Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations — TEI-tagged view

Amir ArbabipersName, Ehsan ArbabipersName, Seyedeh Mahsa KamalipersName, Yu HoriepersName, Seunghoon HanpersName, Andrei FaraonpersName (2016date). “Miniature optical planar camera based on a wide-angle metasurface doublet corrected for monochromatic aberrations.” Nature Communicationstitle·j.

Object of study — a monolithic metasurfaceterm·key doublet lensterm·dom integrated with an image sensorterm·key as a miniature camera

Research question — how to correct the off-axis monochromatic aberrationsterm·key that limit metasurfaceterm·key lenses in imaging

Contribution — a cascaded metasurfaceterm·key doublet corrected over a wide range of incident angles, and a planar camera built on it

Full text — tagged

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Miniature optical planar camera based on a wide-angle metasurfaceterm·key doublet corrected for monochromatic aberrationsterm·key Abstract Optical metasurfacesterm·dom are two-dimensional arrays of nano-scatterers that modify optical wavefronts at subwavelength spatial resolution. They are poised to revolutionize optics by enabling complex low-cost systems where multiple metasurfacesterm·key are lithographically stacked and integrated with electronics. For imaging applications, metasurfaceterm·key stacks can perform sophisticated image corrections and can be directly integrated with image sensorsterm·key. Here we demonstrate this concept with a miniature flat camera integrating a monolithic metasurfaceterm·key lens doublet corrected for monochromatic aberrationsterm·key, and an image sensorterm·key. The doublet lensterm·dom, which acts as a fisheyeterm·key photographic objective, has a small f -number of 0.9, an angle-of-view larger than 60° × 60°, and operates at 850 nm wavelength with 70% focusing efficiencyterm·key. The camera exhibits nearly diffraction-limited image qualityterm·mth, which indicates the potential of this technology in the development of optical systems for microscopy, photography, and computer vision.

Optical systems such as cameras, spectrometers and microscopes are conventionally made by assembling discrete bulk optical components like lenses, gratings and filters. The optical components are manufactured separately using cutting, polishing and grinding, and have to be assembled with tight alignment tolerances, a process that is becoming more challenging as the optical systems shrink in size. Furthermore, the continuous progress of mobile, wearable, and portable consumer electronics and medical devices has rapidly increased the demand for high-performance and low-cost miniature optical systems. Optical metasurfacesterm·dom offer an alternative approach for realization of optical components 1 2 3 4 5 . Recent advances have increased their efficiency and functionalities, thus allowing metasurfaceterm·key diffractive optical components with comparable or superior performance than conventional optical components 6 7 8 9 10 . The main advantage of metasurfacesterm·key stems from the capability to make sophisticated planar optical systems composed of lithographically stacked electronic and metasurfaceterm·key layers. The resulting optical system is aligned lithographically, thus eliminating the need for post-fabrication alignments.

The development of the optoelectronic image sensorterm·key has been a significant step towards the on-chip integration of cameras 11 ; however, the camera lenses are yet to be fully integrated with the image sensorterm·key. The freedom in controlling the metasurfaceterm·key phase profiles has enabled the implementation of spherical-aberration-free flat lenses that focus normally incident light to diffraction limitedterm·key spots 7 12 13 14 . Such lenses have been used in applications requiring focusing of an optical beam or collimating emission from an optical fibre 15 or a semiconductor laser 10 . However, the metasurfaceterm·key lenses suffer from other monochromatic aberrationsterm·key (i.e., coma and astigmatism), which reduce their field of view and hinder their adoption in imaging applications where having a large field of view is an essential requirement. A metasurfaceterm·key lens can be corrected for coma if it is patterned on the surface of a sphere 16 17 18 , but direct patterning of nano-structures on curved surfaces is challenging. Although conformal metasurfacesterm·key might provide a solution 19 , the resulting device would not be flat. As we show here, another approach for correcting monochromatic aberrationsterm·key of a metasurfaceterm·key lens is through cascading and forming a metasurfaceterm·key doublet lensterm·dom.

Here we show that a doublet lensterm·dom formed by cascading two metasurfacesterm·key can be corrected over a wide range of incident angles. We also demonstrate an ultra-slim, low f -number camera, composed of two metasurfaceterm·key lenses placed on top of an image sensorterm·key. The camera represents an example of the optical systems enabled by the metasurfaceterm·key vertical integration platform.

