Spiral adaptive Fresnel lens: generalizations, improvements, and augmented-reality/virtual-reality simulations

Two complementary cylindrical lenses, each bent into a spiral, can form the components of an adaptive Fresnel lens whose focusing power can be tuned by rotating the two components relative to each other [Armstrong <i>et al</i>., J. Opt. Soc. Am. A42, 211 (2025)JOAOD60740-323210.1364/JOSAA.540585]. Corresponding windings of the cylindrical-lens spirals form the windings of the resulting adaptive Fresnel lens, and the addition of an Alvarez-Lohmann lens to the cylindrical lenses can improve the device through winding focusing-ensuring that each winding has the same focusing power as the Fresnel lens. Here we extend the type of spiral from logarithmic to Archimedean and hyperbolic; we introduce an alternative type of winding focusing by varying the separation between the two components; and we show how to design our adaptive Fresnel lenses so that, unlike the original design, they work best around non-zero focusing power. Finally, we present <i>SpiralFresnelFrenzy</i>, a web app that allows interactive and immersive raytracing simulations of the view through adaptive Fresnel lenses using augmented reality (AR) or virtual reality (VR). Our work significantly generalizes and improves spiral adaptive Fresnel lenses.