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 jv as besselj |
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17 | #import direct_model.DataMixin as model |
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18 | |
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19 | def make_q(q_max, Rmax): |
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20 | r""" |
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21 | Return a $q$ vector suitable for SESANS covering from $2\pi/ (10 R_{\max})$ |
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22 | to $q_max$. This is the integration range of the Hankel transform; bigger range and |
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23 | more points makes a better numerical integration. |
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24 | Smaller q_min will increase reliable spin echo length range. |
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25 | Rmax is the "radius" of the largest expected object and can be set elsewhere. |
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26 | q_max is determined by the acceptance angle of the SESANS instrument. |
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27 | """ |
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28 | from sas.sascalc.data_util.nxsunit import Converter |
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29 | |
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30 | q_min = dq = 0.1 * 2*pi / Rmax |
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31 | return np.arange(q_min, |
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32 | Converter(q_max[1])(q_max[0], |
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33 | units="1/A"), |
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34 | dq) |
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35 | |
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36 | def make_all_q(data): |
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37 | """ |
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38 | Return a $q$ vector suitable for calculating the total scattering cross section for |
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39 | calculating the effect of finite acceptance angles on Time of Flight SESANS instruments. |
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40 | If no acceptance is given, or unwanted (set "unwanted" flag in paramfile), no all_q vector is needed. |
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41 | If the instrument has a rectangular acceptance, 2 all_q vectors are needed. |
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42 | If the instrument has a circular acceptance, 1 all_q vector is needed |
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43 | |
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44 | """ |
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45 | if not data.has_no_finite_acceptance: |
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46 | return [] |
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47 | elif data.has_yz_acceptance(data): |
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48 | # compute qx, qy |
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49 | Qx, Qy = np.meshgrid(qx, qy) |
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50 | return [Qx, Qy] |
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51 | else: |
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52 | # else only need q |
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53 | # data.has_z_acceptance |
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54 | return [q] |
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55 | |
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56 | def transform(data, q_calc, Iq_calc, qmono, Iq_mono): |
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57 | """ |
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58 | Decides which transform type is to be used, based on the experiment data file contents (header) |
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59 | (2016-03-19: currently controlled from parameters script) |
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60 | nqmono is the number of q vectors to be used for the detector integration |
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61 | """ |
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62 | nqmono = len(qmono) |
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63 | if nqmono == 0: |
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64 | result = call_hankel(data, q_calc, Iq_calc) |
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65 | elif nqmono == 1: |
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66 | q = qmono[0] |
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67 | result = call_HankelAccept(data, q_calc, Iq_calc, q, Iq_mono) |
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68 | else: |
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69 | Qx, Qy = [qmono[0], qmono[1]] |
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70 | Qx = np.reshape(Qx, nqx, nqy) |
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71 | Qy = np.reshape(Qy, nqx, nqy) |
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72 | Iq_mono = np.reshape(Iq_mono, nqx, nqy) |
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73 | qx = Qx[0, :] |
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74 | qy = Qy[:, 0] |
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75 | result = call_Cosine2D(data, q_calc, Iq_calc, qx, qy, Iq_mono) |
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76 | |
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77 | return result |
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78 | |
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79 | def call_hankel(data, q_calc, Iq_calc): |
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80 | return hankel((data.x, data.x_unit), |
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81 | (data.lam, data.lam_unit), |
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82 | (data.sample.thickness, |
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83 | data.sample.thickness_unit), |
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84 | q_calc, Iq_calc) |
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85 | |
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86 | def call_HankelAccept(data, q_calc, Iq_calc, q_mono, Iq_mono): |
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87 | return hankel(data.x, data.lam * 1e-9, |
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88 | data.sample.thickness / 10, |
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89 | q_calc, Iq_calc) |
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90 | |
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91 | def call_Cosine2D(data, q_calc, Iq_calc, qx, qy, Iq_mono): |
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92 | return hankel(data.x, data.y, data.lam * 1e-9, |
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93 | data.sample.thickness / 10, |
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94 | q_calc, Iq_calc) |
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95 | |
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96 | def TotalScatter(model, parameters): #Work in progress!! |
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97 | # Calls a model with existing model parameters already in place, then integrate the product of q and I(q) from 0 to (4*pi/lambda) |
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98 | allq = np.linspace(0,4*pi/wavelength,1000) |
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99 | allIq = 1 |
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100 | integral = allq*allIq |
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101 | |
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102 | |
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103 | |
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104 | def Cosine2D(wavelength, magfield, thickness, qy, qz, Iqy, Iqz, modelname): #Work in progress!! Needs to call model still |
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105 | #============================================================================== |
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106 | # 2D Cosine Transform if "wavelength" is a vector |
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107 | #============================================================================== |
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108 | #allq is the q-space needed to create the total scattering cross-section |
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109 | |
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110 | Gprime = np.zeros_like(wavelength, 'd') |
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111 | s = np.zeros_like(wavelength, 'd') |
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112 | sd = np.zeros_like(wavelength, 'd') |
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113 | Gprime = np.zeros_like(wavelength, 'd') |
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114 | f = np.zeros_like(wavelength, 'd') |
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115 | for i, wavelength_i in enumerate(wavelength): |
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116 | z = magfield*wavelength_i |
