Update ODFTutorial.m

doc/Tutorials/ODFTutorial.m

@@ -2,24 +2,24 @@
 %
 %% Theory
 %
-% The orientation distribution function (ODF) is a function on the
-% orientation space that associates to each orientation $g$ the volume
-% percentage of crystals in a polycrystaline specimen that are in this
+% The orientation distribution function (ODF) is a function in
+% orientation space that associates each orientation $g$ with the volume
+% fraction of crystals in a polycrystaline specimen that are in this
 % specific orientation, i.e.,
 %
 % $$\mathrm{odf}(g) = \frac{1}{V} \frac{\mathrm{d}V(g)}{\mathrm{d}g}.$$
 %
-% In MTEX an entirely random texure will have an ODF constant to one. In
+% In MTEX a perfectly random texure will have an ODF equal to a value of one for all orientations. In
 % other word the values of ODFs in MTEX can be interpreted as multiples of
 % the random distribution (mrd). 
 %
 %% Computing an ODF from Individual Orientations
 %
-% Individual orientations data may be obtained by experimental by EBSD,
-% ACOM or 3d X-ray imaging; or from simulations, like VPSC. In the
-% following we consider an EBSD map of an Titanium alloy.
+% Individual orientation data may be obtained experimentally by EBSD (orientation mapping in a SEM),
+% ACOM (orientation mapping in a TEM) or 3d X-ray imaging; or from computer simulations involving texture modeling, such as VPSC. In the
+% following example we consider an EBSD map of an Titanium alloy.  Note that this test data is based on hexagonal layout rather than the more common x-y grid.
 
-% import the titanium data
+% import the titanium test data downloaded with the MTEX package
 mtexdata titanium
 
 % plot an orientation map
@@ -30,67 +30,67 @@
 % <DensityEstimation.html kernel density estimation> using the command
 % <orientation.calcDensity.html |calcDensity|>.
 
-% extract the orientations
+% copy the EBSD orientations to a separate variable
 ori = ebsd.orientations;
 
 % compute the ODF
 odf = calcDensity(ori)
 
 %%
-% There many different ways to visualize ODF: <EulerAngleSections.html
+% There many different ways to visualize an ODF: <EulerAngleSections.html
 % Euler> or <SigmaSections.html sigma sections>, <ODFPlot.html thee
 % dimensional plots>, <ODFPoleFigure.html pole figures> and
 % <ODFInversePoleFigure.html inverse pole figures>. The most common but not
-% recommended way are sections with respect to the third Euler angle
+% recommended method uses sigma sections, slices with respect to the third Euler angle
 % $\varphi_2$
 
 plot(odf)
 
 %% Computing an ODF from Pole Figure Data
 %
-% Pole figure data arises when textured materials are measured via x-ray,
-% neutron or syncrotron radiation. Generaly, for $3$ to $10$ diffraction
-% planes specified by Miller indices $(hk\ell)$ diffraction intensities are
-% measured at a spherical grid of specimen directions. In the example below
-% each dot corresponds to one diffraction intensity at the plane indicated
-% at the top of the spherical plots measured from the direction
-% corresponding to the pixel position.
-
-% import pole figure data
+% Pole figure data is often generated when textured materials are measured via x-ray,
+% neutron or syncrotron radiation. When performing this type of diffraction experiment, 
+% diffraction intensities are measured over a spherical grid of specimen directions for $3$ to $10$ diffraction
+% planes specified by Miller indices $(hk\ell)$ . In the example below, for each plane indicated
+% at the top of the spherical plot, each dot colour corresponds to a measured diffraction intensity 
+% at the position corresponding to the dot location.
+
+% import the PTX pole figure test data downloaded with the MTEX package
 mtexdata ptx
 
-% plot the data
+% plot the pole figures, representing the experimental data acquired
 plot(pf)
+% show the colour bar.  Note the maximum intensity is different for each pole figure.
 mtexColorbar
 
 %%
 % The <PoleFigure2ODF.html reconstuction> of an ODF from pole figure data
-% requires the solution of an ill posed inverse problem. This mean the
-% reconstruction problem has in general <PoleFigure2ODFAmbiguity.html not a
-% unique solution>, but there are several ODFs that correspond to the same
-% set of pole figure data. MTEX applies <PoleFigure2ODFGhostCorrection.html
-% some heuristics> to identify among all solutions the physically most
-% reasonable.
-
-% compute an ODF with default settings
+% requires the solution of an *ill posed inverse problem*. This means the
+% reconstruction problem generally <PoleFigure2ODFAmbiguity.html does not have a
+% unique solution>, and there are several ODFs that may be constructed from the same
+% set of pole figure data. MTEX generates multiple possibilities, and then applies <PoleFigure2ODFGhostCorrection.html
+% some selection criteria> to identify the physically most
+% reasonable result.
+
+% compute an ODF from the three input pole figures with default settings
 odf = calcODF(pf)
 
 %%
-% Once an ODF is reconstructed we can check how well its pole figures fit
-% the measured pole figures
+% Once an ODF is reconstructed we can check how well the ODF's pole figures fit
+% the experimentally measured pole figures
 
-% plot the recalculated pole figures 
+% plot the pole figures of the calculated ODF
 plotPDF(odf,pf.h)
 
 
 %% ODF Modelling
 %
-% Besides from experimental data MTEX allows also the definition of model
-% ODFS of different type. These include <UnimodalODFs.html unimodal ODFs>,
-% <FibreODFs.html fibre ODF>, <BinghamODFs.html Bingham Distributed ODFs>
+% Aside from using experimental data, MTEX also allows the definition of model
+% ODFs of different types. These include <UnimodalODFs.html unimodal ODFs>,
+% <FibreODFs.html fibre ODFs>, <BinghamODFs.html Bingham Distributed ODFs>
 % and any <ODFModeling.html combination of such ODFs>.
 
-% define a fibre symmetric ODF
+% define a gamma fibre ODF
 odf = fibreODF(fibre.gamma(odf.CS))
 
 % plot it in sigma sections