Results Design and optimization of the metasurfaceterm·key doublet lensterm·dom Figure 1a schematically shows focusing by a spherical-aberration-free metasurfaceterm·key lens. Simulated focal spots for such a lens are shown in Fig. 1b , exhibiting diffraction limitedterm·key focusing for normal incidence and significant aberrations for incident angles as small as a few degrees. The proposed doublet lensterm·dom ( Fig. 1c ) is composed of two metasurfacesterm·key behaving as polarization insensitive phase plates that are patterned on two sides of a single transparent substrate. The aberrations of two cascaded phase plates surrounded by vacuum have been studied previously in the context of holographic lenses, and it has been shown that such a combination can realize a fisheyeterm·key lens with significantly reduced monochromatic aberrationsterm·key 20 . We used the ray tracing approach to optimize the phase profiles of the two metasurfacesterm·key when they are separated by a 1-mm-thick fused silica substrate. Simulation results of the focal plane spot for different incident angles ( θ ) are presented in Fig. 1d , showing nearly diffraction limitedterm·key focusing by the doublet up to almost 30° incident angle. The doublet lensterm·dom has an input aperture diameter of 800 μm and a focal length of 717 μm corresponding to an f -number of 0.9. In the optimum design, the first metasurfaceterm·key operates as a corrector plate and the second one performs the significant portion of focusing; thus, we refer to them as correcting and focusing metasurfacesterm·key, respectively. The metasurfacesterm·key are designed for the operation wavelength of 850 nm, and are implemented using the dielectric nano-postterm·key metasurfaceterm·key platform shown in Fig. 2a (ref. 7 ). The metasurfacesterm·key are composed of hexagonal arrays of amorphous silicon nano-poststerm·key with different diameters that rest on a fused silica substrate and are covered by the SU-8 polymer. The nano-poststerm·key behave as truncated waveguides with circular cross sections supporting Fabry–Pérot resonances 7 9 19 . The high refractive index between the nano-poststerm·key and their surroundings leads to weak optical coupling among the nano-poststerm·key and allows for the implementation of any phase profile with subwavelength resolution by spatially varying the diameters of the nano-poststerm·key. Simulated intensity transmission and phase of the transmission coefficient for different nano-postterm·key diameters are presented in Fig. 2b , showing that 2 π phase coverage is achieved with an average transmission over 96% (see Methods for details).

Device fabrication We fabricated the metasurfacesterm·key on both sides of a fused silica substrate by depositing amorphous silicon and defining the nano-postterm·key pattern using e-beam lithography and dry etching (see Methods for the details). First, the correcting metasurfacesterm·key were patterned on the top side of the substrate, and then the focusing metasurfacesterm·key were aligned and patterned on the substrate's bottom side (as schematically shown in Fig. 2c ). To protect the metasurfacesterm·key while processing the other side of the substrate, the metasurfacesterm·key were cladded by a layer of cured SU-8 polymer. Aperture and field stops were formed by depositing and patterning opaque metal layers on the top and bottom sides of the substrate, respectively, and anti-reflection layers were coated on both sides of the device. Photos of the top and bottom sides of a set of fabricated metasurfaceterm·key doublet lensesterm·dom are shown in Fig. 2c . Scanning electron microscope images of the nano-poststerm·key are shown in Fig. 2d .

Focal spot and focusing efficiencyterm·key characterizations We characterized the fabricated metasurfaceterm·key doublet by illuminating it with an 850 nm laser beam at different incident angles (as shown in Fig. 3a ), and measuring its focal spot and focusing efficiencyterm·key. For comparison, a spherical-aberration-free singletterm·dom metasurfaceterm·key lens with the same aperture diameter and focal length as the doublet lensterm·dom (phase profile , ρ : radial coordinate, f =717 μm: focal length, D =800 μm: aperture diameter) was also fabricated and characterized. The focal spots of the metasurfaceterm·key doublet and singletterm·dom lenses were measured with two different polarizations of incident light and are shown along with the corresponding simulation results in Fig. 3b,c , respectively (see Methods for details). The doublet lensterm·dom has a nearly diffraction limitedterm·key focal spot for incident angles up to more than 25° (with the criterion of Strehl ratio of larger than 0.9, see Supplementary Fig. 1 ) while the singletterm·dom exhibits significant aberrations even at incident angles of a few degrees. As Fig. 3b,c shows, simulated and measured spot shapes agree well. For the doublet lensterm·dom, a small asymmetry in the 0° spot shape and slightly larger aberrations are observed in the measured spots compared with the simulation results, which we attribute to a misalignment (estimated ∼2 μm along both x and y directions) between the top and bottom side patterns ( Supplementary Fig. 2 ).

