Orientation Matrices calculations Crystal re orientation
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1 Orientation Matrices calculations Crystal re orientation Pierre LEGRAND Synchrotron SOLEIL Proxima1 Beamline Scientist 2004 hp
2 Diversity of goniometers (handling of the sample) Rotation (Intersecting Axes) Single Axis Eulerian Goniometers Kappa Goniometers Robots arms 4 to 6 axis Mini Kappa Translation Motorized Goniometer (XY, Z, XYZ) Motorized Head Translation (XY, Z, XYZ) Complex rotation/translations Tripods Hexapods Rotation (Not intersecting) [Jacquamet L. et al Actad D ] page 2
3 A robot as a goniometer (handling of the sample++) Beam positioning Sample changer Multi axis goniometer Gain of space [Jacquamet L. et al Actad D ] BM30A FIP CRG French Beamline ESRF page 3
4 A robot as a goniometer (handling of the sample++) Emulating a Kappa goniometer... (rotation around an arbitrary axis) page 4
5 What is used on synchrotron BL? Why aren't multi axes used more extensively? page 5
6 Lack of space... collisions and lack of software! page 6
7 Three Axis Orientation Coordinate rotation by a three axis rotation system Virtual three circles goniosta 3 rotations around successive axes Axes can be defined by any set of 3 vectors ex = Vector(1,0,0), ey = Vector(0,1,0), ez = Vector(0,0,1) StandardAxes = ex, ey, ez NoniusKappaAxes = ez, kappavector(50), ez EMBLKappaAxes = ez, kappavector(24), ez EulerAxes = ez, ex, ez DenzoAxes = ez, ey, ex page 7
8 Python class Based on the Geometrical classes of the ScientificPython module made by Konrad Hinsen Vectors objects Tensor objects Transformation Tensor Analysis module Transformation Rotation Rotation Quaternions Translation ThreeAxisRotation Rotation+Translation Uses Numerical Python page 8
9 Constructor ThreeAxisRotation(init,rotationAxes=(ex, ey, ez), inversaxesorder=0) - rotationaxes is a tupple of 3 vectors (e1, e2, e3) defining the three rotation axes. - init can be either: - a tensor object containing the rotation matrix - a Rotation object, - a set of three angles (a1, a2, a3) in radian 3 immuable axes + A Tensor Object (3x3) Rotation Object Set of 3 angles page 9
10 setangles((a1,a2,a3)) addangles((a1,a2,a3)) getangles() Methodes Get angles from the tensor (2 solutions) This a reimplementation of the David Thomas's algorithm [1] described by Gerard Bricogne in [2] [1] "Modern Equations of Diffractometry. Goniometry." D.J. Thomas Acta Cryst. (1990) A46 Page [2] "The ECC Cooperative Programming Workshop on Position-Sensitive Detector Software." G. Bricogne, Computational aspect of Protein Crystal Data Analysis, Proceedings of the Daresbury Study Weekend (23-24/01/1987) Page Methods added to Rotation in ScientificPython version >= 2.4.9: Rotation.threeAngles(axes) return a 3 angles representation Rotation.asQuaternion() return a quaternion representation page 10
11 Operations Rot = Rot1 * Rot2 Rot.inverse(), Rot.dot(X), Rot.transpose() Transformation = Rot * Translation Vector2 = Rot(Vector1) Other python Classes class CrystalVector(Vector) class OrthogonalizationMatrix(Tensor) class CrystalOrienationMatrix() class DegreeOfFreedom() page 11
12 Applications Virtual goniometer HKL tango device server (6-cercles) c++ library (done by PICCA Frédéric-Emmanuel) Interonversion of OM to different program conventions Conversion of MR rotation solutions to different program conventions page 12
13 Applications Virtual goniometer The Virtual Goniometer will simulate any type of goniometer composed of 3 consecutive axes. Optionaly translations can be defined before (pre-translation holding the first axis) or after the axes (posttranslation holded by the last axis). = Combining DOFs (by holding order) + Intercept changes (hard limit, collision maps, self shadow maps, strastegy) + Integrating orientation methods (gonset.py) + Calibration methods (positioning of the maps) page 13
14 Crystal Orientation Matrices Conversion Data Processing Programs use different convention and frame reference Mosflm uses 2 different representations for the OM and 2 different laboratory frame conventions (Detector and Crystal) Denzo uses 3 different representations for the OM and 2 different laboratory frame convention (Detector and Crystal). Very difficulte to understand... XDS uses only one representations for the OM and one laboratory frame convention page 14
15 Crystal Orientation Matrices Conversion Needs: Numerical Python (could be replaced by another library) ScientificPython Interconversion: Needs rewrite to us the new classes xds2mos.py (can start mosflm) xds2dnz.py mos2dnz.py dnz2mos.py dnx2xds.py mos2xds.py page 15
16 Thanks! Questions? page 16
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