Chip-scale metalens microscope for wide-field and depth-of-field imaging

Abstract. Microscopy is very important in research and industry, yet traditional optical microscopy suffers from the limited field-of-view (FOV) and depth-of-field (DOF) in high-resolution imaging. We demonstrate a simultaneous large FOV and DOF microscope imaging technology based on a chip-scale metalens device that is implemented by a SiNx metalens array with a co- and cross-polarization multiplexed dual-phase design and dispersive spectrum zoom effect. A 4-mm  ×  4-mm FOV is obtained with a resolution of 1.74  μm and DOF of 200  μm within a wavelength range of 450 to 510 nm, which definitely exceeds the performance of traditional microscopes with the same resolution. Moreover, it is realized in a miniaturized compact prototype, showing an overall advantage for portable and convenient microscope technology.


Introduction
Microscopes are important imaging tools that effectively expand the human eyes to the microworld for applications in scientific research, biomedical diagnosis, and industry. Besides the ultimate goal of superresolution, a new direction of this technique aims for wide field-of-view (FOV), large depth-offield (DOF), high throughput, and compactly portable performance. [1][2][3][4][5][6] Traditional optical microscopes are established based on refractive optical elements 7,8 that are usually bulky and heavy with limitations in FOV and DOF, although they have been substantially developed. A possible solution to miniaturizing the imaging system is to use flat diffractive lenses, but the quite low efficiency and poor imaging quality prevent its imaging applications. 9 Recent lensless imaging technology considerably revolutionizes the manner of imaging technology and enables the possibility of highly compact imaging devices. 3,[10][11][12] Nevertheless, it strongly depends on the postprocess computation that requires large resources and prior information with risk of artifacts in some cases.
In this work, we developed a polarizer-embedded metalens imaging device (PMID) that is implemented based on geometric silicon nitride (SiN x ) metasurfaces directly mounted on a CMOS image sensor. It is proved to significantly improve the imaging quality by eliminating the background noise, which enables zoomed-in imaging to reach a higher resolution. After a systematic characterization of the imaging performances from the singlet metalens, we extended it to a metalens array with two sets of polarization multiplexed focusing phases that work in coand cross-polarizations, respectively. Based on this design, the embedded circular polarization filter (CPF) can work for both orthogonal polarization illuminations to construct two sets of compensated subimages, which enables a stitched high-quality large FOV microscope image. Thanks to the broadband property, this metalens array inherits the dispersive spectral zoom effect 32,43 and shows the capability of large DOF imaging by tuning the illumination wavelength. A chip-scale (4 mm × 4 mm) FOV is obtained with the resolution of 1.74 μm (∼1.37 μm in theory, limited by the size of the image sensor pixel), DOF of ∼200 μm within a wavelength of 450 to 510 nm, which definitely exceeds the performance of traditional microscopes with the same resolution. Furthermore, it is fully implemented in a compact prototype with a light-emitting diode (LED) light source and a liquid-crystal polarization switch, which provides a non-mechanical, stable, and miniaturized microscope technique for portable and convenient applications. The chip-scale metalens and fixed CPF with a thickness of 220 μm are fixed on the CMOS image sensor (Imaging source: DMM 27UJ003-ML, pixel size: 1.67 μm × 1.67 μm) by two layers of optically clear adhesive tapes (OCA, thickness: 50 μm and 100 μm, Tesa, 69402). Here, the OCA works both as the connector and the spacer that determine the imaging distance (v), which is fixed in our chip-scale PMID. A photographic image is depicted in Fig. 1(b).

