Optical spatial differential device for target extraction, inverse design method and application

Abstract

The application belongs to the technical field of photonic artificial micro-nano structure design and image processing, and discloses an optical spatial differential device for target extraction, a reverse design method and application. The method comprises the following steps: setting a target transfer function according to the functional requirement of an optical device; establishing an optimization model according to the design parameters of a super surface, the design parameters being dielectric constant distribution, and performing certain constraint and binary processing on the design parameters in each iteration process; judging whether the loss function converges or not, outputting an optimization scheme if the loss function converges, and otherwise, performing gradient calculation and continuing the next iteration optimization process. The optical spatial differential device is based on the diffraction optical angular spectrum theory and the Fourier transform property, directly acts on an incident light field image, realizes spatial frequency regulation of the light field image in the wave vector space, and thus achieves the purpose of processing the image in the optical domain. The obtained patterns of the application can be directly applied to a double photopolymerization 3D printing technology, so as to prepare a sample.

Description

Technical Field

[0001] This invention belongs to the field of photonic artificial micro / nano structure design and image processing technology, and particularly relates to optical spatial differentiating devices for target extraction, reverse design methods and applications. Background Technology

[0002] Spatial differentiation of images is commonly used as a preprocessing method in image processing to extract image features and compress image data. Fast and efficient spatial differentiation of images is fundamental for real-time edge detection, target recognition, and tracking, playing a crucial role in fields such as artificial intelligence, autonomous driving, and machine vision. Traditional image processing involves steps such as acquiring images with optical cameras, converting light signals into electrical signals, and performing calculations in the electrical domain. This involves optical sensors and photoelectric converters, which not only occupy a large volume but also generate power consumption due to heat. With the increasing demand for smaller, lower-power, and faster devices, optical devices capable of directly calculating light fields have demonstrated significant research value and importance. In 2014, Silva et al. first introduced optical metasurfaces into the design of optical computing devices. With the improvement of micro-nano optics theory and the development of nanofabrication technology, optical metasurfaces, due to their unique optical response and small size and ease of integration, have been widely studied and applied in the design of optical devices.

[0003] Early research focused on the optical response of optical metasurfaces. Metasurfaces, composed of periodically arranged subwavelength resonant units, can flexibly and precisely control the amplitude, phase, and polarization of light waves at the subwavelength scale, making them a hot research topic in analog optical computing devices. The design of these devices relies on rigorous physical theories and requires designers to combine prior physical effects with empirical and theoretical adjustments to specific structural parameters to obtain a specific optical response and achieve the desired function. Metasurfaces designed using this research method, consisting of simple structures such as nanocylinders and square prisms, have been applied to the design of optical computing devices for differentiation, integration, and equation solving. However, this method cannot be transferred to designs with different requirements; designers need to redesign based on their intuition and experience.

[0004] With the advancement of computing technology, many algorithms have been developed to solve optimization problems. The design of optical devices can also be viewed as a problem of finding the optimal structure based on the target functional requirements. Therefore, inverse optimization algorithms have been applied to the design of optical devices.

[0005] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0006] (1) Existing technologies rely on the geometric characteristics of optical structures and the experience of designers in the design of optical devices, which limits the practical application of optical devices.

[0007] (2) Existing optical devices have poor design freedom and large overall size, poor structural compactness, and are not convenient for use in integrated systems.

[0008] (3) In the existing technology, the device contains a variety of dielectric materials, which is not conducive to the direct use of dual-photopolymerization 3D printing technology to prepare samples. Summary of the Invention

[0009] To overcome the problems existing in related technologies, the present invention discloses embodiments of optical spatial differentiating devices for target extraction, reverse design methods, and applications. Specifically, it relates to a target-driven reverse design method suitable for generating optical spatial differentiating devices, and proposes a specific form of an optical spatial differentiating device designed based on this method that can perform spatial differentiation operations on light field images. This device is used to perform spatial differentiation operations on light field images, achieving edge extraction, edge enhancement, and segmentation, thus realizing all-optical computation of images.

[0010] The technical solution is as follows: A reverse design method for optical spatial differentiating devices oriented towards target extraction includes the following steps:

[0011] S1, Set the target spatial spectrum transfer function according to the functional requirements of the optical device;

[0012] S2, Establish an optimization model based on the design parameters of the metasurface, wherein the design parameters are the dielectric constant distribution, and the design parameters are subject to certain constraints and binarization in each iteration;

[0013] S3: Determine if the loss function has converged. If it has converged, output the optimization scheme. Otherwise, perform gradient calculation to update the design parameters and then continue to the next iteration of the optimization process.

