1 | """ |
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2 | Conversion of scattering cross section from SANS in absolute |
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3 | units into SESANS using a Hankel transformation |
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4 | |
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5 | Everything is in units of metres except specified otherwise |
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6 | |
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7 | Wim Bouwman (w.g.bouwman@tudelft.nl), June 2013 |
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8 | """ |
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9 | |
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10 | from __future__ import division |
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11 | |
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12 | import numpy as np |
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13 | from numpy import pi, exp |
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14 | |
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15 | from scipy.special import jv as besselj |
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16 | |
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17 | def make_q(q_zmax, Rmax): |
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18 | q_min = dq = 0.1 * 2*pi / Rmax |
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19 | #q_min = 0.00003 |
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20 | return np.arange(q_min, q_zmax, dq) |
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21 | |
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22 | # TODO: dead code; for now the call to the hankel transform happens in BumpsModel |
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23 | class SesansCalculator: |
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24 | def __init__(self, kernel, q_zmax, Rmax, SElength, wavelength, thickness): |
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25 | self._set_kernel(kernel, q_zmax, Rmax) |
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26 | self.SElength = SElength |
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27 | self.wavelength = wavelength |
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28 | self.thickness = thickness |
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29 | |
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30 | def _set_kernel(self, kernel, q_zmax, Rmax): |
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31 | kernel_input = kernel.make_input([make_q(q_zmax, Rmax)]) |
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32 | self.sans_calculator = kernel(kernel_input) |
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33 | |
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34 | def __call__(self, pars, pd_pars, cutoff=1e-5): |
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35 | Iq = self.sans_calculator(pars, pd_pars, cutoff) |
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36 | P = hankel(self.SElength, self.wavelength, self.thickness, self.q, Iq) |
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37 | self.Iq = Iq |
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38 | return P |
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39 | |
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40 | def hankel(SElength, wavelength, thickness, q, Iq): |
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41 | """ |
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42 | Compute the expected SESANS polarization for a given SANS pattern. |
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43 | |
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44 | Uses the hankel transform followed by the exponential. The values |
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45 | for zz (or spin echo length, or delta), wavelength and sample thickness |
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46 | information should come from the dataset. *q* should be chosen such |
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47 | that the oscillations in *I(q)* are well sampled (e.g., 5*2*pi/d_max). |
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48 | |
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49 | *SElength* [A] is the set of z points at which to compute the hankel transform |
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50 | |
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51 | *wavelength* [m] is the wavelength of each individual point *zz* |
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52 | |
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53 | *thickness* [cm] is the sample thickness. |
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54 | |
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55 | *q* [A^{-1}] is the set of q points at which the model has been computed. |
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56 | These should be equally spaced. |
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57 | |
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58 | *I* [cm^{-1}] is the value of the SANS model at *q* |
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59 | """ |
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60 | G = np.zeros(len(SElength), 'd') |
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61 | for i in range(len(SElength)): |
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62 | integr = besselj(0,q*SElength[i])*Iq*q |
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63 | G[i] = np.sum(integr) |
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64 | dq=(q[1]-q[0])*1e10 # [m^-1] step size in q, needed for integration |
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65 | G *= dq*1e10*2*pi # integr step, conver q into [m**-1] and 2 pi circle integr |
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66 | P = exp(thickness*wavelength**2/(4*pi**2)*(G-G[0])) |
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67 | |
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68 | return P |
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