[0] - qmax))
return data[:, minIndex:maxIndex + 1]
####################################################################
# Fit Function #
####################################################################
def relative_difference(sim, exp):
result = (exp - sim)/(exp + sim)
return numpy.sum(result*result)/len(sim)
def create_Parameter_dictionary(parameterNames, *args):
return {name: value for name, value in zip(parameterNames, *args)}
class FitObjective:
def __init__(self, q_axis, rdata, simulationFactory, parameterNames):
if isinstance(q_axis, list) and isinstance(rdata, list) and \
isinstance(simulationFactory, list):
self._q = q_axis
self._r = rdata
self._simulationFactory = simulationFactory
elif not isinstance(q_axis, list) and not isinstance(rdata, list) \
and not isinstance(simulationFactory, list):
self._q = [q_axis]
self._r = [rdata]
self._simulationFactory = [simulationFactory]
else:
raise Exception("Inconsistent parameters")
self._parameterNames = parameterNames
def __call__(self, *args):
fitParameters = create_Parameter_dictionary(self._parameterNames,
*args)
print(f"FitParamters = {fitParameters}")
result_metric = 0
for q, r, sim in zip(self._q, self._r, self._simulationFactory):
sim_result = sim(q, fitParameters).array()
result_metric += relative_difference(sim_result, r)
return result_metric
def run_fit_differential_evolution(q_axis, rdata, simulationFactory,
startParams):
bounds = [(par[1], par[2]) for n, par in startParams.items()]
parameters = [par[0] for n, par in startParams.items()]
parameterNames = [n for n, par in startParams.items()]
print(f"Bounds = {bounds}")
objective = FitObjective(q_axis, rdata, simulationFactory,
parameterNames)
chi2_initial = objective(parameters)
result = differential_evolution(objective,
bounds,
maxiter=200,
popsize=len(bounds)*10,
mutation=(0.5, 1.5),
disp=True,
tol=1e-2)
resultParameters = create_Parameter_dictionary(parameterNames,
result.x)
chi2_final = objective(resultParameters.values())
print(f"Initial chi2: {chi2_initial}")
print(f"Final chi2: {chi2_final}")
return resultParameters
####################################################################
# Main Function #
####################################################################
if __name__ == '__main__':
fixedParams = {
"sld_PyOx_imag": (0, 0, 0),
"sld_Py2_imag": (0, 0, 0),
"sld_Py1_imag": (0, 0, 0),
"sld_SiO2_imag": (0, 0, 0),
"sld_Si_imag": (0, 0, 0),
"sld_SiO2_real": (3.47, 3, 4),
"sld_Si_real": (2.0704, 2, 3),
"dq": (0.018, 0, 0.1),
}
if len(sys.argv) > 1 and sys.argv[1] == "fit":
# some sensible start parameters for fitting
startParams = {
"intensity": (1.04, 0, 3),
"t_PyOx": (77, 60, 100),
"t_Py2": (56, 40, 70),
"t_Py1": (64, 50, 80),
"t_SiO2": (16, 10, 30),
"sld_PyOx_real": (1.915, 1.6, 2.2),
"sld_Py2_real": (5, 3, 6),
"sld_Py1_real": (4.62, 3, 6),
"r_PyOx": (27, 5, 35),
"r_Py2": (12, 5, 20),
"r_Py1": (12, 5, 20),
"r_SiO2": (17, 2, 25),
"r_Si": (18, 2, 25),
"msld_PyOx": (0.25, 0, 1),
"msld_Py2": (0.63, 0, 1),
"msld_Py1": (0.64, 0, 1),
"ms150": (1, 0.9, 1.1),
