  Over the recent years, there have been many reports of achromatic metalenses
and diffractive lenses. However, very few (if any) practical applications of
such achromatic flat lenses have been demonstrated, which raises questions
about the potential of these lenses to provide solutions for real world cases
which involve broadband illumination. A recent paper placed limits on the
performance of achromatic metalenses. However, is this limit also valid for a
diffractive lens? Not necessarily so. In this paper we derive the limits on the
performance of achromatic diffractive lenses. In particular, we show that
achromatic diffractive lenses can cover 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 achromatic diffractive 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 may set the ground for better evaluation of
flat lens performance, understanding of their capabilities and limitations, and
for exploring novel design concepts and applications.
