Full prescription corrected near-eye displays using two-dimensionally displaced Alvarez lenses

Vision correction needs to be integrated into near-eye displays (NEDs) because people with refractive errors cannot view NEDs while wearing spectacles. In particular, full prescription including spherical (defocused) and cylindrical (astigmatic) optical powers should be dynamically corrected. This study considers the Alvarez lenses due to their compactness and scalable fabrication; however, they cannot achieve full prescription correction because the traditional one-dimensional (1D) displacement only modulates a defocused wavefront. This study introduces displacement direction as an additional parameter to develop 2D Alvarez lenses. A mathematical framework is established to derive a surface equation that can correct arbitrary combinations of defocus and astigmatism. A pancake-based NED was adopted to verify the proposed Alvarez lenses through simulation and experiment for four typical prescriptions. Finally, an Apple Vision Pro integrated with fabricated Alvarez lenses (diameter: 36 mm; thickness: 6.5 mm) demonstrated that image quality was almost corrected to normal vision.