Continuous variation in Fresnel lens focal length

An optical structure which combines a Fresnel zone plate with an induced convex lens on a PLZT substrate has been proposed to enable initial focusing under no applied potential, a continuous range of short focal distances, and the ability to switch the focal point to infinity. The transmitted optical field was analytically described and a simple formula was derived that demonstrated the dependence of the new focal length on each focusing mechanism. The numerical example provided showed a continuous change of focal length of about 16% while maintaining a good parabolic shape of the induced lens.