Multifocal metalens and image scanning microscope including same

Abstract

The present invention relates to a high-density and uniform multifocal arrangement method, a multifocal metalens, and an image scanning microscope including same. When the multifocal arrangement method of the present invention is used, focal points can be uniformly arranged at high density, and when a metalens to which the method is applied is used, an ultra-high-resolution image scanning microscope can be manufactured.

Description

Multifocal metalens and image scanning microscope including the same

[0001] The present invention was carried out under project number 1711198556 with the support of the Ministry of Science and ICT of the Republic of Korea, the research management agency for the said project is the National Research Foundation of Korea, the research project name is "Development of Leading Convergence Technology in Brain Science," the research project name is "Development of Spatiotemporal Integrated Analysis Pipeline (iTRAP) for Brain Disease Organoid-Based Precision Medicine," the lead institution is the Industry-Academic Cooperation Foundation of Sungkyunkwan University, and the research period is 2024.01.01-2024.12.31.

[0002] The present invention was carried out under project number 2710006474 with the support of the Ministry of Science and ICT of the Republic of Korea, the research management agency for the said project is the National Research Foundation of Korea, the research project name is "STEAM Global Convergence Research Support", the research project name is "Implementation of Ultralightweight High-Resolution Multidimensional Metasurface-Based Bioimaging and Sensing System", the lead organization is the Industry-Academic Cooperation Foundation of Pohang University of Science and Technology, and the research period is July 1, 2024 - December 31, 2024.

[0003] This patent application claims priority to Korean Patent Application No. 10-2025-0010475 filed with the Korean Intellectual Property Office on January 23, 2025, the disclosures of said patent application are incorporated herein by reference.

[0004] The present invention relates to a high-density and uniform multi-focus array method, a multi-focus metalens, and an image scanning microscope including the same.

[0005]

[0006] Image Scanning Microscopy (ISM) is a super-resolution imaging technique that doubles resolution through pixel reassignment and deconvolution. Theoretically, confocal detection improves optical resolution, and this improvement becomes greater as the pinhole size is reduced. However, reducing the pinhole size decreases the amount of light collected, resulting in a lower Signal-to-Noise Ratio (SNR). ISM was proposed as an alternative technique that provides enhanced resolution and optical sectioning effects without SNR loss by employing an array detector so that each pixel acts as a small confocal pinhole. ISM has evolved into a promising technique that offers substantial resolution improvements and high compatibility with other imaging technologies. Among various implementation methods, scanning with a multi-focus array has been reported as the most common approach (Fig. 1a).

[0007] In practice, to achieve a fast and wide field of view (FOV) in ISM, it is important to generate high-density and uniform multi-focus arrays. Traditionally, Digital Micromirror Devices (DMDs) and Microlens Arrays (MLAs) have been used to generate multi-focus arrays. However, DMDs are not cost-effective and require complex alignment, making the system difficult to configure and maintain. On the other hand, while MLAs are relatively cost-effective and simple to use, their Numerical Aperture (NA) is limited to less than 0.6, and there are difficulties in reducing the pitch to less than 100 μm due to manufacturing process limitations. Furthermore, because it is difficult to independently control the pitch and NA of MLAs, significant reduction is required to achieve high resolution and high-density multi-focus arrays, which can lead to aberrations.

[0008] To overcome these limitations, metalens, which are planar optical devices composed of nanostructures, were introduced. Metalens provide excellent optical modulation capabilities. Several types of multifocal metasurfaces have been reported, such as Dammann gratings and metalens arrays. However, Dammann gratings have problems such as low NA (<0.4), difficulty in adjusting spacing, non-uniform intensity, and a limited number of focal points. Furthermore, metalens arrays exhibit a trade-off between the number of available focal points, lens size, and NA. One effective method for generating multifocal arrays is to simply add phase profiles. In this invention, this is referred to as the "Phase Addition Method." Multifocal metalens can be realized by integrating multiple phase profiles of metalens. However, in this method, reducing the spacing is limited due to interference between adjacent focal points. Another existing method is the "Random Multiplexing Method," which is widely used for combining multiple holograms. This method allows for the design of multifunctional metalens by combining phase profiles through multiplication by a binary random matrix. While random multiplexing is less sensitive to interference between adjacent focal points, it has the disadvantage that focus quality degrades as the number of integrated phase profiles increases due to the multiplication of random matrices.

[0009] Therefore, there is an urgent need to develop a high-density and uniform multi-focus array method that overcomes the aforementioned disadvantages.

[0010] In this study, we propose a new multiplexing strategy named the "Hybrid Multiplexing Method." This method combines two existing methods to leverage the strengths of each. First, the target multi-focus array was divided into even foci and odd foci to increase the distance between adjacent foci and prevent interference (Fig. 1b). The phase profiles generating the even and odd foci were created using a phase summing method and subsequently combined through random multiplexing. This approach minimizes beam quality degradation while reducing interference by using only two random matrices (Fig. 1b). Wave propagation simulations using various parameters confirmed that the proposed method enables multi-focus arrays that are more uniform, have smaller spacing, and possess higher NAs than existing design methods. For simulation verification, a silicon nitride (SiN) multi-focus metalens was fabricated to generate 40 x 40 foci designed to operate at 488 nm with a spacing of 3 μm and an NA of 0.7. Furthermore, it was demonstrated that the spacing could be further reduced using polarization modulation. Since orthogonally polarized light does not interfere with each other, adopting polarization modulation can generate a denser multi-focus array, which was named the "Polarization Hybrid Multiplexing Method."

[0011] As a proof of concept, a multifocal metalens-based image scanning microscopy (MMISM) was constructed using the proposed multifocal metalens (Fig. 1c). Through MMISM, performance exceeding the diffraction limit was demonstrated in phantom imaging. MMISM imaging, using 0.03 μm fluorescent beads at NA 0.5, achieved a resolution of approximately 290–390 nm based on the full width at half maximum (FWHM), which is about twice the resolution of approximately 550–600 nm obtained from wide-field microscopy (WF). Furthermore, the complex structure of neurons was successfully visualized in 40 μm-thick forebrain organoid sections stained with MAP2 and pTau antibodies. Detailed observation of neuronal structures is crucial for elucidating the functionality of the nervous system. MMISM provides improved resolution and optical cross-sectioning effects compared to wide-field microscopy, and more clearly represents neuronal fiber structures. MMISM successfully resolved sub-diffraction limit fine structures separated to approximately 300-400 nm, which were indistinguishable under wide-field microscopy. The hybrid multiplexing method proposed in this study provides a promising strategy for implementing novel optical modulation applications such as MMISM.

[0012] Throughout this specification, numerous papers and patent documents are referenced and cited. The disclosures of the cited papers and patent documents are incorporated by reference into this specification in their entirety to more clearly explain the state of the art to which the present invention pertains and the content of the present invention.

[0013]

[0014] The inventors have made diligent research efforts to develop a high-density and uniform multi-focus array method. As a result, the present invention was completed by identifying that a high-density and uniform multi-focus array is possible by dividing the target multi-focus array into an even foci and an odd foci to increase the distance between adjacent foci to prevent interference, forming a phase profile that generates the even and odd foci using a phase summing method, and then combining them through random multiplexing.

[0015] Therefore, the objective of the present invention is to provide a multi-focus array method.

[0016] Another objective of the present invention is to provide a multi-focus metalens.

[0017] Another objective of the present invention is to provide a microscope comprising the metalens.

[0018] Other objects and advantages of the present invention will become more apparent from the following detailed description of the invention, claims, and drawings.

[0019]

[0020] In one aspect of the present invention, the present invention provides a multi-focus array method comprising the following steps:

[0021] (a) combining phase profiles for light sources corresponding to positions where x+y+z is even or odd in three-dimensional grid coordinates (x,y,z), respectively, to form an even phase map and an odd phase map for generating a focus array corresponding to said even position or odd position; and

[0022] (b) A step of integrating the formed even phase map and odd phase map.

[0023] The inventors have made diligent research efforts to develop a high-density and uniform multi-focus array method. As a result, it was discovered that a high-density and uniform multi-focus array is possible by dividing the target multi-focus array into an even foci and an odd foci to increase the distance between adjacent foci to prevent interference, forming a phase profile that generates the even and odd foci using a phase summing method, and then combining them through random multiplexing.

