Three-dimensional (3D) microscopic imaging [1–3] is a widely used technique to explore the depth information and surface topography of microscopic objects. Some representative methods are confocal scanning microscopy [4,5], light-field microscopy [6,7], structured illumination microscopy [8,9], and binocular stereoscopic microscopy [10,11]. Among these methods, stereoscopic microscopy is one of the simplest ways to record the surface and depth information of the objects in real time, with applications in the biosciences [12], medical research [13], and industrial detection [14].

Stereoscopic microscopes rely on two oblique optical axes to generate a pair of microscopic images with parallax. They can be classified into Greenough types and common main objective (CMO) types. The former uses two objectives to form light paths for left and right images, but their physical dimensions have to be restricted, to prevent contact between the lenses. Consequently, numerical apertures (NAs) are limited to ∼0.2. Higher NAs (∼0.35) can be achieved with the CMO type, which uses a single and large aperture objective to handle the two light paths. However, CMO microscopes are more expensive than Greenough microscopes because of the complex design and fabrication of the objectives. Thus, it is important to find alternative strategies to enable high-resolution and low-cost stereoscopic microscopes.

Metasurfaces [15–17], which use ultrathin meta-atoms to accurately modulate amplitude, phase, and polarization of the local electromagnetic fields, can achieve diverse functions such as light bending [18,19], holograms [20,21], and polarization conversion [22,23]. They are also used to enhance the quality of the stereoscopic systems, e.g., 3D stereoscopic holography [24,25]. Metalens [26–28] is a special category of metasurfaces that has been receiving much attention due to their excellent focusing and imaging abilities. Researchers have used metalenses as core elements to build various microscopic systems for biomedical and chemical imaging, such as for ex vivo mice intestine tissues [29], fluorescent polyethylene microspheres [30], and frog egg cells [31]. Furthermore, compared with the bulky glass lenses, metalenses are also able to implement multiple functions, such as multi-focus generation [32,33], spectral analysis [34], chiral imaging [35], and depth sensing [36]. Another major advantage of metalenses over their bulky counterparts is their ability to distinguish between polarization states, which opens up new possibilities of applications. For example, a Stokes camera based on metalenses [37], and a birefringent metalens encoding two phase profiles for corrections of aberrations were recently demonstrated [38]. Thus, the extra degree of freedom afforded by polarization control is poised to play a crucial role in the next steps of metalens research and development.

In this paper, we propose a birefringent metalens to improve the imaging performance of a Greenough-type stereoscopic microscope [Fig. 1(a)]. The designed metalens encodes two phase profiles in a single layer, thus removing the physical restrictions limiting the NA in conventional stereoscopic microscopes. Our stereoscopic metalens has an NA of 0.4 and can produce two symmetrical focal points for stereoscopic imaging at the wavelength of 532 nm. We demonstrate stereoscopic microscopic imaging by embedding the metalens in a commercial stereoscopic microscope, thus increasing its NA from 0.15 to 0.4. The system achieves a resolution of 870 nm. As a proof of concept, we use the metalens-based stereoscopic microscope to image pollen grains and silk fibers. Furthermore, a high-resolution autostereoscopic display, which can display stereoscopic microscopic images vividly without the aid of extra equipment, is assembled to enhance the viewing experience. Our approach paves the way toward high-resolution and low-cost stereoscopic microscopes.

The metalens-based stereoscopic system is illustrated in Fig. 1(a). The inset shows the metalens surface, where the colors indicate the two-phase profiles, which partially overlap in the yellow region. This overlap is significant to achieve high NA. The phase profiles are encoded in two orthogonal linear polarizations, with the left one corresponding to x-polarized and the right one for y-polarized. The metalens is designed for operation at the single wavelength of 532 nm; thus, the system does not suffer from chromatic aberrations. To make the design compatible with the commercial stereoscopic microscope setup, the center of each metalens is positioned assuming an angle of incidence of 6° [see inset Fig. 1(a)]; the diameter and NA of the metalens are 400 μm and 0.4, respectively. This birefringent metalens can image two aspects of the same object using the parallax effect.

