Tutorial¶
In a first time, you need to install the library
$ pip install ImagingReso
then you need to import it
>>> import ImagingReso
Initialization¶
we first define our stack of elements. Each layer of the stack can be a single element, or a compound and is defined by a dictionary where the thickness is defined in mm, the density in g/cm3 and the ratio is the stochiometric coefficient of each element.
example:¶
>>> _stack = {'CoAg': {'elements': ['Co','Ag'],
'stoichiometric_ratio': [1,1],
'thickness': {'value': 0.025,
'units': 'mm'},
'density': {'value': 0.5,
'units': 'g/cm3'},
},
'U': {'elements': ['U'],
'stoichiometric_ratio': [1],
'thickness': {'value': 0.3,
'units': 'mm'},
'density': {'value': np.NaN,
'units': 'g/cm3'},
},
}
Then you can now initialize the object as followed, in this case we use a energy range of 0 to 300 eV with 10 eV of energy step.
As noted that if the density is omitted, the program will use the stochiometri_ratio and theoretical density of each element to estimage the density of the compound (layer), and changing the isotope density, or isotopic coefficient will affect the layer/compound density. But if you provide the density, this value won’t be affected by any other changes. If you provide the density, we suppose that you know what you are doing and that you know your component enough to make sure its density value should not be changed.
>>> o_reso = ImagingReso.Resonance(stack = _stack, energy_min=0.001, energy_max=300, energy_step=10)
It is also possible to define the layers (stack) one by one using their formula as demonstrated here
>>> o_reso = ImagingReso.Resonance(energy_min=0.001, energy_max=300, energy_step=10)
>>> stack1 = 'CoAg'
>>> thickness1 = 0.025 #mm
>>> density1 = 0.5 #g/cm3
>>> o_reso.add_layer(formula=stack1, thickness=thickness1, density=density1)
>>> stack2 = 'U'
>>> thcikness2 = 0.3
>>> o_reso.add_layer(formula=stack2, thcikness=thickness2)
All the parameters defined can be checked as followed
The list of stack displays the input information, but also reported the list of isotopes, mass, etc, for the elements you defined, for each layer.
>>> import pprint
>>> pprint.pprint(o_reso.slack)
{'CoAg': {'Ag': {'density': {'units': 'g/cm3', 'value': 10.5},
'isotopes': {'density': {'units': 'g/cm3',
'value': [10.406250187729098,
10.600899412431097]},
'file_names': ['Ag-107.csv', 'Ag-109.csv'],
'isotopic_ratio': [0.51839, 0.48161000000000004],
'list': ['107-Ag', '109-Ag'],
'mass': {'units': 'g/mol',
'value': [106.905093, 108.904756]}},
'molar_mass': {'units': 'g/mol', 'value': 107.8682}},
'Co': {'density': {'units': 'g/cm3', 'value': 8.9},
'isotopes': {'density': {'units': 'g/cm3',
'value': [8.749367803547068,
8.900000030203689]},
'file_names': ['Co-58.csv', 'Co-59.csv'],
'isotopic_ratio': [0.0, 1.0],
'list': ['58-Co', '59-Co'],
'mass': {'units': 'g/mol',
'value': [57.9357576, 58.9332002]}},
'molar_mass': {'units': 'g/mol', 'value': 58.9332}},
'atoms_per_cm3': {'Ag': 1.8051829472054791e+21,
'Co': 1.8051829472054791e+21},
'density': {'units': 'g/cm3', 'value': 0.5},
'elements': ['Co', 'Ag'],
'stoichiometric_ratio': [1, 1],
'thickness': {'units': 'mm', 'value': 0.025}},
'U': {'U': {'density': {'units': 'g/cm3', 'value': 18.95},
'isotopes': {'density': {'units': 'g/cm3',
'value': [18.552792392319066,
18.632509467526443,
18.712358690988417,
18.951741325328925]},
'file_names': ['U-233.csv',
'U-234.csv',
'U-235.csv',
'U-238.csv'],
'isotopic_ratio': [0.0,
5.4999999999999995e-05,
0.0072,
0.992745],
'list': ['233-U', '234-U', '235-U', '238-U'],
'mass': {'units': 'g/mol',
'value': [233.039628,
234.0409456,
235.0439231,
238.0507826]}},
'molar_mass': {'units': 'g/mol', 'value': 238.02891}},
'atoms_per_cm3': {'U': 4.7943575106128917e+22},
'density': {'units': 'g/cm3', 'value': 18.949999999999999},
'elements': ['U'],
'stoichiometric_ratio': [1],
'thickness': {'units': 'mm', 'value': 0.3}}}
or you can also simply print the object
>>> print(o_reso)
{
"CoAg": {
"elements": [
"Co",
"Ag"
],
"stoichiometric_ratio": [
1,
1
],
...