Device Architecture and Metalens Design
The phase profile of the metalens is designed according to the following hyperbolic distribution: 13 where λ is the design wavelength, x and y are the coordinates of each nanofin, and f is the focal length. This phase profile is imparted via the Pancharatnam-Berry (PB) phase. 16 Each nanofin of the metasurface is designed with a high-aspect-ratio rectangle with the same height (h ¼ 1 μm), length (l x ¼ 240 nm), width (l y ¼ 95 nm), and arranged in period of p ¼ 300 nm to satisfy the Nyquist-Shannon sampling theorem, 44 which operates as a half-wave-plate with a high transmission efficiency. SiN x (refractive index of 2.0 at 470 nm) was chosen because of its low loss in visible light and its potential compatibility with full CMOS-based devices. The polarization conversion ratio (PCR) of nanofins, which is the ratio of the transmitted optical power with opposite helicity to the total incident power, is calculated to be 99% at 470 nm by a commercial finite-difference time-domain (FDTD) solver (Lumerical Inc., Vancouver, Canada). Three distinct 250-μm-diameter metalenses were fabricated with focal lengths equal to 360, 330, and 250 μm, corresponding to magnifications of 1×, 2×, and 3×, respectively. All metalenses were fabricated using standard electron-beam lithography and dry etching in a 1-μm-thick SiN x film deposited on a fused silica substrate (refractive index of 1.48 at 470 nm, see Secs. S1 and S2 of the Supplementary Material). The inset of Fig. 1(b) shows the sideview scanning electron microscope (SEM) images of a fabricated SiN x metalens.

Imaging Characterization of Singlet-Metalens PMID
Before getting to the large FOV imaging device, first, we characterized the imaging performances of a singlet-metalens PMID, including the resolution, signal-to-noise ratio (SNR), modulation transfer function (MTF), and imaging bandwidth. The experimental details are provided in Sec. S1 and Fig. S2 Fig. 1(g). The MTFs of all metalenses are obtained by the slanted-edge method, 45 as shown in Fig. 1(f), which show a good agreement with theoretical MTF at a low spatial frequency in all metalenses. The discrepancies at a high spatial frequency probably contribute to the background noises. The slanted-edge method is to calculate the Fourier transform of the line spread function, which is the first derivative of the edge spread function (ESF) (i.e., MTF ¼ jF ½dESF∕dxj). Although the PMID has a fixed imaging distance, optical zoom can be realized to obtain depth information by tuning the working wavelength due to the chromatic dispersion of the metalens. The details are provided in Sec. S3 of the Supplementary Material.

Dual-Phase Design for Co-and Cross-Polarization
In our previous work, a polarization multiplexed dual-phase metalens array was proposed and implemented in the CMOS integrated imaging device. 36 It successfully expanded the FOV without increasing the working distance, and the intersecting dual-phase effectively compensated the blind areas in imaging stitching. However, the dual-phase design was based on two orthogonal polarizations that cannot work under a fixed CPF embedded in the integrated device. It led to a relatively poor imaging quality in imaging contrast and SNR, since the PB phase efficiency cannot reach the unity and results in inevitable background noises. Figure 1(d) has shown the significant improvements in PMID imaging quality by adding the CPF compared with that without CPF [see Fig. 1(c)], and it is necessary to validate it in the polarization multiplexed lens array. To circumvent this problem, we proposed a new kind of polarization multiplexed metalens design that can modulate the co-and cross-polarized light independently by combining the propagation and PB phase. In a circle base, the Jones matrix of nanofin in a metasurface describing the relation between the input electric field (E in ) and the output electric field (E out ) can be written as 27 where ϕ RR , ϕ RL , ϕ LR , and ϕ LL are the propagation phases, and RðθÞ is a 2 × 2 rotation matrix. In this work, the widely used rectangular nanofins are chosen, where the phase shift ϕ RR ¼ ϕ LL and ϕ RL ¼ ϕ LR due to the mirror symmetry. So, when the incident light is right-handed circularly polarized (RCP), E out becomes Similarly, for the left-handed circularly polarized (LCP): From Eqs. (3) and (4), we can derive the phase modulations for the output RCP/LCP light respectively under diverse incident RCP or LCP light, which means that co-and cross-polarized light can be independently modulated due to the independent ϕ RR and ϕ RL (ϕ LR and ϕ LL ). By adopting this design to our integrated scheme, two independent phase profiles can be obtained on output with a fixed polarization filter. For example, if the output light is set as RCP, then the incident RCP light can be designed for a special function with the phase profile φ 1 ðx; yÞ ¼ ϕ RR ðx; yÞ and the incident LCP light with another phase profile φ 2 ðx; yÞ ¼ ϕ LR ðx; yÞ þ 2θðx; yÞ. In that case, we can achieve a new polarizationswitchable metasurface. The schematics of the electric field change of our design are shown in Fig. 2(a); the output light can be written as a RR e iϕ RR jRCPi and a LR e ið2θþϕ LR Þ jRCPi under two orthogonal circularly polarized light beams, where a RR and a LR are the corresponding amplitudes of the output beams. For analyzing the amplitudes of the output light, focus on a single nanofin. When illuminated by a circularly polarized light, the transmitted light can be expressed as 46 where t x and t y are the complex amplitudes of the incident light polarized along each axis written as t (5) shows that the helicity of a part of the transmitted light is the same as incidence and the other is the opposite. Then, we can get a RR ¼ jðt x þ t y Þ∕2j and a LR ¼ jðt x − t y Þ∕2j based on which we can obtain the transmitted efficiencies of co-polarization and cross-polarization as a RR 2 and a LR 2 , respectively.
In the PMID, it is best to have a RR 2 ≈ a LR 2 to ensure the PCR ≈ 0.5 to get comparable intensities in two polarization states. The simulated phase responses of nanofins for the transmitted RCP and LCP light are shown in Figs. 2(b) and 2(c), respectively. The red circles and blue squares correspond to co-polarized and cross-polarized manipulations of the selected nanofins with the required phase responses. Figure 2(d) shows the amplitude distribution of the selected nanofins. By selecting a suitable size and orientation angle of nanofins, the phase manipulation is completely decoupled for two incident circularly polarized light beams. As a proof of concept, we simulated the response of a transverse bifocal metalens with a focal length of 9 μm, radius r of 3.75 μm, and focal shift distance of AEr∕2 by FDTD. The simulation intensity profiles on the focal plane with CPF for x-polarized, LCP, and RCP light incidence are shown in Figs. 2(e)-2(g), respectively, and are exactly consistent with the design.