}
fit = True
else:
# result from our own fitting
startParams = {
'intensity': 0.9482344993285265,
't_PyOx': 74.97056190221168,
't_Py2': 61.75823766477464,
't_Py1': 54.058310970786316,
't_SiO2': 23.127048588278402,
'sld_PyOx_real': 2.199791584033569,
'sld_Py2_real': 4.980316982224387,
'sld_Py1_real': 4.612135848532186,
'r_PyOx': 31.323366207013787,
'r_Py2': 9.083768897940645,
'r_Py1': 5,
'r_SiO2': 14.43455709065263,
'r_Si': 14.948233893986075,
'msld_PyOx': 0.292684104601585,
'msld_Py2': 0.5979447434271339,
'msld_Py1': 0.56376339230351,
'ms150': 1.083311702077648
}
startParams = {d: (v, ) for d, v in startParams.items()}
fit = False
fixedParams = {d: v[0] for d, v in fixedParams.items()}
paramsInitial = {d: v[0] for d, v in startParams.items()}
def run_Simulation_300_p(qzs, params):
return run_simulation(qzs, params, sign=1)
def run_Simulation_300_m(qzs, params):
return run_simulation(qzs, params, sign=-1)
def run_Simulation_150_p(qzs, params):
return run_simulation(qzs, params, sign=1, ms150=True)
def run_Simulation_150_m(qzs, params):
return run_simulation(qzs, params, sign=-1, ms150=True)
qzs = numpy.linspace(qmin, qmax, scan_size)
q_300_p, r_300_p = qr(run_Simulation_300_p(qzs, paramsInitial))
q_300_m, r_300_m = qr(run_Simulation_300_m(qzs, paramsInitial))
q_150_p, r_150_p = qr(run_Simulation_150_p(qzs, paramsInitial))
q_150_m, r_150_m = qr(run_Simulation_150_m(qzs, paramsInitial))
data_300_p = get_Experimental_data("honeycomb/300_p.dat", qmin, qmax)
data_300_m = get_Experimental_data("honeycomb/300_m.dat", qmin, qmax)
data_150_p = get_Experimental_data("honeycomb/150_p.dat", qmin, qmax)
data_150_m = get_Experimental_data("honeycomb/150_m.dat", qmin, qmax)
plot_sld_profile(paramsInitial,
"Honeycomb_Fit_sld_profile_initial.pdf")
plot([q_300_p, q_300_m, q_150_p, q_150_m],
[r_300_p, r_300_m, r_150_p, r_150_m],
[data_300_p, data_300_m, data_150_p, data_150_m], [1, 1, 10, 10],
["300K $+$", "300K $-$", "150K $+$", "150K $-$"],
"Honeycomb_Fit_reflectivity_initial.pdf")
# fit and plot fit
if fit:
dataSimTuple = [[
data_300_p[0], data_300_m[0], data_150_p[0], data_150_m[0]
], [data_300_p[1], data_300_m[1], data_150_p[1], data_150_m[1]],
[
run_Simulation_300_p, run_Simulation_300_m,
run_Simulation_150_p, run_Simulation_150_m
]]
fitResult = run_fit_differential_evolution(*dataSimTuple,
startParams)
print("Fit Result:")
print(fitResult)
q_300_p, r_300_p = qr(run_Simulation_300_p(qzs, fitResult))
q_300_m, r_300_m = qr(run_Simulation_300_m(qzs, fitResult))
q_150_p, r_150_p = qr(run_Simulation_150_p(qzs, fitResult))
q_150_m, r_150_m = qr(run_Simulation_150_m(qzs, fitResult))
plot([q_300_p, q_300_m, q_150_p, q_150_m],
[r_300_p, r_300_m, r_150_p, r_150_m],
[data_300_p, data_300_m, data_150_p, data_150_m],
[1, 1, 10, 10],
["300K $+$", "300K $-$", "150K $+$", "150K $-$"],
"Honeycomb_Fit_reflectivity_fit.pdf")
plot_sld_profile(fitResult, "Honeycomb_Fit_sld_profile_fit.pdf")
plt.show()
|
BornAgain
≻ 20
≻ Documentation ≻ Python scripting ≻ Fitting ≻ Extended examples ≻ Reflectometry: Fit honeycomb
