Metasurface holographic grating for computing tomographic spectrometer and its design method

Abstract

The present invention relates to a metasurface holographic grating for a computed tomography spectrometer and a design method thereof. First, a diffraction pattern, a system focal length, and a detector target surface are selected to determine the initial structural parameters of the metasurface holographic grating. Then, a phase compensation distribution is obtained according to the initial structural parameters. Next, a simulation software is used to simulate the small-period unit of the metasurface holographic grating to obtain a relationship between the phase compensation and the diameter of the surface unit structure. Finally, the phase distribution is converted into the metasurface holographic grating array structure through the relationship. The metasurface holographic grating designed by this method can miniaturize the spectrometer and produce a good diffraction effect. This design method uses a phase optimization algorithm to convert the discrete phase distribution of the metasurface holographic grating into a continuous phase distribution, improving the accuracy of simulating the far-field response of the metasurface holographic grating.

Description

Technical Field

[0001] The present invention relates to the field of micro-nano optical technologies, and particularly to a metasurface holographic grating for a computed tomography spectrometer and a design method thereof. Background Art

[0002] Computed tomography spectroscopy borrows the principle of computed tomography and combines it with imaging spectroscopy technology to detect a projection of a target data cube or projection images in multiple projection directions, and then reconstructs the spectral information and spatial image information of the target from these projection images.

[0003] However, the key component of the computed tomography spectrometer, the holographic grating, needs to be manufactured by electron beam exposure, with a complex process and a relatively high manufacturing cost. Moreover, since the minimum step of the traditional holographic grating is in the micron order, it will result in a relatively large volume of the computed tomography spectrometer. Therefore, the miniaturization of the computed tomography spectrometer is also a problem that needs to be solved.

[0004] An optical metasurface is made of sub-wavelength metal or high refractive index dielectric units, and these units modulate the phase of the transmitted light through resonance or waveguide effects. By adjusting the geometric shape of the nano-units, the phase of the light transmitted through the metasurface can be adjusted extremely flexibly with sub-wavelength spatial resolution. In addition, the metasurface manufacturing process is relatively mature and compatible with traditional semiconductor processes, having the advantage of being easy to manufacture. Compared with a low refractive index binary phase grating, the thickness of the metasurface can also be designed to be relatively thin, with greater degrees of freedom.

[0005] At the same time, in the current iteration process of the metasurface phase, discrete phase distributions are basically used. However, the actual phase distribution of the metasurface is continuous, so in the actual optical path, it will bring changes in the diffraction effect, making the iteration process require further optimization through algorithms. Summary of the Invention

[0006] For this reason, the present invention provides a metasurface holographic grating for a computed tomography spectrometer and a design method thereof. The metasurface holographic grating designed by this method has a relatively small volume, is insensitive to the polarization of incident light, and has a relatively high transmission efficiency, and can realize the functions of beam splitting and dispersion in a computed tomography spectrometer.

[0007] To achieve the above object, the technical solution proposed by the present invention is:

[0008] On the one hand, the present invention provides a design method for a metasurface holographic grating for a computed tomography spectrometer, characterized by including the following steps:

[0009] S1: Select a diffraction pattern, a system focal length, and a detector target surface to determine the initial structural parameters of the metasurface holographic grating;

[0010] S2: Obtain the phase compensation distribution according to the initial structural parameters, the transmission phase principle, and the phase hologram optimization algorithm;

[0011] S3: Simulate the small-period unit of the metasurface holographic grating using simulation software according to the initial structural parameters to obtain the relationship between the phase compensation and the diameter of the surface unit structure;

[0012] S4: Convert the phase distribution into the metasurface holographic grating array structure according to the relationship between the phase compensation and the diameter of the surface unit structure.

