Classical optical design techniques are oriented toward optimizing imaging system response at a single image plane. Recently, researchers have proposed to greatly extend the imaging system depth of field, by introducing large deformations of the optical wavefront, coupled with subsequent post-detection image restoration. In one case, a spatially separable cubic phase plate is placed at the pupil plane of an imaging system to create an extremely large effective depth of field. The price for this extended performance is noise amplification in the restored imagery relative to a perfectly focused image. In this paper we perform a series of numerical design studies based on information theoretic analyses to determine when a cubic phase system is preferable to a standard optical imaging system. The amount of optical path difference (OPD) associated with the cubic phase plate is directly related to the amount of achievable depth of field. A large OPD allows greater depth of field at the expense of greater noise in the restored image. The information theory approach allows the designer to study the effect of the cubic phase OPD for a given depth of field requirement.