Index: src/sas/qtgui/Perspectives/Corfunc/media/corfunc_help.rst
===================================================================
--- src/sas/qtgui/Perspectives/Corfunc/media/corfunc_help.rst	(revision 417c03f075685f86777838c8c717dec8e0ed8965)
+++ src/sas/qtgui/Perspectives/Corfunc/media/corfunc_help.rst	(revision 417c03f075685f86777838c8c717dec8e0ed8965)
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+.. corfunc_help.rst
+
+.. _Correlation_Function_Analysis:
+
+Correlation Function Analysis
+=============================
+
+Description
+-----------
+
+This currently performs correlation function analysis on SAXS/SANS data, 
+but in the the future is also planned to generate model-independent volume 
+fraction profiles from the SANS from adsorbed polymer/surfactant layers. 
+The two types of analyses differ in the mathematical transform that is 
+applied to the data (Fourier vs Hilbert). However, both functions are 
+returned in *real space*.
+
+A correlation function may be interpreted in terms of an imaginary rod moving
+through the structure of the material. Î(x) is the probability that a rod of 
+length x has equal electron/neutron scattering length density at either end. 
+Hence a frequently occurring spacing within a structure will manifest itself 
+as a peak in Î(x). *SasView* will return both the one-dimensional ( Î\ :sub:`1`\ (x) ) 
+and three-dimensional ( Î\ :sub:`3`\ (x) ) correlation functions, the difference 
+being that the former is only averaged in the plane of the scattering vector.
+
+A volume fraction profile :math:`\Phi`\ (z) describes how the density of polymer 
+segments/surfactant molecules varies with distance, z, normal to an (assumed 
+locally flat) interface. The form of :math:`\Phi`\ (z) can provide information 
+about the arrangement of polymer/surfactant molecules at the interface. The width 
+of the profile provides measures of the layer thickness, and the area under 
+the profile is related to the amount of material that is adsorbed.
+
+Both analyses are performed in 3 stages:
+
+*  Extrapolation of the scattering curve to :math:`Q = 0` and toward 
+   :math:`Q = \infty`
+*  Smoothed merging of the two extrapolations into the original data
+*  Fourier / Hilbert Transform of the smoothed data to give the correlation
+   function or volume fraction profile, respectively
+*  (Optional) Interpretation of Î\ :sub:`1`\ (x) assuming the sample conforms 
+   to an ideal lamellar morphology
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+
+Extrapolation
+-------------
+
+To :math:`Q = 0`
+................
+
+The data are extrapolated to q = 0 by fitting a Guinier function to the data
+points in the low-q range.
+
+The equation used is:
+
+.. math::
+    I(q) = A e^{Bq^2}
+
+Where the parameter :math:`B` is related to the effective radius-of-gyration of 
+a spherical object having the same small-angle scattering in this region.
+	
+Note that as q tends to zero this function tends to a limiting value and is 
+therefore less appropriate for use in systems where the form factor does not 
+do likewise. However, because of the transform, the correlation functions are 
+most affected by the Guinier back-extrapolation at *large* values of x where 
+the impact on any extrapolated parameters will be least significant.
+
+To :math:`Q = \infty`
+.....................
+
+The data are extrapolated towards q = :math:`\infty` by fitting a Porod model to
+the data points in the high-q range and then computing the extrapolation to 100 
+times the maximum q value in the experimental dataset. This should be more than 
+sufficient to ensure that on transformation any truncation artefacts introduced 
+are at such small values of x that they can be safely ignored.
+
+The equation used is:
+
+.. math::
+    I(q) = K q^{-4}e^{-q^2\sigma^2} + Bg
+
+Where :math:`Bg` is the background, :math:`K` is the Porod constant, and :math:`\sigma` (which 
+must be > 0) describes the width of the electron/neutron scattering length density 
+profile at the interface between the crystalline and amorphous regions as shown below.
+
+.. figure:: fig1.png
+   :align: center
+
+
+Smoothing
+---------
+
+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 then the Porod tail-fit beyond this. The joins between the original data and 
+the Guinier/Porod extrapolations are smoothed using the algorithm below to try 
+and avoid the formation of truncation ripples in the transformed data:
+
+Functions :math:`f(x_i)` and :math:`g(x_i)` where :math:`x_i \in \left\{
+{x_1, x_2, ..., x_n} \right\}`, are smoothed over the range :math:`[a, b]`
+to produce :math:`y(x_i)`, by the following equations:
+
+.. math::
+    y(x_i) = h_ig(x_i) + (1-h_i)f(x_i)
+
+where:
+
+.. math::
+    h_i = \frac{1}{1 + \frac{(x_i-b)^2}{(x_i-a)^2}}
+
+
+Transformation
+--------------
+
+Fourier
+.......
