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We proposed the use of relative encircled power as a measure of focusing efficiency [Optica7,252(2020)OPTIC82334-253610.1364/OPTICA.388697]. The comment [Optica8,1009(2021)OPTIC82334-253610.1364/OPTICA.416017] has raised useful questions, which we address briefly here and provide some clarifications.

We designed, fabricated, and characterized a flat multi-level diffractive lens comprised of only silicon with$\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}=15.2\mathrm{m}\mathrm{m}$, focal$\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}=19\mathrm{m}\mathrm{m}$, numerical aperture of 0.371, and operating over the long-wave infrared (LWIR)$\mathrm{s}\mathrm{p}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{m}=8\text{µ<\#comment/>}\mathrm{m}$to 14 µm. We experimentally demonstrated a field of view of 46°, depth of focus$><\#comment/>5\mathrm{m}\mathrm{m}$, and wavelength-averaged Strehl ratio of 0.46. All of these metrics were comparable to those of a conventional refractive lens. The active device thickness is only 8 µm, and its weight (including the silicon substrate) is less than 0.2 g.

Multilevel diffractive lenses (MDLs) have emerged as an alternative to both conventional diffractive optical elements (DOEs) and metalenses for applications ranging from imaging to holographic and immersive displays. Recent work has shown that by harnessing structural parametric optimization of DOEs, one can design MDLs to enable multiple functionalities like achromaticity, depth of focus, wide-angle imaging, etc. with great ease in fabrication. Therefore, it becomes critical to understand how fabrication errors still do affect the performance of MDLs and numerically evaluate the trade-off between efficiency and initial parameter selection, right at the onset of designing an MDL, i.e., even before putting it into fabrication. Here, we perform a statistical simulation-based study on MDLs (primarily operating in the THz regime) to analyse the impact of various fabrication imperfections (single and multiple) on the final structure as a function of the number of ring height levels. Furthermore, we also evaluate the performance of these same MDLs with the change in the refractive index of the constitutive material. We use focusing efficiency as the evaluation criterion in our numerical analysis; since it is the most fundamental property that can be used to compare and assess the performance of lenses (and MDLs) in general designed for any application with any specific functionality.

Compound eyes found in insects provide intriguing sources of biological inspiration for miniaturized imaging systems. Inspired by such insect eye structures, we demonstrate an ultrathin arrayed camera enabled by a flat multi-level diffractive microlens array for super-resolution visible imaging. We experimentally demonstrate that the microlens array can achieve a large fill factor (hexagonal close packing with$\mathrm{p}\mathrm{i}\mathrm{t}\mathrm{c}\mathrm{h}=120\text{µ<\#comment/>}\mathrm{m}$), thickness of 2.6 µm, and diffraction-limited ($\mathrm{S}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{h}\mathrm{l}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}=0.88$) achromatic performance in the visible band (450 to 650 nm). We also demonstrate super-resolution imaging with resolution improvement of$\sim <\#comment/>1.4$times by computationally merging 1600 images in the array.