Optimization Method for Multilayer Stereoscopic Display System Based on Polarization Dual-Channel Metasurface

Abstract

An optimization method for a multi-layer three-dimensional display system based on a polarization dual-channel metasurface, belonging to the fields of micro-nano optics and three-dimensional display optical imaging. In the present invention, a polarization dual-channel metasurface with multi-layer three-dimensional display function is arranged at the spectrum plane position of a 4F system, and the two-dimensional image source information is arranged in three-dimensional space through the polarization dual-channel metasurface to expand the display dimension of the image information; the three-dimensional display metasurface forms a planar misalignment and a controllable fixed interval of multi-layer image information based on the spatial distribution position of the diffraction orders of the light beam emitted by the 4F system controlled by a twisted grating; by utilizing the resonance phase characteristics of the metasurface, the light beam emitted by the 4F system realizes symmetric display of the spatial sorting of diffraction orders under the condition of polarization dual channels for the same image source information, so that the emitted three-dimensional pattern produces a mirror three-dimensional display effect in the orthogonal polarization channels, which can enhance the modulation flexibility and controllable dimension of the display optical path of the 4F system and enrich the imaging control means.

Description

Technical Field

[0001] The present invention relates to an optimization method for a stereoscopic display optical system, and particularly to an optimization method for a multi-layer stereoscopic display system based on a polarization dual-channel metasurface, belonging to the fields of micro-nano optics and stereoscopic display optical imaging. Background Art

[0002] With the gradual widespread application of virtual reality and augmented reality technologies in social life, people's enthusiasm for pursuing micro-structured 3D display technologies has been increasing day by day. As a practical virtual reality means, 3D display technologies usually require a large-scale device. Therefore, the exploration of 3D display elements with more precise dimensions has attracted people's attention. To achieve this goal, people have made various attempts and explorations on 3D display technologies by using means such as spatial light modulators, diffraction gratings, DOE elements, and so on.

[0003] For ordinary gratings, the focal length characteristics brought by the lens system act uniformly on all diffraction orders, and it is impossible to achieve the focal plane separation of each diffraction order. For zone plates, the multi-focal separation characteristics in the Z direction have limitations in the pitch variation, do not have a high design flexibility, and it is generally difficult to combine with spatial distribution characteristics to form a complex and interesting diffraction effect. The twisted grating is an extended grating concept. Based on the basic grating equation and combined with the Z-direction control method of the zone plate, it further expands the X-Y plane distribution of the grating diffraction orders into a multi-focal distribution in 3D space. Different from the concept of the zone plate, the twisted grating tilts and deforms the spatial grating diffraction orders, so as to achieve the consistent control of the spatial distribution and focal length characteristics. As a light field modulation means, the twisted grating has the ability to transform plane single-layer image information into spatial multi-layer information, thus forming the effect of 3D display. It utilizes the design freedom of the multi-focal in the Z direction of the zone plate to obtain multi-layers of planes, and also utilizes the diffraction angles of the grating orders to achieve the synthesis of multi-layers of independent information targets, truly realizing free multi-focal imaging in space. The design method of the twisted grating has been widely applied to the design of spatial multi-focal imaging. Whether in 3D display technologies, laser cutting technologies, or optical tweezer technologies, the characteristics of spatially distributed light beams can be designed to be freely distributed. Combining the design method of the twisted grating with the design of 3D display technologies is an important method for people to explore 3D display using micro-nano structures. Through preliminary attempts, people have been able to achieve 3 - 6 layers of spatial multi-foci, and 3D display technologies with more precise depth and more complex light field characteristics are still under exploration. Summary of the Invention

[0004] To solve the problems of large volume, complex structure, inflexible modulation means, and low available dimensions in the existing three-dimensional imaging systems, the main objective of the present invention is to provide an optimization method for a multi-layer three-dimensional display system based on a polarization dual-channel metasurface. A polarization dual-channel metasurface with multi-layer three-dimensional display functions is arranged at the spectral plane position of a 4F system. The two-dimensional image source information is arranged in three-dimensional space through the polarization dual-channel metasurface to expand the display dimension of the image information; the three-dimensional display metasurface forms a planar misalignment and controllable fixed interval of multi-layer image information based on the spatial distribution position of the diffraction orders of the output beam of the controlled 4F system; by utilizing the resonance phase characteristics of the metasurface, symmetric display of the spatial sorting of diffraction orders for the same image source information under the condition of polarization dual channels is realized for the output beam of the 4F system, so that a mirror three-dimensional display effect is generated for the output three-dimensional pattern in the orthogonal polarization channels, and further, the modulation flexibility and controllable dimensions of the display optical path of the 4F system can be enhanced, and the control means of the imaging system can be enriched.

