EELS_Tools: Spectroscopy
Analysis of EDS Spectra#
part of
a pycroscopy ecosystem package
Notebook by Gerd Duscher, 2024
Microscopy Facilities
Institute of Advanced Materials & Manufacturing
The University of Tennessee, Knoxville
Model based analysis and quantification of data acquired with transmission electron microscopes
Content#
An Introduction into displaying and analyzing EDS spectrum images and spectra This works also on Google Colab.
Prerequesites#
Install pyTEMlib#
If you have not done so in the Introduction Notebook, please test and install pyTEMlib and other important packages with the code cell below.
import sys
import importlib.metadata
def test_package(package_name):
"""Test if package exists and returns version or -1"""
try:
version = importlib.metadata.version(package_name)
except importlib.metadata.PackageNotFoundError:
version = '-1'
return version
# pyTEMlib setup ------------------
if test_package('pyTEMlib') < '0.2024.02.0':
print('installing pyTEMlib')
!{sys.executable} -m pip install pyTEMlib -q --upgrade
# ------------------------------
print('done')
done
In Google Colab: Please restart runtime Ctrl+M
Loading of necessary libraries#
Please note, that we only need to load the pyTEMlib library, which is based on sidpy Datsets.
%matplotlib widget
import numpy as np
import matplotlib.pylab as plt
import sys
if 'google.colab' in sys.modules:
from google.colab import output
output.enable_custom_widget_manager()
from google.colab import drive
%load_ext autoreload
%autoreload 2
sys.path.insert(0,'../../../SciFiReaders/')
import SciFiReaders
print(SciFiReaders.__version__)
sys.path.insert(0,'../../')
import pyTEMlib
import pyTEMlib.file_tools # File input/ output library
import pyTEMlib.eels_tools
import pyTEMlib.eds_tools
import scipy
import pyTEMlib.image_tools
if 'google.colab' in sys.modules:
drive.mount("/content/drive")
# For archiving reasons it is a good idea to print the version numbers out at this point
print('pyTEM version: ',pyTEMlib.__version__)
__notebook__ = '2_Image_Registration'
__notebook_version__ = '2024_6_28'
You don't have igor2 installed. If you wish to open igor files, you will need to install it (pip install igor2) before attempting.
You don't have gwyfile installed. If you wish to open .gwy files, you will need to install it (pip install gwyfile) before attempting.
0.12.0
Symmetry functions of spglib enabled
Qt dialogs are not available
SimpleITK not installed; Registration Functions for Image Stacks not available
install with: conda install -c simpleitk simpleitk
pyTEM version: 0.2025.04.2
Open File#
Load File#
Select a main dataset and any additional data like reference data and such.
fileWidget = pyTEMlib.file_tools.FileWidget3()
Select and Plot Dataset#
Select a dataset from the drop down value and display it with the code cell below.
v = fileWidget.selected_dataset.plot()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Cell In[4], line 1
----> 1 v = fileWidget.selected_dataset.plot()
AttributeError: 'FileWidget3' object has no attribute 'selected_dataset'
spectrum = None
for key in fileWidget.datasets.keys():
if 'Super' in fileWidget.datasets[key].title:
if spectrum == None:
spectrum = fileWidget.datasets[key]
else:
spectrum += fileWidget.datasets[key]
view = spectrum.plot()
spectrum
|
||||||||||||||||
spectrum.data_type = 'spectral_image'
view = spectrum.sum(axis=[1]).plot()
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call last)
Cell In[13], line 2
1 spectrum.data_type = 'spectral_image'
----> 2 view = spectrum.sum(axis=[1]).plot()
File c:\Users\gduscher\AppData\Local\anaconda3\Lib\site-packages\sidpy\sid\dataset.py:651, in Dataset.plot(self, verbose, figure, **kwargs)
649 self.view = PointCloudVisualizer(self, figure=figure, **kwargs)
650 else:
--> 651 raise NotImplementedError('Datasets with data_type {} cannot be plotted, yet.'.format(self.data_type))
652 elif len(self.shape) == 3:
653 if verbose:
NotImplementedError: Datasets with data_type DataType.SPECTRAL_IMAGE cannot be plotted, yet.