Wide-Field and Depth-of-Field Imaging by Chip-Scale PMID
Based on the co-and cross-polarization multiplexed metalens array, we proposed and implemented a chip-scale PMID in a 4f system with an FOVof 4 mm × 4 mm. The phase profiles of the metalens satisfy the requirements of two different focusing lenses for two orthogonal circularly polarized light beams, as schematically shown in Fig. 3 Fig. 3(b). The middle and right images of Fig. 3(b) show the top-view photographic image of the whole metalens array and the zoomed-in image of the metalens array, respectively. By simply switching the polarization station of incident light, we can obtain two independent images of the USAF resolution test chart taken by the imaging device, as displayed in Fig. 3(c). Figure 3(d) shows a stitched image by combining two sets of subimages after certain image processing (the detailed proceeding is provided in Sec. S5 of the Supplementary Material), of which the region in the red circle corresponds to the FOV of an Olympus microscope with a 10× objective (NA ¼ 0.25).
The stitched image has a wide FOV area the same as the metalens array region (4 mm × 4 mm) with the same resolution of a single metalens (∼1.74 μm, g8e2). Here, we calculated the space-bandwidth product (SBP) to compare the performance of the chip-scale PMID and traditional Olympus microscope, which refers to the effective number of pixels required to represent an image and is a measure of the information content of the imaging system. 44 The SBP of the chip-scale PMID is ∼21.1, which is >18.4 of the traditional microscope with a 10× objective. Figure 3(e) shows the zoomed-in image with the same imaging resolution taken through the PMID (right) and a commercial Olympus microscope (left), respectively. The performance of this PMID is comparable to that of the traditional microscope with the same resolution, and it evidently shows the great improvement (∼4 times) in FOVof PMID without decreasing the imaging quality. This chip-scale PMID is further employed to image different biospecimens. To observe the cells in the solution, we made a cell solution container with glass cover (0.13 to 0.16 mm) and ultraviolet (UV) adhesive, of which the diagram and photographic image are displayed in Figs. 4(a) and 4(b), respectively. Figure 4(c) shows the stitched image of human umbilical vein endothelial cells (HUVECs) in a solution at λ ¼ 470 nm. This stitched image covers 256× times the area of a singlet metalens without decreasing the resolution. Next, we changed the working wavelength from 450 to 510 nm to derive DOF information owing to the spectral zooming effect. Zoomed-in images of the HUVECs at different operating wavelengths are shown in Fig. 4(d) from which different microscopic cell information at different depths in the solution can be distinguished. According to our characterization, the total DOF is measured at about 200 μm. (More details are provided in Sec. S6 of the Supplementary Material.) Note that compared with the previous version of the metalens microscope, 36 this PMID integrating the CPF gives rise to a high SNR and imaging quality and makes it possible to achieve broadband imaging to resolve the DOF information in a wide-field scheme. So far, based on this chip-scale PMID we have achieved good resolution, high SNR, large FOV, and tunable DOF imaging simultaneously. Moreover, this device also enables wide view living videos for microscopic observations; see Video 1 for flowing HUVECs in a solution as an example.
To further demonstrate the advantage of the chip-scale PMID for integration, we implemented a miniaturized compact prototype with a combination of the LED light source, liquid crystal polarizer, and sample holder as its image shown in Fig. 5(b). It has a very compact size of 3 cm × 3.5 cm × 4 cm, with a 1000fold reduction in size and weight as compared with the bulky Olympus microscope [see Fig. 5(a)], so it is termed as a portable microscope system (PMS). Note that in this PMS, a liquid crystal (LC) is adopted together with a polarizer and blue-light LED (λ ∼ 470 nm) source to provide a non-mechanical switch of illumination polarization. Based on this PMS, a wide-field microscopic image can be achieved as well. For example, Fig. 5(c) shows the results of the pine stem cross section (c.s.), where all feature sizes can be clearly distinguished with a high imaging quality by comparing with the image (decolored) taken by the Olympus microscope (10×). Meanwhile, the full FOV of the PMS is ∼7.5 times the FOV of the Olympus microscope camera with a 10× objective. Undoubtedly, this PMID-enabled PMS prototype has shown its overwhelming advantage in portable and convenient microscope imaging. There are more details about PMS in Sec. S7 of the Supplementary Material and Video 2.

