Evolution of the transverse response of an optical system with complex filters

In many optical systems a specific axial behaviour is needed. It is very common to search for high focal depth and an almost constant distribution along the axial coordinate. An additional condition to be required could be symmetrical axial response. The transverse response in the best image plane is also of great importance, for instance to produce superresolution. Moreover, the invariance of the transverse response in defocused planes could be a requirement for an optical system. In this paper, we study the transverse response at defocused planes produced by complex filters with high focal depth. In order to analyze the transverse responses we extend the transverse gain factor for defocused planes. Here, we derive several conditions that complex filters may satisfy to produce symmetrical axial response. Numerical examples of transverse responses for some filters that produce high depth of focus are shown.