[c97724e] | 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 | from scipy.special import jv as besselj |
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[02e70ff] | 15 | #import direct_model.DataMixin as model |
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| 16 | |
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[09ebe8c] | 17 | def make_q(q_max, Rmax): |
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[384d114] | 18 | r""" |
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[09ebe8c] | 19 | Return a $q$ vector suitable for SESANS covering from $2\pi/ (10 R_{\max})$ |
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| 20 | to $q_max$. |
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| 21 | """ |
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[c97724e] | 22 | q_min = dq = 0.1 * 2*pi / Rmax |
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[09ebe8c] | 23 | return np.arange(q_min, q_max, dq) |
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[02e70ff] | 24 | |
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| 25 | def make_allq(data): |
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| 26 | if not data.needs_all_q: |
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| 27 | return [] |
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| 28 | elif needs_Iqxy(data): |
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| 29 | # compute qx, qy |
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| 30 | Qx, Qy = np.meshgrid(qx, qy) |
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| 31 | return [Qx, Qy] |
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| 32 | else: |
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| 33 | # else only need q |
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| 34 | return [q] |
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| 35 | |
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| 36 | def transform(data, q_calc, Iq_calc, qmono, Iq_mono): |
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| 37 | nqmono = len(qmono) |
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| 38 | if nqmono == 0: |
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| 39 | result = call_hankel(data, q_calc, Iq_calc) |
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| 40 | elif nqmono == 1: |
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| 41 | q = qmono[0] |
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| 42 | result = call_HankelAccept(data, q_calc, Iq_calc, q, Iq_mono) |
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| 43 | else: |
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| 44 | Qx, Qy = [qmono[0], qmono[1]] |
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| 45 | Qx = np.reshape(Qx, nqx, nqy) |
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| 46 | Qy = np.reshape(Qy, nqx, nqy) |
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| 47 | Iq_mono = np.reshape(Iq_mono, nqx, nqy) |
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| 48 | qx = Qx[0, :] |
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| 49 | qy = Qy[:, 0] |
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| 50 | result = call_Cosine2D(data, q_calc, Iq_calc, qx, qy, Iq_mono) |
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| 51 | |
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| 52 | return result |
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| 53 | |
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| 54 | def call_hankel(data, q_calc, Iq_calc): |
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| 55 | return hankel(data.x, data.lam * 1e-9, |
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| 56 | data.sample.thickness / 10, |
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| 57 | q_calc, Iq_calc) |
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| 58 | |
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| 59 | def call_HankelAccept(data, q_calc, Iq_calc, q_mono, Iq_mono): |
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| 60 | return hankel(data.x, data.lam * 1e-9, |
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| 61 | data.sample.thickness / 10, |
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| 62 | q_calc, Iq_calc) |
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| 63 | |
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| 64 | def Cosine2D(data, q_calc, Iq_calc, qx, qy, Iq_mono): |
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| 65 | return hankel(data.x, data.y data.lam * 1e-9, |
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| 66 | data.sample.thickness / 10, |
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| 67 | q_calc, Iq_calc) |
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| 68 | |
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| 69 | def TotalScatter(model, parameters): #Work in progress!! |
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| 70 | # 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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| 71 | allq = np.linspace(0,4*pi/wavelength,1000) |
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| 72 | allIq = |
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| 73 | integral = allq*allIq |
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| 74 | |
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| 75 | |
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| 76 | |
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| 77 | def Cosine2D(wavelength, magfield, thickness, qy, qz, Iqy, Iqz, modelname): #Work in progress!! Needs to call model still |
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| 78 | #============================================================================== |
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| 79 | # 2D Cosine Transform if "wavelength" is a vector |
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| 80 | #============================================================================== |
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| 81 | #allq is the q-space needed to create the total scattering cross-section |
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| 82 | |
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| 83 | Gprime = np.zeros_like(wavelength, 'd') |
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| 84 | s = np.zeros_like(wavelength, 'd') |
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| 85 | sd = np.zeros_like(wavelength, 'd') |
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| 86 | Gprime = np.zeros_like(wavelength, 'd') |
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| 87 | f = np.zeros_like(wavelength, 'd') |
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| 88 | for i, wavelength_i in enumerate(wavelength): |
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| 89 | z = magfield*wavelength_i |
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| 90 | allq=np.linspace() #for calculating the Q-range of the scattering power integral |
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| 91 | allIq=np.linspace() # This is the model applied to the allq q-space. Needs to refference the model somehow |
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| 92 | alldq = (allq[1]-allq[0])*1e10 |
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| 93 | sigma[i]=wavelength[i]^2*thickness/2/pi*np.sum(allIq*allq*alldq) |
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| 94 | s[i]=1-exp(-sigma) |
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| 95 | for j, Iqy_j, qy_j in enumerate(qy): |
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| 96 | for k, Iqz_k, qz_k in enumerate(qz): |
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| 97 | Iq = np.sqrt(Iqy_j^2+Iqz_k^2) |
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| 98 | q = np.sqrt(qy_j^2 + qz_k^2) |
