Changeset 1404cce in sasview for src


Ignore:
Timestamp:
Oct 8, 2016 4:52:53 PM (8 years ago)
Author:
smk78
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, costrafo411, magnetic_scatt, release-4.1.1, release-4.1.2, release-4.2.2, ticket-1009, ticket-1094-headless, ticket-1242-2d-resolution, ticket-1243, ticket-1249, ticket885, unittest-saveload
Children:
a65042b
Parents:
4ed199e
Message:

corfunc_help.rst thoroughly overhauled. References and new figures
added. Closes #735

Location:
src/sas/sasgui/perspectives/corfunc/media
Files:
6 added
1 edited

Legend:

Unmodified
Added
Removed
  • src/sas/sasgui/perspectives/corfunc/media/corfunc_help.rst

    rda456fb r1404cce  
    1010 
    1111This performs a correlation function analysis of one-dimensional 
    12 SANS data, or generates a model-independent volume fraction profile from a 
    13 one-dimensional SANS pattern of an adsorbed layer. 
    14  
    15 The correlation function analysis is performed in 3 stages: 
     12SAXS/SANS data, or generates a model-independent volume fraction  
     13profile from the SANS from an adsorbed polymer/surfactant layer. 
     14 
     15A correlation function may be interpreted in terms of an imaginary rod moving  
     16through the structure of the material. Γ\ :sub:`1D`\ (R) is the probability that  
     17a rod of length R moving through the material has equal electron/neutron scattering  
     18length density at either end. Hence a frequently occurring spacing within a structure  
     19manifests itself as a peak. 
     20 
     21A volume fraction profile :math:`\Phi`\ (z) describes how the density of polymer segments/surfactant molecules varies with distance from an (assumed locally flat) interface. 
     22 
     23Both functions are returned in *real space*. 
     24 
     25The analysis is performed in 3 stages: 
    1626 
    1727*  Extrapolation of the scattering curve to :math:`Q = 0` and 
    1828   :math:`Q = \infty` 
    19 *  Fourier/Hilbert Transform of the extrapolated data to give the correlation 
    20    function/volume fraction profile 
    21 *  Interpretation of the 1D correlation function based on an ideal lamellar 
    22    morphology 
     29*  Smoothed merging of the two extrapolations into the original data 
     30*  Fourier / Hilbert Transform of the smoothed data to give the correlation 
     31   function / volume fraction profile, respectively 
     32*  (Optional) Interpretation of the 1D correlation function based on an ideal  
     33   lamellar morphology 
    2334 
    2435.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
     
    2839 
    2940To :math:`Q = 0` 
    30 ^^^^^^^^^^^^^^^^ 
     41................ 
    3142 
    3243The data are extrapolated to Q = 0 by fitting a Guinier model to the data 
    33 points in the lower Q range. 
     44points in the low-Q range. 
     45 
    3446The equation used is: 
    3547 
    3648.. math:: 
    37     I(Q) = e^{A+Bq^2} 
     49    I(Q) = Ae^{Bq^2} 
    3850 
    3951The Guinier model assumes that the small angle scattering arises from particles 
     