[0005] The present invention is realized through the following technical solutions.

[0006] The optimization method for a multi-layer three-dimensional display system based on a polarization dual-channel metasurface disclosed by the present invention includes the following steps:

[0007] Step 1: In order to control the spatial distribution position of the diffraction orders of the output beam of the 4F system to form a planar misalignment and controllable fixed interval of multi-layer image information, a one-dimensional twisted grating is established on the basis of the 4F imaging system structure according to the spatial distribution position regulation target of the output beam diffraction orders. The one-dimensional twisted grating regulates the light field spectral plane information according to the constructed transmittance regulation function, so that a spatial interleaving display effect is generated for the diffraction orders of the output light field of the 4F system.

[0008] The 4F system includes two symmetrically arranged lenses. The two lenses have four front and rear focal points, and the two central focal points coincide. The 4F system is used to reproduce the image information located at the first focal point position at the last focal point position. The focal point position between the two lenses is the spectral plane of the optical system, which can cooperate with the twisted grating regulation to achieve the purpose of controlling the spatial distribution of the diffraction orders of the output beam of the 4F system.

[0009] A one-dimensional twisted grating based on the 4F imaging system structure controls the spatial distribution position of the diffraction orders of the outgoing light beam through multi-focal plane custom distance interleaved display, forming an X-direction misalignment and a controllable fixed interval in the Z-direction of multi-layer image information. Among them, the incident image source information is located at the first focal position in the 4F system, and the metasurface with the function of controlling the one-dimensional twisted grating is located at the second focal position in the 4F system, that is, the central spectral plane position of the optical path. At the third focal position of the 4F system, the image information distributed along the Z-axis shows a regular spatial arrangement. The image information distributed along the Z-axis is the outgoing light field of the 4F system with a multi-layer structure, and the third focal position is the last focal position. The three-dimensional display metasurface controls the spectral plane of the 4F system, making the diffraction orders of the outgoing light field of the 4F system produce a spatially interleaved display effect. The content displayed at different focal positions near the optical axis of the diffraction orders of the outgoing light field is different patterns, and the rest of the pattern information is blocked outside the viewing range.

[0010] The one-dimensional twisted grating regulates the spectral plane information of the light field according to the following transmittance regulation function formula (1), making the diffraction orders of the outgoing light field of the 4F system produce a spatially interleaved display effect.

[0011]

[0012] In the formula, T 1D represents the total transmittance of the one-dimensional twisted grating. Since the twisted grating is a pure phase optical modulation period, the phase distribution represents the modulation function of the transmittance regulation function, which is optimized by the Dammann grating method. The coefficient C m represents the energy distribution of each diffraction order. m represents the diffraction order position in the x direction, x represents the spatial position coordinate of the Cartesian coordinate system, r represents the spatial position coordinate of the cylindrical coordinate system, represents the wave number, λ represents the wavelength, f g represents the defocus coefficient. By the method of phase optimization, the excitation of the target diffraction order is selected, making the diffraction orders of the outgoing light field of the 4F system produce a spatially interleaved display effect. Each diffraction order of the grating is represented by Fourier expansion. In order to achieve the interleaved overlapping effect of different orders, in addition to the characteristic phase of the ordinary grating, the twisted grating also has a regulation limit for each focal position, that is the grating phase controls the spatial angular spread of each diffraction order, that is In the formula, Λ x represents the grating period, that is, Λ x = N×d, d represents the interval of a single antenna pixel of the metasurface. The twisted grating controls the incident pattern in the frequency domain of the image. Combined with the common modulation of the front and rear lens 4f system. The multi-layer focal interval is calculated by the Gaussian formula: Similarly, the misaligned intervals of multiple layers of patterns are expressed as: dx = NAf0. The DMD image source is accurately arranged using the misaligned intervals of the patterns to ensure an ideal interval-aligned spatial pattern at the target observation position.

