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 | |
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18 | class SesansTransform(object): |
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19 | """ |
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20 | Spin-Echo SANS transform calculator. Similar to a resolution function, |
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21 | the SesansTransform object takes I(q) for the set of *q_calc* values and |
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22 | produces a transformed dataset. |
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23 | |
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24 | *SElength* (A) is the set of spin-echo lengths in the measured data. |
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25 | |
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26 | *zaccept* (1/A) is the maximum acceptance of scattering vector in the spin |
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27 | echo encoding dimension (for ToF: Q of min(R) and max(lam)). |
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28 | |
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29 | *Rmax* (A) is the maximum size sensitivity; larger radius requires more |
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30 | computation time. |
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31 | """ |
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32 | #: SElength from the data in the original data units; not used by transform |
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33 | #: but the GUI uses it, so make sure that it is present. |
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34 | q = None # type: np.ndarray |
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35 | |
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36 | #: q values to calculate when computing transform |
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37 | q_calc = None # type: np.ndarray |
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38 | |
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39 | # transform arrays |
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40 | _H = None # type: np.ndarray |
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41 | _H0 = None # type: np.ndarray |
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42 | |
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43 | def __init__(self, z, SElength, lam, zaccept, Rmax): |
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44 | # type: (np.ndarray, float, float) -> None |
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45 | #import logging; logging.info("creating SESANS transform") |
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46 | self.q = z |
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47 | self._set_hankel(SElength, lam, zaccept, Rmax) |
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48 | |
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49 | def apply(self, Iq): |
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50 | G0 = np.dot(self._H0, Iq) |
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51 | G = np.dot(self._H.T, Iq) |
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52 | P = G - G0 |
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53 | return P |
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54 | |
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55 | def _set_hankel(self, SElength, lam, zaccept, Rmax): |
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56 | # type: (np.ndarray, float, float) -> None |
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57 | # Force float32 arrays, otherwise run into memory problems on some machines |
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58 | SElength = np.asarray(SElength, dtype='float32') |
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59 | |
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60 | #Rmax = #value in text box somewhere in FitPage? |
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61 | q_max = 2*pi / (SElength[1] - SElength[0]) |
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62 | q_min = 0.1 * 2*pi / (np.size(SElength) * SElength[-1]) |
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63 | q = np.arange(q_min, q_max, q_min, dtype='float32') |
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64 | dq = q_min |
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65 | |
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66 | H0 = np.float32(dq/(2*pi)) * q |
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67 | |
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68 | repq = np.tile(q, (SElength.size, 1)).T |
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69 | repSE = np.tile(SElength, (q.size, 1)) |
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70 | H = np.float32(dq/(2*pi)) * j0(repSE*repq) * repq |
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71 | |
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72 | replam = np.tile(lam, (q.size, 1)) |
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73 | reptheta = np.arcsin(repq*replam/2*np.pi) |
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74 | mask = reptheta > zaccept |
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75 | H[mask] = 0 |
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76 | |
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77 | self.q_calc = q |
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78 | self._H, self._H0 = H, H0 |
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79 | |
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80 | class OrientedSesansTransform(object): |
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81 | """ |
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82 | Oriented Spin-Echo SANS transform calculator. Similar to a resolution |
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83 | function, the OrientedSesansTransform object takes I(q) for the set |
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84 | of *q_calc* values and produces a transformed dataset. |
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85 | |
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86 | *SElength* (A) is the set of spin-echo lengths in the measured data. |
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87 | |
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88 | *zaccept* (1/A) is the maximum acceptance of scattering vector in the spin |
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89 | echo encoding dimension (for ToF: Q of min(R) and max(lam)). |
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90 | |
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91 | *Rmax* (A) is the maximum size sensitivity; larger radius requires more |
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92 | computation time. |
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93 | """ |
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94 | #: SElength from the data in the original data units; not used by transform |
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95 | #: but the GUI uses it, so make sure that it is present. |
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96 | q = None # type: np.ndarray |
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97 | |
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98 | #: q values to calculate when computing transform |
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99 | q_calc = None # type: np.ndarray |
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100 | |
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101 | # transform arrays |
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102 | _cosmat = None # type: np.ndarray |
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103 | _cos0 = None # type: np.ndarray |
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104 | _Iq_shape = None # type: Tuple[int, int] |
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105 | |
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106 | def __init__(self, z, SElength, zaccept, Rmax): |
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107 | # type: (np.ndarray, float, float) -> None |
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108 | #import logging; logging.info("creating SESANS transform") |
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109 | self.q = z |
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110 | self._set_cosmat(SElength, zaccept, Rmax) |
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111 | |
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112 | def apply(self, Iq): |
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113 | dq = self.q_calc[0][0] |
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114 | Iq = np.reshape(Iq, self._Iq_shape) |
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115 | G0 = self._cos0 * np.sum(Iq) * dq |
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116 | G = np.sum(np.dot(Iq, self._cosmat), axis=0) * dq |
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117 | P = G - G0 |
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118 | return P |
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119 | |
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120 | def _set_cosmat(self, SElength, zaccept, Rmax): |
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121 | # type: (np.ndarray, float, float) -> None |
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122 | # Force float32 arrays, otherwise run into memory problems on some machines |
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123 | SElength = np.asarray(SElength, dtype='float32') |
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124 | |
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125 | # Rmax = #value in text box somewhere in FitPage? |
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126 | q_max = 2 * pi / (SElength[1] - SElength[0]) |
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127 | q_min = 0.1 * 2 * pi / (np.size(SElength) * SElength[-1]) |
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128 | q_min *= 100 |
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129 | |
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130 | q = np.arange(q_min, q_max, q_min, dtype='float32') |
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131 | dq = q_min |
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132 | |
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133 | cos0 = np.float32(dq / (2 * pi)) |
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134 | cosmat = np.float32(dq / (2 * pi)) * np.cos(q[:, None] * SElength[None, :]) |
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135 | |
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136 | qx, qy = np.meshgrid(q, q) |
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137 | self._Iq_shape = qx.shape |
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138 | self.q_calc = qx.flatten(), qy.flatten() |
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139 | self._cosmat, self._cos0 = cosmat, cos0 |
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