[0014] In step one, based on the diffraction optics angular spectrum theory and the properties of spatial Fourier transform, and according to the specific functional requirements of the optical device, its target transfer function in wave vector space is determined. A Gaussian kernel function is added to control the local effect of the transfer function on spatial frequencies of different sizes. The target transfer function is denoted as H. obj (k x ,k y ).

[0015] In one embodiment, the optical device includes a first-order optical spatial differentiator, which performs first-order differentiation operations on the light field image in the x or y direction to extract edge information of the image. The target transfer function of the first-order optical spatial differentiator is as follows:

[0016]

[0017] Where k x ky Let A be the spatial frequency corresponding to the decomposition of the incident light field into elementary plane waves, and let A be the intensity of the transmission coefficient. It controls the local scope of the Gaussian kernel function and adjusts it according to the specific design.

[0018] In one embodiment, the optical device includes a second-order optical spatial differentiator to perform second-order differential operations on the light field image in the x and y directions, thereby enhancing the edge information of the image and sharpening it. The target transfer function of the second-order optical spatial differentiator is as follows:

[0019]

[0020] Where k x k y Let A be the spatial frequency corresponding to the decomposition of the incident light field into elementary plane waves, and let A be the intensity of the transmission coefficient. It controls the local scope of the Gaussian kernel function and is adjusted according to the specific design.

[0021] In one embodiment, in step two, the free-form metasurface is optimized by pixelating each layer of the metasurface. The dielectric constant ε(x,y) of each pixel (x,y) is used as a design parameter, and random coherent noise is set as the initial value of ε(x,y). The range of ε(x,y) is set to [ε...]. min ,ε max [, between two media, one of which is air ε] min =ε air When performing topology optimization for the case where ε(x,y) is continuous, certain constraints are imposed on ε(x,y) and binarization is performed during an optimization iteration.

[0022] In one embodiment, applying certain constraints to the design parameters ε(x,y) and performing binarization processing includes:

[0023] For a target transfer function with symmetry, the structure of the metasurface has a certain symmetry. Certain constraints are imposed on ε(x,y) to satisfy the corresponding symmetry.

[0024] The design parameter ε(x,y) is continuously variable, and its value range is [ε min ,ε max In gradient calculation, ε(x,y) is continuous. When using the full-wave electromagnetic solver to calculate the transmission coefficient of the device, the tanh function binarization algorithm is combined to ensure that the value of ε(x,y) is only the ε of the two component materials. min or ε max .

[0025] In one embodiment, in step three, a full-wave electromagnetic solver is used to calculate the spatial spectral transfer function of the optical device given by ε(x,y) during an optimization iteration process. This transfer function is the response of the optical device to light fields of different spatial frequencies in wave vector space, denoted as H. sim (k x ,k y ); H sim (k x ,k y ) and H obj (k x ,k y The mean square error of ε is used as the loss function L in the optimization iteration process. The gradient of L with respect to ε(x,y) is calculated in each iteration. The design parameters are updated in conjunction with the optimization iteration process until L converges. The results under different period sizes of the metasurface are compared, and the optimized scheme ε is output. o (x,y).

[0026] In one embodiment, the loss function in the optimization iteration process is in the form of:

[0027]

[0028] Where i and j represent the wave vector components k x k y The number of sampling points is n, where n represents the total number of sampling points.

[0029] Another objective of this invention is to provide an optical spatial differential device designed according to the reverse design method of the optical spatial differential device based on the target extraction method. The optical spatial differential device is fabricated by dual-light polymerization 3D printing technology and specifically includes: a metasurface periodic structure of multilayer dielectric; the metasurface periodic structure has a free geometric form and is composed of two dielectric materials, one of which is air.

[0030] Another objective of this invention is to provide an optical device for the fields of artificial intelligence, autonomous driving, and machine vision, wherein the optical device integrates an optical spatial differential device designed by the reverse design method of the optical spatial differential device for target extraction.