The focusing efficiencyterm·key (ratio of the focused power to the incident power) for the metasurfaceterm·key doublet lensterm·dom is shown in Fig. 3d , and is ∼70% for normally incident light. The focusing efficiencyterm·key is polarization dependent, and its value for unpolarized light drops at the rate of ∼1% per degree as the incident angle increases. The measured focusing efficiencyterm·key at normal incidence is lower than the average of the transmission shown in Fig. 2b because of the large numerical aperture (NA) of the focusing metasurfaceterm·key 7 , undesired scattering due to the sidewall roughness of the nano-poststerm·key, residual reflection at the air/SU-8 interfaces, and measurement artefacts (see Methods for details). The metasurfacesterm·key are polarization insensitive at normal incidence, but their diffraction efficiency depends on the polarization of incident light for non-zero incident angles. The focusing efficiencyterm·key is lower for the transverse magnetic polarized light compared with the transverse electric polarized light because of the excitation of some resonances of the nano-poststerm·key with the axial component of the electric field of the incident light 19 . This also causes the slight difference between the transverse electric and transverse magnetic spot shapes for the 30° incident light shown in Fig. 3b . We measured a focusing efficiencyterm·key of ∼75% for the singletterm·dom, and did not observe a detectable difference between the focal spots measured with transverse electric and transverse magnetic polarizations. The measured relative location of the doublet lensterm·dom focal spot as a function of incident angle is shown in Fig. 3e along with the f sin( θ ) curve. The good agreement between the measured data and the curve indicates that the metasurfaceterm·key doublet lensterm·dom can be used as an orthographic fisheyeterm·key lens or a wide angle Fourier transform lens 20 . Also, the specific f sin( θ ) fisheyeterm·key distortion of the image leads to a uniform brightness over the image plane 21 .

Imaging performance We characterized the imaging performance of the metasurfaceterm·key doublet lensterm·dom using the experimental setup shown in Fig. 4a . A pattern printed on a letter-size paper was used as an object. The object was placed ∼25 cm away from the metasurfaceterm·key doublet lensterm·dom and was illuminated by an LED (centre wavelength: 850 nm, bandwidth: 40 nm, spectrum shown in Supplementary Fig. 3 ). The image formed by the doublet lensterm·dom was magnified by approximately × 10 using an objective and a tube lens and captured by a camera. A bandpass filter with 10 nm bandwidth (see Supplementary Fig. 3 for the spectrum) was used to spectrally filter the image and reduce the effect of chromatic aberrationterm·dom on the image qualityterm·mth. Figure 4b shows the image captured by the camera, and its insets depict the zoomed-in views of the image at 0°, 15° and 30° view angles. For comparison, an image captured using the same setup but with the metasurfaceterm·key singletterm·dom lens is shown in Fig. 4c . The objective lens used for magnifying the images has a smaller NA than the metasurfaceterm·key lenses and limits the resolution of the captured images (see Supplementary Fig. 4 for an image taken with a higher NA objective).

Any imaging system can be considered as low pass spatial filter whose transfer function varies across the field of view. For incoherent imaging systems, the transfer function for each point in the field of view can be obtained by computing the Fourier transform of the focal spot intensity. The modulus of this transfer function is referred to as the modulation transfer functionterm·mth (MTFterm·mth) and represents the relative contrast of the image versus the spatial details of the object. The MTFsterm·mth for the metasurfaceterm·key doublet and singletterm·dom lenses were computed using the measured focal spots ( Fig. 3b,c ) and are shown in Fig. 4d,e , respectively. Both the images and the MTFsterm·mth shown in Fig. 4b–e demonstrate the effectiveness of correction achieved by cascading two metasurfacesterm·key, and the diffraction limitedterm·key performance of the metasurfaceterm·key doublet lensterm·dom over a wide field of view.

