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#!/usr/bin/env python3
"""
Generates correlated random rough surfaces for two sample interfaces.
"""
import random
import numpy as np
import bornagain as ba
from bornagain import ba_plot as bp, nm, nm2, nm3
from matplotlib import gridspec
FILM_THICKNESS = 25*nm
CORRELATION_SPLIT_FREQ = 0.035/nm
def correlation(a, b):
return np.corrcoef(a.flatten(), b.flatten())[0, 1]
def frequency_filtered(h, cutoff, keep_low):
fy = np.fft.fftfreq(h.shape[0], d=Ly/h.shape[0])
fx = np.fft.fftfreq(h.shape[1], d=Lx/h.shape[1])
qx, qy = np.meshgrid(fx, fy)
q = np.hypot(qx, qy)
mask = q <= cutoff if keep_low else q >= cutoff
return np.fft.ifft2(np.fft.fft2(h) * mask).real
def psd_line(h):
factor = X_points*Y_points/np.sqrt(Lx*Ly)
n = np.floor(X_points/2 + 1).astype(int)
psd = abs(np.fft.rfft2(h)/factor)**2
psd_points_x = np.array([psd[0][i] for i in range(1, n)])
f_points_x = np.array([i/Lx for i in range(1, n)])
return f_points_x, psd_points_x
def add_map(ax, h, title, vlim):
im = ax.imshow(h, extent=[0, Lx, 0, Ly], cmap='inferno',
vmin=-vlim, vmax=vlim)
ax.set_title(title)
ax.set_xlabel('x, nm')
ax.set_ylabel('y, nm')
bp.plt.colorbar(im, ax=ax, shrink=0.75)
def add_psd(ax, h):
f, psd = psd_line(h)
ax.plot(f, psd)
ax.set_yscale('log')
ax.set_xscale('log')
ax.set_title('PSD')
ax.set_xlabel('$\\nu, nm^{-1}$')
def add_histogram(ax, h):
rms = np.std(h)
ax.hist(h.flatten(), range=[-4*rms, 4*rms], bins=240, color='black')
ax.set_title('Height histogram')
ax.set_xlabel('h, nm')
ax.tick_params(left=False, labelleft=False)
def plot(film_top, substrate_top):
vlim = max(np.max(np.abs(film_top)), np.max(np.abs(substrate_top)))
fig = bp.plt.figure(figsize=(11, 6.5))
gs = gridspec.GridSpec(2, 3)
gs.update(left=0.07, right=0.97, bottom=0.09, top=0.92,
wspace=0.35, hspace=0.35)
add_map(fig.add_subplot(gs[0, 0]), substrate_top,
'Substrate interface', vlim)
add_psd(fig.add_subplot(gs[0, 1]), substrate_top)
add_histogram(fig.add_subplot(gs[0, 2]), substrate_top)
add_map(fig.add_subplot(gs[1, 0]), film_top,
'Film top interface', vlim)
add_psd(fig.add_subplot(gs[1, 1]), film_top)
add_histogram(fig.add_subplot(gs[1, 2]), film_top)
def get_sample():
"""
A sample with one layer on a substrate, with partially
correlated roughnesses.
"""
# defining materials
vacuum_color = (0.90, 0.93, 0.97)
vacuum = ba.RefractiveMaterial("ambience", vacuum_color, 0, 0)
layer_color = (0.05, 0.62, 0.55)
layer_mat = ba.RefractiveMaterial("layer", layer_color, 5e-6, 0)
substrate_color = (0.28, 0.57, 0.82)
substrate_mat = ba.RefractiveMaterial("substrate", substrate_color, 15e-6, 0)
# defining roughness
height_distribution = ba.ErfTransient()
max_spat_freq = 0.5/nm
# for layer
omega = 1*nm3
a1 = 1
a2 = 10*nm
a3 = 100*nm2
a4 = 1000*nm3
autocorr_layer = ba.LinearGrowthModel(omega, a1, a2, a3, a4,
max_spat_freq)
roughness_layer = ba.Roughness(autocorr_layer, height_distribution)
# for substrate
sigma = 0.9*nm
alpha = 0.5
xi = 35*nm
autocorr_sub = ba.SelfAffineFractalModel(sigma, alpha, xi,
max_spat_freq)
roughness_sub = ba.Roughness(autocorr_sub, height_distribution)
# defining layers
l_ambience = ba.Layer(vacuum)
l_layer = ba.Layer(layer_mat, FILM_THICKNESS, roughness_layer)
l_substrate = ba.Layer(substrate_mat, roughness_sub)
# adding layers
my_sample = ba.Sample()
my_sample.addLayer(l_ambience)
my_sample.addLayer(l_layer)
my_sample.addLayer(l_substrate)
return my_sample
if __name__ == '__main__':
# sample size
Lx = 1000*nm
Ly = 1000*nm
X_points = 512
Y_points = 512
sample = get_sample()
seed = random.randrange(2**32) # random every run
# generate both rough interfaces together
maps = ba.RoughnessMap.generateInterfaceMaps(
X_points, Y_points, Lx, Ly, sample, [1, 2], seed)
film_top = maps[0]
substrate_top = maps[1]
film_low = frequency_filtered(film_top, CORRELATION_SPLIT_FREQ, True)
substrate_low = frequency_filtered(substrate_top, CORRELATION_SPLIT_FREQ,
True)
film_high = frequency_filtered(film_top, 2*CORRELATION_SPLIT_FREQ, False)
substrate_high = frequency_filtered(substrate_top,
2*CORRELATION_SPLIT_FREQ, False)
print("seed =", seed)
print("correlation model = LinearGrowthModel")
print("film thickness = {:.1f} nm".format(FILM_THICKNESS))
print("frequency split = {:.3f} nm^-1".format(CORRELATION_SPLIT_FREQ))
print("full-height correlation =",
"{:.3}".format(correlation(film_top, substrate_top)))
print("low-frequency correlation =",
"{:.3}".format(correlation(film_low, substrate_low)))
print("high-frequency correlation =",
"{:.3}".format(correlation(film_high, substrate_high)))
plot(film_top, substrate_top)
ba.showSample3D(sample, sample_size=1000*nm, seed=seed)
bp.plt.show()
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