Source code for sasmodels.sesans

Conversion of scattering cross section from SANS (I(q), or rather, ds/dO) in absolute
units (cm-1)into SESANS correlation function G using a Hankel transformation, then converting
the SESANS correlation function into polarisation from the SESANS experiment

Everything is in units of metres except specified otherwise (NOT TRUE!!!)
Everything is in conventional units (nm for spin echo length)

Wim Bouwman (, June 2013

from __future__ import division

import numpy as np  # type: ignore
from numpy import pi  # type: ignore
from scipy.special import j0

[docs]class SesansTransform(object): """ Spin-Echo SANS transform calculator. Similar to a resolution function, the SesansTransform object takes I(q) for the set of *q_calc* values and produces a transformed dataset *SElength* (A) is the set of spin-echo lengths in the measured data. *zaccept* (1/A) is the maximum acceptance of scattering vector in the spin echo encoding dimension (for ToF: Q of min(R) and max(lam)). *Rmax* (A) is the maximum size sensitivity; larger radius requires more computation time. """ #: SElength from the data in the original data units; not used by transform #: but the GUI uses it, so make sure that it is present. q = None # type: np.ndarray #: q values to calculate when computing transform q_calc = None # type: np.ndarray # transform arrays _H = None # type: np.ndarray _H0 = None # type: np.ndarray def __init__(self, z, SElength, lam, zaccept, Rmax, log_spacing=1.0003): # type: (np.ndarray, float, float, float, float, float) -> None self.q = z self.log_spacing = log_spacing self._set_hankel(SElength, lam, zaccept, Rmax)
[docs] def apply(self, Iq): # type: (np.ndarray) -> np.ndarray """ Apply the SESANS transform to the computed I(q). """ G0 =, Iq) G =, Iq) P = G - G0 return P
def _set_hankel(self, SElength, lam, zaccept, Rmax): # type: (np.ndarray, float, float, float) -> None SElength = np.asarray(SElength) q_max = 2*pi / (SElength[1] - SElength[0]) q_min = 0.1 * 2*pi / (np.size(SElength) * SElength[-1]) q = np.exp(np.arange(np.log(q_min), np.log(q_max), np.log(self.log_spacing))) dq = np.diff(q) dq = np.insert(dq, 0, dq[0]) H0 = dq/(2*pi) * q H = np.outer(q, SElength) j0(H, out=H) H *= (dq * q / (2*pi)).reshape((-1, 1)) reptheta = np.outer(q, lam/(2*pi)) np.arcsin(reptheta, out=reptheta) mask = reptheta > zaccept H[mask] = 0 self.q_calc = q self._H, self._H0 = H, H0