Metasurface holographic display method and device and medium

Abstract

The invention relates to a metasurface holographic display method, metasurface holographic display equipment and a medium. The metasurface holographic display method comprises the following steps: acquiring a high-resolution version and a low-resolution version of a target image set; converting the image set of the high-resolution version into a first composite matrix; based on the image set of the low-resolution version, far-field intensity distribution corresponding to the image set is obtained through phase retrieval and transformation calculation, and the far-field intensity distribution is converted into a second composite matrix; according to the first composite matrix and the second composite matrix, solving to obtain an integrated feature matrix; designing a metasurface structure, and enabling the phase distribution of the metasurface structure to be matched with a target image; obtaining far-field intensity distribution generated by the metasurface structure, and converting the far-field intensity distribution into a column vector; and calculating the column vector by using the integrated feature matrix to obtain a reconstructed high-resolution image. According to the method, crosstalk under a multi-channel condition is effectively suppressed, image reconstruction with high signal-to-noise ratio, high fidelity and high resolution is finally realized, and the method has broadband response and multiplexing capabilities.

Description

Technical Field

[0001] This invention relates to the field of interdisciplinary technology of micro-nano optics and computational imaging, specifically to a metasurface holographic display method, device, and medium. Background Technology

[0002] Holographic display technology can reconstruct three-dimensional images of objects by recording and reproducing the amplitude and phase information of light, and has broad application prospects in scientific research, industrial inspection, data storage, and art design. However, traditional holographic technology relies on bulky optical components, such as spatial light modulators (SLMs) and complex interference optical path systems, resulting in complex system structures, high costs, and difficulties in miniaturization and integration, which limits its widespread adoption in practical applications.

[0003] In recent years, metasurfaces, as artificial two-dimensional materials composed of subwavelength structures, have enabled flexible control of wavefronts by manipulating the phase, amplitude, and polarization response of light waves through the unit structure. This provides a new solution for lightweight and integrated holographic displays. Researchers have already realized various metasurface holograms, including three-dimensional holography, polarization-multiplexed holography, and color holography, across multiple wavelengths such as visible light, infrared, terahertz, and microwaves.

[0004] Despite this, existing metasurface holography techniques still face significant challenges. Due to the limited performance of the modulation transfer function (MTF), reconstructed images often suffer from problems such as blurred edges and loss of detail, resulting in low signal-to-noise ratio and spatial resolution. While increasing the metasurface size can improve pixel density to some extent, it significantly increases fabrication difficulty, especially in the visible and near-infrared bands. Furthermore, channel crosstalk in multichannel holograms further degrades image quality, limiting its application in complex image reconstruction and high-capacity information storage. Summary of the Invention

[0005] This invention provides a metasurface holographic display method, device, and medium, which aims to solve the problems of blurred details, low signal-to-noise ratio, and low resolution in reconstructed images caused by insufficient modulation transfer function performance and channel crosstalk in metasurface holographic displays.

[0006] To achieve the above objectives, the first aspect of the present invention provides a metasurface holographic display method, comprising the following steps: Obtain both high-resolution and low-resolution versions of the target image set; The high-resolution version of the image set is converted into a first composite matrix; Based on the low-resolution version of the image set, the corresponding far-field intensity distribution is obtained through phase retrieval and transformation calculation, and then converted into a second composite matrix; The integrated feature matrix is ​​obtained by solving the first composite matrix and the second composite matrix. Design metasurface structures to match the phase distribution of the target image; Obtain the far-field intensity distribution generated by the metasurface structure and convert it into a column vector; The column vectors are processed using the integrated feature matrix to obtain the reconstructed high-resolution image.

[0007] Furthermore, the method for converting the high-resolution version of the image set into a first composite matrix includes: Each image in the high-resolution grayscale image set is converted into a column vector; Combine all column vectors column by column to form the first composite matrix.