[0013] Step 2: Based on the transmittance modulation function of the one-dimensional twisted grating constructed in Step 1, a two-dimensional twisted grating is constructed to simultaneously control the spatial distribution positions of the diffraction orders of the outgoing light beams in the X and Y directions, so that the diffraction orders of the light field emerging from the 4F system produce a three-dimensional spatial interleaved display effect.

[0014] The one-dimensional grating obtained from formula (1) has achieved the Z-direction display of the one-dimensional distributed image. By simultaneously controlling the spatial distribution positions of the diffraction orders of the outgoing light beams in the X and Y directions, a two-dimensional twisted grating can be constructed, enabling the incident light source information to be emitted in a three-dimensional spatial distribution. The transmittance modulation function of the two-dimensional twisted grating is as shown in formula (2)

[0015]

[0016] In the formula, T 2D represents the total transmittance of the two-dimensional twisted grating, and the phase distribution represents the modulation function of the transmittance modulation, which is obtained by optimizing the Dammann grating method. The coefficient C mn represents the energy distribution of each diffraction order. m represents the diffraction order position in the x direction, n represents the diffraction order position in the y direction, (x, y) represents the spatial position coordinates in the Cartesian coordinate system, r represents the spatial position coordinates in the cylindrical coordinate system, represents the wave number, λ represents the wavelength, f gx , f gy represent the defocus coefficients in the x and y directions. By using the phase optimization method to select the excitation of the target diffraction order, the diffraction orders of the light field emerging from the 4F system produce a spatially interleaved display effect. Each diffraction order of the grating is represented by Fourier expansion. To achieve the interleaved and overlapping effect of different orders, in addition to the characteristic phase of the ordinary grating, the twisted grating also has a control limit for each focal length position, that is The grating phase controls the spatial angular spread of each diffraction order, that is In the formula, Λ represents the grating period, that is Λ = N×d, and d represents the interval of a single antenna pixel of the metasurface. The twisted grating controls the incident pattern in the frequency domain of the image. Combined with the common modulation of the front and rear lens 4f systems. The multi-layer focal length intervals are calculated by the Gaussian formula: Similarly, the misaligned intervals of multiple layers of patterns are expressed as: dx = NAf0, dy = NAf0. The DMD image source is accurately arranged using the misaligned intervals of the patterns to ensure an ideal interval-aligned 3D spatial pattern at the target observation position.

[0017] Step 3: Utilize the dual-channel independent regulation function generated by the metasurface resonance phase characteristics and the above-mentioned transmittance function of the two-dimensional twisted grating to deploy the metasurface. Through the polarization dual-channel metasurface, arrange the two-dimensional image source information in three-dimensional space to expand the display dimension of the image information, and realize the symmetric display of the diffraction order spatial sorting of the 4F system output beam for the same image source information under the polarization dual-channel condition, so that the output three-dimensional pattern produces a mirror three-dimensional display effect in the orthogonal polarization channels, thereby enhancing the modulation flexibility and controllable dimension of the 4F system display optical path and enriching the control means of the imaging system.

[0018] Combined with the polarization channel multiplexing function of the metasurface, the transmittance regulation function of the polarization dual-channel metasurface is shown in formulas (3) and (4).

[0019]

[0020]

[0021] where: T xx , T xx represent the transmittances under two polarization channels, and the phase distribution represents the modulation function of the transmittance regulation function under two polarization channels, which is optimized by the Dammann grating method. m represents the diffraction order position in the x direction, n represents the diffraction order position in the y direction, (x, y) represents the spatial position coordinates of the Cartesian coordinate system, r represents the spatial position coordinates of the cylindrical coordinate system, represents the wave number, λ represents the wavelength, f gx , f gy represent the defocus coefficients in the x direction and y direction. The regulation parameters under the two polarization channels are exactly the same, only the signs of the defocus coefficients are different, so that the effect of orthogonal polarization mirror symmetry of the diffracted light field output beam can be controlled.

