Introduction

In today’s information society, there is a high demand of using optical imaging systems to capture biometric information, such as face, fingerprint, palmprint, and palm vein1,2, to verify human identity. Recently, palm scanning has attracted increasing attention for biometric identifications. Over the past few years, major technology companies including Tencent and Amazon have released palm scanning-based payment systems, which have been applied to various scenarios such as grocery shops, subway stations, and sports venues, reaching tens of millions of registered users3,4,5. Compared to fingerprint scanning, palmprint and palm vein contain richer texture information over a larger area. Furthermore, the collection of palm information is non-invasive and contactless6,7,8. Compared to face recognition, palm scanning provides better privacy protection and can allow the identification of users wearing masks and distinguish users with similar faces, such as twins5,9,10.

In a typical palm scanning system, both palm print and palm vein images are collected for doubly enhanced security. The palm print image can be captured using a conventional RGB camera. On the other hand, the palm vein information can only be collected using a near-infrared camera with the active illumination of a near-infrared light-emitting diode (LED) or a vertical-cavity surface-emitting laser (VCSEL), since infrared light can penetrate deeper into bio-tissues than visible light and allow better visualization of the vein patterns beneath the palm surface11. The key design goal of a palm vein imaging system is to obtain a high-resolution image within an ultrawide field-of-view (FOV) and an extended depth-of-field (DOF)12. A high image resolution is mandatory for the subsequent image processing, feature extraction, and matching13. A wide FOV is critical for capturing the vein image of the entire palm at a close distance. An extended DOF is important for adapting to the habits of different users, who may place their palms at a wide range of distances.

Conventional palm vein imaging systems achieve ultra-wide FOV and extended DOF imaging by using complex fisheye lens designs that include multi-piece spherical lens elements, resulting in a significant size, weight, and cost. In addition, unwanted reflection from multiple lens surfaces leads to flares and ghosts. Furthermore, the system may often encounter unwanted high reflection from the palm surface resulting from water, sweat, or make-up14, resulting in the loss of vein information and deteriorated identification accuracy. To address the issue, Tencent WeChat Pay Lab 33 utilized two orthogonal linear polarizers placed at the light source and the camera module, respectively, to suppress the surface reflection14, yet it further complicates the system.

Metalens is increasingly seen as a potential solution for improving the performance of various imaging systems while reducing their size, weight, and cost. With its exceptional capability to manipulate the vectorial light field, a single metalens may achieve the same performance that would otherwise require multiple conventional optical components15,16,17,18,19,20,21,22,23,24,25. However, despite much progress, most metalenses demonstrated to date have very limited FOV. Metalenses with a wide FOV is an active area of research26,27. It has recently been shown that a single-layer metalens with a quadratic phase profile, instead of the conventional hyperbolic phase profile, can mitigate monochromatic off-axis aberrations, allowing an ultrawide FOV of close to 180°, despite the image resolution being limited by the spherical aberration28,29,30,31. To suppress the spherical aberration and further improve the imaging quality up to the diffraction limit, one may couple a metalens with a front aperture stop32,33,34,35,36,37 or a nonlocal thin film filter38 with relative ease of fabrication. Alternatively, stacked doublet metalenses39,40,41,42, multi-aperture metalenses43,44, and metalenses composed of meta-atoms with nonlocal response45,46 have been explored to achieve wide FOV imaging. To extend the DOF, one may build a metalens with an inverse-designed phase profile47,48 or leverage metalens’ polarization multiplexing capability49.

In this work, we designed and experimentally realized a metalens-integrated system for palm vein imaging in the near-infrared band. Using a metalens with an optimized phase profile coupled to a front aperture stop, we achieved near-diffraction-limited imaging over an ultrawide FOV of 140° and an extended DOF ranging from 33 to 150 mm, which allows clear visualization of vein patterns across the entire palm at various conditions. Furthermore, we showed that one may leverage the polarization selectivity of the metalens to suppress unwanted reflection from the palm surface. Using a VCSEL operating at the wavelength of 850 nm for illumination, we circumvent the issue of chromatic aberration, which is a major challenge for wide FOV metalenses26,27. For the particular application of palm vein imaging, the metalens-integrated system showcased uncompromised imaging performance with a significantly simplified form factor compared to its bulky counterpart.