start = 50
new_spectrum = scipy.ndimage.gaussian_filter(spectrum[start:], sigma=3)
new_energy_scale = spectrum.energy_scale[start:]
major_peaks, _ = scipy.signal.find_peaks(new_spectrum, prominence=40)
minor_peaks, _ = scipy.signal.find_peaks(new_spectrum, prominence=3)
minor_peaks = np.array(minor_peaks)+start
major_peaks = np.array(major_peaks)+start
plt.figure()
plt.plot(spectrum.energy_scale,spectrum, label = 'spectrum 1')
plt.plot(new_energy_scale, new_spectrum, label = 'filtered spectrum 1', color='black')
plt.scatter( spectrum.energy_scale[minor_peaks], spectrum[minor_peaks], color = 'red')
plt.scatter( spectrum.energy_scale[major_peaks], spectrum[major_peaks], color = 'orange')
elements = pyTEMlib.eds_tools.find_elements(spectrum, np.array(minor_peaks))
print(elements)
spectrum.metadata['EDS'] = pyTEMlib.eds_tools.get_x_ray_lines(spectrum, elements)
plt.figure()
plt.plot(spectrum.energy_scale,spectrum, label = 'spectrum')
pyTEMlib.eds_tools.plot_lines(spectrum.metadata['EDS'], plt.gca())
spectrum.metadata['EDS']
spectrum.metadata['EDS'] = {}
spectrum.metadata['EDS']['detector'] = {}
elements[-1] = 'Sb'
elements += ['As']
print(elements)
pyTEMlib.eds_tools.get_x_ray_lines(spectrum, elements)
peaks, p = pyTEMlib.eds_tools.fit_model(spectrum, elements, use_detector_efficiency=False)
for key in spectrum.metadata['EDS']:
print(f"{key}:")
for family in spectrum.metadata['EDS'][key]:
if 'family' in family:
print(f"{family}: {spectrum.metadata['EDS'][key][family]['areal_density']:.3f} atoms/nm^2" )
model = pyTEMlib.eds_tools.get_model(spectrum)
plt.figure()
plt.plot(spectrum.energy_scale, spectrum, label='spectrum')
pyTEMlib.eds_tools.plot_lines(spectrum.metadata['EDS'], plt.gca())
plt.plot(spectrum.energy_scale, model, label='model')
plt.plot(spectrum.energy_scale, spectrum-model, label='residual')
plt.legend()
pyTEMlib.eds_tools.get_eds_cross_sections(79)
6915.004936267494 *0.011799/16, 5088.57172585567*0.015317/13, 6915.004936267494 *0.011799/ 5088.57172585567/0.015317
144.5/16/7, 153.6376070726737/16.049676955798695/7
5259.605 / 4536.087 , 4339.124 / 3337.746
3028.209 / 2392.879 , 2474.216 / 1894.291
spectrum.metadata['EDS']
2100.835 , 5.689*36
xs = pyTEMlib.eds_tools.get_eds_cross_sections(31)
xs['L']/xs['K'], 18/13
13
spectrum.metadata['EDS']['Ga']['L-family']['areal_density']/19.2, (spectrum.metadata['EDS']['Ga']['K-family']['areal_density']/16.05)
spectrum.metadata['EDS']['As']['L-family']['areal_density']/18.06 , (spectrum.metadata['EDS']['As']['K-family']['areal_density']/13.05)
model = np.zeros(len(spectrum))
for i in range(len(p)-4):
model += peaks[i]*p[i]
pass
plt.figure()
plt.plot(spectrum.energy_scale, spectrum, label='spectrum')
plt.plot(spectrum.energy_scale, model, label='model')
plt.plot(spectrum.energy_scale, spectrum-model, label='residual')
plt.legend()
from pyTEMlib.xrpa_x_sections import x_sections
alpha_K = .9e6
alpha_L = 6.e7
alpha_M = 6*1e8 # 2.2e10
# omega_K = Z**4/(alpha_K+Z**4)
# omega_L = Z**4/(alpha_L+Z**4)
# omega_M = Z**4/(alpha_M+Z**4)
out_tags = {}
energy_scale = spectrum.get_spectral_dims(return_axis=True)[0].values
for element in elements:
atomic_number = pyTEMlib.eds_tools.elements_list.index(element)
out_tags[element] ={'Z': atomic_number}
if 'K-L3' in x_sections[str(atomic_number)]['lines']:
if x_sections[str(atomic_number)]['lines']['K-L3']['position'] < energy_scale[-1]:
height = spectrum[np.searchsorted(energy_scale, x_sections[str(atomic_number)]['lines']['K-L3']['position'] )]