[0024] In this specification, the term "grid coordinates (x,y,z)" refers to criteria for specifying the positions of a multi-focus array. In the grid structure, the coordinates of each position are classified into even positions and odd positions based on whether the x+y+z value is even or odd. This classification is intended to reduce interference by physically separating the focus arrays and to increase the density of the arrays. For example, positions where x+y+z is even correspond to even focus arrays, and positions where x+y+z is odd correspond to odd focus arrays. This increases the distance between focus arrays and minimizes interference between arrays, thereby enabling the creation of a uniform multi-focus array.

[0025] The above x, y, and z represent three-dimensional spatial coordinates for implementing a multi-focus array in the present invention, and each coordinate is used to define a grid structure or specify a particular location. Array groups can be distinguished based on even and odd numbers using the x+y+z values, and this includes regular or random arrays. x and y define coordinates in a two-dimensional plane, while z is used as an axis indicating the depth or position of the focus.

[0026] In one embodiment of the present invention, x, y, and z are integers. For example, x, y, and z are positive integers, negative integers, 0, or a combination thereof.

[0027] In one embodiment of the present invention, z is a constant. When z is a constant, the focus array method is a two-dimensional or planar focus array method. For example, by setting the surface z value of the plane to be observed to an arbitrary constant value and arranging the focus for the case where z is the constant, a two-dimensional multiple focus formed on the surface of the plane to be observed can be arranged.

[0028] In one aspect of the present invention, the present invention provides a multi-focus array method comprising the following steps:

[0029] (a) combining phase profiles for light sources corresponding to positions where x+y is even or odd in 2D grid coordinates (x,y), respectively, to form an even phase map and an odd phase map for generating a focus array corresponding to said even position or odd position; and

[0030] (b) A step of integrating the formed even phase map and odd phase map.

[0031] In this specification, the term "phase profile for a light source" refers to the phase distribution of light from a specific light source and is a key element of metalens design. The phase profile defines the phase corresponding to the position of each focal array. This phase design is necessary to generate phase maps for both even and odd positions, thereby optimizing the uniformity and density of the focal array.

[0032] The above even phase map is formed based on a phase profile corresponding to an even position in grid coordinates, and the odd phase map is formed based on a phase profile corresponding to an odd position. Each phase map is designed independently and possesses different phase characteristics to generate a multi-focus array. The independent design of the even and odd phase maps contributes to reducing interference between focus arrays and improving the quality (uniformity, density) of the array.

[0033] In one embodiment of the present invention, the multiple focal points are arranged on the same plane.

[0034] In one embodiment of the present invention, the distance between the nearest phases is 1 to 5 AU (Airy unit). The distance between the nearest phases may be, for example, 1 to 5 AU, 1 to 4.5 AU, 1 to 4 AU, 1 to 3.5 AU, 1 to 3 AU, 1 to 2.5 AU, 1 to 2 AU, 1 to 1.5 AU, 1.5 to 5 AU, 2 to 5 AU, 2.5 to 5 AU, 3 to 5 AU, 3.5 to 5 AU, 4 to 5 AU, 4.5 to 5 AU, 1.5 to 4.5 AU, 2 to 4.5 AU, 2 to 3.5 AU, 2.5 to 4.5 AU, 3 to 4 AU, 3 to 3.5 AU, or 3.5 to 4 AU.

[0035] In one embodiment of the present invention, the wavelength of the light source is 100 to 1500 nm. For example, the wavelength of the light source is 100 to 1500 nm, 100 to 1400 nm, 100 to 1300 nm, 100 to 1200 nm, 100 to 1100 nm, 100 to 1000 nm, 100 to 900 nm, 100 to 800 nm, 100 to 700 nm, 100 to 600 nm, 100 to 500 nm, 100 to 400 nm, 100 to 300 nm, 100 to 200 nm, 200 to 1500 nm, 300 to 1500 nm, 400 to 1500 nm, 500 to 1500 nm, 600 to 1500 nm, 700 to 1500 nm, 800 to It may be 1500 nm, 900 to 1500 nm, 1000 to 1500 nm, 1100 to 1500 nm, 1200 to 1500 nm, 1300 to 1500 nm, 1400 to 1500 nm, 200 to 1200 nm, 200 to 900 nm, 300 to 700 nm, 300 to 400 nm, 400 to 700 nm, 400 to 500 nm, or 600 to 700 nm.

[0036] In one embodiment of the present invention, the focus array method may additionally include conventional methods that a person skilled in the art can adopt to improve the density, uniformity, accuracy, etc. of the focus array. For example, it may additionally include steps of removing out-of-focus light through macro pinholes, pixel rearrangement and image summation, resolution enhancement through deconvolution using a Gaussian kernel, or a combination thereof, but is not limited thereto.

[0037] In one embodiment of the present invention, step (a) is performed repeatedly for different polarization states of the light source.

[0038] Step (a) of the present invention can be performed repeatedly for different polarization states of a light source to generate independent focal arrays for different polarization states in the same lens. In one embodiment of the present invention, phase profiles are generated for right-circularly polarized (RCP) and left-circularly polarized (LCP) states, respectively, to independently form focal arrays corresponding to RCP and LCP. This iterative process can suppress interference between focal arrays and provide optimal array characteristics for each polarization state. Specifically, by independently designing and combining phase maps for each polarization state, multifunctional optical performance can be achieved in a single metalens.

[0039] In one embodiment of the present invention, the different polarization states are polarization states that are orthogonal to each other.

[0040] In the present invention, the term "orthogonal polarization state" refers to the polarization state of two light sources that do not physically interfere with each other, and may be composed, for example, of right-sided light and left-sided light (RCP and LCP) or linear polarization states perpendicular to each other.

[0041] In one embodiment of the present invention, the different polarization states are mutually orthogonal circular polarization, linear polarization, or elliptical polarization.

[0042] The aforementioned circular polarization is most effective for interference suppression within optical devices, while linear and elliptical polarization can utilize their unique properties in specific applications. For example, elliptical polarization is advantageous in asymmetric optical structures, and linear polarization is useful in systems requiring polarization sensitivity.

[0043] In one embodiment of the present invention, step (b) is integrated so that the phases regarding different polarization states are arranged in an alternating grid shape.

[0044] The focus array formed in the multi-focus array method of the present invention is arranged in a form where the phases of different phase maps are intersected. This is a design intended to optimize the distance between foci and suppress interference between arrays through physical separation between even and odd phase maps. In addition, when integrating phase maps for multiple polarization states, the phases regarding different polarization states are arranged in an alternating grid form, thereby increasing the density of the focus array while maintaining uniformity. The arrangement of the phases of different polarization states in an intersecting form means that the phase of the first polarization state is surrounded by the phase of the second polarization state, which is the closest phase.

[0045] In one embodiment of the present invention, the step of forming a phase map by combining the phase profiles is performed through a method selected from the group consisting of a phase addition method, a phase optimization method, a periodic phase array method, a random phase distribution method, a harmonic phase combination method, a phase inverse design, and combinations thereof. However, it is not limited thereto and includes any method capable of forming a phase map by combining phase profiles.

[0046] In this specification, the term "Phase Addition Method" refers to a technique for combining individual phase profiles to generate a multi-focus array in metalens design. In this method, individual phase profiles corresponding to each focus array are calculated and then linearly added to form a single integrated phase map. The Phase Addition Method is widely used in various multi-focus metalens designs due to its simple implementation and low computational cost. However, this method may result in interference between adjacent foci; in particular, as the spacing between foci decreases, such interference intensifies, which can degrade the uniformity of the array and the quality of the focus.

[0047] In one embodiment of the present invention, the even phase map and the odd phase map are integrated through random multiplexing.

[0048] In the present invention, the term "Random Multiplexing" refers to a method used to suppress interference and improve the uniformity of a focal array during the process of combining multiple phase maps to generate a multi-focal array. In this method, each phase map is multiplied by a binary random matrix and then summed to form a final integrated phase map. The random matrix is ​​designed so that only one phase map is activated at each location and satisfies the condition L1(x,y)+L2(x,y)=1 at all locations. This prevents interference between different phase maps at the same location.

[0049] In one embodiment of the present invention, the even phase map and the odd phase map are integrated using random matrices L1(x,y) and L2(x,y) that indicate whether each phase map is active at a corresponding location, and the random matrix is ​​a binary matrix satisfying L1(x,y)+L2(x,y)=1 at all locations.

[0050] In one embodiment of the present invention, (c) additionally includes the step of arranging the focus according to the phase of the integrated phase map.

[0051] In one embodiment of the present invention, the multi-focus array method minimizes mutual interference between adjacent focal points.