Results

Palm vein imaging framework

The framework of the palm vein imaging system is schematically illustrated in Fig. 1a. Based on the habits of different users, the imaging DOF is designed to extend a wide range from 33 to 150 mm. Linearly y-polarized light illumination covering a wide FOV can be provided by two symmetrically placed 850-nm VCSELs, each coupled to a diffuser and a polarizer. At the receiving end, a conventional near-infrared camera module is composed of a polarizer polarized along x-direction, multi-piece refractive lens elements, and a near-infrared image sensor. Existing palm vein imaging system has limited FOV. To achieve ultrawide FOV operation for a better user experience, bulky fisheye lens is required, as schematically shown in Fig. 1b. Here we aim to replace the polarizer and the bulky fisheye lens with a single-layer metalens coupled to an aperture stop, which is much more compact, as schematically shown in Fig. 1c. To achieve polarization selectivity and remove unwanted reflection, the metalens is designed to focus x-polarized light and deflect y-polarized light out of the imaging area.

Fig. 1: Framework of the palm vein imaging system.
figure 1

a Linearly polarized light from the light source illuminates the palm across a wide FOV and extended DOF. Light reflected and scattered from the palm is collected by a near-infrared camera. b Schematic of a conventional palm vein imaging system, including a polarizer, a fisheye lens with multi-piece spherical lens elements, and an image sensor. The fisheye lens is based on a sample from Zebase library (F016). c Schematic of a metalens-integrated palm vein imaging system. The system consists of an aperture stop, a solid substrate, a metalens, and an image sensor. The metalens splits light emitted from the palm, with x-polarized light focused on the image plane and y-polarized light deflected out of the imaging area.

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Metalens design and fabrication

A conventional metalens is designed to have a hyperbolic phase profile, such that spherical aberration at normal incidence can be eliminated16. However, for off-normal incidence, third-order (Seidel) aberrations, including coma, astigmatism, and field curvature, become prominent26,27. One way to address the issue is to replace the hyperbolic phase profile with a quadratic phase profile, such that when a beam illuminates on the metalens with an oblique angle-of-incidence (AOI) \({\theta }_{\text{i}}\), a focal spot can still be formed with a lateral shift of \(f\sin {\theta }_{\text{i}}\), where \(f\) is focal length28. Nonetheless, a single-layer metalens with a quadratic phase profile suffers from significant spherical aberration. The spherical aberration results in a low modulation transfer function (MTF) and resolution of the imaging system, which is unacceptable for subsequent image processing and recognition. An alternative method to achieve wide FOV imaging is by placing an aperture stop in front of the metalens. For such a scheme, recently an analytical form of the ideal phase function has been derived, which can allow near-diffraction-limited imaging at a given object distance50. To further achieve simultaneous wide FOV and extended DOF imaging with near-diffraction-limited resolution, based on the scheme of a single-layer metalens incorporating an aperture stop on a fused silica substrate, as illustrated in Fig. 2a, we performed optimization of the metalens phase profile, expressed in a polynomial form:

$${\phi }_{{\rm{m}}}\left(r\right)={M}\mathop{\sum}\limits_{i=1}^{N}{A}_{{\rm{i}}}{\left(\frac{r}{R}\right)}^{2{\rm{i}}}$$
(1)

where \(r\) is the radial distance to the lens center, \({A}_{\text{i}}\) is the coefficient on the 2ith power of \(r/R\), which is the normalized radial coordinate, \(N\) is the number of polynomial coefficients in the series, and \(M\) is the diffraction order. The first term of the polynomial series is equivalent to a quadratic phase and determines the focal length of the metalens. The additional terms could be optimized to further enhance the image quality. The goal is to orthogonally project a 180° hemispherical space onto the focal plane following the \(f\sin {\theta }_{\text{i}}\) spatial mapping relation. The orthogonal projection causes image points at large AOIs to be compressed, leading to noticeable barrel distortion, as shown in Fig. 2b. Nonetheless, the distortion does not deteriorate the image resolution and can be corrected using established image processing techniques (see “Methods”)51.

