1 | """ |
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2 | Conversion of scattering cross section from SANS (I(q), or rather, ds/dO) in absolute |
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3 | units (cm-1)into SESANS correlation function G using a Hankel transformation, then converting |
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4 | the SESANS correlation function into polarisation from the SESANS experiment |
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5 | |
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6 | Everything is in units of metres except specified otherwise (NOT TRUE!!!) |
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7 | Everything is in conventional units (nm for spin echo length) |
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8 | |
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9 | Wim Bouwman (w.g.bouwman@tudelft.nl), June 2013 |
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10 | """ |
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11 | |
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12 | from __future__ import division |
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13 | |
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14 | import numpy as np # type: ignore |
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15 | from numpy import pi, exp # type: ignore |
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16 | from scipy.special import j0 |
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17 | #from mpmath import j0 as j0 |
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18 | |
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19 | class SesansTransform(object): |
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20 | #: Set of spin-echo lengths in the measured data |
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21 | SE = None # type: np.ndarray |
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22 | #: Maximum acceptance of scattering vector in the spin echo encoding dimension (for ToF: Q of min(R) and max(lam)) |
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23 | zaccept = None # type: float |
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24 | #: Maximum size sensitivity; larger radius requires more computation |
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25 | Rmax = None # type: float |
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26 | #: q values to calculate when computing transform |
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27 | q = None # type: np.ndarray |
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28 | |
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29 | # transform arrays |
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30 | _H = None # type: np.ndarray |
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31 | _H0 = None # type: np.ndarray |
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32 | |
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33 | def set_transform(self, SE, zaccept, Rmax): |
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34 | if self.SE is None or len(SE) != len(self.SE) or np.any(SE != self.SE) or zaccept != self.zaccept or Rmax != self.Rmax: |
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35 | self.SE, self.zaccept, self.Rmax = SE, zaccept, Rmax |
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36 | self._set_q() |
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37 | self._set_hankel() |
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38 | |
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39 | def apply(self, Iq): |
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40 | G0 = np.dot(self._H0, Iq) |
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41 | G = np.dot(self._H.T, Iq) |
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42 | P = G - G0 |
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43 | return P |
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44 | |
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45 | def _set_q(self): |
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46 | #q_min = dq = 0.1 * 2*pi / self.Rmax |
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47 | |
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48 | q_max = 2*pi / (self.SE[1]-self.SE[0]) |
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49 | q_min = dq = 0.1 *2*pi / (np.size(self.SE) * self.SE[-1]) |
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50 | |
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51 | #q_min = dq = q_max / 100000 |
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52 | q=np.arange(q_min, q_max, q_min) |
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53 | self.q = q |
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54 | self.dq = dq |
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55 | |
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56 | def _set_hankel(self): |
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57 | #Rmax = #value in text box somewhere in FitPage? |
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58 | q = self.q |
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59 | dq = self.dq |
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60 | SElength = self.SE |
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61 | |
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62 | H0 = dq / (2 * pi) * q |
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63 | q=np.array(q,dtype='float32') |
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64 | SElength=np.array(SElength,dtype='float32') |
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65 | |
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66 | # Using numpy tile, dtype is conserved |
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67 | repq=np.tile(q,(SElength.size,1)) |
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68 | repSE=np.tile(SElength,(q.size,1)) |
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69 | H = dq / (2 * pi) * j0(repSE*repq.T)*repq.T |
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70 | |
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71 | # Using numpy meshgrid - meshgrid produces float64 from float32 inputs! Problem for 32-bit OS: Memerrors! |
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72 | #H0 = dq / (2 * pi) * q |
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73 | #repSE, repq = np.meshgrid(SElength, q) |
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74 | #repq=np.array(repq,dtype='float32') |
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75 | #repSE=np.array(repSE,dtype='float32') |
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76 | #H = dq / (2 * pi) * j0(repSE*repq)*repq |
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77 | |
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78 | self._H, self._H0 = H, H0 |
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79 | |
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80 | class SESANS1D(SesansTransform): |
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81 | def __init__(self, data, _H0, _H, q_calc): |
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82 | # x values of the data (Sasview requires these to be named "q") |
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83 | self.q = data.x |
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84 | self._H0 = _H0 |
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85 | self._H = _H |
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86 | # Pysmear does some checks on the smearer object, these checks require the "data" object... |
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87 | self.data=data |
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88 | # q values of the SAS model |
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89 | self.q_calc = q_calc # These are the MODEL's q values used by the smearer (in this case: the Hankel transform) |
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90 | def apply(self, theory): |
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91 | return SesansTransform.apply(self,theory) |
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