[0031] Combining all the above technical solutions, the advantages and positive effects of this invention are as follows:

[0032] First, in view of the technical problems existing in the prior art and the difficulty of solving these problems, and closely combining the technical solution to be protected by this invention with the results and data during the research and development process, this paper analyzes in detail how the technical solution of this invention solves the technical problems, and the inventive technical effects brought about after solving the problems, as described in detail below:

[0033] The optical spatial differentiating device for target extraction provided by this invention is based on the diffraction optical angular spectrum theory and Fourier transform properties. It does not require an additional lens to perform Fourier transform on the light field. The optical spatial differentiating device directly acts on the incident light field image and realizes spatial frequency modulation of the light field image in wave vector space, thereby achieving the purpose of image processing in the optical domain.

[0034] This device consists of multiple dielectric metasurfaces, each with a freely distributed dielectric material. The thickness of each metasurface layer is on the order of hundreds of nanometers, resulting in a very compact volume. The design method employs a goal-driven inverse optimization approach, offering versatility and applicability to various types of spatial spectral filtering (e.g., spatial Gaussian filtering) functional device designs. It has low dependence on the designer's prior knowledge and experience, and the obtained layer patterns can be directly applied to dual-photonic polymerization 3D printing technology for sample fabrication.

[0035] Compared to existing technologies, the advantages of this invention further include: This invention provides a target-driven reverse design method that targets the mean square error between the spatial spectral transfer function of an optical device and the target spatial spectral transfer function. Therefore, it is not limited to a specific optical structure or a specific target function. Optical devices that can be designed by controlling the light field of different spatial frequencies in wave vector space can all be designed using the method provided by this invention, without relying on the geometric characteristics of the optical structure or the designer's experience.

[0036] The design method provided by this invention uses the dielectric constant distribution ε(x,y) of the metasurface as a parameter, and combines topology optimization algorithm and tanh function binarization algorithm to iteratively process the dielectric constant distribution ε(x,y), which is beneficial for optimization using free-form metasurface structures. It has a higher degree of design freedom than the existing technology of designing optical spatial differential devices using scattering array structures, and can generate transfer function forms with richer functions.

[0037] The optical spatial differentiating device provided by this invention acts directly on the incident light field without the need for an additional lens. The overall size of the device is on the order of micrometers, and it features a compact structure and small size, making it easy to apply in integrated systems.

[0038] The optical spatial differentiating device provided by this invention operates in the near-infrared wavelength. After pixelation of the metasurface within the unit periodic structure, the scale of each pixel unit is on the sub-hundred nanometer scale. The device contains only two dielectric materials and is divided into a multi-layer structure with the same thickness. Within each layer, basic units are repeatedly arranged according to an optimized period, which is beneficial for directly using dual-photonic polymerization 3D printing technology to prepare samples.

[0039] Secondly, considering the technical solution as a whole or from the perspective of the product, the technical effects and advantages of the technical solution to be protected by this invention are specifically described as follows:

[0040] This invention provides a target-driven reverse design method for optical spatial differentiators. The method reverse designs optical differentiating devices by combining diffraction optical angular spectrum theory and topology optimization algorithm. It also proposes a first-order optical spatial differentiator that performs first-order spatial differentiation operation on light field images and a second-order optical spatial differentiator that performs second-order spatial differentiation operation on light field images.

[0041] Furthermore, the design method for spatial differentiable devices provided by this invention is based on the principle of using a specific optical response as the optimization objective to inversely solve for the structural parameters of the optical device. This method does not require prior knowledge to select a special optical structure, does not require manual adjustment of structural parameters, and can be applied to the design of devices with other functions, thereby designing optical devices with more complex functions.

[0042] Third, as supplementary evidence of the inventive step of the claims of this invention, it is also reflected in the following important aspects:

[0043] (1) The technical solution of the present invention can be used for the design of micro-nano optical products, not only limited to optical spatial differentiators, but also including any optical device that modulates the spatial frequency light field. The designed products can be integrated into optoelectronic systems and further applied in the fields of artificial intelligence, autonomous driving and machine vision.

[0044] (2) Existing technologies either use scattering array structures to design spatial spectrum transfer functions through resonance principles, or design optical devices in real space optical field response. This invention provides an optical spatial differential device and reverse design method for target extraction, which reverse designs the optical field response of free geometric metasurfaces in wave vector space, filling the gap in designing optical devices in wave vector space through reverse methods.

[0045] (3) The technical solution of the present invention performs reverse design of free geometric metasurface based on the generated target, which solves the problem of low design freedom due to the use of scattering array structure in the prior art, and also solves the problem of low design efficiency due to the reliance on the designer's intuition and experience in the prior art.

