Micro-Alvarez lenses for a variable dynamic range Shack-Hartmann wavefront sensor

The well-known Alvarez lenses consist of a pair of aspheric surfaces such that their relative lateral displacement results in an equivalent quadratic phase inducing lens that can be tuned from positive to negative powers by controlling the amount and direction of the displacements. In applications requiring a range of only positive powers, the use of the Alvarez lenses in their original design results in an inefficient use of plate size and equivalent lens aperture. We show formulas to shape the surfaces overcoming this inefficient problem. The design parameters to construct an array of micro-Alvarez lenses to compose a Shack-Hartmann wavefront sensor with variable dynamic range is given.