[0052]

[0053] In one embodiment of the present invention, the present invention provides a metalens comprising a plurality of focal points arranged in a grid shape, wherein the distance between the nearest focal points is 1 to 5 AU (Airy unit).

[0054] In the present invention, the term "metalens including a focus" means that the focus of the metalens is formed or arranged in an observation target plane or space. In one embodiment of the present invention, the term "metalens including a focus" may be used with the same meaning as "metalens having a focus," "metalens forming a focus," or "metalens arranging a focus."

[0055] In this invention, the term "AU (Airy Unit)" refers to a spatial unit associated with the diffraction pattern of a focal point in an optical system and is used to define the spacing or size of focal points within the diffraction limit. The AU is calculated based on the wavelength of light (λ) and the numerical aperture (NA) of the optical system, and is generally expressed as 1 AU = 1.22λ / NA. Here, λ represents the wavelength of the light source, and NA represents the numerical aperture of the lens. The AU is useful for evaluating the spacing between focal points or optical resolution, and is utilized as a criterion for optimizing focal density or reducing interference, particularly in the design of multi-focus arrays. As the AU value decreases, the spacing between focal points narrows and density increases; however, since this can lead to increased interference, a balance is required during design. The AU is used to quantitatively compare optical performance and serves as an important indicator in the design of ultra-high-resolution optical devices such as metalens.

[0056] The distance between the nearest focal points may be, for example, 1 to 5 AU, 1 to 4.5 AU, 1 to 4 AU, 1 to 3.5 AU, 1 to 3 AU, 1 to 2.5 AU, 1 to 2 AU, 1 to 1.5 AU, 1.5 to 5 AU, 2 to 5 AU, 2.5 to 5 AU, 3 to 5 AU, 3.5 to 5 AU, 4 to 5 AU, 4.5 to 5 AU, 1.5 to 4.5 AU, 2 to 4.5 AU, 2 to 3.5 AU, 2.5 to 4.5 AU, 3 to 4 AU, 3 to 3.5 AU, or 3.5 to 4 AU, but is not limited thereto.

[0057] The term "metasurface" in this specification refers to an artificially designed, extremely thin surface, generally composed of nanoscale structures. These nanostructures can manipulate interactions with electromagnetic waves, particularly light, to control optical properties such as refraction, reflection, polarization, and phase change. Metasurfaces are much smaller than traditional optical elements and can manipulate light more efficiently; thanks to these characteristics, they are applicable in various fields such as optics, sensors, communications, and imaging. Furthermore, metasurfaces can be applied to lenses that allow light to pass through while adjusting focus based on optical properties (amplitude, phase, etc.), and such lenses are referred to as metalenses.

[0058] In this specification, the substrate of the meta-lens may be made of any one of the materials among glass (fused silica, BK7, etc.), quartz, polymer (PMMA, SU-8, etc.) and plastic, and may also be a semiconductor substrate.

[0059] In one embodiment of the present invention, the meta-lens may be formed by a nanostructure comprising hydrogenated amorphous silicon (a-Si:H), SiN (silicon nitride), or a combination thereof, on a silicon dioxide glass substrate.

[0060] In one embodiment of the present invention, a meta-lens may be manufactured using a lithography technique utilizing an electron or photon beam, etc. In the lithography technique for manufacturing the meta-lens, a focused beam may be scanned across the surface of a substrate to create a pattern corresponding to a desired meta-surface structure. In some cases, the surface of the substrate may be coated with a resist material that changes properties when exposed to beam energy. Depending on the type of resist material used, either the exposed resist material or the unexposed resist material may be selectively removed, while the other portion remains on the surface of the substrate. When the resist material is selectively removed, the substrate may be exposed and etched (e.g., by wet etching, dry etching, reactive-ion etching (RIE), etc.) to remove a portion of the substrate material. In some cases, the etching process may create geometric features of a meta-surface on the surface of the substrate material to form the meta-lens. In some cases, the manufacturing process can be time-consuming and costly because geometric features of the meta-surface must be patterned onto the resist material by directing a focused beam onto the resist material.

[0061] Systems, devices, processes (also referred to as methods), and computer-readable media (collectively referred to as systems and techniques) are described herein for manufacturing meta-lenses and optical systems including meta-lenses in a scalable manner. For example, semiconductor manufacturing technology is used to simultaneously produce multiple devices (e.g., microprocessors, application-specific integrated circuits, etc.) on a single silicon wafer. In contrast to the lithography technique described above, features manufactured on the surface of the silicon wafer are not drawn individually.

[0062] Instead, features of the device (or negative representations of the features) can be patterned onto a mask. Features of a single device can be repeated in an array to fill an area (or part of an area) of the surface of a silicon wafer having multiple devices. By a single exposure to light, the pattern on the mask can be transferred to a photosensitive resist (photoresist) material. In semiconductor manufacturing, multiple masks may be used to manufacture different features of the device, such as metal layers, transistors, passivation layers, mechanical structures, etc. Therefore, it would be advantageous if the photolithography process used to manufacture semiconductors could also be used to manufacture meta-lenses.

[0063] In some embodiments, silicon materials used in many semiconductor manufacturing applications are transparent to certain wavelengths of light. In some cases, optical applications can detect light at wavelengths to which silicon is transparent. Therefore, silicon can be a suitable substrate material for manufacturing meta-lenses for image sensing applications, where silicon is transparent to the wavelengths of light being detected. For example, applications use short-wave infrared (SWIR). In some cases, SWIR-sensitive image sensors can be manufactured using semiconductor manufacturing techniques. For example, SWIR-sensitive imagers can be manufactured on silicon wafers using germanium-silicon (GeSi)-based complementary metal-oxide-semiconductor (CMOS) technology. In some cases, the semiconductor manufacturing techniques described above can be used to manufacture meta-lenses on silicon wafers.

[0064] For some optical applications, silicon may not be a suitable substrate for manufacturing meta-lenses because the wavelengths of light relevant to the application may not be able to pass through silicon. For example, silicon is opaque at visible light wavelengths. Many optical applications detect light at visible wavelengths. In such cases, materials that are transparent at visible light wavelengths may be suitable substrates for manufacturing meta-lenses. In one exemplary example, meta-lenses can be fabricated on a glass substrate. In some cases, nanoimprinting lithography techniques can be used to fabricate meta-lenses on a glass substrate.

[0065] In one embodiment of the present invention, the diameter of the metalens is 100 to 1000 μm. The diameter of the metalens is, for example, 100 to 1000 µm, 100 to 900 µm, 100 to 800 µm, 100 to 700 µm, 100 to 600 µm, 100 to 500 µm, 100 to 400 µm, 100 to 300 µm, 100 to 200 µm, 200 to 1000 µm, 300 to 1000 µm, 400 to 1000 µm, 500 to 1000 µm, 600 to 1000 µm, 700 to 1000 µm, 800 to 1000 µm, 900 to 1000 µm, 200 to 900 µm, 300 to 800 µm, It is 400 to 700 μm, 400 to 600 μm, or 450 to 550 μm, but is not limited thereto.

[0066] In one embodiment of the present invention, the height of the metalens is 100 to 1000 nm. The height of the metalens is, for example, 100 to 1000 nm, 100 to 900 nm, 100 to 800 nm, 100 to 700 nm, 100 to 600 nm, 100 to 500 nm, 100 to 400 nm, 100 to 300 nm, 100 to 200 nm, 200 to 1000 nm, 300 to 1000 nm, 400 to 1000 nm, 500 to 1000 nm, 600 to 1000 nm, 700 to 1000 nm, 800 to 1000 nm, 900 to 1000 nm, 200 to 900 nm, 300 to 800 nm, 400 to 700 nm, 400 to 600 nm nm, or 450 to 550 nm, but is not limited thereto.

[0067] In one embodiment of the present invention, the metalens has 10 to 2500 focal points. For example, it may have 10 to 2500, 10 to 2000, 10 to 1500, 10 to 1000, 10 to 500, 100 to 2500, 500 to 2500, 1000 to 2500, 1500 to 2500, 2000 to 2500, or 1000 to 2000 focal points, but is not limited thereto. The number of focal points included in the metalens may vary depending on the area of ​​the metalens within the distance range between the closest focal points.

[0068] In one embodiment of the present invention, the numerical aperture (NA) of the metalens is 0.5 to 2.0. The term numerical aperture as used herein measures the ability of a lens to collect light and refers to an important parameter, mainly in microscopes or other optical instruments. The numerical aperture can be calculated using the formula NA = n x sin(θ). Here, n represents the refractive index of the medium, and θ represents the maximum angle (half-angle) between the light ray passing through the lens and the lens optical axis.

