An acoustic metamaterial-based phase holographic imaging device and design method

Abstract

This invention relates to the field of acoustic imaging technology, specifically to a phase holographic imaging device based on acoustic metamaterials, comprising a sound wave generator, a LAM metasurface, and a control unit. The sound wave generator generates planar sound waves; the LAM metasurface receives the sound waves and modulates their phase and amplitude; the control unit controls the structure and geometry of the internal cells of the LAM metasurface, ensuring that under frontal sound illumination, the sound waves reach a decoupling point within the internal structural space of the LAM metasurface; achieving decoupling modulation of the phase and amplitude of the reflected sound waves from the surface by the cells; and includes a processor that calculates the sound pressure at the phase position projected onto the holographic surface based on the input image, and adjusts the dimensional parameters of the internal cells of the LAM metasurface via the controller. In this invention, after the incident sound wave interacts with the LAM metasurface, it undergoes demodulation and remodulation, and is reflected at an angle perpendicular to the LAM subsurface. The LAM metasurface does not impose any angular constraints on the incident sound wave; the angle of the reflected wave is always perpendicular to the LAM surface. This results in a phase acoustic hologram imaging quality that meets the required amplitude compensation.

Description

Technical Field

[0001] This invention relates to the field of acoustic imaging technology, and in particular to a phase holographic imaging device and design method based on acoustic metamaterials. Background Technology

[0002] Acoustic holography is an advanced method of sound wave manipulation that achieves precise control and imaging of sound fields by recording and reconstructing complete wavefield information. Recent research has demonstrated its enormous application potential, holding significant importance for various applications such as particle manipulation, improved medical imaging, and ultrasound therapy. In the past few years, considerable efforts have been made in the study of acoustic holographic control. Holograms are typically constructed using active transducer arrays or passive metamaterials to achieve pixel-by-pixel modulation of the phase and amplitude of sound waves. However, achieving complete control over sound remains challenging, requiring completely independent modulation of the amplitude and phase in two degrees of freedom within the acoustic hologram, which together determine any signal. Figure 1 The diagram illustrates the acoustic holographic imaging mechanism; where a) amplitude holography with phase modulation (AH by PM); b) amplitude holography with amplitude and phase decoupling modulation (AH by APM); and c) phase holography with amplitude and phase decoupling modulation (PH by APM). However, when the incident wave interacts with a complex metasurface, a complex coupling effect must occur between amplitude and phase. Previous pure phase holography (PM) methods neglected the errors caused by the unavoidable amplitude information changes during phase modulation. Figure 1 As shown in (a), while phase modulation can adjust the sound field, it cannot address the impact of amplitude on the image. In high-resolution imaging, strict reliance on phase control can lead to distortion. To overcome this limitation, amplitude-phase holography (APM) is proposed, which simultaneously controls amplitude and phase, thereby effectively improving the ability to manipulate the holographic sound field. Figure 1 (as shown in b), especially for creating complex 3D patterns. Although the APM method increases the degree of freedom in sound field control, its systems tend to introduce computational complexity and energy loss due to inherent amplitude manipulation, thus affecting the overall efficiency of sound propagation.

[0003] LAM metasurfaces, or LossyAcoustic Metamaterials, are metasurfaces made of lossy acoustic metamaterials. LAM metasurfaces are artificial composite material surfaces with special acoustic properties; by designing their microstructure, effective manipulation of sound waves can be achieved. This type of material surface has broad application prospects in the field of acoustics, such as sound wave cloaking, sound wave focusing, and sound wave absorption. In acoustic holographic imaging, the design of phase holographic LAM metasurfaces with coupled amplitude compensation is key to achieving sound wave manipulation. The accuracy of the hologram is crucial to the accuracy of sound field reconstruction, and the manufacturing accuracy of the hologram is affected by various factors, including errors in the manufacturing process. In the process of manufacturing LAM metasurfaces using 3D printing technology, 3D printing errors may lead to distortion and unexpected regions in the hologram projected from the LAM metasurface onto the image plane. Based on this, a design method for LAM metasurfaces based on acoustic metamaterials is proposed. Summary of the Invention

[0004] The purpose of this invention is to address the problems existing in the background technology by proposing a phase holographic imaging device and design method based on acoustic metamaterials, so as to improve the performance of acoustic holograms in sound field reconstruction, especially in complex sound fields and multipath environments.

[0005] The technical solution of the present invention:

[0006] A first aspect of the present invention provides a phase holographic imaging device based on acoustic metamaterials, comprising a sound wave generator, an LAM metasurface, and at least one control unit;

[0007] Among them, the sound wave generator is used to generate plane sound waves;

[0008] The LAM metasurface is used to receive sound waves and modulate their phase and amplitude; the LAM metasurface consists of multiple independent cells, which are distributed in a rectangular array.

