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Quaternions

Table of quaternions was generated using methods in pyimgalgos/src/Quaternion.py

Quaternion.py is tested by self-test using chain of conversions:

  • angles -> rotation matrix -> quaternion -> rotation matrix -> angles,

where in and out angles and rotation matrix coincide.

Script cxif5315/make-quaternions.py generates file with a list of quaternions from file with table of angles

List of few quaternions 
Angles around x,y,z:     0.0     0.0     0.0   quaternion: w, x, y, z:   1.000000   0.000000   0.000000   0.000000
Angles around x,y,z:    30.0     0.0     0.0   quaternion: w, x, y, z:   0.965926   0.258819   0.000000   0.000000
Angles around x,y,z:    60.0     0.0     0.0   quaternion: w, x, y, z:   0.866025   0.500000   0.000000   0.000000
Angles around x,y,z:    90.0     0.0     0.0   quaternion: w, x, y, z:   0.707107   0.707107   0.000000   0.000000
Angles around x,y,z:   120.0     0.0     0.0   quaternion: w, x, y, z:   0.500000   0.866025   0.000000   0.000000
Angles around x,y,z:   150.0     0.0     0.0   quaternion: w, x, y, z:   0.258819   0.965926   0.000000   0.000000
Angles around x,y,z:     0.0     0.0     0.0   quaternion: w, x, y, z:   1.000000   0.000000   0.000000   0.000000
Angles around x,y,z:     0.0    30.0     0.0   quaternion: w, x, y, z:   0.965926   0.000000   0.258819   0.000000
Angles around x,y,z:     0.0    60.0     0.0   quaternion: w, x, y, z:   0.866025   0.000000   0.500000   0.000000
Angles around x,y,z:     0.0    90.0     0.0   quaternion: w, x, y, z:   0.707107   0.000000   0.707107   0.000000
Angles around x,y,z:     0.0   120.0     0.0   quaternion: w, x, y, z:   0.500000   0.000000   0.866025   0.000000
Angles around x,y,z:     0.0   150.0     0.0   quaternion: w, x, y, z:   0.258819   0.000000   0.965926   0.000000
Angles around x,y,z:     0.0     0.0     0.0   quaternion: w, x, y, z:   1.000000   0.000000   0.000000   0.000000
Angles around x,y,z:     0.0     0.0    30.0   quaternion: w, x, y, z:   0.965926   0.000000   0.000000   0.258819
Angles around x,y,z:     0.0     0.0    60.0   quaternion: w, x, y, z:   0.866025   0.000000   0.000000   0.500000
Angles around x,y,z:     0.0     0.0    90.0   quaternion: w, x, y, z:   0.707107   0.000000   0.000000   0.707107
Angles around x,y,z:     0.0     0.0   120.0   quaternion: w, x, y, z:   0.500000   0.000000   0.000000   0.866025
Angles around x,y,z:     0.0     0.0   150.0   quaternion: w, x, y, z:   0.258819   0.000000   0.000000   0.965926

Unit cell

cell-fiber.cell 
CrystFEL unit cell file version 1.0
lattice_type = triclinic
centering = I
a = 18.36 A
b = 26.65 A
c = 4.81 A
al = 90.0 deg
be = 90.0 deg
ga = 102.83 deg

pattern_sim

command to generate simulated events:

cat quaternion_basis.txt | pattern_sim -g simple.geom -p cell-fiber.cell --photon-energy=6000 -o result04 -n 4 -s 1 --background=1

Results

rotation around X by 0, 30, 60, 90, 120, 150 degree

rotation around Y by 0, 30, 60, 90, 120, 150 degree

 

rotation around Z by 0, 30, 60, 90, 120, 150 degree

Summary

  • No sensitivity to crystal rotation around Y and Z
  • any of crystal orientations do not resemble fiber sample
  • Thomas White did not advice to use pattern_sim due to potential bugs. In stead he suggested to use diffraction.

 

 

 

 

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