The design of phase profiles is based on the spherical wave method [31,36,39], which is suitable for our imaging conditions based on metalenses without tube lenses and helps to eliminate spherical aberration. The phase profiles for each metalens are encoded as an aplanatic phase distribution [31] as follows: φl−m(x,y)=2πλ0(scosθ−x2+y2+s2)+2π·nsubλ0⁢[vcosθ−(x+d)2+y2+v2],(1)φr−m(x,y)=2πλ0(scosθ−x2+y2+s2)+2π·nsubλ0⁢[vcosθ−(x−d)2+y2+v2],(2)where d is the shift distance and θ is the angle of inclination; λ0 is the wavelength in air; and s and v are, respectively, the object and image distances [see inset of Fig. 1(a)]. In our design, these parameters are set to be s/v=3; nsub is the refractive index of the substrate. To simplify the design, we treat the thickness of the substrate as infinite and uniform; hence, the image plane is inside the substrate. It is noted that, unlike the hyperbolic metalens, the NAs of these aplanatic metalenses are defined by the object distance s and the diameter w of each metalens as NA=w/w2+4s2 [31].

The focusing performance of the designed birefringent metalens is evaluated using 3D finite-difference time-domain (FDTD). The refractive index of c-Si used in the simulation is 4.15. To save computation time, we consider a birefringent metalens with an NA of 0.4 and sizes of l×w=12.8μm×10μm [inset of Fig. 1(a)], which correspond to the diameter of the single left or right metalens, to be w=10μm. The phase profiles of the proposed metalens are shown in Fig. 3(a). Notice that only the yellow region, where both phase profiles overlap, requires simultaneous lensing effect for both polarizations, whereas the red (blue) region requires lensing effect only for x-polarized (y-polarized) light. The deviation between the designed and ideal phase profiles introduces imaging aberrations. To optimize the matching between the design and ideal phase profiles, the metalens in the red region is designed so that its phase for x-polarized light satisfies Eq. (1), but no constraints are imposed on the y polarization. Likewise, the metalens in the blue region is designed to satisfy Eq. (2) for y-polarized incidence. Dipole sources with linear x and y polarizations are placed on the left and right of the designed image points and utilized in the simulation for focusing characterization.

As shown in Figs. 3(b) and 3(d), the metalens successfully discriminates between the polarization of the incident beam, correctly focusing it in the target position. By fitting with Airy functions, the full width at half-maximum of the two focal spots is calculated to be 655.2 nm and 608.4 nm, respectively [Figs. 3(c) and 3(e)]. The simulated focusing efficiencies of the left and right metalenses are 33.2% and 32.2%, respectively.

To fabricate the metalens, a bonding process [19,42] is carried out on a silicon-on-insulator wafer with a 400 nm c-Si thin-film and a 375 nm thick silicon dioxide layer. First, inductively coupled plasma (ICP, Oxford Instruments Plasma Pro System 100 ICP180) is used to etch down the c-Si layer to 300 nm. The pattern is defined in a high-resolution negative resist (HSQ) with 230 nm thickness using electron beam lithography (Raith Vistec EBPG-5000plusES). After exposure, the pattern is transferred to a c-Si layer by ICP etching. The HSQ is spun onto the structures, followed by hard baking at 300°C for 5 h to flatten the surface. Whereas SiO2 and other common materials are developed by chemical vapor deposition, the HSQ layer is processed by spin coating and hard baking, which can easily infiltrate into the gaps between the meta-atoms and has better back-filling performance [43]. Then a silica buffer layer is deposited on the sample by inductively coupled plasma chemical vapor deposition (ICP-CVD, Oxford Instruments Plasma Pro System 100 ICP180-CVD). The UV light curable adhesive NOA61 is spin-coated on the sample to bond with the glass substrate by subsequent ultraviolet LED light illumination. Finally, the opaque silicon substrate is removed by the precise grinding machine Logitech PM6 and ICP. Scanning electron microscope (SEM) images of the metalens with a diameter of 400 μm are shown in Fig. 4.

The designed birefringent metalens is embedded in a commercial stereoscopic microscope according to the optical setup of Fig. 1(a) to perform high-resolution stereoscopic microscope imaging operating in the transmission mode. The stereoscopic microscope (Yong Heng XTZ-05T) is of Greenough-type with an NA of 0.15. It has two individual light paths and two objectives. A white-light LED source associated with a 532 nm filter with 10 nm bandwidth is used for incoherent and unpolarized green light illumination. The sample is placed near the object distance, which is s=450μm, in accordance with the diameter w of 400 μm and NA of 0.4. The images from the birefringent metalenses are matched with the parallax angles of the stereoscopic microscope so that the left and right images with x- and y-polarized light can be collected by the microscope objectives of the stereoscopic microscope.

