Conventional lenses are ultimately limited by geometry. Available design parameters are a single index of refraction (n) per lens element, variations in the element surface profile, including continuous surfaces (lens curvature) and/or discontinuous surfaces (diffractive optics). Light rays undergo refraction at the surfaces of each element, but travel in straight lines within the lens. Since the design space of conventional optics is limited to a combination of refractive index and surface structure, correcting for aberrations (for example through the use of achromatic or diffractive optics) leads to large, heavy, complex designs, and/or greater losses, lower image quality, and manufacturing difficulties.