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We demonstrate the implementation of a low-power, low-profile, varifocal liquid-crystal Fresnel lens stack suitable for tunable imaging in smart contact lenses. The lens stack consists of a high-order refractive-type liquid crystal Fresnel chamber, a voltage-controlled twisted nematic cell, a linear polarizer and a fixed offset lens. The lens stack has an aperture of 4 mm and thickness is ∼980 µm. The varifocal lens requires ∼2.5 V_RMSfor a maximum optical power change of ∼6.5 D consuming electrical power of ∼2.6 µW. The maximum RMS wavefront aberration error was 0.2 µm and the chromatic aberration was 0.008 D/nm. The average BRISQUE image quality score of the Fresnel lens was 35.23 compared to 57.23 for a curved LC lens of comparable power indicating a superior Fresnel imaging quality.

 

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.

 

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.

 

A lens performs an approximately one-to-one mapping from the object to the image plane. This mapping in the image plane is maintained within a depth of field (or referred to as depth of focus, if the object is at infinity). This necessitates refocusing of the lens when the images are separated by distances larger than the depth of field. Such refocusing mechanisms can increase the cost, complexity, and weight of imaging systems. Here we show that by judicious design of a multi-level diffractive lens (MDL) it is possible to drastically enhance the depth of focus by over 4 orders of magnitude. Using such a lens, we are able to maintain focus for objects that are separated by as large a distance as$\sim <\#comment/>6\mathrm{m}$in our experiments. Specifically, when illuminated by collimated light at$\mathrm{\lambda <\#comment/>}=0.85\text{µ<\#comment/>}\mathrm{m}$, the MDL produced a beam, which remained in focus from 5 to 1200 mm. The measured full width at half-maximum of the focused beam varied from 6.6 µm (5 mm away from the MDL) to 524 µm (1200 mm away from the MDL). Since the side lobes were well suppressed and the main lobe was close to the diffraction limit, imaging with a horizontal × vertical field of view of${40}^{\circ <\#comment/>}\times <\#comment/>{30}^{\circ <\#comment/>}$over the entire focal range was possible. This demonstration opens up a new direction for lens design, where by treating the phase in the focal plane as a free parameter, extreme-depth-of-focus imaging becomes possible.

 

Flat lenses enable thinner, lighter, and simpler imaging systems. However, large-area and high-NA flat lenses have been elusive due to computational and fabrication challenges. Here we applied inverse design to create a multi-level diffractive lens (MDL) with thickness$<<\#comment/>1.35\text{µ<\#comment/>}\mathrm{m}$, diameter of 4.13 mm, and$\mathrm{N}\mathrm{A}=0.9$at wavelength of 850 nm (bandwidth$\sim <\#comment/>35\mathrm{n}\mathrm{m}$). Since the MDL is created in polymer, it can be cost-effectively replicated via imprint lithography.

 

We experimentally demonstrate imaging in the long-wave infrared (LWIR) spectral band (8 μm to 12 μm) using a single polymer flat lens based upon multilevel diffractive optics. The device thickness is only 10 μm, and chromatic aberrations are corrected over the entire LWIR band with one surface. Due to the drastic reduction in device thickness, we are able to utilize polymers with absorption in the LWIR, allowing for inexpensive manufacturing via imprint lithography. The weight of our lens is less than 100 times those of comparable refractive lenses. We fabricated and characterized 2 different flat lenses. Even with about 25% absorption losses, experiments show that our flat polymer lenses obtain good imaging with field of view of 35° and angular resolution less than 0.013°. The flat lenses were characterized with 2 different commercial LWIR image sensors. Finally, we show that, by using lossless, higher-refractive-index materials like silicon, focusing efficiencies in excess of 70% can be achieved over the entire LWIR band. Our results firmly establish the potential for lightweight, ultrathin, broadband lenses for high-quality imaging in the LWIR band.