Fig. 2: Design of the metalens-integrated palm vein imaging system.
figure 2

a System layout and ray-tracing simulation. b Designed image height as a function of the AOI (blue solid line) compared to the target image height following the \(f\sin {\theta }_{\text{i}}\) spatial mapping relation (orange dashed line) and a conventional pinhole model following the \(f\tan {\theta }_{\text{i}}\) spatial mapping relation (yellow dashed line). c Simulated MTF of the metalens-integrated imaging system as a function of the object distance and FOV along the sagittal (S) and tangential (T) direction, respectively. d Simulated Strehl ratio and focusing efficiency within the FOV and DOF. e, f Comparison of simulated point spread functions (PSFs) between a conventional metalens with hyperbolic phase (e) and our metalens with optimized phase coupled to an aperture stop (f).

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The metalens is designed to operate at a near-infrared wavelength of 850 nm, which is ideally suited for vein visualization52. The damped least-squares method is employed to optimize the system by adjusting the phase profile and structure parameters, including the size of the aperture stop, substrate thickness, and back focal length (see “Methods”). The optimized aperture size of 400 μm enables near-diffraction-limited imaging within the entire FOV and DOF. Further increasing the aperture size beyond 400 μm may result in a noticeable decrease in the MTF. The optimized system has an MTF of greater than 0.2 at 227.3 cycles/mm within the entire FOV and DOF, as shown in Fig. 2c. A near-diffraction-limited Strehl ratio of greater than 0.75 with a focusing efficiency of greater than 0.7 can be obtained within the entire ultrawide FOV of 140° and an extended DOF ranging from 33 to 150 mm, as shown in Fig. 2d. In the final stage of the metalens design, we incorporate polarization selectivity to address the issue of unwanted surface reflection for palm vein imaging. While the metalens is optimized to focus the x-polarized light, the additional design goal is to deflect the y-polarized light carrying surface reflection out of the imaging area. Therefore, for y-polarized light, we design the following phase profile:

$${\phi}_{\text{y}}\left(r\right)={k}_{0}r\sin {\theta }_{\text{d}}-n{k}_{0}\sqrt{{r}^{2}+{h}^{2}}$$
(2)

where \({k}_{0}\) is the wavenumber in free \({\theta_d}\) = 60° space, is the deflection angle of the chief ray, n is the refractive index of the substrate, and h is the thickness of the substrate.

A metalens with a polarization-multiplexed response can be realized by designing each meta-atom with an anisotropic response53,54. Here, the meta-atom is composed of 600-nm-tall amorphous silicon nanopillars of rectangular in-plane cross-section, as shown in Fig. 3a. The width and length of nanopillars can be adjusted to independently control the transmission phase of x- and y-polarized incident light, respectively, as shown in Fig. 3b, c. The metalens with a diameter of 3 mm was fabricated via standard electron-beam lithography and reactive-ion etching process, after aligning it with the aperture stop made of chromium, fabricated via photolithography on the back side of the substrate. A photograph, an optical microscopy image, and a representative scanning electron microscopy image of the fabricated sample are shown in Fig. 3d–f, respectively.

Fig. 3: Metalens design and fabrication.
figure 3

a Meta-atom composed of silicon nanopillar of rectangular in-plane cross-section on a fused silica substrate. The nanopillar is designed to have height H = 600 nm, period U = 300 nm, and width Wx and length Wy ranging from 100–220 nm. b, c Designed metalens phase profiles that can split light emitted from the palm, with x-polarized light focused on the image plane and y-polarized light deflected out of the imaging area. d Photograph of the aperture stop. e–g Photograph (e), optical microscopy image (f), and scanning electron microscopy image (g) of the fabricated metalens sample, respectively.