[0022] It further includes Step 4: Utilize the advantages of flexible, multi-dimensional optical parameter combination, and thin, light, and compact structure of the metasurface modulation means. Based on the polarization dual-channel metasurface, a multi-layer three-dimensional display system is realized by arranging the optical path according to Step 2. Based on the multi-layer three-dimensional display system, it can support optical imaging scenarios such as wearable display and virtual reality, as well as optical integrated display devices to improve control flexibility and integration compactness.

[0023] The multi-dimensional optical parameters include three-dimensional spatial information, frequency characteristics, polarization characteristics, phase characteristics, etc. of the light field.

[0024] Beneficial effects:

[0025] 1. The present invention discloses an optimization method for a multi-layer three-dimensional display system based on a polarization dual-channel metasurface. A polarization dual-channel metasurface with multi-layer three-dimensional display function is arranged at the spectrum plane position of a 4F system. The two-dimensional image source information is arranged in three-dimensional space through the polarization dual-channel metasurface to expand the display dimension of the image information.

[0026] 2. The present invention discloses an optimization method for a multi-layer three-dimensional display system based on a polarization dual-channel metasurface. Based on the control of the diffraction order spatial distribution position of the output beam of the 4F system by a twisted grating, a planar misalignment and controllable fixed interval of multi-layer image information are formed; by utilizing the resonance phase characteristics of the metasurface, symmetric display of the diffraction order spatial sorting for the same image source information under the polarization dual-channel condition of the output beam of the 4F system is realized, so that a mirror three-dimensional display effect is generated for the output three-dimensional pattern under the orthogonal polarization channels, and further, the modulation flexibility and controllable dimension of the display optical path of the 4F system can be enhanced, and the control means of the imaging system can be enriched.

[0027] 3. The present invention discloses an optimization method for a multi-layer three-dimensional display system based on a polarization dual-channel metasurface. By utilizing the advantages of flexible modulation means, multi-dimensional optical parameter combination, and thin, light, and compact structure of the metasurface, the multi-layer three-dimensional display system based on the polarization dual-channel metasurface can support optical imaging scenarios such as wearable display and virtual reality, as well as optical integrated display devices to improve control flexibility and integration compactness. The multi-dimensional optical parameters include three-dimensional spatial information, frequency characteristics, polarization characteristics, phase characteristics, etc. of the light field. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is a flowchart of an optimization method for a multi-layer three-dimensional display system based on a polarization dual-channel metasurface disclosed by the present invention;

[0029] Figure 2 is a schematic conceptual diagram of the imaging system of the method of the present invention;

[0030] Figure 3 is a schematic diagram of the basic principle of a one-dimensional twisted grating corresponding to Step 1 of the method of the present invention;

[0031] Figure 4 is a schematic diagram of phase optimization corresponding to Step 3 of the method of the present invention; FIG. a is a schematic diagram of the energy ratio distribution of the optimized target diffraction order; FIG. b is a schematic diagram of the optimized phase period distribution of the Dammann grating; FIGS. c and d are schematic diagrams of the optimized phase arrangements of the Txx and Tyy dual-channel twisted gratings respectively;

[0032] Figure 5 is the experimental effect diagram provided by the embodiment of the present invention; FIG. a is the two-dimensional digital information carried by the incident light source; FIG. b is the experimental result diagram of the axial multi-layer display of the digital information; FIG. c is the two-dimensional letter information carried by the incident light source; FIG. d is the experimental result diagram of the axial multi-layer display of the letter information;

[0033] Figure 6 It is a schematic diagram for comparing experimental observation positions provided by an embodiment of the present invention. Specific implementation manners

[0034] The following further elaborates on the method of the present invention in detail in conjunction with the accompanying drawings and embodiments.

[0035] Embodiment 1:

[0036] As shown in the attached Figure 1 figure, the optimization method of the multi-layer three-dimensional display system based on the polarization dual-channel metasurface disclosed in this embodiment regulates the phase of the outgoing light beam under the illumination of light with a wavelength of 680 nm. The specific implementation steps are as follows:

[0037] Step 1: In order to control the planar misalignment and controllable fixed interval of the spatial distribution positions of the diffraction orders of the outgoing light beam of the 4F system to form multi-layer image information, according to the regulation target of the spatial distribution positions of the diffraction orders of the outgoing light beam, a one-dimensional twisted grating is established on the structure of the 4F imaging system. The one-dimensional twisted grating regulates the light field spectrum plane information according to the constructed transmittance regulation function, so that the diffraction orders of the outgoing light field of the 4F system produce a spatially staggered display effect, such as Figure 3 .

