time spectrum fit
time spectrum of a ~3 µm stainless steel foil
95% enriched in 57Fe
a small line broadening needs to be included, here done via an isomer distribution
[1]:
import nexus as nx
import numpy as np
import matplotlib.pyplot as plt
load data
[2]:
time_data, intensity_data = nx.data.Load('time_spectrum_stainless_steel_foil.dat',
x_index = 1,
intensity_index = 2,
x_start = 19,
x_stop = 191,
intensity_threshold=0.1
)
plt.semilogy(time_data, intensity_data)
plt.show()
sample
[3]:
dist = nx.lib.distribution.Gaussian(points = 51,
fwhm = nx.Var(0.1, min = 1e-6, max = 0.8, fit = True, id = "gauss fwhm")
)
site = nx.Hyperfine(# isomer = 0,
# magnetic_field = 0,
# quadrupole = 0,
isomer_dist = dist,
isotropic = True)
SSt = nx.Material.Template(nx.lib.material.SS_enriched)
SSt.hyperfine_sites = [site]
layer_SSt = nx.Layer(id = "SSt layer",
material = SSt,
thickness = nx.Var(3000, min = 2500, max = 3500, fit = True, id = "thickness"),
# thickness_fwhm = nx.Var(100, min= 0, max = 600, fit = True, id = "thickness fwhm")
)
sample = nx.Sample(id = "sample",
layers = [layer_SSt],
geometry = "f" # forward scattering geometry
)
experiment
[4]:
beam = nx.Beam()
beam.LinearSigma()
exp = nx.Experiment(beam = beam,
objects = [sample],
isotope = nx.lib.moessbauer.Fe57)
time spectrum
[5]:
time_spectrum = nx.TimeSpectrum(id = "time spectrum",
experiment=exp,
time_length=600,
time_step=0.2,
# max_detuning=400,
# electronic=False,
time_data = time_data,
intensity_data = intensity_data,
scaling=nx.Var(2000, min = 1e-16, max = 1e8, fit = True, id = "scaling"),
# background=0.0,
# offset=0.0
# resolution=0.7,
# distribution_points=31, # uncomment if thickness_fwhm is used
bunch_spacing = 192.1, # PETRA III spacing in timing mode
# residual= nx.lib.residual.Sqrt(),
# fft_window='auto',
# coherence=False
)
time_spectrum()
time_spectrum.Plot()
fit
[6]:
fit = nx.Fit(id = "time spectrum fit",
measurements = [time_spectrum]
)
fit.options.file_output = False
fit.Evaluate()
Run Fit instance with id: time spectrum fit
Starting fit with 1 measurement data set(s) and 3 fit parameter(s):
no. | id | initial value | min | max
0 | scaling | 2000 | 1e-16 | 1e+08
1 | thickness | 3000 | 2500 | 3500
2 | gauss fwhm | 0.1 | 1e-06 | 0.8
Using 0 equality constraint(s) on parameter(s):
Using 0 inequality constraint(s).
Calling ceres solver with fit method LevMar
Ceres Solver Report: Iterations: 4, Initial cost: 3.546737e+03, Final cost: 2.435848e+02, Termination: CONVERGENCE
Gradient error analysis.
Fit performed with algorithm:
LevMar
Error analysis:
Gradient
Using 3 fit parameter(s):
no. | id | fit value | +/- std dev | initial value | min | max
0 | scaling | 2500.76 | 7.71484 | 2000 | 1e-16 | 1e+08
1 | thickness | 3394.83 | 6.33984 | 3000 | 2500 | 3500
2 | gauss fwhm | 0.245553 | 0.00221591 | 0.1 | 1e-06 | 0.8
Correlation matrix:
no. | 0 1 2
-----|---------------------------
0 | 1.000 -0.359 0.557
1 | -0.359 1.000 -0.686
2 | 0.557 -0.686 1.000
Using 0 equality constraint(s) on parameter(s):
and 0 inequality constraint(s).
Total cost = 2.436e+02
cost for each FitMeasurement is:
no. | id | cost | %
0 | time spectrum | 2.436e+02 | 100.000
Fit instance with id "time spectrum fit" finished.
[7]:
time_spectrum.Plot()
