Using the Calibration class
The pulse height histogram generated by a Multi Channel Analyzer (MCA) is related to the gamma photon energy by some proportionality relation. To interpret the gamma energy spectrum the spectrum must be calibrated using some reference isotope with well defined gamma energies.
The Calibration class provides a simple tool to define the proportionality relation between channels and energy values. The class performs a polynomial fitting with a oder set by the user. The class uses the numpy.polyfit funcion to perform the operation.
An instance of the calibration class can be constructed by providing a dictionary listing the values of the channel index together with the corresponding enerrgy (in \(\text{keV}\)). Once constructed the Calibration object can be used to calibrate a GammaSpectrum or to set the energy scale of a plot.
To show how the procedure works let us first load the background and sample spectra previously used in the GammaSpectrum class tutorial.
from pygammaspec.spectrum import GammaSpectrum
from pygammaspec.visualization import plot_spectrum
background = GammaSpectrum.from_PRA_histogram("../utils/background.txt", 25851)
sample = GammaSpectrum.from_PRA_histogram("../utils/weak_radium.txt", 25851)
plot_spectrum(sample, background, chrange=(0, 30))
The sample spectrum, even if very weak, shows the characteristic peaks of \(^{226}\text{Ra}\) and its daughters (\(^{214}\text{Pb}\), \(^{214}\text{Bi}\)). Let us use these peaks as calibration. To do so let us define a dictionary correlating the channel index with the energy of the corresponding photo-peak and then let us create a calibration object by using a second order polynomial:
from pygammaspec.spectrum import Calibration
data = {
14.41: 609.312, # Bi-214
9.12: 351.932, # Pb-214
7.86: 295.224, # Pb-214
6.59: 241.997, # Pb-214
5.21: 186.211, # Ra-226
}
calibration = Calibration(data, 2)
The calibration curve can be visualized using the plot_calibration function from the pygammaspec.visualization module:
from pygammaspec.visualization import plot_calibration
plot_calibration(calibration)
Once the calibration object has been created it can be applied to a GammaSpectrum object by using the built-in calibration property setter. Once the calibration has been applied the energy scale of the spectrum can be accessed directly, as a list of float values, using the property energy.
background.calibration = calibration
sample.calibration = calibration
print("Sample energy scale (in keV):")
print(sample.energy)
Sample energy scale (in keV):
[-0.8927299296031618, -0.5703788367679863, -0.247887277644266, 0.07474474776799922, 0.3975172394688097, 0.7204301974581647, 1.0434836217360646, 1.36667751230251, 1.6900118691575, 2.0134866923010346, 2.3371019817331145, 2.6608577374537394, 2.9847539594629087, 3.308790647760624, 3.632967802346884, 3.9572854232216876, 4.281743510385038, 4.606342063836932, 4.931081083577371, 5.255960569606356, 5.580980521923885, 5.9061409405299585, 6.231441825424578, 6.556883176607743, 6.8824649940794504, 7.208187277839704, 7.534050027888503, 7.860053244225847, 8.186196926851736, 8.512481075766168, 8.838905690969147, 9.16547077246067, 9.492176320240741, 9.819022334309354, 10.146008814666512, 10.473135761312214, 10.800403174246462, 11.127811053469255, 11.455359398980594, 11.783048210780477, 12.110877488868905, 12.438847233245877, 12.766957443911394, 13.095208120865458, 13.423599264108066, 13.752130873639219, 14.080802949458917, 14.409615491567157, 14.738568499963945, 15.067661974649278, 15.396895915623157, 15.726270322885577, 16.055785196436542, 16.385440536276057, 16.715236342404115, 17.045172614820714, 17.375249353525863, 17.70546655851955, 18.035824229801786, 18.36632236737257, 18.6969609712319, 19.02774004137977, 19.358659577816187, 19.689719580541148, 20.020920049554658, 20.352260984856706, 20.683742386447303, 21.015364254326443, 21.34712658849413, 21.679029388950358, 22.011072655695134, 22.343256388728456, 22.675580588050323, 23.008045253660732, 23.340650385559687, 23.673395983747188, 24.006282048223238, 24.339308578987826, 24.672475576040963, 25.005783039382642, 25.339230969012867, 25.67281936493164, 26.006548227138953, 26.34041755563481, 26.674427350419215, 27.008577611492168, 27.342868338853663, 27.677299532503703, 28.01187119244229, 28.346583318669417, 28.681435911185094, 29.016428969989313, 29.351562495082078, 29.68683648646339, 30.02225094413324, 30.35780586809164, 30.693501258338582, 31.02933711487407, 31.365313437698106, 31.701430226810686, 32.03768748221181, 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The obtained calibation object can also be used to scale the spectrum plots providing the object to the plot_spectrum function:
plot_spectrum(sample, background, chrange=(0, 30), external_calibration=calibration)
Tip
If the same valid calibration object is applied to both the sample and background spectra given to plot_spectrum, the funtion will automatically switch the x-axis to the energy scale. If a different calibration object is given as external_calibration this will override the previously given calibrations. As such, in the previous example the same result would have been obtained without specifying the external_calibration argument.