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Metalens characterization and palm vein imaging experiments

To accurately assess the resolution and FOV of the imaging system, we initially measured the MTF of the metalens within the FOV of ±65° at infinity distance utilizing a commercially-available MTF test station (ImageMaster HR, TriOptics). The measured MTFs (Fig. 4a) showed good agreement with simulated ones. To evaluate the depth-dependent imaging performance of the metalens, we built an experimental setup as shown in Fig. 4b, and quantify the system’s MTFs using the edge-based spatial frequency response (e-SFR) method (see “Methods”). The imaging target is a pre-distorted SFRplus test chart (Imatest), as illustrated in the inset of Fig. 4b. The test chart is designed with built-in pincushion distortion (the inverse of barrel distortion) so that the image used for the SFR analysis has relatively small distortion and a statistically adequate pixel quantity55. On the test chart, we marked a rectangular area with eight red crosses, covering the diagonal FOV of 140° (130° horizontal and 120° vertical), as shown in Fig. 4c. Two VCSELs with a central wavelength of 850 nm are placed symmetrically on two sides of the imaging system to provide relatively uniform illumination on the test chart. The receiving end is composed of the metalens and a near-infrared CMOS image sensor with a pixel size of 2.2 μm (OG01A1B, OmniVision).

Fig. 4: Characterization of the metalens-integrated imaging system.
figure 4

a Simulated and measured MTF of the metalens within the FOV of ±65° at infinity distance. b Photograph of the metalens-integrated imaging system. c Image of the test chart at a distance of 33 mm. d Simulated and measured MTF of the metalens as a function of the object distance at the AOI of 40° based on the e-SFR method. e, f Images of a test chart for x-polarized light and y-polarized light, respectively.

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To evaluate the DOF of the imaging system, we characterized the MTF of the system over a distance ranging from 33 to 150 mm at an AOI of 40°. The measured MTFs exceed 0.3 at half Nyquist frequency of 114 cycles/mm spanning the entire DOF, as shown in Fig. 4d. The discrepancy between the measured and simulated MTFs may be due to the sensor noise, non-uniform illumination, and defects in the fabricated metalens. The polarization selectivity of the metalens was evaluated by placing a wire grid polarizer (WGF-HC12N, AsahiKASEI) between the test chart and the metalens, with no polarizer placed in front of the VCSELs. As shown in Fig. 4e, when the polarizer is transmissive along the x-direction, a bright image of the test chart can be obtained. In contrast, when the polarizer is transmissive along the y-direction, as shown in Fig. 4f, the image is mostly dark in the center. The bright part near the edge of the image may be attributed to the limited extinction ratio of the wire grid polarizer at a large AOI.

Finally, to demonstrate palm vein imaging using the metalens-integrated imaging system, a polarizer was positioned between the VCSEL and the palm to generate linearly polarized illumination. It was rotated until the intensity of palm reflection was minimized, at which point the palm was illuminated with y-polarized light and imaged with x-polarized light. We captured palm vein images at a distance of 75 and 120 mm, respectively, and corrected distortions for convenient vein observation, with results shown in Fig. 5a–d. The circularly shaped background noise may be attributed to the stray light of the reflective chromium aperture stop as well as higher-order diffraction. The stray light may be suppressed by replacing chromium with more absorptive material for constructing the aperture stop. Moreover, we captured images of a wet palm with the polarization direction of the illumination beam along the x- and y-direction, as shown in Fig. 5e, f, respectively. It is evident that the system can effectively suppress high reflection from the palm and provide an enhanced vein image through polarization filtering. The circularly shaped background noise still exists but is less obvious with a different exposure setting. The decrease of brightness for the outer zone of the wide field scene is due to the limited FOV of the illumination optics. The VCSEL used as illumination in the system has a FOV of 90° × 70°, which is not enough to cover the entire imaging FOV of 130° × 120°. Therefore, two separately placed VCSELs are used, which may result in non-uniform illumination, especially towards the edge of the FOV. To address the issue of non-uniform illumination, in the future, it is possible to closely integrate the illumination and imaging optics on the same circuit board. The VCSEL’s illumination FOV may be further expanded via advanced diffractive optics design56.

Fig. 5: Palm vein imaging experiments.
figure 5

a, b Palm image before (a) and after (b) distortion correction, respectively, at a distance of 75 mm with y-polarized illumination. c, d Palm image before (c) and after (d) distortion correction, respectively, at a distance of 120 mm with y-polarized illumination. e, f Palm image after distortion correction at a distance of 85 mm with x-polarized (e) and y-polarized (f) illumination, respectively.

