Changeset 41345d7e in sasview


Ignore:
Timestamp:
Jul 12, 2016 5:33:14 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, 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:
d03228e
Parents:
eb320682
Message:

Add more info to corfunc perspective docs page

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

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

    rfb7fcec r41345d7e  
    1515*  Extrapolation of the scattering curve to :math:`Q = 0` and 
    1616   :math:`Q = \infty` 
    17 *  Fourier Transform of the extrapolated data to give the correlation function 
     17*  Fourier/Hilbert Transform of the extrapolated data to give the correlation 
     18   function/volume fraction profile 
    1819*  Interpretation of the 1D correlation function based on an ideal lamellar 
    1920   morphology 
     
    6061   :align: center 
    6162 
    62    ``Figure 1`` The value of :math:`\sigma` is a measure of the electron 
     63   **Figure 1** The value of :math:`\sigma` is a measure of the electron 
    6364   density profile at the interface between crystalline and amorphous regions. 
    6465 
     
    8384.. math:: 
    8485    h_i = \frac{1}{1 + \frac{(x_i-b)^2}{(x_i-a)^2}} 
     86 
     87Transform 
     88--------- 
     89 
     90Fourier 
     91^^^^^^^ 
     92 
     93If Fourier is selected for the transform type, the perspective will perform a 
     94discrete cosine transform to the extrapolated data in order to calculate the 
     95correlation function. The following algoritm is applied: 
     96 
     97.. math:: 
     98    \Gamma(x_k) = 2 \sum_{n=0}^{N-1} x_n \cos{\left[ \frac{\pi}{N} 
     99    \left(n + \frac{1}{2} \right) k \right] } \text{ for } k = 0, 1, \ldots, 
     100    N-1, N 
     101 
     102Hilbert 
     103^^^^^^^ 
     104If Hilbert is selected for the transform type, the perspective will perform a 
     105Hilbert transform to the extraplated data in order to calculate the Volume 
     106Fraction Profile. 
     107 
     108Interpretation 
     109-------------- 
     110Once the correlation function has been calculated by transforming the 
     111extrapolated data, it may be interpreted by clicking the "Compute Parameters" 
     112button. The correlation function is interpreted in terms of an ideal lamellar 
     113morphology, and structural parameters are obtained as shown in Figure 2 below. 
     114It should be noted that a small beam size is assumed; no de-smearing is 
     115performed. 
     116 
     117.. figure:: fig2.gif 
     118   :align: center 
     119 
     120   **Figure 2** Interpretation of the correlation function. 
     121 
     122The structural parameters obtained are: 
     123 
     124*   Long Period :math:`= L_p` 
     125*   Average Hard Block Thickness :math:`= L_c` 
     126*   Average Core Thickness :math:`= D_0` 
     127*   Average Interface Thickness :math:`\text{} = D_{tr}` 
     128*   Polydispersity :math:`= \Gamma_{\text{min}}/\Gamma_{\text{max}}` 
     129*   Local Crystallinity :math:`= L_c/L_p` 
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