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Calculate the standard deviation of the gaussian distribution in defocus caused by chromatic aberration in the STEM
import matplotlib.pyplot as plt
import numpy as np
import sympy as sp
E0, dE, Cc = sp.symbols('E0, dE, C_c, ')
deltaZ_sigma = Cc*dE/E0#*2*sp.sqrt(2*sp.log(2))
zlp = 0.9
voltage = 3e5
chrom = 1.6e-3
f = sp.lambdify([Cc, dE, E0], deltaZ_sigma)
sigma = f(chrom, zlp, voltage) / 1e-9
mu = 0
x = np.linspace(-20,20,1000)
def gaussian(x, mu, sigma, normalise = False):
gauss = np.exp((-(x-mu)**2)/(2*sigma**2))
if normalise:
gauss = gauss * 1/(sigma*np.sqrt(2*np.pi)) # normalise
return gauss
gauss = gaussian(x, mu, sigma)
defocus = np.array([-2*sigma, -sigma, 0, sigma, 2*sigma])
weighting = gaussian(defocus, mu, sigma)
print("Standard deviation of defocus is: {}".format(sigma))
print("Chosen five steps of 1sigma apart:")
print('Weighted by:')
fig, ax = plt.subplots()
ax.plot(x, gauss, color='grey', zorder=-1, lw=4)
plt.fill_between(x, gauss, color='lightgrey')
plt.scatter(defocus, weighting,color='green')
plt.xlabel('Temporal distribution in defocus / nm')
plt.ylabel('Gaussian weights')
data_coords = np.array([[0, i] for i in weighting])
figure_coords = ax.transData.transform(data_coords)
axes_coords = ax.transAxes.inverted().transform(figure_coords).T[1]
for x0, ymax in zip(defocus, axes_coords):
plt.axvline(x0, ymax = ymax, ls='--', color='green')
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