[0038] In the embodiment, the target diffraction orders m = (-2, -1, 0, 1, 2) in the x direction are selected, the focal length f0 of the 4F system lens is 150 mm, the defocus coefficient f gx of the one-dimensional Dammann grating is 15 / 4f0, the working wavelength λ = 680 nm, the grating period Λ x = 12 * 350 nm = 4.2 um, and the multi-layer pattern misalignment interval dx = NAf0 = 24 m. The DMD image source is accurately arranged using the pattern misalignment interval to ensure an ideally spaced-aligned spatial pattern at the target observation position.

[0039] Step 2: Based on the transmittance regulation function of the one-dimensional twisted grating constructed in Step 1, a two-dimensional twisted grating is constructed to regulate the spatial distribution positions of the diffraction orders of the outgoing light beam in both the X direction and the Y direction simultaneously, so that the diffraction orders of the outgoing light field of the 4F system produce a three-dimensional spatially staggered display effect.

[0040] The one-dimensional grating obtained by formula (1) has achieved the Z-direction display of the one-dimensional distributed image. By regulating the spatial distribution positions of the diffraction orders of the outgoing light beam in both the X direction and the Y direction simultaneously, a two-dimensional twisted grating can be constructed, enabling the incident light source information to be emitted in a three-dimensional spatial distribution. In the embodiment, the target diffraction orders m = (-2, -1, 0, 1, 2) in the x direction and m = (-1, 1) in the y direction, a total of 10 diffraction orders, are selected as the optimization targets. The optimization results and the phase distribution of the transmittance function in the case of orthogonal polarization are asFigure 4 。The focal length f0 of the lens in the 4F system is 150 mm, and the defocus coefficient f of the one-dimensional Dammann grating gx = 15 / 4f0, f gx = 15 / f0, the working wavelength λ = 680 nm, the grating period Λ x = 12 * 350 nm = 4200 nm. The misalignment intervals of the multi-layer patterns are dx = NAf0 = 24 mm and dy = NAf0 = 24 mm. The focal length intervals of the multi-layers are calculated by the Gaussian formula: dz = 2f0 / 15 = 20 mm. The misalignment intervals of the patterns are used to accurately arrange the DMD image sources to ensure that an ideal spatially aligned pattern is obtained at the target observation position. The comparison between the experimental observation positions and the set positions of each layer is as Figure 5 shown.

[0041] Step 3: Use the dual-channel independent regulation function generated by the metasurface resonance phase characteristics and the above-mentioned transmittance function of the two-dimensional twisted grating to arrange the metasurface. Through the polarization dual-channel metasurface, the two-dimensional image source information is arranged in three-dimensional space to expand the display dimension of the image information, and realize the symmetric display of the diffraction order spatial sorting of the 4F system output beam for the same image source information under the polarization dual-channel condition, so that the output three-dimensional pattern generates a mirror three-dimensional display effect in the orthogonal polarization channels, thereby enhancing the modulation flexibility and controllable dimension of the 4F system display optical path and enriching the control means of the imaging system.

[0042] In the embodiment, numbers and letters are input as the image source information of the DMD into the three-dimensional display optical path system. At the output light field position, it can be observed that 10 parts of the pattern are symmetrically arranged in different polarization channels, as Figure 6 .

[0043] Step 4: Utilize the advantages of flexible metasurface modulation means, multi-dimensional optical parameter combination, and thin, light, and compact structure. Based on the polarization dual-channel metasurface, the multi-layer three-dimensional display system is arranged according to Step 2. Based on the multi-layer three-dimensional display system, it is possible to support optical imaging scenarios such as wearable display and virtual reality, as well as optical integrated display devices to improve control flexibility and integration compactness. The multi-dimensional optical parameters include the three-dimensional spatial information, frequency characteristics, polarization characteristics, phase characteristics, etc. of the light field.