[0013] In some embodiments, optimize the metasurface holographic grating array structure based on the interior point method and the vector electromagnetic method, including the steps of:

[0014] S1: Compare the far-field pattern of the metasurface holographic grating array structure with the diffraction pattern required in reality, perform iterative optimization until the far-field pattern is consistent with the diffraction pattern distribution, obtain the optimized arrangement of the metasurface holographic grating array, and the corresponding phase distribution of the metasurface holographic grating array;

[0015] S2: Import the phase distribution into optical design software, input the real three-dimensional data cube and simulate the complete optical path of the metasurface holographic grating to obtain the diffraction pattern on the focal plane array;

[0016] S3: Use data processing software to superimpose the diffraction patterns of different wavelengths, and obtain the restored three-dimensional data cube through the expectation maximization algorithm. Compare the parameters of the restored three-dimensional data cube and the real three-dimensional data cube. If the difference is small, the overall imaging process of the metasurface holographic grating is correct, otherwise, reselect the diffraction pattern, system focal length, and target surface.

[0017] Among them, in S1 of

[0009] , the vector electromagnetic method is combined with the interior point method to optimize the diameter of each surface unit structure of the metasurface holographic grating, so that the energy distribution of each order is as uniform as possible. By using the Fraunhofer diffraction formula as the propagation function, the vector electromagnetic method can consider the coupling between the surface unit structures of the metasurface holographic grating and simulate the far-field response of the continuous phase distribution of the metasurface.

[0018] The interior point method defines the figure of merit f(x1, x2, …, x M ) = FOM = RMSE + (1 - Eff) as the optimization function to design and optimize the metasurface, where x j is the diameter of the surface unit structure, and x j ∈R, j = 1, 2, …, M, 20nm ≤ x j ≤ 250nm; is the root mean square error, reflecting the uniformity of the diffraction points; is the diffraction efficiency, reflecting the overall efficiency of light diffraction onto the target surface, where I i is the diffraction intensity of the i-th order normalized to the incident light intensity, and N is the total number of target diffraction orders.

[0019] The diameter of the surface unit structure in the (n + 1)-th iteration of the interior point method where the diameter of the surface unit structure The Hessian matrix H f (X) = A T DA, The gradient of the objective function Δx j is the step size for taking the derivative of the objective function, j = 1, 2, …, M.

[0020] On the other hand, the present invention provides a metasurface holographic grating for a computed tomography spectrometer, characterized in that it is composed of a substrate and a surface unit structure, wherein the substrate has a surface extending in a first direction and a second direction perpendicular to the first direction, and the surface unit structure is a cylinder perpendicular to the substrate.

[0021] In some embodiments, the surface unit structures have equal heights, are arranged in a matrix, and are composed of one or more large periods.

[0022] Furthermore, in some embodiments, the large periods are arranged in a matrix in the first direction and the second direction of the substrate, and the large period is composed of small periods of 15 * 15.

[0023] In some embodiments, the substrate is silica, and the surface unit structure is a sub-wavelength metal or a high refractive index medium.

[0024] As a preferred solution, the surface unit structure is titanium dioxide.

[0025] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention can miniaturize the metasurface holographic grating and produce a good diffraction effect. Due to the use of a symmetric structure for design, the polarization direction of the incident light can be unrestricted. The design method of the present invention combines the vector electromagnetic method and the interior point method, and uses a phase optimization algorithm to convert the discrete phase distribution of the metasurface holographic grating into a continuous phase distribution, improving the accuracy of simulating the far-field response of the metasurface holographic grating. And this optimization algorithm is based on the far-field response pattern, which can make the energy distribution of each order as uniform as possible. Brief Description of the Drawings

[0026] Figure 1 is the principle block diagram of the present invention.

[0027] Figure 2It is the phase distribution diagram of the embodiment of the present invention.

[0028] Figure 3 It is a schematic diagram of the small period of the metasurface holographic grating of the embodiment of the present invention.

[0029] Figure 4 It is the function of FOM with respect to the number of iterations in the embodiment of the present invention.

[0030] Figure 5 It is a schematic diagram of the initial structure of the metasurface holographic grating structure of the embodiment of the present invention.

[0031] Figure 6 It is a schematic diagram of the structure of the metasurface holographic grating structure after optimization in the embodiment of the present invention. Detailed implementation manners

[0032] The following further elaborates on the detailed implementation manners of the present invention in conjunction with the accompanying drawings and examples. It should be noted that only the parts related to the present invention are shown in the drawings, not all the results. And the specific examples are only for explaining the present invention, not for limiting the scope of the invention.

