# Eulerian to Kappa Geometry Calculator

Enter a chie angle in Eulerian geometry and press the "Calculate" button to get the required kappa, phi, and omega movements in kappa geometry for the equivalent movement of the desired chie angle rotation. You can also enter an initial position as shown on the dials of the Beam Line 9-3 goniometer, and the two possible final positions will be given.

Alternatively, you can enter a vector, press "Rotate", and the required kappa, omega, and phi rotations will be given to rotate that particular vector to lie along the z-axis.

 Initial Kappa Initial Omega Initial Phi Chie angle Vector: x y z δ Kappa δ Omega δ Phi Alt δ Kappa Alt δ Omega Alt δ Phi Final Kappa Final Omega Final Phi Alt Final Kappa Alt Final Omega Alt Final Phi

All values are in degrees, except for vector components.

For converting a chie rotation to kappa geometry, the normal solution can be found by solving the following three equations (where delta = 90° + ome - omk = -90° + phie - phik, and ome and phie are rotations in eulerian geometry, and omk and phik are rotations in kappa geometry):

• sin(alpha)*sin(0.5*kappa) = sin(0.5*chie)
• cos(alpha)*sin(0.5*kappa) = sin(delta)*cos(0.5*chie)
• cos(0.5*kappa) = cos(delta)*cos(0.5*chie)

Note: The dials on the Beam Line 9-3 goniometer are backwards. However, since the two sets of solutions are simply opposites of each other, this simply has the effect of switching the values for the normal and alternate solutions, which should not have an impact when applying the equivalent movement of the desired chie rotation. Due to physical limitations, though, one or both solutions may not be feasible.

When performing the necessary movements, positive rotations on the three axes are defined as follows:

• kappa axis: when facing the goniometerhead straight on, a positive kappa rotation will rotate the goniometerhead up and to the left
• omega/phi axes: when facing the goniometerhead straight on, a positive omega/phi rotation will be a clockwise rotation

In addition, the xyz coordinate axes are defined as follows (according to the MOSFLM User Guide) in relation to the goniometer on Beam Line 9-3:

• x axis: when facing the goniometerhead straight on, the positive x axis points in the same direction in which the beam is traveling
• y axis: when facing the goniometerhead straight on, the positive y axis points towards the ceiling
• z axis: when facing the goniometerhead straight on, the positive z axis points away from you

An illustration showing the positive directions of all 6 axes in relation to SSRL's goniometer setup is provided here.

Again, when performing movements, a positive rotation on all three axes will appear as a negative rotation on the goniometer dials. For more information on the calculations for converting chie rotations to kappa geometry movements, see Chapter 2 of the CAD4 user manual.

Also, please note that in the CAD4 user manual, the beam is coming from a different direction in relation to the goniometer when compared to SSRL's setup. As a result, to obtain the correct values for the equivalent kappa geometry movoment, a rotation of 90 degrees about the omega axis in Eulerian geometry needs to be applied before any other transformations, and a rotation of -90 degrees about the omega axis in Eulerian geometry also needs to be applied at the end of all transformations. This correctly compensates for the difference between the SSRL setup and the CAD4 user manual setup.