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FitIncidentSpectrum v1

Summary

Calculate a fit for an incident spectrum using different methods. Outputs a workspace containing the functionalized fit, its first derivative and (optionally) its second 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’]
DerivOrder	Input	number	1	Whether to return the first or first and second derivative of the fit function. Allowed values: [‘1’, ‘2’]

Description

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

• GaussConvCubicSpline: A fit with Cubic Spline using a Gaussian Convolution to get weights.

• CubicSpline: A fit using a cubic spline.

• 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]

4. 6. 18. 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

Source

Python: FitIncidentSpectrum.py