[0033] 1. Design method of the metasurface holographic grating for a computational tomographic spectrometer

[0034] The present invention provides a design method of a metasurface holographic grating for a computational tomographic spectrometer. Figure 1 As a schematic diagram of the flow of the specific design method, it includes the following steps:

[0035] S1: Select the diffraction pattern, system focal length, and detector target surface to determine the initial structural parameters of the metasurface holographic grating;

[0036] S2: Obtain the phase compensation distribution according to the initial structural parameters, transmission phase principle, and phase hologram optimization algorithm.

[0037] In the specific embodiment of the present invention, the phase compensation in S2 is designed based on the transmission phase. When light with a wavelength of λ0 propagates in a medium with an effective refractive index of n eff and the thickness of the medium is d, the phase accumulation generated is:

[0038] In the specific embodiment of the present invention, by applying the scalar diffraction theory and the Gerchberg - Saxton algorithm, the initial phase distribution diagram can be obtained through multiple iterations. As shown in the attached Figure 2 figure, each large period is set to be composed of 15 * 15 phase points, and the large period is repeated 15 times in both the x and y directions to form this distribution diagram.

[0039] S3: Use simulation software to simulate the small-period unit of the metasurface holographic grating according to the initial structural parameters, and obtain the relationship between phase compensation and the diameter of the surface unit structure.

[0040] In a specific embodiment of the present invention, as shown in the appendix Figure 3 The surface unit structure is a cylinder. The substrate thickness h2 = 150 nm, the side length of the substrate unit d = 250 nm. The height of the surface unit structure h1 = 700 nm. The relationship between phase compensation and the diameter of the surface unit structure of the surface unit structure is: phase where, the diameter of the surface unit structure in the small unit of the surface unit structure array 20 nm ≤ D i ≤ 250 nm.

[0041] When designing the parameters of the surface unit structure inside the unit structure, the phase modulation amount of the metasurface holographic grating array should satisfy a phase coverage of 2π at the designed central wavelength, and under this condition, try to achieve a larger phase coverage at each wavelength within the designed wavelength band as much as possible.

[0042] S4: According to the relationship between phase compensation and the diameter of the surface unit structure, convert the phase distribution into the metasurface holographic grating array structure.

[0043] In a specific embodiment of the present invention, the metasurface holographic grating array structure is optimized based on the interior point method and the vector electromagnetic method, including the steps:

[0044] S1: Compare the far-field pattern of the metasurface holographic grating array structure with the diffraction pattern required in practice, and perform iterative optimization until the far-field pattern is consistent with the diffraction pattern distribution, to obtain the optimized arrangement of the metasurface holographic grating array and the corresponding phase distribution of the metasurface holographic grating array.

[0045] Since adjacent different antennas will affect the electromagnetic field inside the antenna, thereby affecting the transmission function response, by combining the vector electromagnetic method with the interior point method, comprehensively considering the phase compensation generated by each surface unit structure and the coupling between adjacent surface unit structures, the discrete phase distribution is converted into a continuous phase distribution for design, and the diameter of each surface unit structure of the metasurface holographic grating is optimized to make the energy distribution of each order as uniform as possible.

[0046] By using the Fraunhofer diffraction formula as the propagation function, the vector electromagnetic method can consider the coupling between the surface unit structures of the metasurface holographic grating and simulate the far-field response of the continuous phase distribution of the metasurface.

[0047] The interior point method defines the figure of merit f(x1, x2,..., x M ) = FOM = RMSE + (1 - Eff) as the optimization function to design and optimize the metasurface, where xj is the diameter of the surface unit structure, and x j ∈R, j = 1, 2, …, M, 20 nm ≤ x j ≤ 250 nm; is the root mean square error, reflecting the uniformity of the diffraction points; is the diffraction efficiency, reflecting the overall efficiency of light diffraction onto the target surface, where I i is the diffraction intensity of the i-th order normalized to the incident light intensity, and N is the total number of target diffraction orders.