Miniature metasurfaceterm·key camera To further demonstrate the use of this technology in imaging applications, we realized a miniature planar camera by using a metasurfaceterm·key doublet lensterm·dom and a CMOS image sensorterm·key as schematically shown in Fig. 4f . To compensate for the light propagating through the cover glass protecting the image sensorterm·key, another doublet lensterm·dom was optimized (see Metasurfaceterm·key Doublet Lensterm·dom II in Supplementary Fig. 5 ). The total dimensions of the camera (including the image sensorterm·key) are 1.6 mm × 1.6 mm × 1.7 mm. The miniature camera was characterized using the setup shown in Fig. 4g and by imaging the object shown in Fig. 4a , which was illuminated by a filtered LED (centre wavelength: 850 nm, bandwidth: 10 nm, see Supplementary Fig. 3 for the spectrum). The image captured by the image sensorterm·key is also shown in Fig. 4g , which shows a wide field of view. The camera's image qualityterm·mth is reduced by the nonuniform sensitivity of the image sensorterm·key pixels to the 850 nm light due to the colour filters, and by its larger-than-optimal pixel size. Therefore, the image qualityterm·mth can be improved by using a monochromatic image sensorterm·key with a smaller pixel size (the optimum pixel size for the miniature camera is ∼0.4 μm based on the MTFsterm·mth shown in Fig. 4d ). Thus, the miniature camera benefits from the current technological trend in pixel size reduction.

The intensity of the image formed by a camera only depends on the NA of its lens (it is proportional to 1/ f -number 2 =4NA 2 (ref. 22 )); therefore, the metasurfaceterm·key miniature camera collects a small optical power but forms a high brightness image. Furthermore, the metasurfaceterm·key doublet lensterm·dom is telecentric in the image space, and light is incident on the image sensorterm·key with the uniform angular distribution ( Supplementary Fig. 5 ), and thus removing the need for the variable incident angle correction in the image sensorterm·key.

Correcting chromatic abberations The metasurfaceterm·key doublet lensterm·dom suffers from chromatic aberrationsterm·dom that reduce the image qualityterm·mth of the miniature camera as the illumination bandwidthterm·mth increases. Simulated focal spots of the metasurfaceterm·key doublet lensterm·dom for different illumination bandwidthsterm·mth and the corresponding MTFsterm·mth are shown in Fig. 5a,b , respectively. See Supplementary Fig. 6 for the off-axis MTFsterm·mth. As it can be seen from the MTFsterm·mth, the imaging resolutionterm·mth decreases as the illumination bandwidthterm·mth increases. This effect can be seen as reduced contrast and lower resolution in the image shown in Fig. 5c (40 nm bandwidth illumination) compared with the image shown in Fig. 5d (10 nm bandwidth illuminations). For the imaging purpose, the fractional bandwidth of a metasurfaceterm·key lens is proportional to ( Supplementary Note 1 ) and can be increased by reducing the NA of the metasurfaceterm·key lens and its focal length. Also, since the MTFsterm·mth of the metasurfaceterm·key doublet lensterm·dom shown in Fig. 5b have significant high-frequency components, the unfavourable effect of chromatic aberrationterm·dom can to some extent be corrected using Wiener deconvolution 23 . Figure 5e shows the deconvolution results of the image shown in Fig. 5c that is taken with a 40-nm-bandwidth illumination (see Methods for the details). As expected, the deconvolved image appears sharper and has a higher contrast than the original image; however, deconvolution also amplifies the noise, limiting its applicability for correcting the chromatic aberrationsterm·dom over a significantly wider bandwidth.

Discussion The metasurfaceterm·key doublet lensterm·dom and camera can be further miniaturized by reducing the thickness of the substrate, the diameters of the metasurfaceterm·key lenses, the focal length of the lens, and the distance to the image sensorterm·key by the same scale factor, while using the same nano-postterm·key metasurfaceterm·key design presented in Fig. 2 . For example, a 10 × smaller camera (160 μm × 160 μm × 170 μm) can be designed and fabricated using a similar procedure on a 100-μm-thick fused silica substrate. Such a camera would have 10 × larger bandwidth compared with the miniature camera presented here, the same image plane intensity, but with 10 × smaller image and 100 × lower number of distinguishable pixels (94 × 94 pixels instead of 940 × 940). Compared with other miniature lenses reported previously 24 25 26 and Awaiba NanEye camera ( http://www.awaiba.com ), the metasurfaceterm·key doublet offers significantly smaller f -number and better correction for monochromatic aberrationsterm·key that lead to brighter images with higher resolution; however, they have larger chromatic aberrationterm·dom (that is, narrower bandwidth).

