The PLANCK SURVEYOR is a European Space Agency satellite mission to image the very faint anisotropies in the temperature of the Cosmic Microwave Background (CMB) radiation. Maynooth is actively participating in an international collaboration of scientists involved with the optical design of the High Frequency Instrument (HFI). This paper outlines research which has been undertaken in Maynooth concerned with numerical modelling of the optical characteristics of the multi-frequency array of detectors making up the HFI instrument. In the study the commercial software package ZEMAX was used to model the coupling of the focal plane HFI detectors to the PLANCK telescope. This package is particularly useful in the optical design of PLANCK because of the powerful optimisation features of the software. It is thus possible to readily determine the optimum positioning of the detectors in the focal plane of the telescope. Although the package is based on a numerical ray tracing approach, diffraction effects can be included making it possible to model the beam patterns for the HFI array on the sky. As a method of validating this approach the results of the ZEMAX model of the system were compared with that of a more rigorous physical optics simulation. It was concluded from the study that the level of agreement between the two approaches support the proposed use of ZEMAX. Once the detector positions were optimised using ZEMAX the physical optics approach was used to determine a more accurate set of beam patterns for the array.