With the emergence of new radio telescopes promising larger fields-of-view at lower observation frequencies (e.g., SKA), addressing direction-dependent effects (DDE) (e.g., direction-specific beam responses; sector-based ionosphere corruptions) has become all the more important. Be it through A-projection or major-cycle calibration strategies, addressing DDE often requires reliable representations of antenna/station beams; yet, these require significant amounts of computational memory as they are baseline-, frequency-, time- and polarisation-dependent. A novel prototype is reported here to approximate antenna beams suitable to SKA-MID using Zernike polynomials. It is shown that, beam kernels can be approximated up to 3 lobes with sufficiently few
coefficients, thereby replacing the memory-intensive sampled beams. It is hoped that these results facilitate more efficient beam-dependent solutions and approaches to tackling polarisation leakage; all of which are essential for large-scale radio telescopes.