out_tags[element]['K-family'] = {'height': height}
if 'K' in x_sections[str(atomic_number)]['fluorescent_yield']:
out_tags[element]['K-family']['yield'] = x_sections[str(atomic_number)]['fluorescent_yield']['K']
else:
out_tags[element]['K-family']['yield'] = atomic_number**4/(alpha_K+atomic_number**4)/4/1.4
out_tags
from numba import jit
# @jit(nopython = False)
def get_array(data, xv, yv, z_length):
profile = np.zeros([xv.shape[1], 2, z_length], dtype='float')
for index_x in range(xv.shape[1]):
for index_y in range(xv.shape[0]):
x = int(xv[index_y, index_x])
y = int(yv[index_y, index_x])
if x< data.shape[0] and x>0 and y < data.shape[1] and y>0:
profile[index_x, 0] +=data[x, y]
return profile
def get_profile(dataset, line):
xv, yv = get_line_selection_points(line)
if dataset.data_type.name == 'IMAGE':
dataset.get_image_dims()
profile = scipy.ndimage.map_coordinates(np.array(dataset.T), [xv,yv])
profile_dataset = sidpy.Dataset.from_array(profile.sum(axis=0))
profile_dataset.data_type='spectrum'
profile_dataset.units = dataset.units
profile_dataset.quantity = dataset.quantity
profile_dataset.set_dimension(0, sidpy.Dimension(np.linspace(xv[0,0], xv[-1,-1], profile_dataset.shape[0]),
name='x', units=dataset.x.units, quantity=dataset.x.quantity,
dimension_type='spatial'))
profile_dataset
if dataset.data_type.name == 'SPECTRAL_IMAGE':
spectral_axis = dataset.get_spectral_dims(return_axis=True)[0]
profile = get_array(np.array(dataset), xv, yv, dataset.shape[2])
profile_dataset = sidpy.Dataset.from_array(profile)
profile_dataset.data_type='spectral_image'
profile_dataset.units = dataset.units
profile_dataset.quantity = dataset.quantity
profile_dataset.set_dimension(0, sidpy.Dimension(np.linspace(xv[0,0], xv[-1,-1], profile_dataset.shape[0]),
name='x', units=dataset.x.units, quantity=dataset.x.quantity,
dimension_type='spatial'))
profile_dataset.set_dimension(2, spectral_axis)
return profile_dataset
def get_line_selection_points(line):
start_point = line.line_verts[3]
right_point = line.line_verts[0]
low_point = line.line_verts[2]
if start_point[0] > right_point[0]:
start_point = line.line_verts[0]
right_point = line.line_verts[3]
low_point = line.line_verts[1]
m = (right_point[1] - start_point[1]) / (right_point[0] - start_point[0])
length_x = int(abs(start_point[0]-right_point[0]))
length_v = int(np.linalg.norm(start_point-right_point))
linewidth = int(abs(start_point[1]-low_point[1]))
x = np.linspace(0,length_x, length_v)
y = np.linspace(0,linewidth, line.line_width)
xv, yv = np.meshgrid(x, y)
yy = yv +x*m+start_point[1]
xx = (xv.T -y*m ).T + start_point[0]
return xx, yy
def select(b):
pass
v = d.plot()
selected_area = pyTEMlib.image_tools.LineSelector(v.axes[0], select, 100)
selected_area.set_linewidth(100)
dataset.original_metadata
dataset.metadata['experiment']
tags = dataset.metadata['experiment']
tags['acceleration_voltage_V'] = tags['acceleration_voltage']
tags['microscope']['acceleration_voltage']
tags = dataset.metadata['experiment']
spectrum = dataset
spectrum.metadata = dataset.metadata
tags['acceleration_voltage_V'] = float(tags['acceleration_voltage'])
print(tags['acceleration_voltage_V'])
start = np.searchsorted(spectrum.energy_scale, 150)
detector_efficiency = np.zeros(len(spectrum))
detector_efficiency+= pyTEMlib.eds_tools.detector_response(spectrum)
plt.figure()
plt.plot(spectrum.energy_scale, detector_efficiency),
