Changeset ccbbc3b in sasmodels


Ignore:
Timestamp:
Mar 28, 2019 12:41:49 PM (4 months ago)
Author:
awashington
Branches:
master
Children:
1c8ff89
Parents:
3f3df6c
Message:

Remove out of date documentation

File:
1 edited

Legend:

Unmodified
Added
Removed
  • doc/guide/sesans/sans_to_sesans.rst

    rd7af1c6 rccbbc3b  
    3131 
    3232in which :math:`t` is the thickness of the sample and :math:`\lambda` is the wavelength of the neutrons. 
    33  
    34 Log Spaced SESANS 
    35 ----------------- 
    36  
    37 For computational efficiency, the integral in the Hankel transform is 
    38 converted into a Reimann sum 
    39  
    40  
    41 .. math:: G(\delta) \approx 
    42           2 \pi 
    43           \sum_{Q=q_{min}}^{q_{max}} J_0(Q \delta) 
    44           \frac{d \Sigma}{d \Omega} (Q) 
    45           Q \Delta Q \! 
    46  
    47 However, this model approximates more than is strictly necessary. 
    48 Specifically, it is approximating the entire integral, when it is only 
    49 the scattering function that cannot be handled analytically.  A better 
    50 approximation might be 
    51  
    52 .. math:: G(\delta) \approx 
    53           \sum_{n=0} 2 \pi \frac{d \Sigma}{d \Omega} (q_n) 
    54           \int_{q_{n-1}}^{q_n} J_0(Q \delta) Q dQ 
    55           = 
    56           \sum_{n=0} \frac{2 \pi}{\delta} \frac{d \Sigma}{d \Omega} (q_n) 
    57           (q_n J_1(q_n \delta) - q_{n-1}J_1(q_{n-1} \delta))\!, 
    58  
    59 Assume that vectors :math:`q_n` and :math:`I_n` represent the q points 
    60 and corresponding intensity data, respectively.  Further assume that 
    61 :math:`\delta_m` and :math:`G_m` are the spin echo lengths and 
    62 corresponding Hankel transform value. 
    63  
    64 .. math:: G_m = H_{nm} I_n 
    65  
    66 where 
    67  
    68 .. math:: H_{nm} = \frac{2 \pi}{\delta_m} 
    69           (q_n J_1(q_n \delta_m) - q_{n-1} J_1(q_{n-1} \delta_m)) 
    70  
    71 Also not that, for the limit as :math:`\delta_m` approaches zero, 
    72  
    73 .. math:: G(0) 
    74           = 
    75           \sum_{n=0} \pi \frac{d \Sigma}{d \Omega} (q_n) (q_n^2 - q_{n-1}^2) 
Note: See TracChangeset for help on using the changeset viewer.