[0008] Furthermore, methods for obtaining the corresponding far-field intensity distribution through phase retrieval and transformation calculations include: For the low-resolution version of the image set, the Gerchberg-Saxton algorithm is used to calculate the phase space distribution corresponding to each image; Perform a Fourier transform on each phase spatial distribution to obtain the corresponding far-field intensity distribution.

[0009] Furthermore, the method for converting the far-field intensity distribution into a second composite matrix includes: Transform each far-field intensity distribution matrix into a column vector; Combine all column vectors column by column to form a second composite matrix.

[0010] Furthermore, methods for obtaining the integrated feature matrix include: Based on the second composite matrix, its Moore-Penrose pseudo-inverse matrix is ​​calculated using the singular value decomposition method. The first composite matrix is ​​multiplied by the Moore-Penrose pseudo-inverse matrix to obtain the integrated feature matrix.

[0011] Further methods for matching its phase distribution with the target image include: Based on the target image of the low-resolution version image set, the Gerchberg-Saxton phase retrieval algorithm is used to calculate the spatial phase distribution corresponding to the target image. Based on the spatial phase distribution, a unit structure of the metasurface is selected, and the geometric parameters of the unit structure are adjusted to make the transmission or reflection phase distribution of the metasurface structure consistent with the spatial phase distribution.

[0012] Furthermore, the metasurface structure is composed of periodically arranged TiO2 rectangular nanopillars.

[0013] Furthermore, the method for obtaining the reconstructed high-resolution image by performing operations on the column vectors using the integrated feature matrix includes: The column vector is multiplied by the integrated feature matrix to obtain the reconstructed high-resolution image column vector; The column vectors of the reconstructed high-resolution image are rearranged into a two-dimensional image matrix to obtain the final reconstructed high-resolution image.

[0014] To achieve the above objectives, a second aspect of the present invention provides an electronic device including a memory and a processor, the memory being used to store a program supporting the processor in executing the metasurface holographic display method, and the processor being configured to execute the program stored in the memory.

[0015] To achieve the above objectives, a third aspect of the present invention provides a computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, performs the steps of the metasurface holographic display method.

[0016] The beneficial effects of this invention are: Compared with existing technologies, the present invention provides a metasurface holographic display method, device, and medium that separates and preserves the high-frequency spatial features of the original image set by constructing an integrated feature matrix, while using the metasurface micro / nano structure to encode the low-frequency features and phase distribution of the target image. In the reconstruction stage, the low-resolution far-field intensity distribution generated by the metasurface is obtained, and matrix operations are performed on it using the pre-calculated integrated feature matrix to directly map the low-resolution intensity information into a high-resolution image. This bypasses the limitation on resolution caused by the insufficient performance of the modulation transfer function in traditional methods and effectively suppresses crosstalk in multi-channel cases. Ultimately, it achieves high signal-to-noise ratio, high fidelity, and high-resolution image reconstruction, while also possessing broadband response and multiplexing capabilities. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below.

[0018] Figure 1 This is a flowchart of a metasurface holographic display method disclosed in an embodiment of the present invention.

[0019] Figure 2 This is a flowchart of obtaining an integrated feature matrix disclosed in an embodiment of the present invention.

[0020] Figure 3 This is a reconstructed image of an ultra-high quality metasurface hologram disclosed in an embodiment of the present invention, wherein... Figure 3(a) is the target image. Figure 3 (b) represents a metasurface micro / nano structure. Figure 3 (c) shows the far-field intensity distribution. Figure 3 (d) is the reconstructed image. Detailed Implementation

[0021] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0022] According to embodiments of the present invention, it should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the following manufacturing method, in some cases the steps shown or described may be performed in a different order than that shown here.