}
or using only the object name
>>> o_reso
{
"CoAg": {
"elements": [
"Co",
"Ag"
],
"stoichiometric_ratio": [
1,
1
],
...
}
The energy range defined
>>> print("Energy min {} eV".format(o_reso.energy_min))
Energy min 0.001 eV
>>> print("Energy max {} eV".format(o_reso.energy_max))
Energy max 300 eV
>>> print("Energy step {} eV".format(o_reso.energy_step))
Energy step 10 eV
During the initialization process, the following things take place behind the scene - the number of atoms per cm3 of each element is calculated - the density of each layer (if not provided is estimated) - the arrays of Sigma (barns) vs Energy for each isotope is retrieved
>>> pprint.pprint(o_reso.stack_sigma)
{'CoAg': {'Ag': {'107-Ag': {'energy_eV': array([ 1.00000000e-05, 1.03401821e+01, 2.06803541e+01,
...
2.79184656e+02, 2.89524828e+02, 2.99865000e+02]),
'sigma_b': array([ 1938.91 , 6.69765395, 6.9742027 , 5.28153402,
...
4.73100823, 4.11286 ])},
'109-Ag': {'energy_eV': array([ 1.00000000e-05, 1.03446648e+01, 2.06893197e+01,
...
2.79305690e+02, 2.89650345e+02, 2.99995000e+02]),
'sigma_b': array([ 4.51167000e+03, 1.19932847e+01, 5.51138934e+00,
...
4.32864623e+00, 1.19208304e+01, 5.41247000e+00])},
'energy_ev': array([ 1.00000000e-05, 1.03424234e+01, 2.06848369e+01,
...
2.79245173e+02, 2.89587587e+02, 2.99930000e+02]),
'sigma': array([ 3177.9769436 , 9.24808268, 6.26969716, 64.29044465,
...
8.19369849, 4.73876517])},
…
}}}
Modify Isotopic Ratio¶
Let’s presume that the U layer of our sample does not have the default isotopic_ratio reported
`
U-233 -> 0
U-234 -> 5.5e-5
U-235 -> 0.007
U-238 -> 0.99
`
but instead
`
U-233 -> 0
U-234 -> 0
U-235 -> 0.15
U-238 -> 085
`
Display current isotopic ratio¶
It’s possible to display the current list of isotopic ratio
To display the entire list
>>> pprint.pprint(o_reso.get_isotopic_ratio())
{'CoAg': {'Ag': {'107-Ag': 0.51839, '109-Ag': 0.48161000000000004},
'Co': {'58-Co': 0.0, '59-Co': 1.0}},
'U': {'U': {'233-U': 0.0,
'234-U': 5.4999999999999995e-05,
'235-U': 0.0072,
'238-U': 0.992745}}}
From there, it’s possible to narrow down the search to the compound and element we are looking for
>>> pprint.pprint(o_reso.get_isotopic_ratio(compound='U', element='U'))
{'233-U': 0.0,
'234-U': 5.4999999999999995e-05,
'235-U': 0.0072,
'238-U': 0.992745}
if compound is composed of only 1 element, element paremeter can be omitted >>> pprint.pprint(o_reso.get_isotopic_ratio(compound=’U’)) {‘233-U’: 0.0,
‘234-U’: 5.4999999999999995e-05, ‘235-U’: 0.0072, ‘238-U’: 0.992745}
Define new set of isotopic ratio¶
Let’s presume our new set of ‘U’ ratio is
>>> new_list_ratio = [0.2, 0.3, 0.4, 0.1]