[0069] In one embodiment of the present invention, the metalens has the characteristic of manipulating the phase of a light source so that when a first light and a second light having different wavelengths are transmitted, the phase change is the same, and the difference in wavelength between the first light and the second light is 10 nm to 100 nm. The difference in wavelength between the first light and the second light may be, for example, 10 nm to 100 nm, 10 nm to 90 nm, 10 nm to 80 nm, 10 nm to 70 nm, 10 nm to 60 nm, 10 nm to 50 nm, 10 nm to 40 nm, 10 nm to 30 nm, 10 nm to 20 nm, 20 nm to 100 nm, 30 nm to 100 nm, 40 nm to 100 nm, 50 nm to 100 nm, 60 nm to 100 nm, 70 nm to 100 nm, 80 nm to 100 nm, 90 nm to 100 nm, 20 nm to 80 nm, 30 nm to 70 nm, 30 nm to 60 nm, 30 nm to 50 nm, or 30 nm to 40 nm. However, it is not limited to this.

[0070] In one embodiment of the present invention, the material of the metalens or the nanostructure included in the metalens is selected from the group consisting of hydrogenated amorphous silicon (a-Si:H), hydrogenated amorphous silicon nitride (a-SiNx:H), and hydrogenated amorphous silicon oxide (a-SiOx).

[0071] When fabricating meta-lenses using hydrogenated amorphous silicon, deposition can be performed at low temperatures, and absorption in the visible light region can be reduced compared to amorphous silicon (a-Si). Hydrogenated amorphous silicon (a-Si:H) offers low manufacturing costs and high efficiency, and can provide efficient meta-surfaces in the visible light region.

[0072] In one embodiment of the present invention, the plurality of focal points are formed according to the multi-focus array method.

[0073] In one embodiment of the present invention, the distance between the nearest focal points of the metalens is 1 to 10 μm. The distance between the nearest focal points is, for example, 1 to 10 µm, 1 to 9.5 µm, 1 to 9 µm, 1 to 8.5 µm, 1 to 8 µm, 1 to 7.5 µm, 1 to 7 µm, 1 to 6.5 µm, 1 to 6 µm, 1 to 5.5 µm, 1 to 5 µm, 1 to 4.5 µm, 1 to 4 µm, 1 to 3.5 µm, 1 to 3 µm, 1 to 2.5 µm, 1 to 2 µm, 1 to 1.5 µm, 1.5 to 10 µm, 2 to 10 µm, 2.5 to 10 µm, 3 to 10 µm, 3.5 to 10 µm, 4 to 10 µm, 4.5 to 10 µm, 5 It may be up to 10 µm, 6 to 10 µm, 6.5 to 10 µm, 7 to 10 µm, 7.5 to 10 µm, 8 to 10 µm, 8.5 to 10 µm, 9 to 10 µm, 9.5 to 10 µm, 2 to 8 µm, 2 to 6 µm, 2 to 4 µm, or 3 to 4 µm, but is not limited thereto.

[0074] In one embodiment of the present invention, the numerical aperture (NA) of the metalens is 0.5 to 1.0. For example, the numerical aperture of the metalens may be 0.5 to 1.0, 0.5 to 0.9, 0.5 to 0.8, 0.5 to 0.7, 0.5 to 0.6, 0.6 to 1.0, 0.7 to 1.0, 0.8 to 1.0, 0.9 to 1.0, 0.6 to 0.9, 0.6 to 0.8, or 0.7 to 0.8, but is not limited thereto.

[0075]

[0076] In one embodiment of the present invention, the present invention provides a microscope comprising the metalens.

[0077] In one embodiment of the present invention, the microscope may include parts, accessories, software, configurations, etc. of a general microscope that can be adopted by a person skilled in the art. For example, it may include, but is not limited to, a light source, an objective lens, an eyepiece, a stage, an optical filter and aperture, a camera, or a sensing device.

[0078] Specifically, it may include at least one of the following components, but is not limited thereto:

[0079] Light Sources and Illumination Systems: Laser source, LED source, optical fiber light transmission system, condenser, Kohler illumination device

[0080] Optical systems: Beam splitter, relay lens, tube lens, various aberration-corrected lenses

[0081] Machinery and Control Systems: Auto-Focusing System, Anti-vibration Table, Incubator System for Live Cell Imaging

[0082]

[0083] In one embodiment of the present invention, the microscope is an image scanning microscope.

[0084] In one embodiment of the present invention, the image scanning microscope may include components, accessories, software, configurations, etc. of a conventional image scanning microscope that can be adopted by a person skilled in the art. For example, it may include a scanning module, an array detector, a computer control and data processing system, a sophisticated optical filter system, and a motorized stage. Specifically, it may include a system characterized by providing a resolution exceeding the diffraction limit through pixel reassignment and deconvolution, including a multi-focus metalens, an intermediate image plane, a beam expander, a dichroic mirror, a bandpass filter, a tube lens, and an sCMOS camera, but is not limited thereto.

[0085]

[0086] The features and advantages of the present invention are summarized as follows:

[0087] (a) The present invention provides a multi-focus array method.

[0088] (b) The present invention provides a multi-focus metalens.

[0089] (c) The present invention provides a microscope comprising the metalens.

[0090] (d) When using the multi-focus array method of the present invention, the focus can be uniformly distributed at high density, and when using a metalens to which the method is applied, an ultra-high resolution image scanning microscope can be manufactured.

[0091]

[0092] Figure 1 shows an overview of a multi-focus metalens-based image scanning microscope system. (Figure 1a) Illustration of a multi-focus metalens. (Figure 1b) Schematic representation of a hybrid multiplexing method for multi-focus metalens design. Hybrid multiplexing is a novel method that combines existing phase addition and random multiplexing techniques to generate a dense array of multiple focal points. Odd and even phase maps are generated through the phase addition method, and the two phase maps are subsequently integrated through random multiplexing to minimize coherent interference between focal points. d min represents the minimum spacing between odd or even focal points, and the spacing s of a multifocal metalens is d min It is smaller than. (Fig. 1c) Illustration of a multifocus metalens-based image scanning microscope system. MM; multifocus metalens, IP; intermediate image plane, BE; beam expander, DM; dichroic mirror, BP; bandpass filter, TL; tube lens. (Fig. 1d) Data acquisition and image processing workflow of a multifocus metalens-based image scanning microscope system. Deconv means deconvolution.

[0093] Figure 2 relates to the characterization and comparison of conventional and hybrid multiplexing methods. (Figure 2a) Schematic representation of the conventional multiplexing method (phase addition and random multiplexing) and the proposed hybrid multiplexing method. (Figure 2b) Representative simulation PSFs of multifocal arrays generated by the phase addition (top), random multiplexing (middle), and hybrid multiplexing (bottom) methods. The multifocal arrays were designed at 20 x 20 focal points, 3 μm spacing, 0.7 NA, and 488 nm wavelength. Scale bar: 10 AU. (Figure 2c) Quality comparison of multifocal arrays generated by the three multiplexing methods in terms of resolution and SNR. (Figure 2d) Quality analysis of the multifocal arrays in terms of uniformity and intensity.

[0094] Figure 3 shows the experimental verification results of the fabricated multifocus metalens. Figure 3a shows (a) the phase profile of the multifocus metalens generating 40 x 40 focal points at 3 μm intervals and 0.7 NA under 488 nm light illumination, (b) an optical microscope image of the fabricated multifocus metalens, (c) a scanning electron microscope (SEM) image of the SiN meta-atom of the fabricated multifocus metalens, (d) a PSF image obtained from numerical simulation of the designed multifocus metalens, and (e) an experimentally obtained PSF image of the fabricated multifocus metalens. For accurate comparison with the simulation, binary linear interpolation was applied to the experimentally obtained PSF image to match the pixel size with the simulation data. Scale bar: 20 μm. Figure 3b shows (f) the PSF image obtained from simulation (top). This is the image cropped from (d), and the cropping location is indicated by the magenta arrow. The bottom shows the corresponding horizontal intensity profile. Scale bar: 400 nm. (g) the experimentally obtained PSF image (top). This is the image cropped from (e), and the cropping location is indicated by the magenta arrow. The bottom shows the corresponding horizontal intensity profile. Scale bar: 400 nm.

[0095] Figures 3c to 3e show the quantitative analysis results of multi-focus array PSFs obtained from simulation and experiment. (Figure 3c) Normalized average peak intensity of the multi-focus array. (Figure 3d) Absolute intensity difference between simulation and experimentally obtained multi-focus array images related to distance from the center. (Figure 3e) Absolute difference in FWHM related to distance from the center.