[0046] (4) Existing technologies, for the purpose of integrating optical and electronic devices, are limited to the design of optical devices using single-layer scattering array metasurface structures. The technical solution of the present invention designs multi-layer metasurface structures, the overall structure of the device is on the micrometer scale, compact in size, easy to integrate, and can be designed with richer functions compared to single-layer structures. Attached Figure Description

[0047] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure;

[0048] Figure 1 A flowchart illustrating the reverse design method for an optical spatial differentiating device oriented towards target extraction, provided in an embodiment of the present invention.

[0049] Figure 2 A schematic diagram illustrating the reverse design method for an optical spatial differentiating device oriented towards target extraction, provided in an embodiment of the present invention.

[0050] Figure 3 This is a schematic diagram of the structure and working principle of the optical spatial differentiating device provided in the embodiment of the present invention. The actual device mainly utilizes the 0th order diffraction output.

[0051] Figure 4 The basic unit design output of the periodic microstructure of the first-order optical spatial differential device provided in the embodiment of the present invention is shown. The black area represents the medium and the white area represents the air. The structure is composed of 40 layers of free geometric metasurfaces stacked together. The right side shows the spatial distribution diagram of the medium material of four of the metasurface layers.

[0052] Figure 5 A comparison of the target transfer function and the transfer function of the optimized scheme for the first-order optical spatial differentiating device provided in the embodiments of the present invention;

[0053] Figure 6(a) is a schematic diagram of the input image of the first-order optical spatial differentiator provided in an embodiment of the present invention;

[0054] Figure 6(b) is a schematic diagram of the output effect of the first-order optical spatial differential device provided in the embodiment of the present invention performing first-order spatial differential operation on the input image 1;

[0055] Figure 6(c) is a schematic diagram of the second input image of the first-order optical spatial differentiator provided in the embodiment of the present invention;

[0056] Figure 6(d) is a schematic diagram of the output effect of the first-order optical spatial differentiator device provided in the embodiment of the present invention performing first-order spatial differentiating operation on the input image 2;

[0057] Figure 7 The basic unit design of the periodic microstructure of the second-order optical spatial differentiating device provided in the embodiments of the present invention;

[0058] Figure 8 A comparison of the target transfer function and the transfer function of the optimized scheme for the second-order optical spatial differentiating device provided in the embodiments of the present invention;

[0059] Figure 9(a) is a schematic diagram of the input image of the second-order optical spatial differentiator provided in an embodiment of the present invention;

[0060] Figure 9(b) is a schematic diagram of the output effect of the second-order optical spatial differentiator device provided in the embodiment of the present invention performing first-order spatial differential operation on the input image 1;

[0061] Figure 9(c) is a schematic diagram of the output effect of a second-order optical spatial differential device designed using existing technology to perform second-order spatial differential operation on input image 1.

[0062] Figure 9(d) is a schematic diagram of the second-order optical spatial differentiator provided in an embodiment of the present invention;

[0063] Figure 9(e) is a schematic diagram of the output effect of the second-order optical spatial differential device provided in the embodiment of the present invention performing first-order spatial differential operation on the input image 2.

[0064] Figure 9(f) is a schematic diagram of the output effect of a second-order optical spatial differential device designed using existing technology to perform second-order spatial differential operation on the input image 2; Detailed Implementation

[0065] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0066] I. Explanation of the Implementation Example:

[0067] like Figure 1 As shown, the reverse design method for an optical spatial differentiating device for target extraction provided in this embodiment of the invention includes the following steps:

[0068] Step 1: Set the target spatial spectral transfer function according to the functional requirements of the optical device;

[0069] Step 2: Establish an optimization model based on the design parameters of the metasurface. The design parameters are the dielectric constant distribution. In each iteration, the design parameters are subject to certain constraints and binarization.

[0070] Step 3: Determine if the loss function has converged. If it has converged, output the optimization scheme; otherwise, perform gradient calculation to update the design parameters and continue to the next iteration of the optimization process.

[0071] In a preferred embodiment of the present invention, in step one, based on the diffraction optical angular spectrum theory and the spatial Fourier transform properties, and according to the specific functional requirements of the optical spatial differential device, its target transfer function in wave vector space is determined, and a Gaussian kernel function is added to control the local effect of the transfer function on spatial frequencies of different sizes. The target transfer function is denoted as H. obj (k x ,k y );

[0072] In a preferred embodiment of the present invention, in step two, the free-form metasurface is optimized by pixelating each layer of the metasurface. The dielectric constant ε(x,y) of each pixel (x,y) is used as a design parameter, and random coherent noise is set as the initial value of ε(x,y). The range of ε(x,y) is set to [ε...]. min ,ε max ], that is, between two media (one of which may be air ε min =ε air For topology optimization problems where ε(x,y) is continuous, certain constraints are imposed on ε(x,y) and tanh function binarization is performed during an optimization iteration.