[0044] The above specific description further details the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. Optimization method for a multi-layer three-dimensional display system based on a polarization dual-channel metasurface, characterized in that: Including the following steps: Step 1: In order to control the planar misalignment and controllable fixed interval of the multi-layer image information formed by the spatial distribution position of the diffraction orders of the output beam of the 4F system, based on the regulation target of the spatial distribution position of the diffraction orders of the output beam, a one-dimensional twisted grating is established on the structure of the 4F imaging system. The one-dimensional twisted grating regulates the light field spectrum plane information according to the constructed transmittance regulation function, so that the diffraction orders of the output light field of the 4F system produce a spatially staggered display effect; Step 2: Based on the transmittance regulation function of the one-dimensional twisted grating constructed in Step 1, a two-dimensional twisted grating is constructed to regulate the spatial distribution position of the diffraction orders of the output beam in both the X and Y directions simultaneously, so that the diffraction orders of the output light field of the 4F system produce a three-dimensional spatial staggered display effect; Step 3: Utilize the dual-channel independent regulation function generated by the metasurface resonance phase characteristics and the transmittance function of the above two-dimensional twisted grating to arrange the metasurface. Through the polarization dual-channel metasurface, the two-dimensional image source information is arranged in three-dimensional space to expand the display dimension of the image information, realizing the symmetric display of the diffraction order spatial sorting of the output beam of the 4F system for the same image source information under the polarization dual-channel condition, so that the output three-dimensional pattern produces a mirror three-dimensional display effect in the orthogonal polarization channels, thereby enhancing the modulation flexibility and controllable dimension of the 4F system display optical path.

2. The optimization method of the multi-layer three-dimensional display system based on the polarization dual-channel metasurface according to claim 1, wherein: It further includes Step 4. Utilizing the advantages of flexible metasurface modulation means, multi-dimensional optical parameter combination, and thin, light, and compact structure, based on the polarization dual-channel metasurface, a multi-layer three-dimensional display system is arranged for the optical path according to Step 2. Based on the multi-layer three-dimensional display system, it can support optical imaging scenarios such as wearable display and virtual reality, as well as optical integrated display devices to improve control flexibility and integration compactness; The multi-dimensional optical parameters include the three-dimensional spatial information, frequency characteristics, polarization characteristics, and phase characteristics of the light field.

3. The optimization method of the multi-layer three-dimensional display system based on the polarization dual-channel metasurface according to claim 1 or 2, characterized in that: In Step 1, The 4F system includes two symmetrically arranged lenses. The two lenses have four front and rear focal points, and the two central focal points coincide; the 4F system is used to reproduce the image information located at the first focal point position at the last focal point position. The focal point position between the two lenses is the spectrum plane of the optical system, which can cooperate with the twisted grating regulation to achieve the purpose of controlling the spatial distribution of the diffraction orders of the output beam of the 4F system; A one-dimensional twisted grating based on the 4F imaging system structure controls the spatial distribution position of the diffraction orders of the outgoing light beam through multi-focal plane custom distance staggered display, constituting the X-direction misalignment and the controllable fixed interval in the Z-direction of the multi-layer image information; among them, the incident image source information is located at the first focal position in the 4F system, and the metasurface with the one-dimensional twisted grating control function is located at the second focal position in the 4F system, that is, the central spectral plane position of the optical path; at the third focal position of the 4F system, the image information distributed along the Z-axis shows a regular spatial arrangement. The image information distributed along the Z-axis is the outgoing light field of the 4F system with a multi-layer structure, and the third focal position is the last focal position; the three-dimensional display metasurface controls the spectral plane of the 4F system to make the diffraction orders of the outgoing light field of the 4F system produce a spatially staggered display effect; the content displayed at different focal positions near the optical axis of the diffraction orders of the outgoing light field are different same patterns, and the rest of the pattern information is blocked outside the observation range; The one-dimensional twisted grating regulates the spectral plane information of the light field according to the following transmittance regulation function formula (1) to make the diffraction orders of the outgoing light field of the 4F system produce a spatially staggered display effect; where T 1D represents the total transmittance of the one-dimensional twisted grating; since the twisted grating is during pure phase optical modulation, the phase distribution represents the modulation function of the transmittance regulation function, which is obtained by optimizing the Dammann grating method; the coefficient C m represents the energy distribution of each diffraction order; m represents the diffraction order position in the x direction, x represents the spatial position coordinate of the Cartesian coordinate system, r represents the spatial position coordinate of the cylindrical coordinate system, represents the wave number, λ represents the wavelength, f g represents the defocus coefficient; the target diffraction order excitation is selected by the phase optimization method to make the diffraction orders of the output light field of the 4F system produce a spatially staggered display effect; each diffraction order of the grating is represented by Fourier expansion; in order to achieve the effect of staggered overlap of different orders, in addition to the characteristic phase of the ordinary grating in addition, the twisted grating also has the regulation limit for each focal position, that is the grating phase controls the spatial angular spread of each diffraction order, that is where Λ x represents the grating period, that is Λ x = N×d, d represents the interval of a single antenna pixel of the metasurface; the twisted grating controls the incident pattern in the frequency domain of the image; combined with the common modulation of the front and rear lens 4F system; the multi-layer focal interval is calculated by the Gaussian formula: Similarly, the multi-layer pattern misalignment interval is expressed as: dx = NAf0; the DMD image source is accurately arranged using the pattern misalignment interval to ensure an ideal interval-aligned spatial pattern at the target observation position.