A 1951 USAF resolution chart is used to measure the resolution and magnification of the proposed setup. Figure 5(a) shows the images obtained with the stereoscopic microscope without the metalens. The resolution is limited and only the fringes in Group 7 Element 6 (228.1 lp/mm, corresponding to a resolution of 2192 nm) can be distinguished. After embedding the metalens, the fringes in Group 9 Element 2 (574.7 lp/mm, corresponding to the resolution of 870 nm) can be imaged clearly, as shown in Figs. 5(b) and 5(c). Thus, the resolution of the system is higher than 870 nm, which is close to the Rayleigh criterion for an NA of 0.4 at the wavelength of 532 nm (0.61λ/NA). Besides the optical resolution and magnification, the stereoscopic depth z=bf/Md and the depth resolution Δz=z(Md)−z(Md+MΔd) are other important metrics for characterizing the performance of stereoscopic microscopes [44]. In the experiment, b=95.1μm is the separation baseline of the centers of the two metalenses, f=310.5μm is the focal length, M=13.6 is the magnification, d=43.2μm is the disparity, and Δd=3.6μm is the disparity step which equals the pixel size. Accordingly, the stereoscopic depth z is 50.3 μm and the depth resolution Δz is about 3.9 μm.

To demonstrate the application of the metalens assisted stereoscopic microscope, micro-samples of pollen grains and silk fibers are chosen as targets. The dimensions of pollens are around 18 μm to 30 μm, while the width of a silk fiber is around 10 μm to 20 μm. Their featured sizes are compatible with the resolution of the setup, and they are stacked or staggered with suitable depth information.

To better understand our stereoscopic microscope compared with conventional optical microscopes, we used both systems to image pollen grains and silk fibers. As shown in Fig. 6, the birefringent metalens can enhance the resolution and magnification of the stereoscopic microscope to the level of a conventional optical microscope.

The left and right parallax images of the pollen grains [Figs. 6(b) and 6(c)] and silk fibers [Figs. 6(f) and 6(g)] are further sent to the autostereoscopic display (Fig. 7), which follows the principle of temporal–spatial multiplexing directional backlight design [45]. Assisted by this autostereoscopic display, vivid and full high-definition stereoscopic microscopic images can be perceived without wearing extra equipment, thus greatly simplifying the system and improving the perceptual experience [46,47].

Since the stereo perception can only be reached with a specialized display, we transform the full-color stereoscopic microscopic images into anaglyph images [Figs. 6(i) and 6(j)], so that stereo perception can be obtained with the assistance of red–blue glasses via normal screens. Other stereoscopic displays, such as polarized-glasses assisted displays [48] and virtual reality equipment [49,50], are also compatible with our proposed stereoscopic microscope.

In terms of the image quality, it is worth noting that our stereoscopic microscopic images are obtained under the transmission mode. Since the pollen grains and silk fibers are not completely transparent, the contrast of the images is decreased and some superficial details are missing, resulting in inevitable deterioration of image quality. The reflection mode metalens [51,52] or the hybrid of the metalens [53–56] and the conventional refractive lens [57] will assist in increasing the ability to operate in reflection, which can improve the image quality further. Furthermore, in the phase design, we assume that a spherical wave is emitted by a single point. An improved design could be obtained by taking into account emission from multiple points, so as to eliminate comatic aberrations.

In addition, the NA and magnification are closely related to the depth of field of the microscopic image. Our metalens has an NA of 0.4, which can resolve the sizes and depth positions of the pollen grains and silk fibers samples. Higher resolution can be achieved by reducing the distance between the birefringent metalens and the object plane. In principle, the resolution can be further improved by compounding birefringent metalens with higher NA metalenses for imaging [31,58–61], and theoretically the NA can reach 1.33 according to the Nyquist sampling NA≤λ/(2·a) [58]. However, the corresponding stereoscopic depth will decrease accordingly, which is significant for smaller targets with smaller depth positions. For example, for the hemoglobin with the size of 7 μm, a metalens with NA of 0.6 is more suitable.

In conclusion, we propose a birefringent metalens to improve the imaging resolution in the stereoscopic microscope. The designed single-layer metalens encodes two lensing phase profiles together, thereby removing the physical limitations of the bulk lens and thus achieving a higher NA than objectives used in the conventional stereoscopic microscopes. The demonstration shows that the birefringent metalens is compatible with commercial stereoscopic systems and can improve its resolutions while maintaining low cost.

Acknowledgment. H. L. acknowledges support by Innovation Group Project of Southern Marine Science and Engineering (Guangdong). E. R. M. acknowledges support by FAPESP and CNPq.