The coherence parameters associated with the electron impact excitation of the He 3¹P state are studied for a Monte Carlo simulation of an experiment consisting of crossed electron and atom beams. The effects of changes in gas pressure and interaction region geometry are monitored by a fixed polarimeter analysing radiation resulting from the 3¹P to 1¹S (53.7 nm) transition. This work extends the simulations of Humphrey with the incorporation of a finite electron detector, a region of background gas and angular dispersion in the electron beam. Humphrey found that with an infinitesimal electron detector, the measured polarizations were not strongly dependent on interaction region geometry. In this work, however, it is found that the coherence parameters are very strongly dependent on interaction region geometry, pressure and the solid angle of the electron detector. Even very small solid angles can adversely affect the measured parameters. While angular correlations are not specifically studied, there are indications from simulations of electron scattering angle integrated polarizations that it is most important that any measurements involving a rotation of the photon detector should rotate about a symmetry axis of the gas source.