In the late 1960s Alvarez and Lohmann independently suggested cubic phase plates as varifocal elements. A variety of different theoretical as well as experimental approaches have been discussed since. Today compact tunable optics is of specific interest e.g. in miniaturized optical systems. Recently developed fabrication technologies like diamond turning or milling nowadays enable the fabrication of higher order freeform surface profiles as implementation of efficient phase plates for an optimization of the imaging properties. We present a non-paraxial analysis of the imaging behavior of diffractive, refractive and hybrid Alvarez-Lohmann lenses with increased numerical aperture. Our analysis includes the influence of lateral focus shifts as well as monochromatic and polychromatic aberrations over the tuning range. Experimental results with phase plates fabricated by diamond milling and lithographic techniques will be presented.