The importance of antenna beam width in detecting enhanced backscatter in a layer of vegetation is studied. First, the vegetation is modeled as a layer of random media over a flat dielectric half space. The random media consists of thin dielectric discs and cylinders. The polarimetric bistatic scattering coefficients are calculated using the Distorted Born Approximation (DBA) taking into account scattering mechanisms such as direct scatter, direct-reflected scatter, and double ground reflected scatter. The polarimetric bistatic scattering coefficients can have an enhancement factor that is positive for like-polarized returns or can be negative for cross polarized returns at and around the backscatter angle for the direct-reflected scattering component. Depending on model parameters, the magnitude and the angular width of the scattering coefficients can vary. In order to maximize received power due to the enhancement factor at backscatter, an antenna with a narrow beam width with respect to the angular width of the scattering coefficients for the layer is required. Conversely, an antenna beam width that is on the order of the angular width, will receive a fraction of the enhancement backscattered power, and this can cause inaccuracies in problems such as soil moisture retrieval through a vegetation canopy.