[0023] like Figure 1 As shown, this invention provides a metasurface holographic display method. This method, on the one hand, obtains an integrated feature matrix of an image set through optimized calculation, preserving the high-frequency spatial features of the image set; on the other hand, it utilizes metasurface micro / nano structures to preserve the low-frequency spatial features of the target image, thereby realizing an ultra-high-quality metasurface hologram driven by the integrated feature matrix. A schematic diagram illustrating the principle of obtaining the integrated feature matrix T of the image set is shown below. Figure 2 As shown, the detailed steps of this method are as follows: Step S100: Obtain the high-resolution and low-resolution versions of the target image set; First, a raw image set containing multiple target images is collected. Then, each image is preprocessed and converted into a grayscale image to ensure data format uniformity. Next, two resolution versions of the same image are generated by setting different spatial sampling scales. The high-resolution version (e.g., 256×256 pixels) aims to preserve the fine structure and high-frequency detail features of the image, while the low-resolution version (e.g., 64×64 pixels, which can be obtained through image scaling operations such as downsampling) is used to correspond to the lower spatial frequency information that the metasurface can provide in the actual diffraction process.

[0024] Step S200: Convert the high-resolution version of the image set into a first composite matrix; The two-dimensional image data (i.e., a two-dimensional matrix) of each image in the preprocessed high-resolution grayscale image set (e.g., each image is 256×256 pixels) is rearranged into a column vector according to a specific order (e.g., column-major or row-major). The dimension of this column vector is (Represents the total number of pixels in a single image); if the image set contains This image will then... The column vectors are concatenated and combined in column order to form a vector of size. The first composite matrix (denoted as matrix M, The first composite matrix here can be mathematically regarded as a data matrix composed of all pixel information of all high-resolution images, with each column corresponding to all gray values ​​of an image.

[0025] Step S300: Based on the low-resolution version of the image set, obtain its corresponding far-field intensity distribution through phase retrieval and transformation calculation, and convert it into a second composite matrix; For each image in the low-resolution grayscale image set (e.g., each image is 64×64 pixels), the Gerchberg-Saxton (GS) phase retrieval algorithm (a numerical method that recovers the phase distribution from intensity information by iteratively applying constraints between the spatial and frequency domains) is used to calculate its corresponding spatial phase distribution. Then, a Fourier transform (a mathematical tool for converting signals from the spatial / temporal domain to the frequency domain, used here to simulate light wave diffraction and calculate its far-field complex amplitude) is performed on the recovered spatial phase distribution of each image to obtain its corresponding far-field intensity distribution (i.e., the intensity pattern formed by the light field on the far-field observation plane, mathematically a 64×64 real matrix, denoted as ). Then, each far-field intensity distribution matrix is ​​rearranged into a column vector in a specific order. Its dimensions are (in If the image set contains This image will ultimately... The column vectors are concatenated and combined in column order to form a vector of size. The second composite matrix (denoted as matrix) The second composite matrix stores the far-field intensity information of all low-resolution images after being mapped by the diffraction physical process.

[0026] Step S400: Solve for the integrated feature matrix based on the first composite matrix and the second composite matrix; The two composite matrices corresponding to the resolution versions obtained in steps S200 and S300 (i.e., the first composite matrix composed of the high-resolution image set) The second composite matrix formed by the low-resolution far-field intensity distribution According to the matrix equation The established mathematical model (which describes the linear mapping between high-resolution images and low-resolution far-field distributions) is used to solve the integrated feature matrix through numerical computation. .

[0027] The specific solution process is as follows: first, for the second composite matrix... Perform singular value decomposition (a stable algorithm that decomposes a matrix into the product of three specific matrices, often used to solve the pseudo-inverse of ill-conditioned linear systems), and then calculate its Moore-Penrose pseudo-inverse matrix. (A generalized inverse matrix, even if) (It can provide stable approximate solutions even when the matrix is ​​not square or the condition number is large), and finally, matrix multiplication is used to solve the problem. Obtain the integrated feature matrix (its dimensions are) This ensemble feature matrix essentially learns a linear transformation operator from a low-resolution far-field intensity space to a high-resolution image space, thereby extracting and encoding high-frequency features from the original image into the ensemble feature matrix. This provides a core mapping basis for subsequent high-quality image reconstruction.