Fit Spectrum#
#elements = ['C', 'O', 'Cu', 'Al', 'Ni', 'Zn', 'Mn', 'Ce', 'Mg']
# spectrum.metadata = chooser.dataset.metadata
spectrum.metadata['EDS'] = {}
pyTEMlib.eds_tools.get_x_ray_lines(spectrum, elements)
peaks, p = pyTEMlib.eds_tools.fit_model(spectrum, elements, use_detector_efficiency= False)
results = {}
from tqdm.notebook import trange, tqdm
for i in trange(len(prof[:,0])):
spectrum = prof[i, 0]
spectrum.metadata = chooser.dataset.metadata
spectrum.metadata['EDS'] = {}
peaks, p = pyTEMlib.eds_tools.fit_model(spectrum, elements, use_detector_efficiency= True)
for element in chooser.dataset.metadata['EDS']['lines'].keys():
for family in chooser.dataset.metadata['EDS']['lines'][element].keys():
if family !='Z':
if 'height' in chooser.dataset.metadata['EDS']['lines'][element][family].keys():
if element+': '+family not in results:
results[element+': '+family] = []
results[element+': '+family].append(chooser.dataset.metadata['EDS']['lines'][element][family]['height'])
else:
for line in chooser.dataset.metadata['EDS']['lines'][element][family]:
if element+': '+line not in results:
results[element+': '+line] = []
results[element+': '+line].append(chooser.dataset.metadata['EDS']['lines'][element][family][line]['height'])
model = np.zeros(len(spectrum))
for i in range(len(p)-4):
model += peaks[i]*p[i]
pass
start = np.searchsorted(spectrum.energy_scale, 150)
energy_scale = spectrum.energy_scale[start:]
#p[-3:] = [100, 3, .007]
print(p[-4:])
E_0 = spectrum.metadata['experiment']['acceleration_voltage_V'][0]
#model[start:] += (detector_efficiency[start:] * (p[-3] + p[-2] * (E_0 - energy_scale) / energy_scale + p[-1] * (E_0-energy_scale) ** 2 / energy_scale))
bgd = p[-4] / (energy_scale + p[-3] * energy_scale ** 2 + p[-2] * energy_scale ** .5) - p[-1]
model[start:] += detector_efficiency[start:] * bgd
plt.figure()
plt.plot(spectrum.energy_scale, spectrum, label='spectrum')
plt.plot(spectrum.energy_scale,model, label='model')
# plt.plot(spectrum.energy_scale[start:], bgd*detector_efficiency[start:])
plt.plot(spectrum.energy_scale,spectrum-model, label='difference')
plt.ylim(0, 400)
p[:-4], E_0
for element in chooser.dataset.metadata['EDS']['lines'].keys():
for family in chooser.dataset.metadata['EDS']['lines'][element].keys():
if family !='Z':
if 'height' in chooser.dataset.metadata['EDS']['lines'][element][family].keys():
print(element, family, chooser.dataset.metadata['EDS']['lines'][element][family]['height'])
else:
for line in chooser.dataset.metadata['EDS']['lines'][element][family]:
print(element, line, chooser.dataset.metadata['EDS']['lines'][element][family][line]['height'])
print(results.keys())
plt.figure()
for key in ['C: K-L2', 'Cu: K-family', 'Ni: K-family', 'Zn: K-family', 'O: K-family', 'Mn: L-family', 'Mg: K-family']:
plt.plot(results[key], label=key)
plt.legend()
len(p)
print(results.keys())
plt.figure()
for key in ['Cu: K-family', 'Ni: K-family', 'Mn: L-family']:
plt.plot(results[key], label=key)
plt.legend()
len(p)
plt.figure()
for key in ['Ce: L-family', 'Ce: M-family', 'Al: K-family', 'Mn: L-family', 'Mg: K-family']:
plt.plot(results[key], label=key)
plt.legend()
plot.close('all')
pyTEMlib.eds_tools.get_phases(chooser.dataset, number_of_phases=5)
fig = pyTEMlib.eds_tools.plot_phases(chooser.dataset, image_chooser.dataset, survey_image_chooser.dataset)
Spectrum Image#
Select the HAADF image reference
# elements = pyTEMlib.eds_tools.find_elements(spectrum, minor_peaks)