[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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[3f3df6c] | 16 | from scipy.special import j0 |
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[d7af1c6] | 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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[ac995be] | 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 | self.q = z |
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[9f91afe] | 47 | self._set_hankel(SElength, lam, zaccept, Rmax) |
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[54f1d96] | 48 | |
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| 49 | def apply(self, Iq): |
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[b297ba9] | 50 | # type: (np.ndarray) -> np.ndarray |
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| 51 | """ |
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| 52 | Apply the SESANS transform to the computed I(q). |
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| 53 | """ |
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[94d13f1] | 54 | G0 = np.dot(self._H0, Iq) |
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| 55 | G = np.dot(self._H.T, Iq) |
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[54f1d96] | 56 | P = G - G0 |
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| 57 | return P |
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| 58 | |
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[9f91afe] | 59 | def _set_hankel(self, SElength, lam, zaccept, Rmax): |
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[94d13f1] | 60 | # type: (np.ndarray, float, float) -> None |
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[3f3df6c] | 61 | SElength = np.asarray(SElength) |
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[94d13f1] | 62 | q_max = 2*pi / (SElength[1] - SElength[0]) |
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| 63 | q_min = 0.1 * 2*pi / (np.size(SElength) * SElength[-1]) |
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[3f3df6c] | 64 | q = np.exp(np.arange(np.log(q_min), np.log(q_max), np.log(1.0003))) |
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| 65 | |
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| 66 | dq = q[1:]-q[:-1] |
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| 67 | dq = np.hstack([[dq[0]], dq]) |
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[54f1d96] | 68 | |
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[3f3df6c] | 69 | H0 = dq/(2*pi) * q |
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[54f1d96] | 70 | |
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[38935ec] | 71 | H = np.outer(q, SElength) |
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[3f3df6c] | 72 | j0(H, out=H) |
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| 73 | H *= (dq * q).reshape((-1, 1)) |
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| 74 | H /= 2*pi |
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| 75 | |
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| 76 | reptheta = np.outer(q, lam) |
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| 77 | reptheta /= 2*np.pi |
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[38935ec] | 78 | np.arcsin(reptheta, out=reptheta) |
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[9f91afe] | 79 | mask = reptheta > zaccept |
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[3f3df6c] | 80 | H[mask] = 0 |
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[38935ec] | 81 | |
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[3f3df6c] | 82 | self.q_calc = q |
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[94d13f1] | 83 | self._H, self._H0 = H, H0 |
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