[0009] The control unit controls the structure and geometry of the internal cells of the LAM metasurface, enabling sound waves to reach a decoupling point within the internal structure of the LAM metasurface under frontal sound illumination, and achieving decoupling modulation of the phase and amplitude of the sound waves reflected from the surface by the cells. The control unit also includes a processor that calculates the sound pressure at the phase position projected onto the holographic surface based on the input image, and adjusts the dimensional parameters of the internal cells of the LAM metasurface through the controller.

[0010] Preferably, each cell has the same external dimensions but different internal dimensions; the cells are set to a fixed structure or an adjustable structure.

[0011] When the cell has a fixed structure, the specific parameters of each cell are calculated by the processor, and the corresponding LAM metasurface with the specified size parameters is produced by additive manufacturing.

[0012] When a cell is set to an adjustable structure, the position of the internal structure of the cell is adjusted by the control unit in conjunction with the action structure so that it meets the specific parameters of each cell obtained by the processor.

[0013] Preferably, the cell of the LAM metasurface consists of three channels, namely C1, C2, and C3, with heights of h1, h2, and h3 respectively.

[0014] The widths of channels C1 and C3 are d = βD;

[0015] The air channel fill ratio is defined as β = 0.8, D = λ / 4 is the cell width, and λ is the wavelength of the sound wave; the speed of sound in air is C0 = 340 m / s. -1 The sound wave frequency was chosen to be 1.7kHz, resulting in D = 5mm.

[0016] Preferably, the width of the middle cell is w; the channel wall is acoustically rigid, and the total height of the cell is h = h1 + h2 + h3, with h2 = 5mm fixed.

[0017] The length h1 of the incident acoustic channel and the width w of the intermediate channel modulate the phase and amplitude of the acoustic wave. The relationship between h1 and w and the phase and amplitude can be represented by the following formula.

[0018]

[0019]

[0020] Preferably, the cell width D has subwavelength properties, and the amplitude A and phase φ of the reflected sound wave are independent of the incident direction.

[0021] Preferably, the incident sound wave on the LAM metasurface is at an arbitrary angle; the angle of the reflected wave is always perpendicular to the LAM surface.

[0022] Preferably, the LAM metasurface is manufactured using 3D printing equipment; the precision of the 3D printing equipment is 0.2mm.

[0023] Preferably, the fabricated LAM metasurface is scanned in three dimensions using a confocal microscope with a scanning accuracy of λ / 4; this is to assess errors in the manufacturing process and the quality of holographic reconstruction, and to optimize the design to reduce errors in the 3D printing process.

[0024] Preferably, the control unit further includes a processor, and controls the imaging device to achieve acoustic phase holographic imaging according to the following steps:

[0025] S1. Discretize the hologram to be imaged into a subwavelength scale image pixel sequence and place it at the phase position;

[0026] S2. The amplitude and phase distribution of the LAM metasurface required for holographic reconstruction are calculated using the time reversal method;

[0027] S3. The optimal coupling compensation amplitude is solved using the horned lizard optimization algorithm to optimize the calculation of the compensation amplitude and improve the accuracy of sound field reconstruction.

[0028] S4. The incident sound wave is reflected by the LAM metasurface, and the phase and compensation amplitude information of the coupled image are encoded to reconstruct an acoustic hologram that matches the pre-designed image, thereby realizing phase imaging.

[0029] A second aspect of the present invention provides a design method for a phase holographic imaging device based on acoustic metamaterials, comprising:

[0030] The acoustic holographic image to be encoded is discretized into a subwavelength scale pixel sequence;

[0031] The cell structure of the LAM metasurface is designed based on the phase and compensation amplitude information of the acoustic holographic image to be encoded;

[0032] The LAM metasurface cell includes three channels: upper, middle, and lower, each with different heights and widths to ensure its subwavelength characteristics.

[0033] The amplitude and phase information corresponding to the holographic image are encoded on the LAM metasurface to achieve decoupled modulation of the acoustic wave.

[0034] Compared with the prior art, the present invention has the following beneficial technical effects:

[0035] This invention utilizes a confocal microscope to perform three-dimensional scanning of printed holographic surfaces with a scanning precision of λ / 4, or one-quarter of the wavelength. This high-precision scanning allows for detailed analysis of the printed holograms and comparison with theoretical holograms to assess manufacturing process errors and the quality of holographic reconstruction. This method enables quantitative evaluation of holographic accuracy and optimization of designs to reduce errors during 3D printing. This is significant for improving the performance of acoustic holograms in sound field reconstruction, particularly in complex sound fields and multipath environments. Furthermore, this high-precision manufacturing and evaluation method opens up new possibilities for the application of acoustic holograms in other fields, such as high-capacity acoustic volumetric displays and dynamic particle manipulation. Attached Figure Description

[0036] Figure 1 Diagram of acoustic holographic imaging mechanism;

[0037] Figure 2The diagram illustrates the iterative optimization process of the HLOA algorithm for finding the optimal amplitude compensation.