The miniature metasurfaceterm·key camera concept can be extended for colour and hyperspectral imaging by using a set of metasurfacesterm·key that are designed for different centre wavelengths and fabricated side by side on the same chip. Each of the metasurfaceterm·key doublet lensesterm·dom forms an image on a portion of a single monochromatic image sensorterm·key. High-quality thin-film colour filters with different centre wavelengths can be directly deposited on the correcting metasurfaceterm·key of each doublet lensterm·dom, and the colour filter efficiency issues associated with small size colour filters will be avoided 27 28 . Also, multiwavelength metasurfaceterm·key lenses that work at multiple discrete wavelengths have been demonstrated 29 30 31 32 . However, the multiwavelength metasurfacesterm·key exhibit the same chromatic dispersion (that is, ) and thus similar chromatic aberrationsterm·dom as the single wavelength metasurfaceterm·key lenses. The amorphous silicon metasurfacesterm·key have negligible absorption loss for wavelengths above 650 nm. For shorter wavelengths, materials with lower absorption loss such as polycrystalline silicon, gallium phosphide, titanium dioxide 33 34 or silicon nitride 35 36 can be used.

The metasurface-enabled camera we reported here has a flat and thin form factor, small f -number, and exhibits nearly diffraction limitedterm·key performance over a large field of view. From a manufacturing standpoint, the metasurfaceterm·key doublets have several advantages over conventional lens modules. Conventional lens modules are composed of multiple lenses that are separately manufactured and later aligned and assembled together to form the module. On the other hand, the metasurfaceterm·key doublets are batch manufactured with simultaneous fabrication of tens of thousands of doublets on each wafer, and with the metasurfacesterm·key aligned to each other using lithographic steps during fabrication. Furthermore, the assembly of the conventional lens modules with the image sensorsterm·key has to be done in a back-end step, but the metasurfaceterm·key doublet can be monolithically stacked on top of image sensorsterm·key. More generally, this work demonstrates a vertical on-chip integration architecture for designing and manufacturing optical systems, which is enabled through high performance metasurfacesterm·key. This architecture will enable low-cost realization of conventional optical systems (for example, spectrometers, 3D scanners, projectors, microscopes and so on), and systems with novel functionalities in a thin and planar form factor with immediate applications in medical imaging and diagnostics, surveillance and consumer electronics.

Methods Simulation and design The phase profiles of the two metasurfacesterm·key composing the doublet lensesterm·dom were obtained through the ray tracing technique using a commercial optical design software (Zemax OpticStudio, Zemax LLC). The phase profiles were defined as even order polynomials of the radial coordinate ρ as where R is the radius of the metasurfaceterm·key, and the coefficients a n were optimized for minimizing the focal spot size (root mean square spot size) at incident angles up to 30°. Two different metasurfaceterm·key doublet lensesterm·dom were designed. The first doublet lensterm·dom (metasurfaceterm·key doublet lensterm·dom I) is optimized for focusing incident light in air, and was used in measurements shown in Figs 3 and 4b,d . The second doublet lensterm·dom (metasurfaceterm·key doublet lensterm·dom II) is optimized for focusing through the ∼445-μm-thick cover glass of the CMOS image sensorterm·key, and was used in the implementation of the miniature camera as shown in Fig. 4f,g . The optimal values of the coefficients for the two doublet lensesterm·dom are listed in Supplementary Tables 1 and 2 , and the corresponding phase profiles are plotted in Supplementary Fig. 7 . The phase profile for the spherical-aberration-free metasurfaceterm·key singletterm·dom is given by , where f =717 μm is the focal length of the singletterm·dom (which is the same as the focal length of the doublet lensterm·dom I).

The simulation results shown in Figs 1b,d and 2b,c and Supplementary Fig. 2 were computed assuming the metasurfacesterm·key operate as ideal phase masks (that is, their phase profile is independent of the incident angle). Incident light was modelled as a plane wave and optical waves passing through the metasurfacesterm·key were propagated through the homogeneous regions (that is, fused silica and air) using the plane wave expansion technique 37 . The simulated focal plane intensity results for wideband incident light, which are shown Fig. 5a , were obtained by computing a weighted average of the optical intensity at several discrete wavelengths in the bandwidth of the incident light. The weights were chosen according to the power density of incident light ( Fig. 5a , bottom) assuming the diffraction efficiency of the metasurfacesterm·key is constant over the incident light's bandwidth. This assumption is justified because the efficiency of dielectric nano-postterm·key metasurfacesterm·key does not vary significantly over ∼10% fractional bandwidth 7 . The simulated bandwidth-dependent modulation transfer functionterm·mth of the metasurfaceterm·key doublet lensterm·dom shown in Fig. 5b and Supplementary Fig. 6 were obtained by taking the Fourier transform of the simulated focal plane intensity distributions presented in Fig. 5a .

