[c97724e] | 1 | """ |
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[d459d4e] | 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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[c97724e] | 5 | |
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[d459d4e] | 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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[c97724e] | 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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[7ae2b7f] | 14 | import numpy as np # type: ignore |
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[fa79f5c] | 15 | from numpy import pi # type: ignore |
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[d7af1c6] | 16 | from scipy.special import j0, j1 |
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| 17 | |
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[94d13f1] | 18 | |
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[54f1d96] | 19 | class SesansTransform(object): |
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[94d13f1] | 20 | """ |
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| 21 | Spin-Echo SANS transform calculator. Similar to a resolution function, |
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| 22 | the SesansTransform object takes I(q) for the set of *q_calc* values and |
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| 23 | produces a transformed dataset |
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| 24 | |
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| 25 | *SElength* (A) is the set of spin-echo lengths in the measured data. |
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| 26 | |
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| 27 | *zaccept* (1/A) is the maximum acceptance of scattering vector in the spin |
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| 28 | echo encoding dimension (for ToF: Q of min(R) and max(lam)). |
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| 29 | |
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| 30 | *Rmax* (A) is the maximum size sensitivity; larger radius requires more |
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| 31 | computation time. |
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| 32 | """ |
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| 33 | #: SElength from the data in the original data units; not used by transform |
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| 34 | #: but the GUI uses it, so make sure that it is present. |
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[54f1d96] | 35 | q = None # type: np.ndarray |
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| 36 | |
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[94d13f1] | 37 | #: q values to calculate when computing transform |
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| 38 | q_calc = None # type: np.ndarray |
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| 39 | |
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[54f1d96] | 40 | # transform arrays |
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[94d13f1] | 41 | _H = None # type: np.ndarray |
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| 42 | _H0 = None # type: np.ndarray |
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[54f1d96] | 43 | |
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[9f91afe] | 44 | def __init__(self, z, SElength, lam, zaccept, Rmax): |
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[94d13f1] | 45 | # type: (np.ndarray, float, float) -> None |
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| 46 | #import logging; logging.info("creating SESANS transform") |
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| 47 | self.q = z |
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[9f91afe] | 48 | self._set_hankel(SElength, lam, zaccept, Rmax) |
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[54f1d96] | 49 | |
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| 50 | def apply(self, Iq): |
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[94d13f1] | 51 | # tye: (np.ndarray) -> np.ndarray |
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| 52 | G0 = np.dot(self._H0, Iq) |
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| 53 | G = np.dot(self._H.T, Iq) |
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[54f1d96] | 54 | P = G - G0 |
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| 55 | return P |
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| 56 | |
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[9f91afe] | 57 | def _set_hankel(self, SElength, lam, zaccept, Rmax): |
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[94d13f1] | 58 | # type: (np.ndarray, float, float) -> None |
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| 59 | # Force float32 arrays, otherwise run into memory problems on some machines |
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| 60 | SElength = np.asarray(SElength, dtype='float32') |
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[54f1d96] | 61 | |
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[d7af1c6] | 62 | # Rmax = #value in text box somewhere in FitPage? |
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[94d13f1] | 63 | q_max = 2*pi / (SElength[1] - SElength[0]) |
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| 64 | q_min = 0.1 * 2*pi / (np.size(SElength) * SElength[-1]) |
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[d7af1c6] | 65 | # q = np.arange(q_min, q_max, q_min, dtype='float32') |
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| 66 | q = np.exp(np.arange(np.log(q_min), np.log(q_max), np.log(2), |
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| 67 | dtype=np.float32)) |
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| 68 | q = np.hstack([0], q) |
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[54f1d96] | 69 | |
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[d7af1c6] | 70 | H0 = np.pi * (q[1:]**2 - q[-1]**2) |
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[54f1d96] | 71 | |
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[38935ec] | 72 | # repq = np.tile(q, (SElength.size, 1)).T |
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| 73 | H = np.outer(q, SElength) |
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[d7af1c6] | 74 | j1(H, out=H) |
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| 75 | H *= q |
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| 76 | H = H[1:] - H[:-1] |
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| 77 | H *= 2 * np.pi / SElength |
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[38935ec] | 78 | |
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| 79 | lam = np.asarray(lam, dtype=np.float32) |
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| 80 | reptheta = np.outer(q, lam) |
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| 81 | reptheta /= np.float32(2*np.pi) |
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| 82 | np.arcsin(reptheta, out=reptheta) |
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| 83 | # reptheta = np.arcsin(repq*replam/2*np.pi) |
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[9f91afe] | 84 | mask = reptheta > zaccept |
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| 85 | H[mask] = 0 |
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| 86 | |
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[38935ec] | 87 | # H = np.zeros((q.size, SElength.size), dtype=np.float32) |
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| 88 | # H0 = q * 0 |
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| 89 | assert(H.shape == (q.size, SElength.size)) |
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| 90 | |
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[94d13f1] | 91 | self.q_calc = q |
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| 92 | self._H, self._H0 = H, H0 |
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