Let’s define the new stochiomettric ratio
>>> o_reso.set_isotopic_ratio(compound='U', list_ratio=new_list_ratio)
>>> pprint.pprint(o_reso.stack)
{'CoAg': {'Ag': {'density': {'units': 'g/cm3', 'value': 10.5},
'isotopes': {'density': {'units': 'g/cm3',
'value': [10.406250187729098,
10.600899412431097]},
'file_names': ['Ag-107.csv', 'Ag-109.csv'],
'isotopic_ratio': [0.51839, 0.48161000000000004],
'list': ['107-Ag', '109-Ag'],
'mass': {'units': 'g/mol',
'value': [106.905093, 108.904756]}},
'molar_mass': {'units': 'g/mol', 'value': 107.8682}},
'Co': {'density': {'units': 'g/cm3', 'value': 8.9},
'isotopes': {'density': {'units': 'g/cm3',
'value': [8.749367803547068,
8.900000030203689]},
'file_names': ['Co-58.csv', 'Co-59.csv'],
'isotopic_ratio': [0.0, 1.0],
'list': ['58-Co', '59-Co'],
'mass': {'units': 'g/mol',
'value': [57.9357576, 58.9332002]}},
'molar_mass': {'units': 'g/mol', 'value': 58.9332}},
'atoms_per_cm3': {'Ag': 1.8051829472054791e+21,
'Co': 1.8051829472054791e+21},
'density': {'units': 'g/cm3', 'value': 0.5},
'elements': ['Co', 'Ag'],
'stoichiometric_ratio': [1, 1],
'thickness': {'units': 'mm', 'value': 0.025}},
'U': {'U': {'density': {'units': 'g/cm3', 'value': 18.680428927650006},
'isotopes': {'density': {'units': 'g/cm3',
'value': [18.552792392319066,
18.632509467526443,
18.712358690988417,
18.951741325328925]},
'file_names': ['U-233.csv',
'U-234.csv',
'U-235.csv',
'U-238.csv'],
'isotopic_ratio': [0.2, 0.3, 0.4, 0.1],
'list': ['233-U', '234-U', '235-U', '238-U'],
'mass': {'units': 'g/mol',
'value': [233.039628,
234.0409456,
235.0439231,
238.0507826]}},
'molar_mass': {'units': 'g/mol', 'value': 234.64285678}},
'atoms_per_cm3': {'U': 4.7943575106128917e+22},
'density': {'units': 'g/cm3', 'value': 18.949999999999999},
'elements': ['U'],
'stoichiometric_ratio': [1],
'thickness': {'units': 'mm', 'value': 0.3}}}
As you can see, the density and molar_mass values of the U compound/element have been updated.
Let’s assume that the Ag element is not perfect and has some voids that changes its density to 8.5 (instead of 10.5). We need to change this value.
First, we can have the current density value for this element
>>> print(o_reso.get_density(compound='CoAg', element='Co'))
10.5
or of all the compounds
>>> pprint.pprint(o_reso.get_density())
{'CoAg': {'Ag': 10.5, 'Co': 8.9}, 'U': {'U': 18.680428927650006}}
Retrieve the Transmission and Attenuation signals¶
Those arrays for each Compound, element and isotopes are calculated during initialization of the object, but also every time one of the parameters is modified, such as density, stochiometric coefficient.