Simulated transmission data of the periodic array of amorphous silicon nano-poststerm·key presented in Fig. 2b were obtained by using the rigorous coupled wave analysis technique using a freely available software package 38 . The simulations were performed at . The amorphous silicon nano-poststerm·key (with refractive index of 3.6 at 850 nm) are 600 nm tall, rest on a fused silica substrate (refractive index of 1.45), and are cladded with a layer of the SU-8 polymer (refractive index of 1.58 at 850 nm). The imaginary part of the refractive index of amorphous silicon is smaller than 10 −4 at 850 nm and was ignored in the simulations. The nano-poststerm·key are arranged in a hexagonal lattice with the lattice constant of a =450 nm. For normal incidence, the array is non-diffractive in both SU-8 and fused silica at wavelengths longer than . The refractive indices of amorphous silicon and SU-8 polymer were obtained through variable angle spectroscopic measurements.

The metasurfaceterm·key patterns were generated using their phase profiles and the relation between the transmission and the diameter of the nano-poststerm·key shown in Fig. 2b . The diameter of the nano-postterm·key at each lattice site ( d ) was chosen to minimize the transmission error defined as , which is the difference between the nano-postterm·key transmission t ( d ) and the desired transmission . The nano-poststerm·key diameters corresponding to low transmission, which are highlighted in Fig. 2b , are automatically avoided in this selection process, as the low transmission amplitude results in a large transmission error.

Device fabrication The metasurfacesterm·key forming the doublet lensesterm·dom shown in Fig. 2c were fabricated on both sides of a 1-mm-thick fused silica substrate. The substrate was cleaned using a piranha solution and an oxygen plasma. A 600-nm-thick layer of hydrogenated amorphous silicon was deposited on each side of the substrate using the plasma enhanced chemical vapour deposition technique with a 5% mixture of silane in argon at 200 °C. Next, the nano-postterm·key patterns for the correcting metasurfacesterm·key were defined on one side of the substrate as follows. First a ∼300-nm-thick positive electron resist (ZEP-520A) was spin coated on the substrate and baked at 180 ° C for 5 min. Then a ∼60-nm-thick layer of a water soluble conductive polymer (aquaSAVE, Mitsubishi Rayon) was spin coated on the resist to function as a charge dissipating layer during electron-beam patterning. The metasurfaceterm·key patterns and alignment marks were written on the resist using electron-beam lithography. The conductive polymer was then dissolved in water and the resist was developed in a resist developer solution (ZED-N50, Zeon Chemicals). A 70-nm-thick layer of aluminium oxide was deposited on the resist and was patterned by lifting-off the resist in a solvent (Remover PG, MicroChem). The patterned aluminium oxide was then used as the hard mask in dry etching of the underlying amorphous silicon layer. The dry etching was performed in a mixture of SF 6 and C 4 F 8 plasmas using an inductively coupled plasma reactive ion etching process. Next, the aluminium oxide mask was dissolved in a 1:1 mixture of ammonium hydroxide and hydrogen peroxide heated to 80 °C. Figure 2d shows scanning electron micrographs of the top and oblique view of the nano-poststerm·key at this step of the fabrication process. The metasurfacesterm·key were then cladded by the SU-8 polymer (SU-8 2002, MicroChem) that acts as a protective layer for the metasurfacesterm·key during the processing of the substrate's backside. A ∼2-μm-thick layer of SU-8 was spin coated on the sample, baked at 90 °C for 5 min, and reflowed at 200 °C for 30 min to achieve a completely planarized surface. The SU-8 polymer was then ultraviolet exposed and cured by baking at 200 °C for another 30 min. The complete planarization of the metasurfacesterm·key, and the void-free filling of the gaps between the nano-poststerm·key were verified by cleaving a test sample fabricated using a similar procedure and inspecting the cleaved cross section using a scanning electron microscope.

