  Wide field-of-view (FOV) optics are widely used in various imaging, display,
and sensing applications. While conventional wide FOV optics rely on cascading
multiple elements to suppress coma and other aberrations, it has recently been
demonstrated that diffraction-limited, near-180 degree FOV operation can be
achieved with a single-piece flat fisheye lens designed via iterative numerical
optimization [Nano Lett. 20, 7429(2020)]. Here we derive an analytical solution
to enable computationally efficient design of flat wide FOV lenses based on
metasurfaces or diffractive optical elements (DOEs). Leveraging this analytical
approach, we further quantified trade-offs between optical performance and
design parameters in wide FOV metalenses.