[0028] Step S500: Design a metasurface structure to match its phase distribution with the target image; Based on a low-resolution version of the target image, the Gerchberg-Saxton (GS) phase retrieval algorithm is used to calculate the spatial phase distribution matching the target image. Subsequently, based on this optimized spatial phase distribution, an appropriate metasurface unit structure (e.g., rectangular nanopillars made of dielectric materials such as TiO2 as the basic unit) is selected. It should be noted that the geometric parameters of the unit structure (such as length and width) directly affect the amplitude and phase response of its scattered field. Therefore, numerical simulation software (such as electromagnetic simulation tools based on the finite element method or the finite-difference time-domain method) is used for systematic simulation calculations to establish a database of one-to-one correspondences between structural units and their emitted phases under different geometric parameters. Based on this, by precisely controlling the geometric parameters of the nanopillars within each unit cell, the transmission or reflection phase delay generated at a specific working wavelength is made consistent with the target spatial phase distribution value calculated by the GS algorithm at the corresponding position, thereby encoding the phase information of the target image into the microstructure of the metasurface. The metasurface is composed of periodically arranged unit cells, and the size of each unit cell and the height of the nanopillars need to be designed according to the working wavelength to ensure that it can effectively control the light wavefront and generate the required far-field diffraction pattern.

[0029] Step S600: Obtain the far-field intensity distribution generated by the metasurface structure and convert it into a column vector; For the metasurface micro / nanostructure designed in step S500, its optical near-field distribution is calculated using the finite-difference time-domain method (a computational electromagnetics method that simulates the interaction between light and matter by directly solving Maxwell's equations numerically). Then, based on this near-field distribution, diffraction derivation is performed using the Fresnel-Kirchhoff diffraction formula (a scalar theoretical model describing the propagation of light waves, used to calculate the intensity distribution in the far field from the near-field complex amplitude distribution) to obtain the intensity distribution formed by the metasurface structure on the far-field observation plane (mathematically represented as a 64×64 real matrix I). Finally, this two-dimensional far-field intensity distribution matrix is ​​rearranged into a column vector according to a specific column-major or row-major order. (in This column vector systematically encodes the low-resolution optical field information generated by the metasurface structure during actual physical diffraction.

[0030] Step S700: Calculate the column vector using the integrated feature matrix to obtain the reconstructed high-resolution image.

[0031] The far-field intensity distribution column vector obtained in step S600 (dimension is) , The integrated feature matrix obtained in step S400 is compared with the integrated feature matrix obtained in advance. (dimension is) ,in Perform matrix multiplication, that is, calculate (in For dimension (column vectors), this operation is essentially performed by integrating the feature matrix. The encoded linear mapping from low-resolution space to high-resolution space will transform the low-resolution physical signals generated by actual metasurface diffraction. Directly transform into column vector representation of a high-resolution image .

[0032] Subsequently, the resulting column vector The images are rearranged into a 256×256 pixel two-dimensional image matrix according to the same image arrangement rules as in step S200 (such as column priority or row priority order), thereby obtaining the final reconstructed high-resolution image. This process bypasses the resolution limitation of the traditional metasurface diffraction limit and directly recovers the image that retains the original high-frequency details by integrating the feature matrix, ultimately achieving high signal-to-noise ratio, high fidelity and high resolution image reconstruction effect.