[0048] The diameter of the surface unit structure in the (n + 1)-th iteration of the interior point method where the diameter of the surface unit structure Hessian matrix H f (X) = A T DA, Gradient of the objective function Δx j is the step size for taking the derivative of the objective function, j = 1, 2, …, M.

[0049] In a specific embodiment of the present invention, the iterative process of the FOM is as shown in the appendix Figure 4 shown. After optimization, the efficiency of the metasurface holographic grating exceeds 80% and the RMSE is lower than 30%. Schematic diagrams of the structure of a large period of the metasurface holographic grating before and after optimization are as shown in the appendix Figure 5 , 6 shown.

[0050] S2: Import the phase distribution into the optical design software, input the real three-dimensional data cube and simulate the complete optical path of the metasurface holographic grating, and obtain the diffraction pattern on the focal plane array;

[0051] S3: Use data processing software to superimpose the diffraction patterns of different wavelengths, and obtain the restored three-dimensional data cube through the expectation maximization algorithm. Compare the parameters of the restored three-dimensional data cube and the real three-dimensional data cube. If the difference is small, the overall imaging process of the metasurface holographic grating is correct; otherwise, reselect the diffraction pattern, system focal length, and target surface.

[0052] In a specific embodiment of the present invention, the Expectation-Maximum algorithm is applied in Matlab to restore the three-dimensional data cube, and the parameters are compared by calculating the peak signal-to-noise ratio.

[0053] The core idea of the Expectation-Maximum algorithm is the iterative reconstruction method, that is, transforming the reconstruction problem into solving an algebraic equation system that reflects the relationship between the voxel values and projection values of the reconstructed data cube. Iterative reconstruction is based on the estimation theory. First, an initial value is assigned to each voxel in the reconstruction area. Starting from the initial cube with the assigned initial values, a cyclic iterative method is adopted. Each iteration is divided into two steps: projection and back-projection. During the projection process, the projection value of the estimated cube, that is, the theoretical projection value, needs to be compared with the actual projection value, and then the comparison result is back-projected into the data cube space to calculate the correction factor to correct the data cube. Then, a new iterative operation is performed on the newly corrected result. This iteration continues until a satisfactory result is obtained. This algorithm can perform multiple iterations on the known two-dimensional image information, enabling the diffraction images to be superimposed and restored, so as to obtain the restored image data.

[0054] 2. Metasurface holographic grating for computing tomographic spectrometer

[0055] The metasurface holographic grating for computing tomographic spectrometer provided by the present invention is composed of a substrate and a surface unit structure. Among them, the substrate has a surface extending in a first direction and a second direction perpendicular to the first direction, and the surface unit structure is a cylinder perpendicular to the substrate. The diameter of the cylinder is D i , the thickness is h1, the thickness of the substrate is h2, and the side length of the small period is d.

[0056] The coordinates referred to in this article are based on the optical axis as the z coordinate, and the x and y coordinates are established in a plane perpendicular to the optical axis.

[0057] In a specific embodiment of the present invention, the surface unit structures have equal heights and are arranged in a matrix, and are composed of one or more large periods.

[0058] The large periods of the metasurface holographic grating are arranged in a matrix in the first direction and the second direction of the substrate, and the number of structural units in each large period is n*n. In the wavelength range of 550nm - 1000nm, by setting the diameter of each surface unit structure in the large period, the corresponding phase delay can be achieved, the incident light can be dispersed, and the diffraction projection of light can be realized, generating two-dimensional diffraction patterns of multiple orders. By changing the size, quantity, etc. of the surface unit structure of the metasurface holographic grating, the order change of the two-dimensional diffraction pattern can be realized.

[0059] In a specific embodiment of the present invention, as shown in the figure, the large period is composed of 15*15 small periods.

[0060] The surface unit structure can be sub-wavelength metal or high refractive index medium. Optional materials include titanium oxide, silicon nitride, fused quartz, amorphous silicon, etc., and optional materials for the plasma structure unit include gold, silver, aluminum, etc.

[0061] In a specific embodiment of the present invention, the substrate is silica and the surface unit structure is titanium dioxide.

