  Recently, there has been an explosion of interest in metalenses for imaging.
The interest is primarily based on their sub-wavelength thicknesses.
Diffractive lenses have been used as thin lenses since the late 19th century.
Here, we show that multi-level diffractive lenses (MDLs), when designed
properly can exceed the performance of metalenses. Furthermore, MDLs can be
designed and fabricated with larger constituent features, making them
accessible to low-cost, large area volume manufacturing, which is generally
challenging for metalenses. The support substrate will dominate overall
thickness for all flat optics. Therefore the advantage of a slight decrease in
thickness (from ~2{\lambda} to ~{\lambda}/2) afforded by metalenses may not be
useful. We further elaborate on the differences between these approaches and
clarify that metalenses have unique advantages when manipulating the
polarization states of light.
