Accurate, low-noise, wideband phased array radar antennas depend on the use of true time delays between microwave elements. A photonic means of generating the required element-to-element phase shifts was developed by Toughlian and Zmuda for systems operating in the VHF frequency range, and extended by Monsay and Caccuitto for operation in the radar C band. The photonic beamformer is based on a heterodyne optical system, in which the reference beam acts as a probe of the acoustic wave in the acousto-optic (AO) cell. It is apparent that the benefits of this photonic system rely greatly on the ability of the probe beam to pick out just the right phase shift/time delay from the acoustic waveform in the AO cell. A basic limitation to system performance could come from intrinsic diffraction effects due to the finite beamwidth of the probe in the AO cell. In addition, the finite size of the photodetector in the system will have an effect on the final SNR. These effects have been studied in detail and their implications for design and performance of the photonic beamformer are discussed.