[0073] In a preferred embodiment of the present invention, in step three, a full-wave electromagnetic solver (e.g., the strictly coupled-wave analysis method RCWA) is used to calculate the spatial spectral transfer function of the optical device given by ε(x,y) during an optimization iteration process. This transfer function is the response of the optical device to light fields of different spatial frequencies in wave vector space, denoted as H. sim (k x ,k y ); H sim (k x ,k y ) and H obj (k x ,k y The mean square error of ε is used as the loss function L in the optimization iteration process. The gradient of L with respect to ε(x,y) is calculated in each iteration. The design parameters are updated in conjunction with the optimization iteration process until L converges. The results under different period sizes of the metasurface are compared, and the optimized scheme ε is output. o (x,y).

[0074] In a preferred embodiment of the present invention, setting the target transfer function according to the functional requirements of the optical device specifically includes the following steps:

[0075] A first-order optical spatial differentiating device performs first-order differential operations on a light field image in the x (or y) direction, which can be used to extract edge information of the image. The target transfer function of the device is as follows:

[0076]

[0077] Where k x k y Let A be the spatial frequency corresponding to the decomposition of the incident light field into elementary plane waves, and let A be the intensity of the transmission coefficient. It controls the local scope of the Gaussian kernel function and can be adjusted according to the specific design;

[0078] A second-order optical spatial differentiating device performs second-order differential operations on the light field image in the x and y directions. This can be used to enhance image edge information and sharpen the image. The target transfer function of the device is as follows:

[0079]

[0080] Where k x k y Let A be the spatial frequency corresponding to the decomposition of the incident light field into elementary plane waves, and let A be the intensity of the transmission coefficient. It controls the local scope of the Gaussian kernel function and can be adjusted according to the specific design.

[0081] In a preferred embodiment of the present invention, step two, which involves applying certain constraints to the design parameters ε(x,y) and performing binarization processing, includes:

[0082] For a target transfer function with symmetry, the structure of the metasurface should have a certain symmetry. Certain constraints are imposed on ε(x,y) to make it satisfy the corresponding symmetry.

[0083] The design parameter ε(x,y) is continuously variable, and its value range is [ε min ,ε max In gradient calculation, ε(x,y) is continuous. When using a full-wave electromagnetic solver to calculate the transmission coefficient of a device, a binarization algorithm is needed to ensure that the value of ε(x,y) is only ε. min or ε max That is, one of the two component materials.

[0084] In a preferred embodiment of the present invention, in step three, the loss function in the optimization iteration process is in the form of:

[0085]

[0086] Where i and j represent the wave vector components k x k y The number of sampling points is n, where n represents the total number of sampling points.

[0087] In embodiments of the present invention, such as Figures 3-7As shown, this embodiment of the invention also provides an optical spatial differentiating device, comprising:

[0088] The metasurface periodic structure of the multilayer medium has a scale on the micrometer scale, and the scale of each pixel after the metasurface is pixelated is on the sub-hundred nanometer scale.

[0089] The metasurface periodic structure consists of only two dielectric materials (one of which can be air), and its morphology has a free geometric form, which can be prepared by dual-photopolymerization 3D printing technology.

[0090] Example 1

[0091] Most existing design methods for optical spatial differential devices are based on the resonance effect of subwavelength scattering structure arrays. Due to the geometric characteristics of the structure, the form of the device transfer function is relatively simple and depends on the designer's prior knowledge. At the same time, the existing design methods are not transferable, and when designing devices with other functions, they need to be designed from scratch, resulting in low design efficiency.

[0092] To solve the above problems, such as Figure 2 As shown, this embodiment of the invention provides a reverse design method for an optical spatial differentiating device oriented towards target extraction, including the following specific steps:

[0093] Step 1: Generate random coherent noise as the initial structure

[0094] This invention optimizes free-form metasurfaces. In one optimization iteration, the metasurface is pixelated, with the dielectric constant ε(x,y) of each pixel used as a design parameter. Random coherent noise is set as the initial value of ε(x,y), and the range of ε(x,y) is set to [ε...]. min ,ε max ], that is, between two media (one of which may be air ε min =ε air For topology optimization problems where ε(x,y) is continuous, certain constraints are imposed on ε(x,y) and binarization is performed during an optimization iteration.

