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source_spectrum.py
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source_spectrum.py
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#
# overwrite the energy in a SHADOW source with values sampled from
# a spectrum (defined as an array)
#
# srio@esrf.eu 2015-07-15
#
import numpy
import Shadow
def sample_from_spectrum(spectrum,npoints=1000,plot=0):
# normalize distribution function
spectrum[:,1] /= spectrum[:,1].sum()
#calculate the cumulative distribution function
a_cdf = numpy.cumsum(spectrum[:,1])
# create randomly distributed npoints
rd = numpy.random.rand(npoints)
# evaluate rd following the inverse of cdf
sampled_energies = numpy.interp(rd,a_cdf,spectrum[:,0])
#plots
if plot:
import matplotlib.pylab as plt
plt.subplot(111)
plt.figure(1)
plt.xlabel("photon energy /eV")
plt.ylabel("normalized spectrum")
plt.plot(a[:,0],a[:,1])
plt.figure(2)
plt.xlabel("a_cdf")
plt.ylabel("photon energy / eV")
plt.plot(a_cdf,a[:,0])
plt.figure(3)
plt.xlabel("index")
plt.ylabel("photon energy / eV")
plt.plot(numpy.linspace(0,npoints-1,npoints), sampled_energies)
plt.show()
return sampled_energies
if __name__ == "__main__":
#define distribution function (spectrum)
a = numpy.array([ \
[1000.00,0.00000 ],\
[2000.00,0.00000 ],\
[3000.00,0.00000 ],\
[4000.00,0.00000 ],\
[5000.00,0.00000 ],\
[6000.00,0.00000 ],\
[7000.00,0.00000 ],\
[8000.00,0.00000 ],\
[9000.00,0.00000 ],\
[10000.0,6.65281 ],\
[11000.0,26.1984 ],\
[12000.0,86.3888 ],\
[13000.0,285.715 ],\
[14000.0,642.834 ],\
[15000.0,1605.83 ],\
[16000.0,2957.33 ],\
[17000.0,6046.30 ],\
[18000.0,9838.37 ],\
[19000.0,12738.8 ],\
[20000.0,16130.6 ],\
[21000.0,19788.5 ],\
[22000.0,23865.6 ],\
[23000.0,27854.9 ],\
[24000.0,32146.1 ],\
[25000.0,35882.3 ],\
[26000.0,39455.6 ],\
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[29000.0,47336.9 ],\
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[31000.0,50532.1 ],\
[32000.0,51625.8 ],\
[33000.0,52335.6 ],\
[34000.0,53043.7 ],\
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[36000.0,53049.9 ],\
[37000.0,52808.1 ],\
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[40000.0,51575.2 ],\
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[48000.0,44310.4 ],\
[49000.0,42984.9 ],\
[50000.0,41634.4 ],\
[51000.0,40430.2 ],\
[52000.0,39222.2 ],\
[53000.0,38071.3 ],\
[54000.0,36896.7 ],\
[55000.0,35945.7 ],\
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[57000.0,42099.2 ],\
[58000.0,49257.8 ],\
[59000.0,55207.9 ],\
[60000.0,61086.8 ],\
[61000.0,46152.4 ],\
[62000.0,31065.0 ],\
[63000.0,28571.1 ],\
[64000.0,26042.6 ],\
[65000.0,25171.6 ],\
[66000.0,24200.1 ],\
[67000.0,28353.4 ],\
[68000.0,32520.8 ],\
[69000.0,27392.2 ],\
[70000.0,22032.3 ],\
[71000.0,19236.8 ],\
[72000.0,16385.0 ],\
[73000.0,15587.5 ],\
[74000.0,14719.0 ],\
[75000.0,14176.4 ],\
[76000.0,13719.6 ],\
[77000.0,13059.6 ],\
[78000.0,12319.1 ],\
[79000.0,11773.1 ],\
[80000.0,10935.6 ],\
[81000.0,10549.2 ],\
[82000.0,9802.11 ],\
[83000.0,9181.41 ],\
[84000.0,8716.42 ],\
[85000.0,8071.86 ],\
[86000.0,7430.28 ],\
[87000.0,6998.92 ],\
[88000.0,6568.78 ],\
[89000.0,5975.87 ],\
[90000.0,5382.43 ],\
[91000.0,4901.83 ],\
[92000.0,4425.00 ],\
[93000.0,3795.52 ],\
[94000.0,3258.13 ],\
[95000.0,2786.15 ],\
[96000.0,2312.45 ],\
[97000.0,1879.51 ],\
[98000.0,1430.59 ],\
[99000.0,920.485 ],\
[100000.,414.051 ],\
[101000.,95.4982 ],\
[102000.,0.00000 ],\
[103000.,0.00000 ] ] )
print("Energy from %f eV to %f eV"%(a[0,0],a[-1,0]))
#
# create SHADOW source
#
src = Shadow.Source()
beam = Shadow.Beam()
beam.genSource(src)
npoints = src.NPOINT
sampled_energies = sample_from_spectrum(a,npoints=npoints,plot=1)
#calculate wavevectors = 2 pi / lambda
codata_h = numpy.array(6.62606957e-34)
codata_ec = numpy.array(1.602176565e-19)
codata_c = numpy.array(299792458.0)
A2EV = 2.0*numpy.pi/(codata_h*codata_c/codata_ec*1e2) #A2EV = 50676.89919
sampled_wavevectors = sampled_energies * A2EV #2 pi / wavelength in cm^-1
#overwrite the energy column with new values
beam.rays[:,10] = sampled_wavevectors
# calculate the histogram for energy of the new source
import Shadow.ShadowTools
Shadow.ShadowTools.histo1(beam,11,nbins=75)