6.4

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FitIncidentSpectrum v1

../_images/FitIncidentSpectrum-v1_dlg.png

FitIncidentSpectrum dialog.

Summary

Calculate a fit for an incident spectrum using different methods. Outputs a workspace containing the functionalized fit and its first derivative.

Properties

Name Direction Type Default Description
InputWorkspace Input MatrixWorkspace Mandatory Incident spectrum to be fit.
OutputWorkspace Output MatrixWorkspace Mandatory Output workspace containing the fit and it’s first derivative.
WorkspaceIndex Input number 0 Workspace index of the spectra to be fitted (Defaults to the first index.)
BinningForCalc Input dbl list   Bin range for calculation given as an array of floats in the same format as Rebin: [Start],[Increment],[End]. If empty use default binning. The calculated spectrum will use this binning
BinningForFit Input dbl list   Bin range for fitting given as an array of floats in the same format as Rebin: [Start],[Increment],[End]. If empty use BinningForCalc. The incident spectrum will be rebined to this range before being fit.
FitSpectrumWith Input string GaussConvCubicSpline The method for fitting the incident spectrum. Allowed values: [‘GaussConvCubicSpline’, ‘CubicSpline’, ‘CubicSplineViaMantid’]

Description

This algorithm fits and functionalizes an incident spectrum and finds its first derivative. FitIncidentSpectrum is able to fit an incident spectrum using:

  • GaussConvCubicSpline: A fit with Cubic Spline using a Gaussian Convolution to get weights. In builds running older versions of SciPy the first derivative is can be less accurate.
  • CubicSpline: A fit using a cubic cline.
  • CubicSplineViaMantid: A fit with cubic spline using the mantid SplineSmoothing algorithm.

Usage

Example: fit an incident spectrum using GaussConvCubicSpline [1]

import numpy as np
import matplotlib.pyplot as plt
from mantid.simpleapi import \
    AnalysisDataService, \
    CalculateEfficiencyCorrection, \
    ConvertToPointData, \
    CreateWorkspace, \
    Divide, \
    FitIncidentSpectrum, \
    Rebin

# Create the workspace to hold the already corrected incident spectrum
incident_wksp_name = 'incident_spectrum_wksp'
binning_incident = "%s,%s,%s" % (0.2, 0.01, 4.0)
binning_for_calc = "%s,%s,%s" % (0.2, 0.2, 4.0)
binning_for_fit = "%s,%s,%s" % (0.2, 0.01, 4.0)
incident_wksp = CreateWorkspace(
    OutputWorkspace=incident_wksp_name,
    NSpec=1,
    DataX=[0],
    DataY=[0],
    UnitX='Wavelength',
    VerticalAxisUnit='Text',
    VerticalAxisValues='IncidentSpectrum')
incident_wksp = Rebin(InputWorkspace=incident_wksp, Params=binning_incident)
incident_wksp = ConvertToPointData(InputWorkspace=incident_wksp)


# Spectrum function given in Milder et al. Eq (5)
def incidentSpectrum(wavelengths, phiMax, phiEpi, alpha, lambda1, lambda2,
                     lamdaT):
    deltaTerm = 1. / (1. + np.exp((wavelengths - lambda1) / lambda2))
    term1 = phiMax * (
        lambdaT**4. / wavelengths**5.) * np.exp(-(lambdaT / wavelengths)**2.)
    term2 = phiEpi * deltaTerm / (wavelengths**(1 + 2 * alpha))
    return term1 + term2


# Variables for polyethlyene moderator at 300K
phiMax = 6324
phiEpi = 786
alpha = 0.099
lambda1 = 0.67143
lambda2 = 0.06075
lambdaT = 1.58

# Add the incident spectrum to the workspace
corrected_spectrum = incidentSpectrum(
    incident_wksp.readX(0), phiMax, phiEpi, alpha, lambda1, lambda2, lambdaT)
incident_wksp.setY(0, corrected_spectrum)

# Calculate the efficiency correction for Alpha=0.693
# and back calculate measured spectrum
eff_wksp = CalculateEfficiencyCorrection(
    InputWorkspace=incident_wksp, Alpha=0.693)
measured_wksp = Divide(LHSWorkspace=incident_wksp, RHSWorkspace=eff_wksp)

# Fit incident spectrum
prefix = "incident_spectrum_fit_with_"

fit_gauss_conv_spline = prefix + "_gauss_conv_spline"
FitIncidentSpectrum(
    InputWorkspace=incident_wksp,
    OutputWorkspace=fit_gauss_conv_spline,
    BinningForCalc=binning_for_calc,
    BinningForFit=binning_for_fit,
    FitSpectrumWith="GaussConvCubicSpline")

# Retrieve workspaces
wksp_fit_gauss_conv_spline = AnalysisDataService.retrieve(
    fit_gauss_conv_spline)

print(wksp_fit_gauss_conv_spline.readY(0))

Output:

[ 66366.97907003  35201.51411451  38022.36591024  61639.70236933
  62200.67498428  48463.5664824   34224.33749995  23402.41931673
  15942.7518712   10958.256381     7639.47147804   5413.27854911
   3900.21888036   2855.91654087   2123.40417572   1601.53146103
   1224.09479598    947.1952884 ]

References

[1]
      1. Mildner, B. C. Boland, R. N. Sinclair, C. G. Windsor, L. J. Bunce, and J. H. Clarke (1977) A Cooled Polyethylene Moderator on a Pulsed Neutron Source, Nuclear Instruments and Methods 152 437-446 doi: 10.1016/0029-554X(78)90043-5

Categories: AlgorithmIndex | Diffraction\Fitting