  Inadequacies in the knowledge of the primary beam response of current
interferometric arrays often form a limitation to the image fidelity. We hope
to overcome these limitations by constructing a frequency-resolved,
full-polarization empirical model for the primary beam of the Westerbork
Synthesis Radio Telescope (WSRT). Holographic observations, sampling angular
scales between about 5 arcmin and 11 degrees, were obtained of a bright compact
source (3C147). These permitted measurement of voltage response patterns for
seven of the fourteen telescopes in the array and allowed calculation of the
mean cross-correlated power beam. Good sampling of the main-lobe, near-in, and
far-side-lobes out to a radius of more than 5 degrees was obtained. A robust
empirical beam model was detemined in all polarization products and at
frequencies between 1322 and 1457 MHz with 1 MHz resolution. Substantial
departures from axi-symmetry are apparent in the main-lobe as well as
systematic differences between the polarization properties. Surprisingly, many
beam properties are modulated at the 5 to 10% level with changing frequency.
These include: (1) the main beam area, (2) the side-lobe to main-lobe power
ratio, and (3) the effective telescope aperture. These semi-sinusoidsal
modulations have a basic period of about 17 MHz, consistent with the natural
'standing wave' period of a 8.75 m focal distance. The deduced frequency
modulations of the beam pattern were verified in an independent long duration
observation using compact continuum sources at very large off-axis distances.
Application of our frequency-resolved beam model should enable higher dynamic
range and improved image fidelity for interferometric observations in complex
fields. (abridged)

Astrophysics