For rotationally symmetric aspheric lenses, one can establish lens design and layout based upon the phase delay function exp[−iφ(ρ)]. An embodiment of the invention is a method for calculating a corresponding variation in focal length denoted by f(ρ). According to an aspect, one can also assert a shape for the focal length f(ρ) and thereafter calculate a phase delay function in order to synthesize a novel lens. New EDoF lens designs are obtained by selection of an inner and outer focal length connected by a simple curve that can be approximate by a polynomial. From the selected f(ρ), one can synthesize a finished EDoF lens design and fabricate the lens. Another aspect of this invention is directed to a method to tailor prior-art EDoF lenses so that their performance over some range is improved.