We review a free parameter in the design of Fresnel zone plate lens antennas. Historically, zone plate antennas have been designed with a specific choice for this parameter, which can be taken as a type of phase reference. Two methods of interpreting the parameter have been identified, either in terms of a reference radius or equivalently a reference phase. Here, for simplicity, we treat this variable parameter as a reference phase. Importantly, the reference phase can be chosen to have non-standard values which have been shown to improve important aspects of antenna performance and to add a new functionality to zone plate antennas.