[0095] Step 2: Calculate the transmission coefficient in wave vector space using a full-wave electromagnetic solver.

[0096] Set the wave vector k of the optical spatial differentiator. x k y Based on the relationship between the wave vector and the incident angle within the incident plane, as well as the azimuth angle between the incident plane and the coordinate axes, the incident angle and azimuth angle of the elementary plane wave are calculated. The relationship between the wave vector and the incident angle is shown in formula (1):

[0097]

[0098]

[0099] The transmission coefficients of a unit-periodic structure with a dielectric constant distribution of ε(x,y) for elementary plane waves of different spatial frequencies are calculated using a full-wave electromagnetic solver (such as the rigorous coupled-wave analysis method RCWA), thus obtaining the spatial spectral transfer function H of the optical device. sim (k x ,k y ).

[0100] Step 3: Determine whether the loss function has reached convergence and extreme values.

[0101] The loss function of the reverse design method provided by this invention is defined as the mean square error between the spatial spectral transfer function of the structure and the target spatial spectral transfer function, as shown below:

[0102]

[0103] In formula (2), i and j represent the wave vector components k. x k y The number of sampling points is n, where n represents the total number of sampling points.

[0104] Step 4: If the loss function in Step 3 reaches convergence and extreme value, the optimization ends and the optimized structure is output. Otherwise, the gradient of the design parameter ε(x,y) is calculated, the distribution of dielectric constant is updated, and then Steps 2-4 above are repeated.

[0105] like Figure 3 This is a schematic diagram illustrating the structure and working principle of an optical spatial differentiating device provided in an embodiment of the present invention. The actual device primarily utilizes 0th-order diffraction output. Based on the diffraction optical angular spectrum theory and the properties of spatial Fourier transform, this invention enables the optical device to perform differential operations on the light field image. The incident light field can be decomposed into a superposition of plane waves with different wave vector components, having the following form:

[0106]

[0107] In formula (3) A0(k x ,k y ) indicates that in the wave vector k x k y The complex amplitude on the wave can also be regarded as the weight of the corresponding wave vector in the superposition of plane waves. Taking the two-dimensional Fourier transform of formula (3) yields the angular spectrum:

[0108]

[0109] Combining formula (4) with the concept of system transfer function, we can obtain that when the light field is incident on the spatial spectrum, the transfer function is H(k x ,k yAfter considering the optical system, the angular spectrum of the system's optical response is expressed as:

[0110] A(k x ,k y )=H(k x ,k y )A0(k x ,k y (5)

[0111] In formula (5), A0(k) x ,k y ) represents the angular spectrum of the incident light field.

[0112] According to formulas (3) and (5), the transmitted light after the incident light passes through a transmission structure is as follows:

[0113]

[0114] In formula (6), H(k) x ,k y () represents the transmission coefficient of the structure to plane wave components on different wave vectors, i.e., the spatial spectral transfer function. According to the properties of the Fourier transform, formula (6) can be expressed in the form of a convolution:

[0115] U′(x,y)=F -1 {A0(k x ,k y )·H(k x ,k y )}=F -1 {A0(k x ,k y )}*F -1 {H(k x ,k y )}(7)

[0116] From equation (7), it can be seen that the real space distribution of the transmitted light field can be regarded as the convolution of the incident light field and the inverse Fourier transform of the wave vector spatial transmission coefficient. Therefore, when H(k x ,k y When it has the form of a differential operator, an optical spatial differential device can perform differential operations on the incident light field.

[0117] Example 2: Exemplary First-Order Optical Spatial Differentiating Device Design Method

[0118] The first-order differential operation of the light field image is shown in the following formula:

[0119]

[0120] The first-order optical spatial differentiating device provided in this embodiment of the invention can perform first-order differential operations on the light field image in the x-direction. The target transfer function of the device is based on the first-order differential operator with the addition of a Gaussian kernel function, as shown below:

[0121]

[0122] In formula (9) It has the function of controlling the range of the Gaussian kernel function; the larger the value, the larger the local influence range of the Gaussian kernel function. The Gaussian kernel function makes the differential effect have specific sensitivity to edges at different scales.

