Optical transfer function design by use of a phase-only coherent transfer function

The design of a desired optical transfer function (OTF) is a common optical problem that has many possible applications. A well-known application for the OTF design is beam shaping for incoherent illumination. However, other applications, such as optical signal processing, can also be addressed with these systems. We derive a mathematical expression for an optimal phase-only filter that, when attached to an imaging lens, provides an optimal approximation in the sense of the minimal mean square error to the desired OTF function. Because of the fact that a phase-only filter is used, high efficiency is achieved.