Combined diffractive optical elements with adjustable optical properties controlled by a relative rotation: tutorial.

A pair of adjacent transmissive diffractive optical elements (DOEs) forms a combined DOE with tunable optical properties, as, for example, a diffractive lens with an adjustable focal length. The optical properties are controlled by a relative movement of the two DOEs, such as a translation or a rotation around the optical axis. Here we discuss various implementations of this principle, such as tunable diffractive lenses, axicons, vortex plates, and aberration correction devices. We discuss the limits of the tuning range and of diffraction efficiency. Furthermore, it is demonstrated how chromatic aberrations can be suppressed by using multi-order DOEs.