4. The method for optimizing a multi-layer three-dimensional display system based on a polarization dual-channel metasurface according to claim 3, wherein: In step two, The one-dimensional grating obtained by formula (1) has realized the Z-direction display of the one-dimensional distributed image. By simultaneously regulating the spatial distribution position of the diffraction orders of the outgoing light beam in the X-direction and the Y-direction, a two-dimensional twisted grating can be constructed so that the incident light source information can be emitted in a three-dimensional space distribution. The transmittance regulation function of the two-dimensional twisted grating is as shown in formula (2) where T 2D represents the total transmittance of the two-dimensional twisted grating, and the phase distribution represents the modulation function of the transmittance regulation function, which is optimized by the Dammann grating method; the coefficient C mn represents the energy distribution of each diffraction order; m represents the diffraction order position in the x direction, n represents the diffraction order position in the y direction, (x, y) represents the spatial position coordinates of the Cartesian coordinate system, and r represents the spatial position coordinates of the cylindrical coordinate system. represents the wave number, λ represents the wavelength, and f gx , f gy represents the defocus coefficients in the x and y directions; the target diffraction order excitation is selected by the method of phase optimization to make the diffraction orders of the output light field of the 4F system produce a spatially staggered display effect; each diffraction order of the grating is represented by Fourier expansion; in order to achieve the effect of staggered overlap of different orders, in addition to the characteristic phase of the ordinary grating in addition, the twisted grating also has the control limit for each focal position, that is the grating phase controls the spatial angular spread of each diffraction order, that is where Λ represents the grating period, that is Λ = N×d, and d represents the interval of a single antenna pixel of the metasurface; the twisted grating controls the incident pattern in the frequency domain of the image; combined with the common modulation of the front and rear lens 4F system; the multi-layer focal interval is calculated by the Gaussian formula: Similarly, the multi-layer pattern misalignment interval is expressed as: dx = NAf0, dy = NAf0; the DMD image source is accurately arranged using the pattern misalignment interval to ensure an ideal interval-aligned 3D spatial pattern at the target observation position.

5. The optimization method of the multi-layer three-dimensional display system based on the polarization dual-channel metasurface according to claim 4, wherein: In step three, Combined with the polarization channel multiplexing function of the metasurface, the transmittance regulation functions of the polarization dual-channel metasurface are as shown in formulas (3) and (4); Where: T xx , T xx represent the transmittances under two polarization channels, and the phase distribution represents the modulation function of the transmittance regulation function under two polarization channels, which is obtained by optimizing the Dammann grating method; m represents the diffraction order position in the x direction, n represents the diffraction order position in the y direction, (x, y) represents the spatial position coordinates of the Cartesian coordinate system, r represents the spatial position coordinates of the cylindrical coordinate system, represents the wave number, λ represents the wavelength, f gx , f gy represents the defocus coefficients in the x direction and y direction; the regulation parameters under the two polarization channels are exactly the same, and only the signs of the defocus coefficients are different, then the effect of orthogonal polarization mirror symmetry of the diffracted light field outgoing beam can be controlled.

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