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Discussion

To summarize, we demonstrated a compact, high-contrast near-infrared palm vein imaging system with a wide FOV of 140° and extended DOF ranging from 33 to 150 mm by using a polarization-selective metalens. Furthermore, the metalens can independently control two orthogonal linearly polarized incident beams for imaging and deflection, effectively addressing challenges posed by undesirable reflections in palm vein collection scenarios. This solution offers a small, lightweight, and potentially low-cost alternative to overcome challenges associated with conventional bulky lenses and polarizers. To further simplify the palm vein imaging system, one may also replace the diffuser and polarizer on the illumination side using a metalens. The operation bandwidth of the metalens may be further improved, potentially leveraging multi-layer or hybrid diffractive–refractive lens design, to allow broadband illumination with an LED source. The proposed approach may not only be applied for biometric authentication but also offer a versatile solution for a range of application areas, including but not limited to endoscopy, microscopy, depth sensing, and security surveillance systems.

Methods

Metalens-integrated imaging system design

We utilized the commercial optical design software Zemax OpticStudio to design and analyze the metalens-integrated imaging system. The sequential surface “binary 2,” whose phase profile expressed in Eq. (1), is used to represent the metalens. To optimize the system’s MTF over the targeted DOF and FOV, we set the phase profile, substrate thickness, aperture diameter, and back focal length as the variables. We set the diffraction order to \(M\text{}=\text{}1\) and the number of polynomial coefficients to \(N\text{}=\text{}2\), as the first two terms turn out to be sufficient for our optimization. The initial phase profile is set as the quadratic phase with \(\frac{{A}_{1}}{{R}^{2}}=-\frac{{\pi}}{{\lambda }_{0}f}\) and \(\frac{{A}_{2}}{{R}^{4}}=0\). The damped least-squared method is implemented to maximize the MTFs for all object points at each object plane.

For the simulation of the PSF and MTF, we utilize the Fast Fourier Transform method, as the focus spots are small enough to ensure accurate results using the Fraunhofer approximation. The simulated PSF is utilized to calculate the focusing efficiency, described as the fraction of the incident light that passes through a circular iris in the focal plane with the radius of Airy disk57:

$${R}_{{\rm{Airy}}}=\frac{1.22{\lambda }{f}}{{D}}$$
(3)

where \(\lambda\) is the free-space wavelength, f is the focal length of metalens, and D is the diameter of the aperture stop. For the estimation of the theoretical focusing efficiency, we assume that there is no energy loss through the aperture stop and the metalens.

MTF measurement

To measure the MTF based on the e-SFR method, a pre-distorted SFRplus test chart was used to provide sufficient data for calculation after being imaged by the system at large AOIs. The employed e-SFR method is a part of the ISO 12233 standard and is widely utilized for edge-gradient analysis of optical systems. This method is adapted to employ slanted edge squares for measuring SFR, which is also known as MTF58,59. The calculation process primarily includes the following steps: (1) generate the edge spread function (ESF) by binning the oversampled edge profile values, (2) compute the line-spread function (LSF) via the derivative of ESF, (3) calculate the discrete Fourier transform (DFT) of the LSF, where SFR is the absolute value of the DFT. These calculation processes can be executed using the commercial software Imatest Master.

Distortion correction

To correct the distortion in the as-captured image, we fit the image height as a function of the AOI (as shown in Fig. 2b) to a polynomial formula, which is

$$y={1.853{\rm{e}}}^{-9}{\theta }_{i}^{4}-{1.103{\rm{e}}}^{-6}{\theta }_{i}^{3}+{\mathrm{3.1.44}{\rm{e}}}^{-8}{\theta }_{i}^{2}+0.02121{\theta }_{{\rm{i}}}-{3.98{\rm{e}}}^{-5}$$
(4)

Subsequently, the captured image can be mapped from its original pixel coordinates along the radial direction to pixel coordinates corresponding to \(y\text{}=\text{}f\tan {\theta }_{\text{i}}\). To obtain the finally displayed undistorted image, we performed scattered data interpolations at a Cartesian grid of integer locations and retained the data within the entire diagonal FOV of 140°.