# Changeset 41345d7e in sasview

Ignore:
Timestamp:
Jul 12, 2016 5:33:14 AM (7 years ago)
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:

Location:
src/sas/sasgui/perspectives/corfunc/media
Files:
 rfb7fcec *  Extrapolation of the scattering curve to :math:Q = 0 and :math:Q = \infty *  Fourier Transform of the extrapolated data to give the correlation function *  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 :align: center Figure 1 The value of :math:\sigma is a measure of the electron **Figure 1** The value of :math:\sigma is a measure of the electron density profile at the interface between crystalline and amorphous regions. .. math:: 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 perspective will perform a discrete cosine transform to the extrapolated data in order to calculate the correlation function. The following algoritm 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 Hilbert ^^^^^^^ If Hilbert is selected for the transform type, the perspective will perform a Hilbert transform to the extraplated data in order to calculate the Volume Fraction Profile. 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 performed. .. figure:: fig2.gif :align: center **Figure 2** Interpretation of the correlation function. The structural parameters obtained 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