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| 99 | Gintegral = Iq*cos(z*Qz_k) |
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| 100 | Gprime[i] += Gintegral |
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| 101 | # sigma = wavelength^2*thickness/2/pi* allq[i]*allIq[i] |
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| 102 | # s[i] += 1-exp(Totalscatter(modelname)*thickness) |
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| 103 | # For now, work with standard 2-phase scatter |
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| 104 | |
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| 105 | |
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| 106 | sd[i] += Iq |
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| 107 | f[i] = 1-s[i]+sd[i] |
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| 108 | P[i] = (1-sd[i]/f[i])+1/f[i]*Gprime[i] |
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| 109 | |
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| 110 | |
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| 111 | |
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| 112 | |
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| 113 | def HankelAccept(wavelength, magfield, thickness, q, Iq, theta, modelname): |
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| 114 | #============================================================================== |
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| 115 | # HankelTransform with fixed circular acceptance angle (circular aperture) for Time of Flight SESANS |
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| 116 | #============================================================================== |
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| 117 | #acceptq is the q-space needed to create limited acceptance effect |
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| 118 | SElength= wavelength*magfield |
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| 119 | G = np.zeros_like(SElength, 'd') |
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| 120 | threshold=2*pi*theta/wavelength |
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| 121 | for i, SElength_i in enumerate(SElength): |
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| 122 | allq=np.linspace() #for calculating the Q-range of the scattering power integral |
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| 123 | allIq=np.linspace() # This is the model applied to the allq q-space. Needs to refference the model somehow |
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| 124 | alldq = (allq[1]-allq[0])*1e10 |
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| 125 | sigma[i]=wavelength[i]^2*thickness/2/pi*np.sum(allIq*allq*alldq) |
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| 126 | s[i]=1-exp(-sigma) |
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| 127 | |
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| 128 | dq = (q[1]-q[0])*1e10 |
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| 129 | a = (x<threshold) |
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| 130 | acceptq = a*q |
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| 131 | acceptIq = a*Iq |
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| 132 | |
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| 133 | G[i] = np.sum(besselj(0, acceptq*SElength_i)*acceptIq*acceptq*dq) |
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| 134 | |
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| 135 | # G[i]=np.sum(integral) |
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| 136 | |
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| 137 | G *= dq*1e10*2*pi |
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| 138 | |
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| 139 | P = exp(thickness*wavelength**2/(4*pi**2)*(G-G[0])) |
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| 140 | |
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[c97724e] | 141 | def hankel(SElength, wavelength, thickness, q, Iq): |
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[384d114] | 142 | r""" |
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[c97724e] | 143 | Compute the expected SESANS polarization for a given SANS pattern. |
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| 144 | |
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[384d114] | 145 | Uses the hankel transform followed by the exponential. The values for *zz* |
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| 146 | (or spin echo length, or delta), wavelength and sample thickness should |
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| 147 | come from the dataset. $q$ should be chosen such that the oscillations |
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| 148 | in $I(q)$ are well sampled (e.g., $5 \cdot 2 \pi/d_{\max}$). |
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[c97724e] | 149 | |
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[384d114] | 150 | *SElength* [A] is the set of $z$ points at which to compute the |
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| 151 | Hankel transform |
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[c97724e] | 152 | |
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| 153 | *wavelength* [m] is the wavelength of each individual point *zz* |
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| 154 | |
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| 155 | *thickness* [cm] is the sample thickness. |
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| 156 | |
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[384d114] | 157 | *q* [A$^{-1}$] is the set of $q$ points at which the model has been |
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| 158 | computed. These should be equally spaced. |
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[c97724e] | 159 | |
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[384d114] | 160 | *I* [cm$^{-1}$] is the value of the SANS model at *q* |
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[c97724e] | 161 | """ |
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[190fc2b] | 162 | G = np.zeros_like(SElength, 'd') |
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[02e70ff] | 163 | #============================================================================== |
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| 164 | # Hankel Transform method if "wavelength" is a scalar; mono-chromatic SESANS |
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| 165 | #============================================================================== |
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[190fc2b] | 166 | for i, SElength_i in enumerate(SElength): |
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| 167 | integral = besselj(0, q*SElength_i)*Iq*q |
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| 168 | G[i] = np.sum(integral) |
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[384d114] | 169 | |
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| 170 | # [m^-1] step size in q, needed for integration |
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[190fc2b] | 171 | dq = (q[1]-q[0])*1e10 |
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[384d114] | 172 | |
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| 173 | # integration step, convert q into [m**-1] and 2 pi circle integration |
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| 174 | G *= dq*1e10*2*pi |
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| 175 | |
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[c97724e] | 176 | P = exp(thickness*wavelength**2/(4*pi**2)*(G-G[0])) |
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| 177 | |
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| 178 | return P |
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