[0033] Steps S100 to S700 together constitute a metasurface holographic display method based on an integrated feature matrix. This method performs dual-resolution preprocessing on the target image set by converting the high-resolution image set into a first composite matrix composed of column vectors, and performs phase retrieval and diffraction calculations on the low-resolution image set to generate a far-field intensity distribution and convert it into a second composite matrix. Then, the integrated feature matrix that can encode high-frequency features is solved using these two matrices. On the physical implementation side, a metasurface structure is designed to match the unit geometry parameters with the target phase distribution, and the actual far-field intensity data generated by the metasurface is obtained and converted into a column vector; finally, the integrated feature matrix is ​​used. Matrix operations are performed on the column vector to reconstruct a high-resolution image, thereby effectively breaking through the traditional diffraction limit on resolution without increasing the size of the metasurface or the processing difficulty, and significantly improving the signal-to-noise ratio, fidelity and detail restoration capability of the reconstructed image.

[0034] The following example uses an apple image set to demonstrate ultra-high quality metasurface holograms. This embodiment selects TiO2 rectangular nanopillars as the basic unit of the metasurface, with a periodicity... p =450 nm, height h =600 nm, the transmission phase of the control structure is controlled by changing the length and width of the nanopillars. For example, for Figure 3 In the target image in (a), the phase space distribution corresponding to the target image is first obtained using the GS algorithm. Then, at a wavelength of 700 nm, a metasurface micro / nano structure is designed by selecting suitable TiO2 nanopillars, such as... Figure 3 As shown in (b), the structure consists of 64×64 unit cells. Based on the finite-difference time-domain method, the near-field distribution of this metasurface structure is calculated, and then the far-field intensity distribution corresponding to the metasurface structure is derived using the Fresnel-Kirchhoff diffraction formula. ),like Figure 3 As shown in (c).

[0035] The column vector is obtained by performing a matrix transformation on the far-field intensity distribution. Then based on the integrated feature matrix According to the matrix equation Solve the matrix ( ), then Perform matrix transformation to reconstruct a 256×256 pixel image, such as Figure 3 As shown in (d), the signal-to-noise ratio and resolution of the reconstructed image are significantly improved, with a signal-to-noise ratio of approximately 11.9 dB and an equivalent resolution of approximately 112.5 nm (~λ / 6). According to the fidelity formula:

[0036] in, This indicates the fidelity between the reconstructed image and the original image, and is used to measure the similarity between the reconstructed result and the original image. The closer the value is to 1 (or 100%), the higher the similarity. It represents the column vector form of the original high-resolution image, which is composed of a 256×256 pixel image matrix arranged in sequence; This indicates that by integrating the feature matrix and far-field intensity column vector The reconstructed image is in column vector form after calculation; , They represent The normalized original distribution and reconstruction results show that the fidelity of the reconstructed image reaches 96.8%, and the fidelity of the reconstructed image exceeds 96% at other incident wavelengths (550-800 nm), indicating that the ultra-high quality metasurface holographic display driven by the integrated feature matrix proposed in this invention has broadband response.

[0037] It should be noted that because the integrated feature matrix has intrinsic multiplexing capability, the above method can also be used to design and implement multi-channel ultra-high quality metasurface holograms.

[0038] The proposed integrated feature matrix construction method extracts and encodes high-frequency spatial features of an image set from the high-resolution original image into a linear transformation matrix (i.e., the integrated feature matrix) using mathematical means. This effectively solves the problem of high-frequency information loss caused by the diffraction limit and insufficient modulation transfer function performance of metasurfaces. This method utilizes the mapping relationship between the high-resolution image matrix and the low-resolution far-field intensity matrix, and achieves the separation and preservation of high-frequency features through stable matrix operations (such as singular value decomposition and pseudo-inverse solving). This not only avoids the processing difficulties caused by simply increasing the metasurface size to improve resolution, but also gives the matrix a natural multiplexing capability, laying a mathematical foundation for subsequent multi-channel, high-capacity metasurface holographic displays.

[0039] On the other hand, by designing metasurface micro / nano structures to match their spatial phase distribution with the target image, the low-frequency features of the image can be accurately preserved and reproduced at the physical level. Combined with the high-frequency compensation provided by the integrated feature matrix, ultra-high-quality holographic reconstruction is achieved. In addition, since the integrated feature matrix itself has multiplexing capabilities, this method can also be extended to multi-channel metasurface holographic displays, which significantly improves information capacity and system integration while improving image quality, providing a reliable path for the realization of high-performance, compact holographic display systems.

