In recent years there has been a lot of interest in flat lenses, a category that includes diffractive lenses and metalenses. These lenses have the potential of reducing the size and cost of optical systems by replacing conventional refractive optical elements. A major obstacle to the widespread use of flat lenses is their inherent large chromatic aberration, associated with diffraction effects. To meet this challenge, achromatic diffractive lenses and metalenses have been developed. In this paper we review previously reported metalens performance limits, derive limits on the performance of achromatic diffractive lenses, and compare the two. We show that such lenses can support a wide spectral range, limited only by loss of efficiency caused by manufacturing limitations related to feature depth and size. On the other hand, we show that these lenses can provide near-diffraction-limited performance only at very low Fresnel numbers, i.e., they cannot provide large focusing power and broadband response simultaneously. We then go on to compare the limits of achromatic metalenses and diffractive lenses, in attempt to understand the potential of different types of flat lenses. Our findings facilitate better understanding of flat lens capabilities and limitations, and the exploration of novel design concepts and applications.
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