The conformity between numerically calculated and the analytically known characteristic far fields can be calculated as
$$zeta_n = displaystyle frac{maxlimits_p displaystyle sumlimits_{q=-p}^{p} Bigg| P_{pq,n}^mathrm{TE/TM} Bigg|^2}{displaystyle sumlimits_{p,q} sumlimits_mathrm{TE/TM}Bigg| P_{pq,n}^mathrm{TE/TM} Bigg|^2}$$
with
$$P_{pq,n}^mathrm{TE/TM} = displaystyle frac{1}{2 Z_0} intlimits_{0}^{2pi} intlimits_{0}^{pi} left( boldsymbol{F}_{pq}^mathrm{TE/TM} right)^ast cdot boldsymbol{F}_n sin vartheta ,mathrm{d}vartheta ,mathrm{d}varphi,$$
where $Z_0$ is the free space impedance, $boldsymbol{F}_n$ is numerically calculated characteristic far field, and $boldsymbol{F}_{pq}^mathrm{TE/TM}$ is the analytically known characteristic far field.
Results:
Coefficient $zeta_n$ for spherical shell discretized into 500 triangles (750 RWG functions) at ka = 1/2:
Matlab script generating characteristic far-fields for TM and TE spherical modes is HERE.
For details see IEEE Trans. Antennas and Propagation paper.
/Edited 21. 04. 2017, MC/