[0096] Figure 4 shows the MMISM imaging results of human forebrain organoids and microbeads. (Figure 4a) Image processing pipeline for MMISM reconstruction. The MMISM reconstruction process includes multi-focus image stack acquisition, macro pinhole application, pixel repositioning, summation, and deconvolution steps. Scale bar: 10 μm. (Figure 4b) WF (top left) and MMISM (bottom left) images of 0.03 μm microbeads and corresponding intensity profiles (right). The resolution measured by MMISM (~290–390 nm) is approximately twice as high as the resolution of WF (~550–600 nm). Images were upsampled by 2x. (Figure 4c) WF (e) and MMISM (f) images of section organoid samples immunostained with MAP2 neuronal markers. The MMISM images show sharper and more distinct fibrous structures compared to the WF images. Scale bar: 10 μm. (Fig. 4d) Intensity profile of the selected region (i-iii) indicated by the dashed line in Fig. 4c. MMISM successfully resolved the microstructure separated to about 300-400 nm, whereas WF could not distinguish these structures.

[0097]

[0098] The present invention will be described in more detail below through examples. These examples are intended solely to explain the invention more specifically, and it will be obvious to those skilled in the art that the scope of the invention is not limited by these examples according to the gist of the invention.

[0099]

[0100] Examples

[0101] Example 1: Materials and Method

[0102] 1-1. Numerical Simulation

[0103] A meta-atom library was created using TORCWA55, a Python library for RCWA (Rigorous Coupled-Wave Analysis) electromagnetic simulations. Silicon dioxide (SiO2) was used as the substrate, and the heights of the meta-atoms were set to 750 nm and 500 nm for SiN and a-Si:H, respectively. All complex refractive index data were measured using ellipsometry.

[0104] The phase profile of the multifocal metalens was calculated using the CuPy Python library, and matrix operations were accelerated using the GeForce TRX 4090 (NVIDIA) GPU. The unpolarized multifocal metalens operating at 488 nm were optimized under various conditions, and a fabrication standard was selected with an NA of 0.7, a spacing of 3.5 AU, a diameter of 1 mm, and 40 x 40 focal lengths. The Airy unit (AU) is expressed as AU = 1.22λ / NA.

[0105] Meanwhile, a polarization-dependent multifocal metalens operating at 633 nm was designed with an NA of 0.7, a spacing of 2 AU, a diameter of 100 μm, and 12 x 12 focals. The Point Spread Function (PSF) of the designed multifocal metalens was numerically simulated using Rayleigh-Sommerfeld propagation.

[0106] The coherently overlapping field strength is It was calculated as. The strength of the incoherently superimposed field is It was calculated as follows. Here, I is the result intensity, and u k represents individual fields participating in the interference.

[0107] Incoherent superposition equations were used for the performance simulation of multifocal metalens designed using a polarization hybrid multiplexing method. This simulation setup enabled precise performance evaluation and optimization of the multifocal metalens design.

[0108]

[0109] 1-2. Metalens Fabrication

[0110] To fabricate a polarization-independent multifocal metalens, a 750 nm thick SiN layer was deposited on a SiO2 substrate using plasma-enhanced chemical vapor deposition (PECVD; Oxford, PlasmaPro 100 Cobra). Subsequently, a 200 nm thick positive photoresist (AR-P 6200.09, Allresist) was spin-coated onto the SiN film at 4000 RPM. To prevent charge accumulation, 100 μL of ESPACER (RESONAC, 300Z) was spin-coated at 2000 RPM for 30 seconds.

[0111] A circular meta-atom design was patterned onto a positive photoresist using electron beam lithography (EBL; NanoBeam, nB5, irradiation dose: 3.75 C / m²). The exposed photoresist was developed for 690 seconds in a 1:3 ratio solution of methyl isobutyl ketone (MIBK) and isopropyl alcohol (IPA). Subsequently, a chromium (Cr) layer with a thickness of 40 nm was deposited using an electron beam deposition system (ULVAC, Ei-5k).

[0112] The unexposed photoresist was removed via a lift-off process using acetone at room temperature for 2 hours. During this process, the Cr layer remains as a hard mask. Patterning was completed by performing an inductively coupled plasma etching (ICP; STS, multiplex ICP) process using SF6 (15 sccm) and C4H8 (40 sccm) gases for 610 seconds. Subsequently, the Cr hard mask was removed using a Cr etchant (TRANSENE, CE-905N) for 5 minutes.

[0113] To fabricate a polarization-dependent multifocal metalens, the same process was used, but rectangular meta-atoms were patterned on an a-Si:H film with a thickness of 500 nm.

[0114]

[0115] 1-3. Optical Characterization

[0116] The focus of the multifocal metalens was characterized using an optical microscope. 450 nm (Thorlabs, CPS450) and 635 nm (Thorlabs, CPS635) lasers were used as light sources, and the beam diameter was adjusted to the metalens diameter using an iris.

[0117] The Point Spread Function (PSF) of the metalens was recorded using a magnification system consisting of a 100x objective lens (Olympus, NA 0.9), a tube lens (Thorlabs, TTL180-A), and an sCMOS camera (Alvium, 1800 U-235). The pixel size of the system is 58.6 nm.

[0118] This configuration was designed to accurately observe the PSF of the metalens at high resolution and was used to experimentally verify the performance of the fabricated metalens.

[0119]

[0120] 1-4. Multifocal Metalens-based Image Scanning Microscopy (MMISM) System Configuration and Data Acquisition

[0121] MMISM imaging was performed using a custom-built system. A 488 nm laser (Coherent OBIS, 488 nm LX 150 mW) was used as the excitation light, and the beam diameter was adjusted to 1 mm using a beam expander and an iris. For multifocus illumination, the PSF of the multifocus metalens was delivered to the sample plane without magnification using two identical 20x objective lenses (Olympus, NA 0.50).

[0122] The imaging system was configured as follows: a 20x objective lens (Olympus, 0.50 NA), a dichroic mirror (Edmund Optics, 67-080), a bandpass filter (Edmund Optics, 67-030), a tube lens (Thorlabs, TTL180-A), and an sCMOS camera (Thorlabs, CS895MU).

[0123] The fluorescence signal was collected through the imaging system. The magnification of the system was 20x, and the pixel size was set to 172.5 nm.

[0124] The 3-axis motor drive stage (Thorlabs, MT3 / M-Z9) was controlled using three DC servo motor controllers (Thorlabs, KDC101), which were synchronized with the sCMOS camera via a trigger I / O breakout board (Thorlabs, TSI-IOBOB2). Before data acquisition, the rotation angle of the multi-focus metalens was adjusted to be parallel to the camera pixels using a rotation mount (Thorlabs, CRM1PT / M).

[0125] MMISM data was acquired by scanning the motor drive stage under multi-focus illumination with a step size of 172.5 nm in the x and y directions. A total of 289 frames (17 x 17) were acquired to smoothly record the entire 120 μm FOV.

[0126] This system ensures accurate focus array alignment and high data quality, and is designed to efficiently collect the data required for MMISM reconstruction.

[0127]

[0128] 1-5. MMISM Reconstruction

[0129] MMISM reconstruction was implemented using open-source Python code for ISM reconstruction. The MMISM reconstruction procedure includes pinholing, pixel reassignment, image summation, and deconvolution steps.

[0130] Out-of-focus light was removed by multiplying the sub-image of each individual focal point by a Gaussian function as a macro pinhole. The standard deviation (STD) of the macro pinhole was empirically determined to be 770 nm and used. After pinholeing, pixel repositioning was performed by locally reducing the pinholed image and repositioning it into a 2x upsampled image.

[0131] The image with rearranged pixels was superimposed and integrated into a single image, and in this process, the resolution It was improved by a factor. Subsequently, the image was deconvolved using a Gaussian kernel, and the resolution was doubled. The standard deviation (STD) of the Gaussian kernel was determined as follows:

[0132]

[0133] This process enabled the realization of ultra-high resolution MMISM imaging and provided structural details that were significantly improved compared to existing optical technologies.

[0134] σ eff , σ ex , and σ em ε₀ and ε₀ represent the standard deviations (STD) of the effective PSF, excitation PSF, and emission PSF, respectively, and mm represents the scaling factor. In practice, a value of 0.5 is widely used as the scaling factor mm value (Equations (1), (2)).

[0135] Wavelengths of 488 nm and 520 nm were used to determine the size of the PSF and the emitted PSF, respectively.

