Fourier transform pupil functions for modifying the depth of focus of optical imaging systems

We use a Fourier transform approach to design pupil functions that modify the axial depth of focus for an optical system. We extend previous research in several ways. We first extend the depth of focus to 4 cm for a 38 cm focal length lens. We show that the transverse size of the focused beam is the same as for an open pupil. We then multiply the pupil function by a circular harmonic window function. The entire depth of focus is now characterized by a vortex beam. Finally we multiply our original pupil function by an edge-enhancing window function. Now the pupil function produces two sharp focus spots at the locations corresponding to the edges of the rectangle function.