[0040] According to another aspect of the embodiments of this application, an electronic device is also provided, including a processor and a memory, wherein the processor is configured to implement the steps of the method when executing a computer program stored in the memory.

[0041] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0042] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. The device embodiments described above are merely illustrative; for example, the division of units can be a logical functional division, and in actual implementation, there may be other division methods. For instance, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual coupling, direct coupling, or communication connection may be through some interfaces; the indirect coupling or communication connection between units or modules may be electrical or other forms.

[0043] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0044] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0045] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A metasurface holographic display method, characterized in that, Includes the following steps: Obtain both high-resolution and low-resolution versions of the target image set; The high-resolution version of the image set is converted into a first composite matrix; Based on the low-resolution version of the image set, the corresponding far-field intensity distribution is obtained through phase retrieval and transformation calculation, and then converted into a second composite matrix; The integrated feature matrix is ​​obtained by solving the first composite matrix and the second composite matrix. Design metasurface structures to match the phase distribution of the target image; Obtain the far-field intensity distribution generated by the metasurface structure and convert it into a column vector; The column vectors are processed using the integrated feature matrix to obtain the reconstructed high-resolution image.

2. The metasurface holographic display method as described in claim 1, characterized in that, The method for converting the high-resolution version of the image set into a first composite matrix includes: Each image in the high-resolution grayscale image set is converted into a column vector; Combine all column vectors column by column to form the first composite matrix.

3. The metasurface holographic display method as described in claim 1, characterized in that, Methods for obtaining the corresponding far-field intensity distribution through phase retrieval and transformation calculations include: For the low-resolution version of the image set, the Gerchberg-Saxton algorithm is used to calculate the phase space distribution corresponding to each image; Perform a Fourier transform on each phase spatial distribution to obtain the corresponding far-field intensity distribution.

4. The metasurface holographic display method as described in claim 3, characterized in that, The method for converting the far-field intensity distribution into a second composite matrix includes: Transform each far-field intensity distribution matrix into a column vector; Combine all column vectors column by column to form a second composite matrix.

5. The metasurface holographic display method as described in claim 1, characterized in that, Methods for obtaining the integrated feature matrix include: Based on the second composite matrix, its Moore-Penrose pseudo-inverse matrix is ​​calculated using the singular value decomposition method. The first composite matrix is ​​multiplied by the Moore-Penrose pseudo-inverse matrix to obtain the integrated feature matrix.

6. The metasurface holographic display method as described in claim 3, characterized in that, Methods for designing metasurface structures whose phase distribution matches that of a target image include: Based on the target image of the low-resolution version image set, the Gerchberg-Saxton phase retrieval algorithm is used to calculate the spatial phase distribution corresponding to the target image. Based on the spatial phase distribution, a unit structure of the metasurface is selected, and the geometric parameters of the unit structure are adjusted to make the transmission or reflection phase distribution of the metasurface structure consistent with the spatial phase distribution.

7. The metasurface holographic display method as described in claim 6, characterized in that, The metasurface structure is composed of periodically arranged TiO2 rectangular nanopillars.

8. The metasurface holographic display method as described in claim 1, characterized in that, The method for obtaining the reconstructed high-resolution image by performing operations on the column vectors using the integrated feature matrix includes: The column vector is multiplied by the integrated feature matrix to obtain the reconstructed high-resolution image column vector; The column vectors of the reconstructed high-resolution image are rearranged into a two-dimensional image matrix to obtain the final reconstructed high-resolution image.

9. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the metasurface holographic display method according to any one of claims 1-8, and the processor is configured to execute the program stored in the memory.

10. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program, when run by a processor, performs the steps of the metasurface holographic display method according to any one of claims 1-8.

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