The focusing metasurfacesterm·key were patterned on the backside of the substrate using a procedure similar to the one used for patterning the correcting metasurfacesterm·key. To align the top and bottom metasurfaceterm·key patterns, a second set of alignment marks was patterned on the backside of the substrate and aligned to the topside alignment marks using optical lithography. The focusing metasurfaceterm·key pattern was subsequently aligned to these alignment marks. The aperture and field stops were then patterned by photo-lithography, deposition of chrome/gold (10 nm/100 nm) layers, and photoresist lift-off. To reduce the reflection at the interface between SU-8 and air, a ∼150-nm-thick layer of hydrogen silsesquioxane (XR-1541 from Dow Corning with refractive index of 1.4 at 850 nm) was spin coated on both sides of the substrate and baked at 180 °C for 5 min.

Systematic fabrication errors due to non-optimal exposure dose in e-beam lithography, or over and under etching will generally increase or decrease the nano-postterm·key diameters almost by the same amount. To compensate for such errors, we fabricated a set of devices (as shown in Fig. 2c ) with all nano-postterm·key diameters biased by the same amount (in steps of 5 nm) from their design values. All the devices in the set showed similar focal spots, but with different focusing efficiencies. The focusing efficiencyterm·key at normal incidence decreased by ∼2.5% for every 5 nm error in the nano-postterm·key diameters.

Measurement procedure and data analysis The measurement results shown in Fig. 3b–e were obtained using the experimental setup schematically shown in Fig. 3a . An 850 nm semiconductor laser (Thorlabs L850P010, measured spectrum shown in Supplementary Fig. 3 ) was coupled to a single mode fibre. The fibre passed through a manual polarization controller and was connected to a fibre collimation package (Thorlabs F220APC-780, 1/ e 2 beam diameter: ∼2.3 mm). The collimated beam was passed through a linear polarizer (Thorlabs LPNIR050-MP) that sets the polarization of light incident on the doublet. The collimator and the polarizer were mounted on a rotation stage whose rotation axis coincides with the metasurfaceterm·key doublet lensterm·dom. The focal plane of the doublet lensterm·dom was imaged using an objective lens, a tube lens (Thorlabs AC254-200-B, focal length: 20 cm) and a camera (Photometrics CoolSNAP K4, pixel size: 7.4 μm). A × 100 objective lens (Olympus UMPlanFl, NA=0.95) was used in measurements shown in Fig. 3b–d , and a × 50 objective lens (Olympus LMPlanFl N, NA=0.5) with a larger field of view was used for obtaining the focal spot position data shown in Fig. 3e . A calibration sample with known feature sizes was used to accurately determine the magnification of the objective/tube lens combination for both of the objectives. The dark noise of the camera was subtracted from the measured intensity images shown in Fig. 3b,c .

The focusing efficiencyterm·key presented in Fig. 3d is defined as the ratio of the optical power focused by the lens to the optical power incident on the lens aperture. The focusing efficiencyterm·key for the normal incidence (zero incident angle) was measured by placing a 15-μm-diameter pinhole in the focal plane of the doublet lensterm·dom and measuring the optical power passed through the pinhole and dividing it by the power of the incident optical beam. For this measurement, the 1/ e 2 diameter of the incident beam was reduced to ∼500 μm by using a lens (Thorlabs LB1945-B, focal length: 20 cm) to ensure that more than 99% of the incident power passes through the aperture of the doublet lensterm·dom (800 μm input aperture diameter). The incident and focused optical powers were measured using an optical power meter (Thorlabs PM100D with Thorlabs S122C power sensor). The pinhole was a 15-μm-diameter circular aperture formed by depositing ∼100 nm chrome on a fused silica substrate and had a transmission of ∼94% (that is, 6% of the power was reflected by the two fused silica/air interfaces), therefore the reported focusing efficiencyterm·key values presented in Fig. 3d underestimate the actual values by a few percent.

The focusing efficiencyterm·key values for non-zero incident angles were found using the focal spot intensity distributions captured by the camera and the directly measured focusing efficiencyterm·key for normal incidence. First, the focused optical powers for different incident angles were obtained by integrating the focal plane intensity distributions within a 15-μm-diameter circle centred at the intensity maximum. The intensity distributions were captured by the camera when the doublet was illuminated by a large diameter beam (1/ e 2 beam diameter of ∼2.3 mm) and the dark noise of the camera was subtracted from the recorded intensities before integration. Next, the focused optical powers for different incident angles were compared with the focused power at normal incidence and corrected for the smaller effective input aperture (that is, a cos( θ ) factor). The measurement was performed for transverse electric (with electric field parallel to the doublet lensterm·dom's surface) and transverse magnetic (with magnetic field parallel to the doublet lensterm·dom's surface) polarizations of the incident beam.