[0123] like Figure 4 The diagram shows the basic unit design output of the periodic microstructure of the first-order optical spatial differential device provided in this embodiment of the invention. The black area represents the medium, and the white area represents air. The structure consists of 40 layers of free-geometric metasurfaces stacked together. The right side shows the spatial distribution diagram of the medium material of four of the metasurface layers (including the 5th, 15th, 25th, and 35th layers).

[0124] like Figure 5 As shown, the left column is the target transfer function defined when optimizing the design of the first-order optical spatial differentiator provided in the embodiment of the present invention, and the right column is the transmission coefficient of the first-order optical spatial differentiator provided in the embodiment of the present invention in wave vector space.

[0125] Figure 6(a) is a schematic diagram of the input image of the first-order optical spatial differentiator provided in an embodiment of the present invention;

[0126] Figure 6(b) is a schematic diagram of the output effect of the first-order optical spatial differential device provided in the embodiment of the present invention performing first-order spatial differential operation on the input image 1;

[0127] Figure 6(c) is a schematic diagram of the second input image of the first-order optical spatial differentiator provided in the embodiment of the present invention;

[0128] Figure 6(d) is a schematic diagram of the output effect of the first-order optical spatial differentiator device provided in the embodiment of the present invention performing first-order spatial differentiating operation on the input image 2;

[0129] In this example, the horizontal (x-direction) differentiation is performed. It can be seen that the first-order optical spatial differentiating device performs a first-order differentiation operation in the x-direction on the incident image, extracting the image's edge information. Furthermore, regardless of the scale of the structures in the image, the optical spatial differentiating device achieves the same effect in differentiating the image.

[0130] Example 3: Exemplary Second-Order Optical Spatial Differentiating Device Design Method

[0131] The second-order differential operation on the light field image is shown in the following formula:

[0132]

[0133] The second-order optical spatial differentiating device provided in this embodiment of the invention can perform second-order differential operations on the light field image in the x and y directions. The target transfer function of the device adds a Gaussian kernel function to the second-order differential operator, as shown below:

[0134]

[0135] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0136] II. Application Examples:

[0137] Application examples

[0138] The optical spatial differentiating device and design method described in the embodiments of the present invention can be applied to the design of optical devices with other target functional requirements.

[0139] Including but not limited to optical Gaussian spatial filters, their spatial spectral transfer functions are shown below:

[0140]

[0141] This includes, but is not limited to, optical spatial integrators, which possess spatial spectral transfer functions.

[0142] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0143] III. Evidence of the relevant effects of the embodiments:

[0144] experiment

[0145] like Figure 7 The figure shows the basic unit design of the periodic microstructure of the second-order optical spatial differentiating device provided in this embodiment of the invention; the black area in the figure represents the medium, and the white area represents air. The structure is composed of 40 layers of free-geometric metasurfaces stacked together, and the right side shows the spatial distribution diagram of the medium material of four of the metasurface layers (including the 5th, 15th, 25th and 40th layers).

[0146] like Figure 8 As shown, the left column is the target transfer function defined during the optimization design of the second-order optical spatial differentiator device according to the embodiment of the present invention, and the right column is the transmission coefficient of the second-order optical spatial differentiator device in wave vector space provided by the embodiment of the present invention.

[0147] Figure 9(a) is a schematic diagram of the input image of the second-order optical spatial differentiator provided in an embodiment of the present invention;

[0148] Figure 9(b) is a schematic diagram of the output effect of the second-order optical spatial differentiator device provided in the embodiment of the present invention performing first-order spatial differential operation on the input image 1;

[0149] Figure 9(c) is a schematic diagram of the output effect of a second-order optical spatial differential device designed using existing technology to perform second-order spatial differential operation on input image 1.

[0150] Figure 9(d) is a schematic diagram of the second-order optical spatial differentiator provided in an embodiment of the present invention;

[0151] Figure 9(e) is a schematic diagram of the output effect of the second-order optical spatial differential device provided in the embodiment of the present invention performing first-order spatial differential operation on the input image 2.

[0152] Figure 9(f) is a schematic diagram of the output effect of a second-order optical spatial differential device designed using existing technology to perform second-order spatial differential operation on the input image 2;

[0153] It can be seen that the second-order optical spatial differentiator performs second-order differentiation operations on the incident image in the x and y directions, increasing the contrast of the image edges and sharpening the image. The technical solution of this invention uses a spatial spectral transfer function with an increased Gaussian kernel. Compared with existing second-order optical spatial differentiator devices, the embodiment provided by this invention achieves clearer results in second-order differentiation of the input image and can also obtain excellent differentiation effects for fine structures in the input image.

