  Modern interferometric imaging relies on advanced calibration that
incorporates direction-dependent effects. Their increasing number of antennas
(e.g. in LOFAR, VLA, MeerKAT/SKA) and sensitivity are often tempered with the
accuracy of their calibration. Beam accuracy drives particularly the capability
for high dynamic range imaging (HDR - contrast > 1:$10^6$). The Radio
Interferometric Measurement Equation (RIME) proposes a refined calibration
framework for wide field of views (i.e. beyond the primary lobe and first null)
using beam models. We have used holography data taken on 12 antennas of the
Very Large Array (VLA) with two different approaches: a `data-driven'
representation derived from Principal Component Analysis (PCA) and a projection
on the Zernike polynomials. We determined sparse representations of the beam to
encode its spatial and spectral variations. For each approach, we compressed
the spatial and spectral distribution of coefficients using low-rank
approximations. The spectral behaviour was encoded with a Discrete Cosine
Transform (DCT). We compared our modelling to that of the Cassbeam software
which provides a parametric model of the antenna and its radiated field. We
present comparisons of the beam reconstruction fidelity vs. `compressibility'.
We found that the PCA method provides the most accurate model. In the case of
VLA antennas, we discuss the frequency ripple over L-band which is associated
with a standing wave between antenna reflectors. The results are a series of
coefficients that can easily be used `on-the-fly' in calibration pipelines to
generate accurate beams at low computing costs.