The images presented in Fig. 4b,c were captured using the experimental setup schematically shown in Fig. 4a . A pattern was printed on a letter-size paper (∼22 cm × 28 cm) and used as an object. The object was placed in front of the metasurfaceterm·key lens at a distance of ∼25 cm from it. Three ruler marks were also printed as a part of the pattern at viewing angles of 0°, 15° and 30°. The object was illuminated by an 850 nm LED (Thorlabs LED851L, measured spectrum shown in Supplementary Fig. 3 ). The images formed by the metasurfaceterm·key lenses were magnified by approximately × 10 using an objective lens (Olympus UMPlanFl, × 10, NA=0.3) and a tube lens (Thorlabs AC254-200-B, focal length: 20 cm). A bandpass filter (Thorlabs FL850-10, centre wavelength: 850 nm, full width at half maximum (FWHM) bandwidth: 10 nm) was placed between the objective lens and the tube lens. The placement of the filter between the objective and the tube lens did not introduce any discernible aberrations to the optical system. The magnified images were captured using a camera (Photometrics CoolSNAP K4) with pixel size of 7.4 μm. The images shown in Fig. 5c,d and Supplementary Fig. 4 were also captured using the same setup but with different objective lenses (Olympus LMPlanFl, × 20, NA=0.4 for Fig. 5c,d and Olympus LMPlanFl N, × 50, NA=0.5 for Supplementary Fig. 4 ).

The miniature camera schematically shown in Fig. 4f is composed of the metasurfaceterm·key doublet lensterm·dom II (with parameters listed in Supplementary Table 2 ) and a low-cost colour CMOS image sensorterm·key (OmniVision OV5640, pixel size: 1.4 μm) with a cover glass thickness of 445±20 μm. An air gap of 220 μm was set between the metasurfaceterm·key doublet lensterm·dom and the image sensorterm·key to facilitate the assembly of the camera. The metasurfaceterm·key doublet was mounted on a 3-axis translation stage during the measurements. To set the distance between the image sensorterm·key chip and the doublet, a far object was imaged and the distance was adjusted until the image was brought into focus.

The modulation transfer functionsterm·mth shown in Fig. 4d,e were computed by taking the Fourier transform of the measured focal plane intensity distributions shown in Fig. 3b,c , respectively. The dark noise of the camera was first subtracted from the recorded intensity distributions. The diffraction limit curves shown in Fig. 4d,e are the simulated modulation transfer functionterm·mth of a diffraction limitedterm·key lens (that is, Fourier transform of the diffraction limitedterm·key Airy disk) with the same focal length ( f =717 μm) and aperture diameter ( D =800 μm) as the metasurfaceterm·key doublet and singletterm·dom lenses used in the measurements.

The image shown in Fig. 5e was obtained using Wiener deconvolution 23 , and by filtering the image shown in Fig. 5c by the Wiener filter where is the spatial frequency, is the on-axis modulation transfer functionterm·mth of the metasurfaceterm·key doublet lensterm·dom for illumination with 40 nm FWHM bandwidth (shown in Fig. 5b ), and and are the power spectral densities of the noise and the image, respectively. The noise was assumed to be white (that is, constant power spectral density), and was assumed to be equal to the power spectral density of an image formed with a diffraction limitedterm·key imaging system with NA=0.4 (that is, the NA of the objective lens used for magnification in the experimental setup). The signal to noise ratio was found as ∼250 by estimating the camera's noise, and was used to set the constant value for .

Data availability The data that support the finding of this study are available from the corresponding author upon request.

Additional information How to cite this article: ArbabipersName, A. et al . Miniature optical planar camera based on a wide-angle metasurfaceterm·key doublet corrected for monochromatic aberrationsterm·key. Nat. Commun. 7, 13682 doi: 10.1038/ncomms13682 (2016).

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Supplementary Material Supplementary Figures 1-7, Supplementary Tables 1-2, Supplementary Note 1 and Supplementary References