[0154] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention and within the spirit and principles of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A reverse design method for optical spatial differentiating devices oriented towards target extraction, characterized in that, The method includes the following steps: S1, Set the target spatial spectrum transfer function according to the functional requirements of the optical device; S2, Establish an optimization model based on the design parameters of the metasurface, wherein the design parameters are the dielectric constant distribution, and constrain and binarize the design parameters in each iteration; S3, determine whether the loss function has converged. If it has converged, output the optimization scheme. Otherwise, perform gradient calculation to update the design parameters, and then continue to the next iteration optimization process. In S1, based on the specific functional requirements of the optical device, its target spatial spectral transfer function in wave vector space is determined, and a Gaussian kernel function is added to control the local effect of the target spatial spectral transfer function on spatial frequencies of different sizes. The target spatial spectral transfer function is denoted as... ; In S2, the free-form metasurface is optimized by pixelating each metasurface layer, and each pixel is... dielectric constant As a design parameter, random coherent noise is set as... initial value, The range of values ​​is set as Between two dielectric materials, one of which is air ,right For topology optimization in the continuous case, during one optimization iteration, for Apply constraints and perform binarization; The dielectric constant Applying constraints and performing binarization processing includes: For a target space spectral transfer function with symmetry, the structure of the metasurface has symmetry. Apply constraints to satisfy the corresponding symmetry; Design parameters The value changes continuously, and the range of values ​​is [missing information]. In gradient calculation It is continuous. When calculating the transmission coefficient of a device using a full-wave electromagnetic solver, the binarization algorithm using the tanh function is combined to make it... The value is one of the two dielectric materials. or .

2. The reverse design method for optical spatial differentiating devices oriented towards target extraction according to claim 1, characterized in that, Optical devices include first-order optical spatial differentiators, which enable the processing of light field images in... or The first-order differential operation in the direction is used to extract the edge information of the image. The target spatial spectrum transfer function of the first-order optical spatial differentiator is as follows: in , The spatial frequencies corresponding to the elementary plane waves that the incident light field is decomposed into. The intensity is the transmission coefficient. It controls the local scope of the Gaussian kernel function and adjusts it according to the specific design.

3. The reverse design method for optical spatial differentiating devices oriented towards target extraction according to claim 1, characterized in that, Optical devices include second-order optical spatial differentiators, enabling the processing of light field images in... , The second-order differential operation in the direction is used to enhance the edge information of the image and sharpen the image. The target spatial spectrum transfer function of the second-order optical spatial differential device is as follows: in , The spatial frequencies corresponding to the elementary plane waves that the incident light field is decomposed into. The intensity is the transmission coefficient. It controls the local scope of the Gaussian kernel function and is adjusted according to the specific design.

4. The reverse design method for optical spatial differentiating devices oriented towards target extraction according to claim 1, characterized in that, In S3, a full-wave electromagnetic solver is used to calculate the optimization iteration process by... The given target spatial spectral transfer function of the optical device represents its response in wave vector space to light fields of different spatial frequencies, denoted as [equation missing]. ;Will and The mean squared error is used as the loss function in the optimization iteration process. During one optimization iteration, the following was calculated: right The gradient, combined with the optimization iteration process, updates the design parameters, so that... Once convergence is achieved, the results for different period sizes of the metasurface are compared, and an optimized solution is output. .

5. The reverse design method for optical spatial differentiating devices oriented towards target extraction according to claim 4, characterized in that, The loss function in the optimization iteration process is in the form of: in express sampling points, This indicates the total number of sampling points.

6. An optical spatial differentiating device designed using the reverse design method for target extraction optical spatial differentiating devices according to any one of claims 1-5, characterized in that, The optical spatial differentiator is fabricated using dual-light polymerization 3D printing technology, specifically comprising: a multilayer dielectric material with a metasurface periodic structure; the metasurface periodic structure has a free geometric form; and the optical spatial differentiator is composed of two dielectric materials, one of which is air.

7. An optical device for the fields of artificial intelligence, autonomous driving, and machine vision, characterized in that, The optical device integrates an optical spatial differential device designed using the reverse design method for target extraction optical spatial differential devices as described in any one of claims 1-5.

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