    4153particles. This has dubious applicability to polymer systems. However, the 
    4254correlation function is affected by the Guinier back-extrapolation to the 
    43 greatest extent at large values of R and so the back-extrapolation only has a 
    44 small effect on the analysis. 
     55greatest extent at large values of R and so only has a 
     56small effect on the final analysis. 
    4557 
    4658To :math:`Q = \infty` 
    47 ^^^^^^^^^^^^^^^^^^^^^ 
     59..................... 
    4860 
    4961The data are extrapolated to Q = :math:`\infty` by fitting a Porod model to 
    50 the data points in the upper Q range. 
     62the data points in the high-Q range. 
    5163 
    5264The equation used is: 
    5365 
    5466.. math:: 
    55     I(Q) = Bg + KQ^{-4}e^{-Q^2\sigma^2} 
    56  
    57 Where :math:`Bg` is the Bonart thermal background, :math:`K` is the Porod 
    58 constant, and :math:`\sigma > 0` describes the electron (or neutron scattering 
    59 length) density profile at the interface between crystalline and amorphous 
    60 regions (see figure 1). 
     67    I(Q) = K Q^{-4}e^{-Q^2\sigma^2} + Bg 
     68 
     69Where :math:`Bg` is the background, :math:`K` is the Porod 
     70constant, 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 
     71regions as shown below. 
    6172 
    6273.. figure:: fig1.gif 
    6374   :align: center 
    6475 
    65    **Figure 1** The value of :math:`\sigma` is a measure of the electron 
    66    density profile at the interface between crystalline and amorphous regions. 
    67  
     76    
    6877Smoothing 
    69 ^^^^^^^^^ 
    70  
    71 The extrapolated data set consists of the Guinier back-extrapolation up to the 
    72 highest Q value of the lower Q range, the original scattering data up to the 
    73 highest value in the upper Q range, and the Porod tail-fit beyond this. The 
    74 joins between the original data and the Guinier/Porod fits are smoothed using 
    75 the algorithm below, to avoid the formation of ripples in the transformed data. 
     78--------- 
     79 
     80The extrapolated data set consists of the Guinier back-extrapolation from Q~0  
     81up 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. 
    7682 
    7783Functions :math:`f(x_i)` and :math:`g(x_i)` where :math:`x_i \in \left\{ 
     
    8793    h_i = \frac{1}{1 + \frac{(x_i-b)^2}{(x_i-a)^2}} 
    8894 
     95         
    8996Transform 
    9097--------- 
    9198 
    9299Fourier 
    93 ^^^^^^^ 
    94  
    95 If Fourier is selected for the transform type, the analysis will perform a 
     100....... 
     101 
     102If "Fourier" is selected for the transform type, the analysis will perform a 
    96103discrete cosine transform on the extrapolated data in order to calculate the 
    97 correlation function. The following algorithm is applied: 
     104correlation function 
     105 
     106.. math:: 
     107    \Gamma _{1D}(R) = \frac{1}{Q^{*}} \int_{0}^{\infty }I(q) q^{2} cos(qR) dq 
     108 
     109where Q\ :sup:`*` is the Scattering Invariant. 
     110 
     111The following algorithm is applied: 
    98112 
    99113.. math:: 
     
    103117 
    104118Hilbert 
    105 ^^^^^^^ 
    106 If Hilbert is selected for the transform type, the analysis will perform a 
     119....... 
     120 
     121If "Hilbert" is selected for the transform type, the analysis will perform a 
    107122Hilbert transform on the extrapolated data in order to calculate the Volume 
    108123Fraction Profile. 
    109124 
     125.. note:: This functionality is not yet implemented in SasView. 
     126 
     127 
    110128Interpretation 
    111129-------------- 
    112 Once the correlation function has been calculated by transforming the 
    113 extrapolated data, it may be interpreted by clicking the "Compute Parameters" 
    114 button. The correlation function is interpreted in terms of an ideal lamellar 
    115 morphology, and structural parameters are obtained as shown in Figure 2 below. 
    116 It should be noted that a small beam size is assumed; no de-smearing is 
     130 
     131Correlation Function 
     132.................... 
     133 
     134Once the correlation function has been calculated it may be interpreted by clicking the "Compute Parameters" button. 
     135 
     136The correlation function is interpreted in terms of an ideal lamellar 
     137morphology, and structural parameters are obtained from it as shown below. 
     138It should be noted that a small beam size is assumed; ie, no de-smearing is 
    117139performed. 
    118140 
    119141.. figure:: fig2.gif 
    120142   :align: center 
    121  
    122    **Figure 2** Interpretation of the correlation function. 
    123143 
    124144The structural parameters obtained are: 
     
