Orientation Finding¶

Azimuthal Integration¶

See Calculate Rotation Angle for more details. Following methods are all based on the histogram gotten in this step.

Gaussian Mixture Model (GMM)¶

Herman Orientation Factor¶

After getting the circular histogram from azimuthal integration, we can calculate Herman Orientation Factor for each degree. The formula is

\(HoF = \frac{3\langle\cos^2\phi\rangle-1}{2}\), where \(\langle\cos^2\phi\rangle = \frac{\sum_{i=0}^{i=x}I_i\cos^2\phi_i\sin\phi_i}{\sum_{i=0}^{i=x}I_i\sin\phi_i}\)

x is either equal to 180 or 90 degrees.

We can get the same number of Herman Factors as the length of the histogram. (See Page 7 for properties of Herman Factor.) Following two figures seperately show results of integration on 90 and 180 degrees.

Note

In Scanning Diffraction program, the area of azimuthal integration is set by ROI. In other programs, the area of azimuthal integration is fixed where the inner radius is 0 and the outer radius is 1/3 max radial length.