XPCS fitting with lmfit

The experimentatl X-ray Photon Correlation Sepectroscopy(XPCS) data are fitted with Intermediate Scattering Factor(ISF) using lmfit Model (http://lmfit.github.io/lmfit-py/model.html)



In [1]:

    
# analysis tools from scikit-xray (https://github.com/scikit-xray/scikit-xray/tree/master/skxray/core)
import skxray.core.roi as roi
import skxray.core.correlation as corr
import skxray.core.utils as utils

from lmfit import minimize, Parameters, Model

# plotting tools from xray_vision (https://github.com/Nikea/xray-vision/blob/master/xray_vision/mpl_plotting/roi.py)
import xray_vision.mpl_plotting as mpl_plot  

import numpy as np
import os, sys
import zipfile

import matplotlib as mpl
import matplotlib.pyplot as plt
from matplotlib.ticker import MaxNLocator
from matplotlib.colors import LogNorm









    



:0: FutureWarning: IPython widgets are experimental and may change in the future.

Easily switch between interactive and static matplotlib plots



In [9]:

    
interactive_mode = False

if interactive_mode:
    %matplotlib notebook
else:
    %matplotlib inline

backend = mpl.get_backend()

This data provided by Dr. Andrei Fluerasu

L. Li, P. Kwasniewski, D. Oris, L Wiegart, L. Cristofolini, C. Carona and A. Fluerasu , "Photon statistics and speckle visibility spectroscopy with partially coherent x-rays" J. Synchrotron Rad., vol 21, p 1288-1295, 2014.



In [3]:

    
#folder = "/Volumes/Data/BeamLines/CHX/Luxi_description_files_for_duke/Duke_data"
folder = os.path.join(*__file__.split(os.sep)[:-1])

#  Get the data and the mask 
try:
    duke_data = np.load(os.path.join(folder, "duke_data", "duke_data.npy"))
    N_mask = np.load(os.path.join(folder, "duke_data", "N_mask.npy"))
except IOError:
    zipfile.ZipFile(os.path.join(folder, "duke_data.zip")).extractall()
    duke_data = np.load(os.path.join(folder, "duke_data", "duke_data.npy"))
    N_mask = np.load(os.path.join(folder, "duke_data", "N_mask.npy"))

#  get the average image
avg_img = np.average(duke_data, axis=0)

# plot the average image data after masking
plt.figure()
plt.imshow(N_mask*avg_img, vmax=1e0, cmap="Dark2" )
plt.title("Averaged masked data for Duke Silica Gel ")
plt.colorbar()
plt.show()

Create the Rings Mask

Use the skxray.core.roi module to create Ring ROIs (ROI Mask)¶ (https://github.com/scikit-xray/scikit-xray/blob/master/skxray/core/roi.py)



In [4]:

    
inner_radius = 24  # radius of the first ring
width = 1        # width of each ring
spacing = 0      # no spacing between rings
num_rings = 5    # number of rings
center = (133, 143)   # center of the spckle pattern

#  find the edges of the required rings
edges = roi.ring_edges(inner_radius, width, spacing, num_rings)
edges









    Out[4]:





array([[ 24.,  25.],
       [ 25.,  26.],
       [ 26.,  27.],
       [ 27.,  28.],
       [ 28.,  29.]])

Convert the edge values of the rings to q ( reciprocal space)



In [5]:

    
dpix = 0.055  # The physical size of the pixels

lambda_ = 1.5498  # wavelength of the X-rays
Ldet = 2200.   #   # detector to sample distance

two_theta = utils.radius_to_twotheta(Ldet, edges*dpix)
q_val = utils.twotheta_to_q(two_theta, lambda_)

q_val









    Out[5]:





array([[ 0.00243251,  0.00253387],
       [ 0.00253387,  0.00263522],
       [ 0.00263522,  0.00273658],
       [ 0.00273658,  0.00283793],
       [ 0.00283793,  0.00293929]])



In [6]:

    
q_ring = np.mean(q_val, axis=1)
q_ring









    Out[6]:





array([ 0.00248319,  0.00258455,  0.0026859 ,  0.00278726,  0.00288861])

Create a labeled array using roi.rings



In [8]:

    
rings = roi.rings(edges, center, avg_img.shape)

mask_data2 = N_mask*duke_data[0:4999]

ring_mask = rings*N_mask

# plot the figure
fig, axes = plt.subplots()
axes.set_title("Ring Mask")
im = mpl_plot.show_label_array(axes, ring_mask, cmap="Dark2")
plt.show()

Find the experimental auto correlation functions

Use the skxray.core.correlation module (https://github.com/scikit-xray/scikit-xray/blob/master/skxray/core/correlation.py)



In [10]:

    
num_levels = 7
num_bufs = 8

g2, lag_steps = corr.multi_tau_auto_corr(num_levels, num_bufs, ring_mask,
                                             mask_data2)

exposuretime=0.001;
deadtime=60e-6;
timeperframe = exposuretime+deadtime
lags = lag_steps*timeperframe

roi_names = ['gray', 'orange', 'brown', 'red', 'green']


fig, axes = plt.subplots(num_rings, sharex=True, figsize=(5, 14))
axes[num_rings-1].set_xlabel("lags")
for i, roi_color in zip(range(num_rings), roi_names):
    axes[i].set_ylabel("g2") 
    axes[i].set_title(" Q ring value " + str(q_ring[i]))
    axes[i].semilogx(lags, g2[:, i], 'o', markerfacecolor=roi_color, markersize=6)
    axes[i].set_ylim(bottom=1, top=np.max(g2[1:, i]))
plt.show()

Do the fitting

One time correlation data is fitted using the model in skxray.core.correlation module (auto_corr_scat_factor) (https://github.com/scikit-xray/scikit-xray/blob/master/skxray/core/correlation.py)



In [11]:

    
mod = Model(corr.auto_corr_scat_factor)



In [12]:

    
out1 = mod.eval(lags=lags, beta=0.2234, relaxation_rate = 6.2567,  baseline=1.0)

result1 = mod.fit(out1, lags=lags, beta=0.2230, relaxation_rate = 6.2500,  baseline=1.0)
plt.figure()
plt.semilogx(lags, g2[:, 0], 'ro')
plt.semilogx(lags, result1.best_fit, '-b')
plt.ylim(1.0, 1.3)
plt.title("Q ring value "+str(q_ring[0]))
plt.show()



In [14]:

    
out2 = mod.eval(lags=lags, beta=0.2234, relaxation_rate=6.9879, baseline=1.000)

result2 = mod.fit(out2, lags=lags, beta=0.22456, relaxation_rate=6.98789, beseline=1.00)
plt.figure()
plt.semilogx(lags, g2[:, 2], 'ro')
plt.semilogx(lags, result2.best_fit, '-b')
plt.ylim(1., 1.3)
plt.title("Q ring value "+ str(q_ring[2]))
plt.show()



In [15]:

    
import skxray
print(skxray.__version__)









    



0.0.4+105.ge27b978



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