[0062] The principle and specific implementation of this structure are elaborated in detail in the text in conjunction with the accompanying drawings. In addition, for those of ordinary skill in the art, there will be changes in the specific implementation manners and application scopes according to the idea of the present invention. In summary, the content of this specification should not be construed as a limitation on the present invention, and all applications and inventions using the idea of the present invention are within the scope of protection.

Claims

1. A design method for a metasurface holographic grating of a computed tomography spectrometer, characterized in that, It includes the following steps: S1: Select a diffraction pattern, system focal length, and detector target surface to determine the initial structural parameters of the metasurface holographic grating; S2: Obtain a phase compensation distribution according to the initial structural parameters, transmission phase principle, and phase hologram optimization algorithm; S3: Use simulation software to simulate the small-period unit of the metasurface holographic grating based on the initial structural parameters to obtain the relationship between phase compensation and the diameter of the surface unit structure; S4: Convert the phase distribution into the metasurface holographic grating array structure according to the relationship between phase compensation and the diameter of the surface unit structure.

2. The design method of the metasurface holographic grating for a computed tomography spectrometer according to claim 1, wherein Optimize the metasurface holographic grating array structure in step S4 based on the interior point method and vector electromagnetic method, including the steps: S4-1: Compare the far-field pattern of the metasurface holographic grating array structure with the diffraction pattern required in practice, and perform iterative optimization until the far-field pattern is consistent with the diffraction pattern distribution, to obtain the optimized arrangement of the metasurface holographic grating array and the corresponding phase distribution of the metasurface holographic grating array; S4-2: Import the phase distribution into optical design software, input real three-dimensional data cubes and simulate the complete optical path of the metasurface holographic grating, and obtain a diffraction pattern on the focal plane array; S4-3: Use data processing software to superimpose the diffraction patterns of different wavelengths, and obtain the restored three-dimensional data cube through the expectation maximization algorithm. Compare the parameters of the restored three-dimensional data cube and the real three-dimensional data cube. If the difference is small, the overall imaging process of the metasurface holographic grating is correct; otherwise, re-select the diffraction pattern, system focal length, and target surface.

3. The design method of the metasurface holographic grating for a computed tomography spectrometer according to claim 2, wherein The defined interior point method defines the quality factor f(x1, x2,..., x M ) = FOM = RMSE + (1 - Eff) as the optimization function to design and optimize the metasurface, where x j is the diameter of the surface unit structure, and x j ∈R, j = 1, 2,..., M, 20nm ≤ x j ≤ 250nm; is the root mean square error, reflecting the uniformity of the diffraction points; is the diffraction efficiency, reflecting the overall efficiency of light diffraction onto the target surface, where I i is the i-th order diffraction intensity normalized to the incident light intensity, and N is the total number of target diffraction orders.

4. The design method of the metasurface holographic grating for a computed tomography spectrometer according to claim 3, wherein The diameter of the surface element structure in the (n + 1)-th iteration of the interior point method where the diameter of the surface element structure Hessian matrix H f (X) = A T DA, Gradient of the objective function Δx j is the step size for taking the derivative of the objective function, j = 1, 2, …, M.

5. A metasurface holographic grating for calculating a tomographic spectrometer, characterized in that, Obtained according to the design method described in any one of claims 1 to 4, composed of a substrate and surface unit structures, wherein the substrate has a surface extending in a first direction and a second direction perpendicular to the first direction, and the surface unit structures are cylinders perpendicular to the substrate.

6. The metasurface holographic grating for calculating a tomographic spectrometer according to claim 5, wherein The surface unit structures have equal heights, are arranged in a matrix, and are composed of one or more large periods.

7. The metasurface holographic grating for calculating a tomographic spectrometer according to claim 6, characterized in that, The large periods are arranged in a matrix in the first direction and the second direction of the substrate, and each large period is composed of 15*15 small periods.

8. The metasurface holographic grating for calculating a tomographic spectrometer according to any one of claims 5 to 7, characterized in that, The substrate is silica, and the surface unit structures are subwavelength metals or high-refractive-index dielectrics.

9. The metasurface holographic grating for calculating a tomographic spectrometer according to claim 8, wherein, The surface unit structure is titanium dioxide.

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