# Changeset e46dde6 in sasmodels

Ignore:
Timestamp:
Jun 12, 2018 5:39:34 AM (4 years ago)
Branches:
master
Children:
02e3c54
Parents:
38935ec
Message:

Start writing up log_sesans theory

File:
1 edited

### Legend:

Unmodified
 rf0fc507 in which :math:t is the thickness of the sample and :math:\lambda is the wavelength of the neutrons. Log Spaced SESANS ----------------- For computational efficiency, the integral in the Hankel transform is converted into a Reimann sum .. math:: G(\delta) \approx 2 \pi \sum_{Q=q_{min}}^{q_{max}} J_0(Q \delta) \frac{d \Sigma}{d \Omega} (Q) Q \Delta Q \! However, this model approximates more than is strictly necessary. Specifically, it is approximating the entire integral, when it is only the scattering function that cannot be handled analytically.  A better approximation might be .. math:: G(\delta) \approx \sum_{n=0} 2 \pi \frac{d \Sigma}{d \Omega} (q_n) \int_{q_n}^{q_{n+1}} J_0(Q \delta) Q dQ = \sum_{n=0} \frac{2 \pi}{\delta} \frac{d \Sigma}{d \Omega} (q_n) (q_{n+1}J_1(q_{n+1} \delta) - q_{n}J_1(q_{n} \delta))\!, Assume that vectors :math:q_n and :math:I_n represent the q points and corresponding intensity data, respectively.  Further assume that :math:\delta_m and :math:G_m are the spin echo lengths and corresponding Hankel transform value. .. math:: G_m = H_{nm} I_n where .. math:: H_{nm} = \frac{2 \pi}{\delta_m} (q_{n+1} J_1(q_{n+1} \delta_m) - q_n J_1(q_n \delta_m))