Changeset d78b5cb in sasview for src/sas/sasgui/perspectives/corfunc

Timestamp:

Jul 19, 2017 5:40:46 AM (7 years ago)

Author:

lewis

Branches:

master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, magnetic_scatt, release-4.2.2, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload

Children:

9b90bf8

Parents:

c728295

Message:

Update corfunc docs to include 3D correlation function

File:

• src/sas/sasgui/perspectives/corfunc/media/corfunc_help.rst (modified) (9 diffs)

src/sas/sasgui/perspectives/corfunc/media/corfunc_help.rst

@@ -10 +10 @@
 
 This performs a correlation function analysis of one-dimensional
-SAXS/SANS data, or generates a model-independent volume fraction 
+SAXS/SANS data, or generates a model-independent volume fraction
 profile from the SANS from an adsorbed polymer/surfactant layer.
 
-A correlation function may be interpreted in terms of an imaginary rod moving 
-through the structure of the material. Γ\ :sub:`1D`\ (R) is the probability that 
-a rod of length R moving through the material has equal electron/neutron scattering 
-length density at either end. Hence a frequently occurring spacing within a structure 
+A correlation function may be interpreted in terms of an imaginary rod moving
+through the structure of the material. Γ\ :sub:`1D`\ (R) is the probability that
+a rod of length R moving through the material has equal electron/neutron scattering
+length density at either end. Hence a frequently occurring spacing within a structure
 manifests itself as a peak.
 
@@ -30 +30 @@
 *  Fourier / Hilbert Transform of the smoothed data to give the correlation
    function / volume fraction profile, respectively
-*  (Optional) Interpretation of the 1D correlation function based on an ideal 
+*  (Optional) Interpretation of the 1D correlation function based on an ideal
    lamellar morphology
 
@@ -74 +74 @@
    :align: center
 
-   
+
 Smoothing
 ---------
 
-The extrapolated data set consists of the Guinier back-extrapolation from Q~0 
+The extrapolated data set consists of the Guinier back-extrapolation from Q~0
 up to the lowest Q value in the original data, then the original scattering data, and the Porod tail-fit beyond this. The joins between the original data and the Guinier/Porod fits are smoothed using the algorithm below to avoid the formation of ripples in the transformed data.
 
@@ -93 +93 @@
     h_i = \frac{1}{1 + \frac{(x_i-b)^2}{(x_i-a)^2}}
 
-        
+
 Transform
 ---------
@@ -102 +102 @@
 If "Fourier" is selected for the transform type, the analysis will perform a
 discrete cosine transform on the extrapolated data in order to calculate the
-correlation function
+1D correlation function:
 
 .. math::
@@ -115 +115 @@
     \left(n + \frac{1}{2} \right) k \right] } \text{ for } k = 0, 1, \ldots,
     N-1, N
+
+The 3D correlation function is also calculated:
+
+.. math::
+    \Gamma _{3D}(R) = \frac{1}{Q^{*}} \int_{0}^{\infty}I(q) q^{2}
+    \frac{sin(qR)}{qR} dq
 
 Hilbert
@@ -165 +171 @@
 .. figure:: profile1.png
    :align: center
- 
+
 .. figure:: profile2.png
    :align: center
-   
+
 
 References
@@ -191 +197 @@
 -----
 Upon sending data for correlation function analysis, it will be plotted (minus
-the background value), along with a *red* bar indicating the *upper end of the 
+the background value), along with a *red* bar indicating the *upper end of the
 low-Q range* (used for back-extrapolation), and 2 *purple* bars indicating the range to be used for forward-extrapolation. These bars may be moved my clicking and
 dragging, or by entering appropriate values in the Q range input boxes.
@@ -221 +227 @@
     :align: center
 
-        
+
 .. note::
     This help document was last changed by Steve King, 08Oct2016