Those arrays are store in the stack_signal dictionary
>>> pprint.pprint(o_reso.stack_signal)
{'CoAg': {'Ag': {'107-Ag': {'attenuation': array([ 8.71204643e-03, 3.02257699e-05, 3.14737842e-05,
...
2.29850072e-05, 2.13506105e-05, 1.85609896e-05]),
'energy_eV': array([ 1.00000000e-05, 1.03401821e+01, 2.06803541e+01,
...
2.79184656e+02, 2.89524828e+02, 2.99865000e+02]),
'transmission': array([ 0.99128795, 0.99996977, 0.99996853, 0.99997616, 0.99823286,
...
0.99997299, 0.99997427, 0.99997701, 0.99997865, 0.99998144])},
'109-Ag': {'attenuation': array([ 2.01550894e-02, 5.41237178e-05, 2.48723558e-05,
...
1.95348051e-05, 5.37967523e-05, 2.44259480e-05]),
...
...
}}}}
You can retrieve any of those arrays, transmission, attenuation and Energy (eV) (x-axis) arrays as followed
for the compound CoAg
>>> transmission_CoAg = o_reso.stack_signal['CoAg']['transmission']
>>> energy_CoAg = o_reso.stack_signal['CoAg']['energy_eV']
for the element Ag
>>> transmission_CoAg_Ag = o_reso.stack_signal['CoAg']['Ag']['transmission']
>>> energy_CoAg_Ag = o_reso.stack_signal['CoAg']['Ag']['energy_eV']
or for the isotope 107-Ag
>>> transmission_CoAg_Ag_107Ag = o_reso.stack_signal['CoAg']['Ag']['107-Ag']['transmission']
>>> energy_CoAg_Ag_107Ag = o_reso.stack_signal['CoAg']['Ag']['107-Ag']['energy_eV']
In case you prefer having the x_axis in Angstroms instead of eV >>> x_axis_ev = energy_CoAg_Ag_107Ag >>> lambda_CoAg_Ag_107Ag = o_reso.convert_x_axis(array=x_axis_ev, from_units=’ev’, to_units=’angstroms’)
Display Transmission and Attenuation¶
Here are the flags available for the final plot (in bold, the default values)
- transmission: True or False. If False, the attenuation signal is plotted
- x_axis: ‘energy’ or ‘lambda’
- mixed: True or False. Display the total signal
- all_layers: True or False. Dislay the signal of each compound/layer
- all_elements: True or False. Display the signal of each element
- all_isotopes: True or False. Display the signal of each isotope
- items_to_plot: Array that defines what to plot. You need to define the path to the compound/element/isotope you want to see.
example:
if we want to display the Co element of the CoAg Compound
>>> items_to_plot = [['CoAg','Co']]
if we want also to display the 107-Ag isotope of the element Al of compound CoAg
>>> items_to_plot = [['CoAg', 'Co'],['CoAg','Ag','107-Ag']]
So here are a few examples of plot commands
>>> o_reso.plot(x_axis='lambda', all_layers=True)
>>> o_reso.plot(transmission=False, items_to_plot= [['CoAg', 'Co'],['CoAg','Ag','107-Ag']])
>>> o_reso.plot(items_to_plot=[['CoAg','Co']])
x-axis unit convertor¶
This library also provides a energy/lambda/time_of_flight convertor, used here to change the x-axis of the plot.
>>> energy_ev = o_reso.stack_signal['CoAg']['Ag']['107-Ag']['energy_eV']
>>> energy_angstroms = o_reso.convert_x_axis(array=energy_ev, from_units='ev', to_units='angstroms')
to convert to time_of_flight, 2 parameters must be provide, the detector_offset (in s, if any) and the distance source to detector (in m)
>>> delay_us = 2.99 #microS
>>> source_to_detector_m = 15.1 #meters
>>> energy_tof = o_reso.convert_x_axis(array=energy_ev, from_units='ev', to_units='s', delay_us=delay_us, source_to_detector_m=source_to_detector_m)