[0136]

[0137] 1-6. Generation of Forebrain Organoids from iPSCs

[0138] Forebrain organoids were derived from human induced pluripotent stem cells (h-iPSCs). In the initial stage, h-iPSCs were cultured in mTeSR Plus medium (Stemcell Technologies, ST100-0276) on plates coated with Matrigel hESC-Qualified Matrix (Corning). To generate embryoid bodies (EBs), h-iPSCs were detached from the plates using ReLeSR, and the resulting colonies were isolated into single cells by adding the ROCK inhibitor Y-27632 (Stemcell Technologies, ST72304) to AggreWell EB Formation Medium (Stemcell Technologies, ST05893). On Day 0, 1.5 x 1061.5 cells / times 10^6 were loaded into each well of an AggreWell800 24-well plate (Stemcell Technologies, 34811). On Day 1, the medium was replaced with EB Formation Medium, and Y-27632 was removed. From Day 2 to Day 5, the medium was replaced daily, and the medium used consisted of the following components: DMEM / F-12 with GlutaMAX (Gibco, 10565-018); 20% KnockOut Serum Replacement (Gibco, A3181501); 1% MEM Non-Essential Amino Acid Solution (Gibco, 11140050); 0.1 mM 2-Mercaptoethanol (Gibco, 21985023); 100 U / mL Penicillin and 100 μg / mL Streptomycin (Merck, P4333); Additionally, SMAD inhibitors Dorsomorphin (10 μM; Merck, P5499) and SB-431542 (10 μM; TOCRIS, 1614).On day 6, a total of 96 EBs were collected, and on day 7, each EB was placed in an individual well of a 96-well ultra-low attachment microplate (Corning, 7007).

[0139] Subsequently, the organoids were maintained in neural medium. The neural medium consisted of the following components: Neurobasal-A Medium (Gibco, 10888-022); B-27 Supplement Minus Vitamin A (Gibco, 12587010); 100 U / mL Penicillin and 100 μg / mL Streptomycin; GlutaMAX (Gibco, 35050-061); 0.5% (v / v) Matrigel Basement Membrane Matrix (Corning, 354234).

[0140] From day 6 to day 15, the medium was replaced daily, and 20 ng / mL of EGF (Peprotech, AF-100-15-500 μg) and 20 ng / mL of bFGF (R&D Systems, 100-18B) were added. From day 16 to day 24, the same medium was used but replaced every two days. From day 25 to day 42, the medium was replaced every two days, and 20 ng / mL of BDNF (Peprotech, 450-02) and 20 ng / mL of NT-3 (Peprotech, 450-03) were added instead of EGF and bFGF. From day 43 onwards, the medium was replaced every four days with a neuro-medium without growth factors.

[0141]

[0142] 1-7. Immunocytochemistry

[0143] The organoids were washed with Phosphate-Buffered Saline (PBS), then fixed overnight at 4°C in a 4% paraformaldehyde (PFA) solution. Afterward, they were washed again with PBS. The fixed organoids were dehydrated in a 30% sugar solution at 4°C for 72 hours. They were then transferred to a cryomold and frozen with FSC 22 Compound (Leica, 3801480). The frozen organoids were sectioned using the cryosection technique, washed with PBS, and then permeabilized in a PBS solution containing 0.3% Triton X-100 (Merck, X100) at room temperature for 30 minutes. The sectioned tissues were blocked in a PBS solution containing 5% Normal Horse Serum (Sigma-Aldrich, H0146) at room temperature for 1 hour.

[0144] The primary antibody (pTau: Thr181 (1:500; Invitrogen, MN1050); MAP2 (1:500; Abcam, ab254143)) was diluted in blocking solution, added to tissue sections, and reacted overnight at 4°C. The fluorescence-conjugated secondary antibody (fluorescence-conjugated antibody (1:500, 3% BSA / PBS)) was diluted 1:500 in PBS solution containing 3% Bovine Serum Albumin (BSA) and reacted for 1 hour at room temperature. After the reaction, the sections were washed and mounted on slides.

[0145]

[0146] Example 2: Multi-focus metalens design strategy

[0147] The generation of high-density multifocal arrays plays a critical role in the implementation of Image Scanning Microscopy (ISM), particularly in terms of scanning speed and reconstruction quality. In the field of metalens, various design methods have been proposed to generate multifocal arrays, including metalens arrays, diffraction gratings, and multiplexing phase profiles. However, metalens arrays exhibit a tradeoff between NA and the number of focal points. Multifocal arrays based on diffraction gratings are limited in uniformity and focal point count due to diffraction angles. Furthermore, in multiplexing phase profiles, the number of available focal points is limited by the metalens size.

[0148] In the present invention, hybrid multiplexing, a novel design strategy combining two existing phase multiplexing techniques (phase addition multiplexing and random multiplexing), was used to generate a high-density multi-focus array (Figs. 1b and 2a). Phase profile addition is the most common method for generating multiple focal points through a single metalens. The integrated phase profile (ψ) of a multi-focus metalens generating focal points of an n x n regular grid array through this phase addition method can be expressed as follows (Fig. 2a):

[0149]

[0150] n, φ_ij, f, (x0, y0), λ, and s represent the number of focal points in the column and row, the phase profile of the individual metalens, the focal length, the center of the n-xn multi-focal array, the wavelength of the incident light, and the spacing between adjacent focal points, respectively. However, the phase addition method has a disadvantage due to interference when the spacing between focal points is narrow. Generating focal points using this method (Equation (3)) is theoretically optically equivalent to coherently overlapping individual focal points, which results in inter-focal interference. This interference becomes more pronounced as the focal points are placed closer together, leading to artifacts such as undesirable side lobes and non-uniformity in the intensity distribution of the focal points.

[0151] Incoherent focals are less sensitive to interference, but achieving them using a single metalens is a challenging task. A promising alternative is random multiplexing, which is commonly used to combine multiple holograms. This method proceeds by multiplying a binary random matrix by the phase map to be integrated, and then summing the phase maps. The phase profile equation for a multi-focus metalens using random multiplexing is expressed as follows:

[0152]

[0153] n² represents the number of multiplexings, and L(x, y) is a set of binary random matrices satisfying the condition that for specific indices i, j at each position (x, y), only the L_ij value is 1 and all other matrix values ​​are 0 (Equation (6)). The sparsity of the random matrix is ​​defined as the ratio of the area where the element value is 1 to the total area of ​​the metalens, which is set to 1 / n² of the total area of ​​the metalens.

[0154] The random multiplexing method is less sensitive to interference than the phase addition method, providing a more uniform multifocus array. According to the 1D multifocus array results, the intensity uniformity of the focal points generated by random multiplexing was similar to that of incoherent focal points. However, this method has the disadvantage that the focus quality deteriorates significantly as the number of multiplexes increases (Fig. 2b). As the number of multiplexes increases, the random matrix becomes sparser, which leads to the degradation of individual phase profiles during the process of multiplying the random matrix by the phase profile. In fact, according to optical propagation theory, the peak intensity of a specific focal point using random multiplexing is proportional to the square of the metalens area and inversely proportional to the number of multiplexes. Therefore, generating a large number of focal points using the random multiplexing method has limitations in terms of focus quality.

[0155] To address this problem, the inventors introduced a hybrid multiplexing method aimed at generating a high-density, homogeneous multi-focus array for MMISM implementation. This method is designed to combine existing multiplexing methods (phase addition and random multiplexing) to leverage the advantages of each method while minimizing their disadvantages. The phase profile of the hybrid multiplexing can be expressed as follows:

[0156]

[0157] ψ_even and ψ_odd represent phase maps for generating mutually intersecting multiple focus arrays, and L1(x, y) and L2(x, y) are binary random matrices satisfying L1(x, y) + L2(x, y) = 1 for all (x, y). In the hybrid multiplexing method, the interval between adjacent focuses is set to s / 2 (Equation (4)).

[0158] First, interference was prevented by separating the regular grid of the multi-focus array into two intersecting multi-focus grids to increase the spacing between adjacent foci (Fig. 1b). In particular, each phase map (ψ_even and ψ_odd) was designed using a phase addition method to maintain the quality of the multi-focus (Equation (7)). Subsequently, the even phase (ψ_even) and the odd phase (ψ_odd) were integrated through random multiplexing to minimize interference between adjacent foci (Equation (8)).

[0159] It is worth noting that only two random matrices were used to combine the even phase (ψ_even) and the odd phase (ψ_odd), which prevents degradation of the multifocus array quality.

