Open Matlab File in the Editor MTEX

The SantaFe example

Simulate a set of pole figures for the SantaFe standard ODF, estimate an ODF and compare it to the inital SantaFe ODF.

Simulate pole figures

CS = crystalSymmetry('m-3m');

% crystal directions
h = [Miller(1,0,0,CS),Miller(1,1,0,CS),Miller(1,1,1,CS),Miller(2,1,1,CS)];

% specimen directions
r = equispacedS2Grid('resolution',5*degree,'antipodal');

% pole figures
pf = calcPoleFigure(SantaFe,h,r);

% add some noise
pf = noisepf(pf,100);

% plot them
plot(pf,'MarkerSize',5)
mtexColorMap LaboTeX

ODF Estimation with Ghost Correction

rec = calcODF(pf)
------ MTEX -- PDF to ODF inversion ------------------
Call c-routine
initialize solver
start iteration
error: 7.2280E-02 1.9648E-02 9.9494E-03 9.2101E-03 8.9175E-03 8.7597E-03 8.6701E-03 8.6138E-03 8.5728E-03 8.5416E-03 8.5161E-03 
Finished PDF-ODF inversion.
error: 8.5161E-03
alpha: 9.9804E+01 9.9821E+01 1.0048E+02 1.0030E+02 
required time: 11s
ghost correction
calculate with fixed background 0.59
initialize solver
start iteration
error: 3.1343E-01 1.2569E-01 5.5515E-02 4.1040E-02 3.9340E-02 3.8633E-02 3.8222E-02 3.7926E-02 3.7716E-02 3.7552E-02 3.7424E-02 
Finished PDF-ODF inversion.
error: 3.7424E-02
alpha: 9.9874E+01 9.9837E+01 1.0057E+02 1.0030E+02 
 
rec = ODF  
  crystal symmetry : m-3m
  specimen symmetry: 222
 
  Uniform portion:
    weight: 0.59116
 
  Radially symmetric portion:
    kernel: de la Vallee Poussin, halfwidth 5°
    center: 1232 orientations, resolution: 5°
    weight: 0.40884
 

ODF Estimation without Ghost Correction

rec2 = calcODF(pf,'NoGhostCorrection')
------ MTEX -- PDF to ODF inversion ------------------
Call c-routine
initialize solver
start iteration
error: 7.2280E-02 1.9648E-02 9.9494E-03 9.2101E-03 8.9175E-03 8.7597E-03 8.6701E-03 8.6138E-03 8.5728E-03 8.5416E-03 8.5161E-03 
Finished PDF-ODF inversion.
error: 8.5161E-03
alpha: 9.9804E+01 9.9821E+01 1.0048E+02 1.0030E+02 
required time: 11s
 
rec2 = ODF  
  crystal symmetry : m-3m
  specimen symmetry: 222
 
  Radially symmetric portion:
    kernel: de la Vallee Poussin, halfwidth 5°
    center: 1232 orientations, resolution: 5°
    weight: 1
 

Error analysis

% calculate RP error
calcError(rec,SantaFe)

% difference plot between meassured and recalculated pole figures
plotDiff(pf,rec)
ans =
    0.0407

Plot estimated pole figures

plotPDF(rec,pf.h,'antipodal')

Plot estimated ODF (Ghost Corrected)

plot(rec,'alpha','sections',18,'resolution',5*degree,...
  'projection','plain','contourf','FontSize',10,'silent')
mtexColorMap white2black
Plotting ODF as alpha sections, range: 0° - 85°

Plot odf

plot(SantaFe,'alpha','sections',18,...
  'projection','plain','contourf','FontSize',10,'silent')
mtexColorMap white2black
Plotting ODF as alpha sections, range: 0° - 85°

Plot Fourier Coefficients

close all;
% true ODF
plotFourier(SantaFe,'bandwidth',32)
% keep plot for adding the next plots
hold all

% With ghost correction:
plotFourier(rec,'bandwidth',32)

% Without ghost correction:
plotFourier(rec2,'bandwidth',32)

legend({'true ODF','with ghost correction','without ghost correction'})
% next plot command overwrites plot
hold off