[0038] Figure 3 This diagram illustrates the relationship between strongly coupled and weakly coupled layers.

[0039] Figure 4 Design diagram of a phase holographic LAM metasurface with coupling compensation amplitude;

[0040] Figure 5 Experimental diagram of phase acoustic holographic scanning field with amplitude compensation;

[0041] Figure 6 This is a holographic correlation verification diagram;

[0042] Figure 7 This is to verify the anti-interference capability of amplitude-compensated phase acoustic holograms. Detailed Implementation

[0043] This paper proposes an Acoustic Phase Hologram (APH) method to adapt to holographic imaging in complex environments, through analytical derivation, numerical simulation, algorithm optimization, and experimental demonstration. The coupling mechanism of phase and amplitude between global pixels in the hologram is investigated in depth. The Hippodrome Optimization Algorithm (HLOA) is introduced to iteratively optimize the optimal coupling compensation amplitude in complex environments, and a time-reversal method is used to calculate the metasurface amplitude and phase distribution required for holographic reconstruction. The design concept utilizes a LossyAcoustic Metamaterial (LAM) structure to encode the phase and compensation amplitude information of the coupled transmitted image. This design concept is based on a different intrinsic mechanism from previous designs, relying on the compensation amplitude of the corresponding phase hologram in complex environments using phase holography. This method simultaneously possesses the advantage of traditional pure phase modulation (PM) methods where phase modulation does not directly cause energy loss, and integrates the characteristic of amplitude-phase modulation (APM) methods, which simultaneously modulate phase and amplitude to increase the degrees of freedom for sound field control. This method addresses the issues of insufficient imaging precision in complex acoustic fields and multipath environments caused by the lack of amplitude control in PM (partial acoustic holograms), and the unnecessary energy loss resulting from direct amplitude control in the APM (amplified acoustic hologram) method, which affects system efficiency. Compared to traditional acoustic metasurface PM and APM, the APH method can obtain high-fidelity and high-quality acoustic holograms in complex acoustic fields despite energy loss, which is of great significance for the practical application of acoustic holography.

[0044] The proposed mechanism enables precise control of the three-dimensional sound field in phase holographic imaging after amplitude compensation, while offering advantages such as simple design, low manufacturing cost, planar profile, high efficiency, and high subwavelength resolution. The effectiveness of this mechanism is demonstrated by obtaining high-fidelity acoustic holograms through amplitude compensation of complex pattern phase holographic imaging under complex environments. Similar to optical holograms, acoustic holography offers new capabilities for particle manipulation and application improvements. However, due to the lack of simultaneous amplitude and phase modulation capabilities, current acoustic hologram production relies on phase modulation methods and complex decoupled amplitude-phase modulation. This paper demonstrates numerically and experimentally that high-fidelity acoustic holograms can be stably generated using phase modulation with coupled amplitude compensation.

[0045] The following specific case study will be used to provide a detailed introduction to this solution:

[0046] Example 1

[0047] This invention proposes an acoustic phase holographic imaging method, such as... Figure 2 As shown, a1 is the phase hologram; a2-a8 are the phase holograms after coupling compensation amplitude; b1 is the initial random amplitude; b2-b8 is the iterative solution process of the coupling compensation amplitude; c1-c8 are local pixels in the compensation amplitude; d1 is the local pixel at the position of letter P in the a1 phase hologram; d2-d8 are the local pixels at the position of letter P in the phase hologram after coupling amplitude compensation; e is the iterative convergence curve; f is the metasurface model encoding amplitude and phase information at different positions; g is a schematic diagram of the LAM metasurface. Figure 2 g demonstrates the LAM metasurface that encodes phase holography; Figure 2 f illustrates the LAM metasurface model after amplitude compensation via coded phase holographic coupling. Considering the general principles of acoustic holographic reconstruction, the hologram is discretized into a subwavelength scale image pixel sequence. The coded amplitude A on the LAM metasurface is... j and phase φ j sound pressure P j The sound pressure level can be calculated by superimposing the wave components of all pixels on the image plane. The calculation is represented by the following formula: where the amplitude A of the coupled hologram... j and phase φ j The information was pre-designed into the unit cell structure of the corresponding LAM metasurface. Under illumination by a plane wave at a fixed frequency of f = 17000 Hz, the unit cells of the LAM metasurface modulate the amplitude A of the incident sound wave. j and phase φ j The sound waves are modulated and reconstructed to match a pre-designed holographic image.