[0160] Simulation results clearly showed that the proposed method produces more uniform, dense, and high-quality focals than the existing method when having the same number of focals and spacing (Fig. 2b).

[0161] This design strategy presents new possibilities for generating high-density multi-focus arrays that overcome the limitations of existing methods while simultaneously achieving interference prevention and quality maintenance.

[0162]

[0163] Example 3: Optimization of Multifocal Metalens Design

[0164] Wave propagation simulations were performed to optimize the performance of multifocal metalens. The key parameters affecting the quality of the multifocal array are wavelength, numerical aperture (NA), metalens diameter, number of focal points, and pitch. In this study, a wavelength of 488 nm and an NA of 0.7 were used unless otherwise specified. Wave propagation simulations were performed at a fixed diameter of 500 μm for various pitches (1–4 Airy units, AU) and numbers of focal points (16–2500) to investigate the effects of these parameters on the quality and uniformity of the multifocal array. Quality, uniformity, and resolution were evaluated by measuring the signal-to-noise ratio (SNR), standard deviation (STD) or relative standard deviation (RSD), and full width at half maximum (FWHM), respectively.

[0165] Since the integration of multiple phase profiles reduces the weights of individual phase profiles, an increasing number of foci led to a tendency for the SNR to decrease regardless of the spacing (Fig. 2c). As previously mentioned, the random multiplexing method was more sensitive to beam quality degradation as the number of foci increased (Fig. 2c). The FWHM of all foci was measured via Gaussian fitting to compare with the theoretical diffraction limit resolution. The fitting results showed that the foci generated by the phase addition and hybrid multiplexing methods fit the Gaussian function well, and the obtained resolution was similar to the theoretical FWHM at the diffraction limit. On the other hand, in random multiplexing, the curve fitting success rate decreased sharply when the number of foci exceeded 300 (Fig. 2c), and the resolution of the successfully fitted foci was up to 20% higher than the diffraction limit (Fig. 2c). In particular, since Gaussian fitting became more difficult with a higher number of foci in random multiplexing, the optimization study focused on comparing the phase addition and hybrid multiplexing methods.

[0166] Unlike SNR, focus uniformity improved as the number of foci increased, and showed a plateau after approximately 1,500 foci (Fig. 2d). Spacing had a significant impact on both average intensity and uniformity (Fig. 2d). Average peak intensity increased with increasing spacing, which is attributed to reduced interference between adjacent foci. Notably, foci generated by the hybrid multiplexing method exhibited higher intensity than those generated by the phase addition method. While the STD of the foci did not show a consistent trend with spacing, the RSD, which reflects both uniformity and brightness, gradually improved with increasing spacing (Fig. 2d).

[0167] In conclusion, increasing the number of focal points offers advantages in terms of ISM uniformity and field of view (FOV), but has the disadvantage of reducing the signal-to-noise ratio (SNR). Reducing the spacing is necessary to improve ISM scanning speed, but this results in disadvantages in terms of uniformity, focal brightness, and FOV. Considering these trade-offs, the inventors fabricated the device by selecting a focal number of 40 x 40 (Fig. 2f) and a spacing of 3.5 AU, at which uniformity reaches a plateau. Although this spacing is not optimized for RSD (Fig. 2d), it provides a balanced setting when considering the ISM FOV. This configuration still offers superior performance compared to the phase-adding method.

[0168] The diameter and NA of a metalens are also important factors in improving beam quality. As the diameter increases, more light is collected, improving the SNR. Additionally, a larger NA reduces the FWHM of the focal point, suppresses inter-focal interference with a narrow spacing, and improves the SNR. To investigate the dependence on NA and diameter, the inventors performed wave propagation simulations for various NAs (0.3-0.7) and diameters (300-1000 μm) while maintaining a fixed number of focal points (40 x 40) and previously optimized values.

[0169] In particular, the inventors used a physical spacing of 3 μm at a wavelength of 488 nm with an NA of 0.7, which corresponds to 3.5 AU. This is to maintain a constant physical spacing to observe only the effect of NA on beam quality, as the physical spacing may vary depending on the NA when using dimensionless optical units (AU). As expected, beam quality was proportional to both the diameter and the NA at a fixed spacing and number of focal points. The inventors decided to construct an ISM by fabricating a metalens with a diameter of 1000 μm and an NA of 0.7. It is expected that an FOV of 120 μm will be achieved through these parameters.

[0170]

[0171] Example 4: Fabrication and Characterization of a Multifocal Metalens

[0172] To generate a meta-atom library, RCWA was performed based on the refractive index of silicon nitride (SiN) measured at 488 nm. Subsequently, the desired meta-atom structure was patterned using electron beam lithography (EBL), and a multifocal metalens was fabricated through lift-off and etching processes (Fig. 3a, see Example 1). The performance of the fabricated multifocal metalens was experimentally verified and compared with simulation results (Fig. 3a).

[0173] Notably, each focal position of the experimentally acquired multi-focus array matched the simulation results well. For a more rigorous analysis, min-max normalization was applied to the multi-focus array images, and the resolution and peak intensity were evaluated by fitting all focal points to a Gaussian function (Fig. 3b). The experimentally measured average peak intensity was approximately 14% lower than the predicted value (Figs. 3c to 3e), and the largest difference occurred at a distance of 20–30 μm from the center of the multi-focus array (Figs. 3c to 3e).

[0174] However, the magnitude of each point diffusion function (PSF) showed a different trend from the peak intensity distribution. The deviation from the simulated value of the PSF magnitude was comparable to a single pixel size (~110 nm) up to a distance of 60 μm from the center, and then decreased as it moved toward the outer region (~80 μm).

[0175] The deviation in intensity and resolution distribution is attributed to manufacturing defects, light source quality, the large pixel size of the camera, and the slight tilt of the metalens. Despite these deviations from the simulation, the performance of the multi-focus metalens generating a 40 χ 40 focus with a 3 μm spacing and NA of 0.7 was superior to that of conventional optical elements such as MLAs.

[0176]

[0177] Example 5: Design and Fabrication of a Polarized Multifocal Metalens

[0178] As previously explained, reducing the pitch offers the advantage of decreasing the number of frames required for ISM reconstruction, but it is limited by interference between coherently generated foci. Generally, it is not feasible to generate incoherent, high-NA foci using conventional diffractive optical elements, spatial light modulators, or metalens designed for unpolarized light. However, Pancharatnam-Berry (PB) phase-based polarization metalens can simultaneously modulate two non-interfering orthogonal polarized lights, enabling the generation of high-NA foci with small pitches.

[0179] The inventors hypothesized that a narrower gap could be achieved by independently modulating right-handed circular polarization (RCP) and left-handed circular polarization (LCP) light, which is a method generally used to create multifunctional or switchable metalens.

[0180] This invention proposes a polarization hybrid multiplexing method that applies independent control of PB phase-based RCP and LCP light to a hybrid multiplexing approach. The key is to generate LCP and RCP multi-focus arrays that intersect each other, designing the array so that each focus is surrounded by other focuses with orthogonal polarization. This prevents interference.

[0181] The orthogonal polarization multifocal array was designed using a hybrid multiplexing method according to the following equation:

[0182]

[0183] ψ_LCP and ψ_RCP represent the target phase profiles for the intersecting multiple focal arrays generated by the respective circularly polarized light. The subscripts 'even' and 'odd' denote even and odd phases for each polarization. In the polarization hybrid multiplexing method, the spacing between adjacent focals is set to s / 2 (Equation (4)).

[0184] To investigate the performance of this method, wave propagation simulations were performed for various focal numbers (25–1600) and spacing (1–4 AU) at a fixed diameter of 500 μm. As expected, the multifocal array generated by the polarization hybrid multiplexing method exhibited higher uniformity than arrays generated by phase addition or conventional hybrid multiplexing methods, even at small spacing (<3 AU).

[0185] For proof of concept, the inventors fabricated a multifocal metalens using a polarization hybrid multiplexing method to generate a denser and more uniform multifocal array. To control the RCP and LCP independently, hydrogenated amorphous silicon (a-Si:H), known for its high refractive index, was selected, and a meta-atom library was generated through RCWA simulation (see Example 1).

[0186] Subsequently, a phase map of a multi-focus metalens was patterned using EBL on a-Si:H with a diameter of 100 μm and a thickness of 500 nm to generate a 12 x 12 focus, the spacing was designed to be 2 AU, and the operating wavelength was set to 633 nm.