+
+If "Fourier" is selected for the transform type, *SasView* will perform a
+discrete cosine transform on the extrapolated data in order to calculate the
+1D correlation function as:
+
+.. math::
+    \Gamma _{1}(x) = \frac{1}{Q^{*}} \int_{0}^{\infty }I(q) q^{2} cos(qx) dq
+
+where Q\ :sup:`*` is the Scattering (also called Porod) Invariant.
+
+The following algorithm is applied:
+
+.. math::
+    \Gamma(x_k) = 2 \sum_{n=0}^{N-1} x_n \cos{\left[ \frac{\pi}{N}
+    \left(n + \frac{1}{2} \right) k \right] } \text{ for } k = 0, 1, \ldots,
+    N-1, N
+
+The 3D correlation function is calculated as:
+
+.. math::
+    \Gamma _{3}(x) = \frac{1}{Q^{*}} \int_{0}^{\infty}I(q) q^{2}
+    \frac{sin(qx)}{qx} dq
+
+.. note:: It is always advisable to inspect Î\ :sub:`1`\ (x) and Î\ :sub:`3`\ (x) 
+    for artefacts arising from the extrapolation and transformation processes:
+	
+	- do they tend to zero as x tends to :math:`\infty`?
+	- do they smoothly curve onto the ordinate at x = 0? (if not check the value 
+	  of :math:`\sigma` is sensible)
+	- are there ripples at x values corresponding to (2 :math:`pi` over) the two 
+	  q values at which the extrapolated and experimental data are merged?
+	- are there any artefacts at x values corresponding to 2 :math:`pi` / q\ :sub:`max` in 
+	  the experimental data? 
+	- and lastly, do the significant features/peaks in the correlation functions 
+	  actually correspond to anticpated spacings in the sample?!!!
+
+Finally, the program calculates the interface distribution function (IDF) g\ :sub:`1`\ (x) as 
+the discrete cosine transform of:
+
+.. math::
+    -q^{4} I(q)
+
+The IDF is proportional to the second derivative of Î\ :sub:`1`\ (x).
+
+Hilbert
+.......
+	
+If "Hilbert" is selected for the transform type, the analysis will perform a
+Hilbert transform on the extrapolated data in order to calculate the Volume
+Fraction Profile.
+
+.. note:: The Hilbert transform functionality is not yet implemented in SasView.
+
+
+Interpretation
+--------------
+
+Correlation Function
+....................
+
+Once the correlation functions have been calculated *SasView* can be asked to 
+try and interpret Î\ :sub:`1`\ (x) in terms of an ideal lamellar morphology 
+as shown below.
+
+.. figure:: fig2.png
+   :align: center
+
+The structural parameters extracted are:
+
+*   Long Period :math:`= L_p`
+*   Average Hard Block Thickness :math:`= L_c`
+*   Average Core Thickness :math:`= D_0`
+*   Average Interface Thickness :math:`\text{} = D_{tr}`
+*   Polydispersity :math:`= \Gamma_{\text{min}}/\Gamma_{\text{max}}`
+*   Local Crystallinity :math:`= L_c/L_p`
+
+Volume Fraction Profile
+.......................
+
+SasView does not provide any automatic interpretation of volume fraction profiles 
+in the same way that it does for correlation functions. However, a number of 
+structural parameters are obtainable by other means:
+
+*   Surface Coverage :math:`=\theta`
+*   Anchor Separation :math:`= D`
+*   Bound Fraction :math:`= <p>`
+*   Second Moment :math:`= \sigma`
+*   Maximum Extent :math:`= \delta_{\text{h}}`
+*   Adsorbed Amount :math:`= \Gamma`
+
+.. figure:: profile1.png
+   :align: center
+
+.. figure:: profile2.png
+   :align: center
+
+The reader is directed to the references for information on these parameters.
+
+References
+----------
+
+Correlation Function
+....................
