I have data for the radiation pattern of antenna, given as the theta and phi components of the electric field (E_theta, E_phi), with 0<theta<180 deg, 0<phi<360 deg. I want to describe this data as a spherical harmonic expansion. So, my task is to find the spherical harmonic expansion coefficients. I assumed the theta and phi components of the electric field can be individually expanded as a sum of spherical harmonics, and found the coefficients by multiplying each (normalized) spherical harmonic term with the data and integrating, since the spherical harmonics are orthonormal. However, this seems incorrect, the error between the reconstructed and measured electric fields increases as the order of the expansion increases. What could be going wrong? I am trying to figure out if the error is conceptual or computational in nature. I saw a paper which says the measured data has to be converted from spherical to Cartesian coordinates (convert (E_theta, E_phi) to (E_x, E_y, E_z)), and then each of Cartesian components has to be expanded in terms of spherical harmonics. Is this necessary, and if so, why? Why doesn't the spherical harmonic expansion hold good in spherical (theta,phi) coordinates?