[0187] When RCP or LCP light was incident on the multifocal metalens, a multifocal array intersecting the focal plane was formed depending on the polarization state. Additionally, when unpolarized light was irradiated onto the metalens, a complete grating-type multifocal array was generated.

[0188] Simulation results confirmed that the multi-focus array generated by the conventional hybrid multiplexing method under the same conditions exhibited lower uniformity of intensity distribution compared to the polarization hybrid multiplexing method.

[0189] This study demonstrates that the polarization hybrid multiplexing method is a promising design strategy that resolves interference issues and provides higher uniformity and dense multi-focus arrays.

[0190]

[0191] Example 6: Multifocus metalens-based image scanning microscope

[0192] ISM (Image Scanning Microscope) is an ultra-high-resolution imaging technique that exceeds the diffraction limit resolution through pixel rearrangement. Theoretically, the resolution of ISM is through pixel rearrangement It can be improved by a factor of 1, and adding deconvolution can improve it by up to a factor of 2 relative to the diffraction limit. To enable pixel rearrangement, it is essential to use an array detector with a pixel size smaller than the Point Spread Function (PSF) so that the PSF is distributed across multiple pixels. Each pixel of the array detector acts as a single detector with a pixel-sized pinhole. A simple method for implementing ISM is to use multi-focus array illumination and an array detector (e.g., sCMOS or CCD).

[0193] In this study, a custom fluorescence ISM was developed using a fabricated multifocal metalens (40 x 40 focals, 3 μm spacing) as a multifocal array illumination, which covers a Field of View (FOV) of 120 μm (see Fig. 1c and Example 1). The multifocal array PSF was delivered to the sample surface without magnification using two 20x objective lenses (NA 0.5).

[0194] To smoothly image the entire FOV for ISM reconstruction, a multi-focus array PSF was scanned horizontally and vertically at single-pixel intervals (172.5 nm) using a motor-driven stage. The number of scans in each direction was determined using the following equation:

[0195]

[0196] NS represents the number of scans in a single direction, p represents the pixel size, and the square brackets denote the flooring function. For example, [x] returns the largest integer less than or equal to x. In this study, the total NS for single ISM reconstruction 2 That is, 289 frames were required. Here, NSNS was 17 frames calculated using a 3 μm interval (3.5 AU@488 nm) and a 172.5 nm pixel size (Equation (12)). It is worth noting that reducing the interval size by half reduces the number of required frames by a factor of 4 (Equation (12)), thereby improving the imaging speed.

[0197] After multi-focus scanning, ISM reconstruction was applied to the acquired image stack (see Fig. 4a and Example 1).

[0198]

[0199] The inventors experimentally demonstrated Multifocal Metalens-based ISM (MMISM) on 0.03 μm fluorescent beads and immunostained organoid tissues. To characterize optical resolution, image stacks of the fluorescent beads were first recorded under multifocal illumination. The FWHM values ​​of the fluorescent beads obtained by wide-field (WF) microscopy were ~550–600 nm, which were slightly higher than the theoretical FWHM (530 nm). However, through MMISM reconstruction, the resolution was nearly doubled, achieving an FWHM of ~290–390 nm (Fig. 4b).

[0200] Next, ultra-high-resolution imaging using MMISM was further validated on biological samples. Precise recording of complex neuronal structures is essential for elucidating neuronal function and connectivity, and for the study of brain dysfunction and neurodegenerative diseases. The inventors recorded image stacks under multifocal illumination and performed ISM reconstruction on forebrain organoid sections stained with MAP2 and pTau antibodies. MAP2 and pTau label microtubule-associated proteins and represent neuronal structures.

[0201] Compared to WF images, the super-resolution MMISM images showed clearer and more distinct structural features (Fig. 4c). As can be seen from the representative intensity profile (Fig. 4d), MMISM resolved neuronal structures separated by ~300-400 nm well, whereas WF failed to resolve them.

[0202] These results demonstrate the performance of the MMISM equipped with a multi-focus metalens designed using the proposed hybrid multiplexing method, and show its potential in the field of ultra-high resolution imaging.

[0203]

[0204] In conclusion, the inventors developed a novel method called hybrid multiplexing for the design of multifocal metalens that generates a dense and uniform multifocal array. Simulation results confirmed that the proposed method provides a greater number of focal points, a smaller pitch, and improved uniformity compared to existing multiplexing techniques. Furthermore, by introducing independent polarization control, it was possible to reduce the pitch while maintaining focal uniformity.

[0205] For a proof of concept, multifocal metalens were fabricated using a hybrid multiplexing method, and a Multifocal Metalens-based ISM (MMISM) system was constructed. The feasibility of MMISM was demonstrated using micro-bead phantoms and sectioned organoid samples. Experimental results showed that MMISM images achieved approximately twice the resolution compared to wide-field (WF) images. Furthermore, neuronal structures exhibited clearer and more distinct features thanks to resolution exceeding the diffraction limit and the optical sectioning effect.

[0206] In this study, a spacing of 3.5 AU was selected to obtain a large field of view (FOV) for the multifocal metalens used in MMISM. However, hybrid multiplexing can provide a uniform multifocal array even at smaller spacings (<3 AU). While the FOV of MMISM can be increased by increasing the number of focal points, this is limited by a degradation in beam quality. This limitation can be overcome by using large metalens with greater multiplexing capabilities, thereby providing a wider FOV. Although only metalens with a diameter of 1–2 mm can be used at the laboratory scale, research on the mass production of large metalens is actively underway. In particular, the mass production of centimeter-scale metalens utilizing nanoimprint lithography has been reported. These advancements suggest the scalability of large multifocal metalens, offering the potential to further expand the speed and range of MMISM.

[0207] Hybrid multiplexing strategies can be used to combine arbitrary phase maps for various purposes. Therefore, the proposed design approach can be applied not only to multifocal metalens but also to the design of various types of multifunctional metalens. This versatility offers the advantage of providing simpler and more compact imaging systems by integrating multiple optical elements into a single thin metalens.

[0208] Although metalens cannot completely replace existing optical elements for general use, they are expected to serve as an alternative to optical components specialized for specific applications, such as MMISM. It is believed that this invention will open up new possibilities for metalens-based imaging systems, such as MMISM as well as advanced optical microscope systems.

Claims

1. A multi-focus array method including the following steps: (a) combining phase profiles for light sources corresponding to positions where x+y+z is even or odd in three-dimensional grid coordinates (x,y,z), respectively, to form an even phase map and an odd phase map for generating a focus array corresponding to said even position or odd position; and (b) A step of integrating the formed even phase map and odd phase map.

2. A multi-focus array method according to claim 1, wherein step (a) is performed repeatedly for different polarization states of the light source.

3. A multi-focus array method according to paragraph 2, wherein the different polarization states are polarization states orthogonal to each other.

4. A multi-focus array method according to paragraph 2, wherein the different polarization states are mutually orthogonal circular polarization, linear polarization, or elliptical polarization.

5. A multi-focus array method according to paragraph 2, wherein step (b) is integrated such that the phases regarding different polarization states are arranged in an alternating grid shape.

6. A multi-focus array method according to claim 1, wherein the step of forming a phase map by combining the phase profiles is performed through a method selected from the group consisting of a phase addition method, a phase optimization method, a periodic phase array method, a random phase distribution method, a harmonic phase combination method, a phase inverse design, and combinations thereof.

7. A multi-focus array method according to claim 1, wherein the even phase map and the odd phase map are integrated through random multiplexing.

8. A multi-focus array method according to claim 1, wherein the even phase map and the odd phase map are integrated using random matrices L1(x,y) and L2(x,y) indicating whether each phase map is active at a corresponding location, and the random matrix is ​​a binary matrix satisfying L1(x,y)+L2(x,y)=1 at all locations.

9. A multi-focus array method according to claim 1, further comprising (c) a step of arranging the focus according to the phase of the integrated phase map.

10. A multi-focus array method according to claim 1, wherein the multi-focus array method minimizes mutual interference between adjacent focal points.

11. A metalens comprising a plurality of focal points arranged in a grid shape, wherein the distance between the nearest focal points is 1 to 5 AU (Airy unit).

12. A metalens according to claim 11, wherein the plurality of focal points are formed according to the multi-focal arrangement method of any one of claims 1 to 10.

13. A metalens according to claim 11, wherein the distance between the nearest focal points of the metalens is 1 to 10 μm.

14. A metalens according to claim 11, wherein the numerical aperture (NA) of the metalens is 0.5 to 1.

0.

15. A microscope comprising the metalens of claim 11.

16. In paragraph 15, the microscope is an image scanning microscope.

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