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117 | allq=np.linspace() #for calculating the Q-range of the scattering power integral |
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118 | allIq=np.linspace() # This is the model applied to the allq q-space. Needs to refference the model somehow |
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119 | alldq = (allq[1]-allq[0])*1e10 |
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120 | sigma[i]=wavelength[i]^2*thickness/2/pi*np.sum(allIq*allq*alldq) |
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121 | s[i]=1-exp(-sigma) |
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122 | for j, Iqy_j, qy_j in enumerate(qy): |
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123 | for k, Iqz_k, qz_k in enumerate(qz): |
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124 | Iq = np.sqrt(Iqy_j^2+Iqz_k^2) |
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125 | q = np.sqrt(qy_j^2 + qz_k^2) |
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126 | Gintegral = Iq*cos(z*Qz_k) |
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127 | Gprime[i] += Gintegral |
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128 | # sigma = wavelength^2*thickness/2/pi* allq[i]*allIq[i] |
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129 | # s[i] += 1-exp(Totalscatter(modelname)*thickness) |
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130 | # For now, work with standard 2-phase scatter |
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131 | |
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132 | |
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133 | sd[i] += Iq |
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134 | f[i] = 1-s[i]+sd[i] |
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135 | P[i] = (1-sd[i]/f[i])+1/f[i]*Gprime[i] |
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136 | |
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137 | |
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138 | |
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139 | |
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140 | def HankelAccept(wavelength, magfield, thickness, q, Iq, theta, modelname): |
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141 | #============================================================================== |
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142 | # HankelTransform with fixed circular acceptance angle (circular aperture) for Time of Flight SESANS |
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143 | #============================================================================== |
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144 | #acceptq is the q-space needed to create limited acceptance effect |
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145 | SElength= wavelength*magfield |
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146 | G = np.zeros_like(SElength, 'd') |
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147 | threshold=2*pi*theta/wavelength |
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148 | for i, SElength_i in enumerate(SElength): |
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149 | allq=np.linspace() #for calculating the Q-range of the scattering power integral |
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150 | allIq=np.linspace() # This is the model applied to the allq q-space. Needs to refference the model somehow |
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151 | alldq = (allq[1]-allq[0])*1e10 |
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152 | sigma[i]=wavelength[i]^2*thickness/2/pi*np.sum(allIq*allq*alldq) |
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153 | s[i]=1-exp(-sigma) |
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154 | |
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155 | dq = (q[1]-q[0])*1e10 |
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156 | a = (x<threshold) |
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157 | acceptq = a*q |
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158 | acceptIq = a*Iq |
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159 | |
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160 | G[i] = np.sum(besselj(0, acceptq*SElength_i)*acceptIq*acceptq*dq) |
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161 | |
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162 | # G[i]=np.sum(integral) |
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163 | |
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164 | G *= dq*1e10*2*pi |
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165 | |
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166 | P = exp(thickness*wavelength**2/(4*pi**2)*(G-G[0])) |
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167 | |
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168 | def hankel(SElength, wavelength, thickness, q, Iq): |
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169 | r""" |
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170 | Compute the expected SESANS polarization for a given SANS pattern. |
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171 | |
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172 | Uses the hankel transform followed by the exponential. The values for *zz* |
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173 | (or spin echo length, or delta), wavelength and sample thickness should |
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174 | come from the dataset. $q$ should be chosen such that the oscillations |
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175 | in $I(q)$ are well sampled (e.g., $5 \cdot 2 \pi/d_{\max}$). |
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176 | |
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177 | *SElength* [A] is the set of $z$ points at which to compute the |
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178 | Hankel transform |
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179 | |
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180 | *wavelength* [m] is the wavelength of each individual point *zz* |
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181 | |
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182 | *thickness* [cm] is the sample thickness. |
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183 | |
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184 | *q* [A$^{-1}$] is the set of $q$ points at which the model has been |
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185 | computed. These should be equally spaced. |
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186 | |
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187 | *I* [cm$^{-1}$] is the value of the SANS model at *q* |
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188 | """ |
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189 | |
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190 | from sas.sascalc.data_util.nxsunit import Converter |
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191 | wavelength = Converter(wavelength[1])(wavelength[0],"A") |
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192 | thickness = Converter(thickness[1])(thickness[0],"A") |
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193 | Iq = Converter("1/cm")(Iq,"1/A") # All models default to inverse centimeters |
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194 | SElength = Converter(SElength[1])(SElength[0],"A") |
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195 | |
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196 | G = np.zeros_like(SElength, 'd') |
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197 | #============================================================================== |
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198 | # Hankel Transform method if "wavelength" is a scalar; mono-chromatic SESANS |
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199 | #============================================================================== |
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200 | for i, SElength_i in enumerate(SElength): |
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201 | integral = besselj(0, q*SElength_i)*Iq*q |
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202 | G[i] = np.sum(integral) |
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203 | G0 = np.sum(Iq*q) |
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204 | |
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205 | # [m^-1] step size in q, needed for integration |
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206 | dq = (q[1]-q[0]) |
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207 | |
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208 | # integration step, convert q into [m**-1] and 2 pi circle integration |
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209 | G *= dq*2*pi |
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210 | G0 = np.sum(Iq*q)*dq*2*np.pi |
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211 | |
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212 | P = exp(thickness*wavelength**2/(4*pi**2)*(G-G0)) |
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213 | |
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214 | return P |
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