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#!/usr/bin/env python3
# /// script
# requires-python = ">=3.10"
# dependencies = ["bornagain>=25,<26", "lmfit"]
# ///
"""
Fitting example: fit with masks
"""
import bornagain as ba
ba.require_versions("bornagain>=25,<26")
from bornagain import deg, nm, nm2
import lmfit
import numpy as np
def get_sample(P):
"""
Uncorrelated cylinders on a substrate, parameterized for fitting.
"""
substrate_color = (0.28, 0.57, 0.82)
particle_color = (0.86, 0.24, 0.18)
substrate_mat = ba.RefractiveMaterial("Substrate", substrate_color, 6e-6, 2e-8)
particle_mat = ba.RefractiveMaterial("Particle", particle_color, 6e-4, 2e-8)
particle = ba.Particle(particle_mat, ba.Cylinder(P["radius"], P["height"]))
particle_layer = ba.Layer(ba.Vacuum())
# Modest coverage keeps material averaging physical over the fit bounds.
particle_layer.deposit2D(ba.Dilute2D(1e-3/nm2, particle))
sample = ba.Sample()
sample.addLayer(particle_layer)
sample.addLayer(ba.Layer(substrate_mat))
return sample
def get_simulation(P):
"""
GISAS simulation for the parameterized cylinder sample.
"""
n = 101
beam = ba.Beam(1e8, 0.1*nm, 0.2*deg)
detector = ba.SphericalDetector(n, -1*deg, 1*deg, n, 0, 2*deg)
simulation = ba.ScatteringSimulation(beam, get_sample(P), detector)
return simulation
def fake_data():
"""
Generate noisy synthetic data for a known cylinder sample.
"""
P = {"radius": 5*nm, "height": 10*nm}
return get_simulation(P).simulate().noisy(0.1, 0.1)
def get_masked_simulation(P):
"""
GISAS simulation with a Python-generated detector mask.
"""
n = 101
beam = ba.Beam(1e8, 0.1*nm, 0.2*deg)
sample = get_sample(P)
detector = ba.SphericalDetector(n, -1*deg, 1*deg, n, 0, 2*deg)
add_mask_to_detector(detector)
simulation = ba.ScatteringSimulation(beam, sample, detector)
return simulation
def add_mask_to_detector(detector):
"""
Adds a Python-generated detector bitmap mask to the detector.
"""
n_phi = detector.axis(0).size()
n_alpha = detector.axis(1).size()
y, x = np.ogrid[:n_alpha, :n_phi]
x0 = 0.5*n_phi
y0 = 0.5*n_alpha
r = 0.32*min(n_phi, n_alpha)
mask = np.ones((n_alpha, n_phi), dtype=bool)
head = (x - x0)**2 + (y - y0)**2 <= r**2
eye = (x - (x0 + 0.22*r))**2 + (y - (y0 + 0.35*r))**2 <= (0.11*r)**2
mouth = (x > x0) & (np.abs(y - y0) < 0.35*(x - x0))
mask[head] = False
mask[eye] = True
mask[mouth] = True
for center in (x0 + 1.15*r, x0 + 1.45*r, x0 + 1.75*r):
snack = (x - center)**2 + (y - y0)**2 <= (0.09*r)**2
mask[snack] = False
detector.setMask(mask)
def get_plotters(exp_data):
"""
Creates the fit-progress plotters.
"""
norm = ba.intensity_norm(exp_data)
experiment_plotter = ba.FitPlotter(
ba.plot_masked_experimental,
context_data=exp_data,
norm=norm,
with_cb=True,
title="Experimental",
)
simulation_plotter = ba.FitPlotter(
ba.plot_heatmap,
norm=norm,
with_cb=True,
title="Simulation",
)
difference_plotter = ba.FitPlotter(
ba.plot_difference,
context_data=exp_data,
with_cb=True,
title="Relative difference",
)
return [
experiment_plotter,
simulation_plotter,
difference_plotter,
]
if __name__ == '__main__':
exp_data = fake_data()
exp_values = exp_data.intensities()
# Fit progress display
monitor = ba.FitMonitor(
get_plotters(exp_data),
ncols=2,
show_best=True,
max_fps=1,
printer=ba.Printer(every_nth=10),
live=True)
def residuals(P):
"""
Simulates and reports residuals; masked pixels contribute zero.
"""
sim_result = get_masked_simulation(P.valuesdict()).simulate()
residuals = ba.valid_pixel_residual(exp_values,
sim_result.intensities())
monitor.update(sim_result, P, residuals)
return residuals
P = lmfit.Parameters()
P.add("radius", value=6*nm, min=4*nm, max=8*nm)
P.add("height", value=9*nm, min=8*nm, max=12*nm)
result = lmfit.minimize(residuals, P, method="leastsq")
finalP = result.params.valuesdict()
# Recompute and report the simulation at the fitted parameters.
residuals(result.params)
# Render the just-reported evaluation as the final fit state.
monitor.render_final(result.params)
print(lmfit.fit_report(result))
ba.showSample3D(get_sample(finalP), sample_size=120*nm, seed=0)
ba.plt.show()
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