Discussion and Conclusion
We have proposed a PMID for wide-field and DOF imaging via integrating both SiN x metalenses and CPF directly to a CMOS image sensor. A new kind of polarization-multiplexed metalens was proposed to modulate the co-and cross-polarized light independently, which rightly enables the fixed polarization filter to work for the integrated device. Detailed characterizations of imaging performances of the singlet SiN x metalenses, including the SNR, MTF, resolution, and imaging bandwidth were systematically performed and carefully compared with the counterpart without CPF. As a result, we successfully demonstrated a chip-scale PMID with the resolution of 1.74 μm, an FOV of 4 mm × 4 mm, and DOF of ∼200 μm, verifying the advantage of wide-field and DOF imaging over the traditional microscope at the same resolution. To the best of our knowledge, this is the first metalens microscope that has an FOV larger than the mature traditional ones, and the DOF tuning without mechanical motion is also a striking feature in large FOV imaging. In the meantime, the miniaturized PMS prototype has a 1000-fold reduction in volume and weight of the traditional. It should be mentioned that the current resolution (1.74 μm) of PMID is not limited by the metalens but the pixel size (1.67 μm) of the CMOS image sensor in our 4f imaging system, which would possibly be improved by employing a smaller pixel-sized CMOS sensor with further development of CMOS technology. The other possibility of improving the resolution could be the booming computational imaging techniques, which have been proved to be an efficient method in many cases of upgrading the imaging performance. Frankly, our microscope imaging function based on two circularly-polarized light will be affected with respect to the circular-polarization sensitive objects, in which some subimages will be possibly weaken or even absent. For these cases, there is still an alternative solution by changing the metalens array design from the circular polarization multiplexing to the linear polarization multiplexing (i.e., x-and y-polarizations), then it is valid to work in the circular polarization-sensitive objects. 21 This chip-scale microscope has shown its overwhelming advantages not only in large FOV and DOF but also the compactness compared with the traditional optical microscope, which will undoubtedly illuminate new revolutionary optical devices by meta-technology.