    131151*   Local Crystallinity :math:`= L_c/L_p` 
    132152 
     153Volume Fraction Profile 
     154....................... 
     155 
     156SasView 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: 
     157 
     158*   Surface Coverage :math:`=\theta` 
     159*   Anchor Separation :math:`= D` 
     160*   Bound Fraction :math:`= <p>` 
     161*   Second Moment :math:`= \sigma` 
     162*   Maximum Extent :math:`= \delta_{\text{h}}` 
     163*   Adsorbed Amount :math:`= \Gamma` 
     164 
     165.. figure:: profile1.png 
     166   :align: center 
     167  
     168.. figure:: profile2.png 
     169   :align: center 
     170    
     171 
     172References 
     173---------- 
     174 
     175Strobl, G. R.; Schneider, M. *J. Polym. Sci.* (1980), 18, 1343-1359 
     176 
     177Koberstein, J.; Stein R. *J. Polym. Sci. Phys. Ed.* (1983), 21, 2181-2200 
     178 
     179Baltá Calleja, F. J.; Vonk, C. G. *X-ray Scattering of Synthetic Poylmers*, Elsevier. Amsterdam (1989), 247-251 
     180 
     181Baltá Calleja, F. J.; Vonk, C. G. *X-ray Scattering of Synthetic Poylmers*, Elsevier. Amsterdam (1989), 257-261 
     182 
     183Baltá Calleja, F. J.; Vonk, C. G. *X-ray Scattering of Synthetic Poylmers*, Elsevier. Amsterdam (1989), 260-270 
     184 
     185:ref:`FDR` (PDF format) 
     186 
    133187.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
     188 
    134189 
    135190Usage 
    136191----- 
    137192Upon sending data for correlation function analysis, it will be plotted (minus 
    138 the background value), along with a red bar indicating the lower Q range (used 
    139 for back-extrapolation), and 2 purple bars indicating the upper Q range (used 
    140 for forward-extrapolation) [figure 3]. These bars may be moved my clicking and 
    141 dragging, or by entering the appropriate values in the Q range input boxes. 
     193the background value), along with a *red* bar indicating the *upper end of the  
     194low-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 
     195dragging, or by entering appropriate values in the Q range input boxes. 
    142196 
    143197.. figure:: tutorial1.png 
    144198   :align: center 
    145199 
    146    **Figure 3** A plot of some data showing the Q range bars 
    147  
    148 Once the Q ranges have been set, click the "Calculate" button next to the 
    149 background input field to calculate the Bonart thermal background level. 
    150 Alternatively, enter your own value into the field. Click the "Extrapolate" 
    151 button to extrapolate the data and plot the extrapolation in the same figure. 
    152 The values of the parameters used for the Guinier and Porod models will also be 
    153 shown in the "Extrapolation Parameters" section [figure 4] 
     200Once 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. 
     201 
     202Click 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. 
    154203 
    155204.. figure:: tutorial2.png 
    156205   :align: center 
    157206 
    158    **Figure 4** A plot showing the extrapolated data and the original data 
    159  
    160 Then, select which type of transform you would like to perform, using the radio 
     207Now select which type of transform you would like to perform, using the radio 
    161208buttons: 
    162209 
    163210*   **Fourier** Perform a Fourier Transform to calculate the correlation 
    164     function of the extrapolated data 
     211    function 
    165212*   **Hilbert** Perform a Hilbert Transform to calculate the volume fraction 
    166     profile of the extrapolated data 
    167  
    168 Clicking the transform button will then perform the selected transform and plot 
    169 it in a new figure. If a Fourier Transform was performed, the "Compute 
    170 Parameters" button can also be clicked to calculate values for the output 
    171 parameters [figure 5] 
     213    profile 
     214 
     215Click the "Transform" button to perform the selected transform and plot 
     216the result in a new graph window. 
     217 
     218If a Fourier Transform was performed, the "Compute Parameters" button can now be clicked to interpret the correlation function as described earlier. 
    172219 
    173220 .. figure:: tutorial3.png 
    174221    :align: center 
    175222 
    176     **Figure 5** The Fourier Transform (correlation function) of the 
    177     extrapolated data, and the parameters extracted from it. 
     223         
     224.. note:: 
     225    This help document was last changed by Steve King, 08Oct2016 
Note: See TracChangeset for help on using the changeset viewer.