



For the pseudoellipse model, the full torsiontilt system is used. The full rotation matrix is given in equation 12.74c on page .
The frame order matrix is
The surface normalisation factor is
The 1 degree frame order matrix with tensor rank2 consists of the following elements
As the trigonometric functions of θ_{max} cannot be integrated, these components must be numerically integrated.
The 2 degree frame order matrix with tensor rank4 consists of the following elements, using Kronecker product double indices from 0 to 8
As the trigonometric functions of θ_{max} cannot be integrated, these components must be numerically integrated. All other frame order matrix elements can be numerically shown to be zero.
The frame order matrix element simulation script from Section 16.2, page was used to compare the implementation of equations 16.52 and 16.53 above. Frame order matrix Daeg^{(1)} and Daeg^{(2)} values were both simulated and calculated, both within and out of the motional eigenframe. The inframe Daeg^{(1)} values are shown in figure 16.15 and Daeg^{(2)} in figure 16.16. The outofframe Daeg^{(1)} values are shown in figure 16.17 and Daeg^{(2)} in figure 16.18.
The relax user manual (PDF), created 20190614.