Changeset ccbbc3b in sasmodels for doc/guide/sesans/sans_to_sesans.rst

Timestamp:

Mar 28, 2019 12:41:49 PM (6 years ago)

Author:

awashington

Branches:

master

Children:

1c8ff89

Parents:

3f3df6c

Message:

Remove out of date documentation

File:

• doc/guide/sesans/sans_to_sesans.rst (modified) (1 diff)

doc/guide/sesans/sans_to_sesans.rst

@@ -31 +31 @@
 
 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-1}}^{q_n} J_0(Q \delta) Q dQ
-          =
-          \sum_{n=0} \frac{2 \pi}{\delta} \frac{d \Sigma}{d \Omega} (q_n)
-          (q_n J_1(q_n \delta) - q_{n-1}J_1(q_{n-1} \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 J_1(q_n \delta_m) - q_{n-1} J_1(q_{n-1} \delta_m))
-
-Also not that, for the limit as :math:`\delta_m` approaches zero,
-
-.. math:: G(0)
-          =
-          \sum_{n=0} \pi \frac{d \Sigma}{d \Omega} (q_n) (q_n^2 - q_{n-1}^2)