-                      rda456fb
+                      r1404cce
 This performs a correlation function analysis of one-dimensional
+SANS data, or generates a model-independent volume fraction profile from a
+one-dimensional SANS pattern of an adsorbed layer.
+The correlation function analysis is performed in 3 stages:
+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. Î\ :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.
+A volume fraction profile :math:`\Phi`\ (z) describes how the density of polymer segments/surfactant molecules varies with distance from an (assumed locally flat) interface.
+Both functions are returned in *real space*.
+The analysis is performed in 3 stages:
 *  Extrapolation of the scattering curve to :math:`Q = 0` and
    :math:`Q = \infty`
+*  Fourier/Hilbert Transform of the extrapolated data to give the correlation
+   function/volume fraction profile
+*  Interpretation of the 1D correlation function based on an ideal lamellar
+   morphology
+*  Smoothed merging of the two extrapolations into the original data
+*  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
+   lamellar morphology
 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
 …
 To :math:`Q = 0`
+^^^^^^^^^^^^^^^^
+................
 The data are extrapolated to Q = 0 by fitting a Guinier model to the data
+points in the lower Q range.
+points in the low-Q range.
 The equation used is:
 .. math::
     I(Q) = e^{A+Bq^2}
+    I(Q) = Ae^{Bq^2}
 The Guinier model assumes that the small angle scattering arises from particles
 …
 particles. This has dubious applicability to polymer systems. However, the
 correlation function is affected by the Guinier back-extrapolation to the
 greatest extent at large values of R and so the back-extrapolation only has a
 small effect on the analysis.
+greatest extent at large values of R and so only has a
+small effect on the final analysis.
 To :math:`Q = \infty`
+^^^^^^^^^^^^^^^^^^^^^
+.....................
 The data are extrapolated to Q = :math:`\infty` by fitting a Porod model to
 the data points in the upper Q range.
+the data points in the high-Q range.
 The equation used is:
 .. math::
+    I(Q) = Bg + KQ^{-4}e^{-Q^2\sigma^2}
+Where :math:`Bg` is the Bonart thermal background, :math:`K` is the Porod
+constant, and :math:`\sigma > 0` describes the electron (or neutron scattering
+length) density profile at the interface between crystalline and amorphous
+regions (see figure 1).
+    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 or neutron scattering length density profile at the interface between the crystalline and amorphous
+regions as shown below.
 .. figure:: fig1.gif
    :align: center
+   **Figure 1** The value of :math:`\sigma` is a measure of the electron
+   density profile at the interface between crystalline and amorphous regions.
 Smoothing
+^^^^^^^^^
+The extrapolated data set consists of the Guinier back-extrapolation up to the
+highest Q value of the lower Q range, the original scattering data up to the
+highest value in the upper Q range, 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.
+---------
+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.
 Functions :math:`f(x_i)` and :math:`g(x_i)` where :math:`x_i \in \left\{
 …
     h_i = \frac{1}{1 + \frac{(x_i-b)^2}{(x_i-a)^2}}
 Transform
 ---------
 Fourier
+^^^^^^^
 If Fourier is selected for the transform type, the analysis will perform a
+.......
+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. The following algorithm is applied:
+correlation function
+.. math::
+    \Gamma _{1D}(R) = \frac{1}{Q^{*}} \int_{0}^{\infty }I(q) q^{2} cos(qR) dq
+where Q\ :sup:`*` is the Scattering Invariant.
+The following algorithm is applied:
 .. math::
 …
 Hilbert
+^^^^^^^
+If Hilbert is selected for the transform type, the analysis will perform a
+.......
+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:: This functionality is not yet implemented in SasView.
 Interpretation
 --------------
+Once the correlation function has been calculated by transforming the
+extrapolated data, it may be interpreted by clicking the "Compute Parameters"
+button. The correlation function is interpreted in terms of an ideal lamellar
+morphology, and structural parameters are obtained as shown in Figure 2 below.
+It should be noted that a small beam size is assumed; no de-smearing is
+Correlation Function
+....................
+Once the correlation function has been calculated it may be interpreted by clicking the "Compute Parameters" button.
+The correlation function is interpreted in terms of an ideal lamellar
+morphology, and structural parameters are obtained from it as shown below.
+It should be noted that a small beam size is assumed; ie, no de-smearing is
 performed.
 .. figure:: fig2.gif
    :align: center
-   **Figure 2** Interpretation of the correlation function.
 The structural parameters obtained are:
 …
 *   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
+References
+----------
+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
+:ref:`FDR` (PDF format)
 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ
 Usage
 -----
 Upon sending data for correlation function analysis, it will be plotted (minus
+the background value), along with a red bar indicating the lower Q range (used
+for back-extrapolation), and 2 purple bars indicating the upper Q range (used
+for forward-extrapolation) [figure 3]. These bars may be moved my clicking and
+dragging, or by entering the appropriate values in the Q range input boxes.
+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.
 .. figure:: tutorial1.png
    :align: center
+   **Figure 3** A plot of some data showing the Q range bars
+Once the Q ranges have been set, click the "Calculate" button next to the
+background input field to calculate the Bonart thermal background level.
+Alternatively, enter your own value into the field. Click the "Extrapolate"
+button to extrapolate the data and plot the extrapolation in the same figure.
+The values of the parameters used for the Guinier and Porod models will also be
+shown in the "Extrapolation Parameters" section [figure 4]
+Once the Q ranges have been set, click the "Calculate" button to determine the background level. Alternatively, enter your own value into the field. If the box turns yellow this indicates that background subtraction has resulted in some negative intensities.
+Click the "Extrapolate" button to extrapolate the data and plot the extrapolation in the same figure. The values of the parameters used for the Guinier and Porod models will also be shown in the "Extrapolation Parameters" section of the window.
 .. figure:: tutorial2.png
    :align: center
+   **Figure 4** A plot showing the extrapolated data and the original data
+Then, select which type of transform you would like to perform, using the radio
+Now select which type of transform you would like to perform, using the radio
 buttons:
 *   **Fourier** Perform a Fourier Transform to calculate the correlation
     function of the extrapolated data
+    function
 *   **Hilbert** Perform a Hilbert Transform to calculate the volume fraction
     profile of the extrapolated data
 Clicking the transform button will then perform the selected transform and plot
+it in a new figure. If a Fourier Transform was performed, the "Compute
+Parameters" button can also be clicked to calculate values for the output
+parameters [figure 5]
+    profile
+Click the "Transform" button to perform the selected transform and plot
+the result in a new graph window.
+If a Fourier Transform was performed, the "Compute Parameters" button can now be clicked to interpret the correlation function as described earlier.
  .. figure:: tutorial3.png
     :align: center
+    **Figure 5** The Fourier Transform (correlation function) of the
+    extrapolated data, and the parameters extracted from it.
+.. note::
+    This help document was last changed by Steve King, 08Oct2016

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