+
+Strobl, G. R.; Schneider, M. *J. Polym. Sci.* (1980), 18, 1343-1359
+
+Koberstein, J.; Stein R. *J. Polym. Sci. Phys. Ed.* (1983), 21, 2181-2200
+
+BaltÃ¡ Calleja, F. J.; Vonk, C. G. *X-ray Scattering of Synthetic Poylmers*, Elsevier. Amsterdam (1989), 247-251
+
+BaltÃ¡ Calleja, F. J.; Vonk, C. G. *X-ray Scattering of Synthetic Poylmers*, Elsevier. Amsterdam (1989), 257-261
+
+BaltÃ¡ Calleja, F. J.; Vonk, C. G. *X-ray Scattering of Synthetic Poylmers*, Elsevier. Amsterdam (1989), 260-270
+
+GÃ¶schel, U.; Urban, G. *Polymer* (1995), 36, 3633-3639
+
+Stribeck, N. *X-Ray Scattering of Soft Matter*, Springer. Berlin (2007), 138-161
+
+:ref:`FDR` (PDF format)
+
+Volume Fraction Profile
+.......................
+
+Washington, C.; King, S. M. *J. Phys. Chem.*, (1996), 100, 7603-7609
+
+Cosgrove, T.; King, S. M.; Griffiths, P. C. *Colloid-Polymer Interactions: From Fundamentals to Practice*, Wiley. New York (1999), 193-204
+
+King, S. M.; Griffiths, P. C.; Cosgrove, T. *Applications of Neutron Scattering to Soft Condensed Matter*, Gordon & Breach. Amsterdam (2000), 77-105
+
+King, S.; Griffiths, P.; Hone, J.; Cosgrove, T. *Macromol. Symp.* (2002), 190, 33-42
+
+.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
+
+
+Usage
+-----
+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
+low-Q range* (used for Guinier back-extrapolation), and 2 *purple* bars indicating 
+the range to be used for Porod forward-extrapolation. These bars may be moved by 
+grabbing and dragging, or by entering appropriate values in the Q range input boxes.
+
+.. figure:: tutorial1.png
+   :align: center
+
+Once the Q ranges have been set, click the "Calculate Bg" button to determine the 
+background level. Alternatively, enter your own value into the box. If the box turns 
+yellow this indicates that background subtraction has created some negative intensities.
+
+Now click the "Extrapolate" button to extrapolate the data. The graph window will update 
+to show the extrapolated data, and the values of the parameters used for the Guinier and 
+Porod extrapolations will appear in the "Extrapolation Parameters" section of the SasView 
+GUI.
+
+.. figure:: tutorial2.png
+   :align: center
+
+Now select which type of transform you would like to perform, using the radio
+buttons:
+
+*   **Fourier**: to perform a Fourier Transform to calculate the correlation
+    functions
+*   **Hilbert**: to perform a Hilbert Transform to calculate the volume fraction
+    profile
+
+and click the "Transform" button to perform the selected transform and plot
+the results.
+
+ .. figure:: tutorial3.png
+    :align: center
+
+If a Fourier Transform was performed, the "Compute Parameters" button can now be 
+clicked to interpret the correlation function as described earlier. The parameters 
+will appear in the "Output Parameters" section of the SasView GUI.
+
+ .. figure:: tutorial4.png
+    :align: center
+
+
+.. note::
+    This help document was last changed by Steve King, 26Sep2017
Index: src/sas/qtgui/Perspectives/Corfunc/media/fdr-pdfs.rst
===================================================================
--- src/sas/qtgui/Perspectives/Corfunc/media/fdr-pdfs.rst	(revision 417c03f075685f86777838c8c717dec8e0ed8965)
+++ src/sas/qtgui/Perspectives/Corfunc/media/fdr-pdfs.rst	(revision 417c03f075685f86777838c8c717dec8e0ed8965)
@@ -0,0 +1,10 @@
+.. fdr-pdfs.rst
+
+.. _FDR:
+
+Fibre Diffraction Review References
+===================================
+
+:download:`Fibre_Diffraction_Review_1994_3_25-29.pdf <Fibre_Diffraction_Review_1994_3_25-29.pdf>`
+:download:`Fibre_Diffraction_Review_2004_12_24.pdf <Fibre_Diffraction_Review_2004_12_24.pdf>`
+:download:`Fibre_Diffraction_Review_2005_13_19-22.pdf <Fibre_Diffraction_Review_2005_13_19-22.pdf>`