[0048]

[0049] Where N is the total number of pixels in the image, A0l and φ 0l They are (x) l ,y l ,z l The magnitude and initial phase at the l-th pixel, A j and φ j These are the amplitude and phase of the j-th pixel on the holographic plane, respectively. The image pixel and the holographic pixel are located at (x... j ,y j ,z j The distance at point () can be characterized as Due to time-reversal symmetry, a pre-designed acoustic hologram can be directly projected, and the hologram can be characterized as...

[0050]

[0051] Where n is the total number of pixels in the holographic image. Let (x, y, z) be a spatial point and (x, y, z) be a holographic pixel on the holographic plane. j ,y j ,z j The distance between them. However, previous schemes for generating pure phase holograms assumed that the amplitudes were all A. j =1, therefore pure phase holography can be characterized as

[0052]

[0053] HLOA algorithm for solving phase holographic compensation amplitude mechanism

[0054] In the study of solving the coupling compensation amplitude problem, this paper introduces a novel swarm-based intelligent optimization algorithm—the Horned Lizard Optimization Algorithm (HLOA). The HLOA algorithm is inspired by the horned lizard's defense strategies when attacked, including concealment, skin color changes, blood spraying, and escape strategies, which help the horned lizard evade predators. Compared to traditional intelligent optimization algorithms, such as genetic algorithms and particle swarm optimization, the HLOA algorithm demonstrates significant advantages in handling high-dimensional optimization problems. By simulating five defense strategies of the horned lizard, the algorithm achieves a good balance between global and local search strategies, making it particularly suitable for solving optimization problems in high-dimensional solution spaces. Taking the acoustic hologram of the initial letter "P" of "Phase" as an example, the pre-designed image of the letter "P" consists of 87×87 pixels, meaning that the globally optimal coupling compensation amplitude matrix needs to be solved based on the 87×87-dimensional phase hologram. In solving for the compensation amplitude, a search strategy that balances the global 7569 pixels of the hologram and only the local location of the letter P in the image must be considered simultaneously to ensure that the loss values ​​at both the global and local locations of the compensation amplitude obtained in each iteration decrease. Finally, a phase hologram with the optimal compensation amplitude is obtained, as shown below. Figure 2 As shown in a8.

[0055] In the reconstruction of acoustic holograms, the horned lizard defense strategy is incorporated into the phase holographic calculation to determine the optimal compensation amplitude of the hologram, thereby improving the accuracy and efficiency of sound field reconstruction. After introducing the compensation amplitude, a complex coupling relationship emerges between the amplitude and phase in the hologram. This coupling relationship is not a simple linear superposition of individual pixels. It involves both direct and indirect interactions, which are reflected in every pixel of the hologram.

[0056] by Figure 2 Taking the central pixel in d1 as an example, when performing amplitude compensation on this pixel, a direct strong coupling effect was observed between the pixel and its phase and the compensation amplitude. Furthermore, the eight pixels surrounding the central pixel also exhibit an indirect weak coupling effect. Further, the outermost 8n pixels also show a slightly smaller indirect weak coupling effect with the central pixel. This complex coupling effect necessitates that the interaction between each pixel and its surrounding pixels be considered when designing the hologram to ensure that the hologram can accurately reconstruct the expected sound field.

[0057] This paper delves into the mechanism of acoustic holography, investigating the strong coupling between imaging pixels and the weak coupling effect of peripheral pixels to the central pixel when a single pixel serves as the radiation source. In an acoustic hologram, each pixel not only acts as a source of sound waves but also interacts with other pixels. This interaction manifests as both direct strong coupling and indirect weak coupling, which collectively determine the reconstruction quality and efficiency of the acoustic hologram.

[0058] Study on the coupling mechanism between amplitude and phase

[0059] In the reconstruction of an acoustic hologram, the spatial variations of amplitude A(x) and phase φ(x) can be coupled through the wave equation of sound waves. Sound pressure can be described by the wave equation or its complex propagation form, expressed as the complex form P(x) = A(x)e iφ(x) The coupling relationship between amplitude A(x) and phase φ(x) can be studied using the derivative of complex sound pressure to reveal the interaction between amplitude and phase. In sound wave propagation, the rate of change of amplitude and the rate of change of phase are correlated through the propagation equation, allowing the amplitude change to be analyzed. and phase change The coupling relationship between them is characterized as follows:

[0060]

[0061] This coupling relationship demonstrates how amplitude and phase influence each other during sound wave propagation. When the phase changes rapidly, the amplitude may decrease, and vice versa. This complex coupling effect necessitates considering the interaction between each pixel and its surrounding pixels when designing holograms to ensure accurate reconstruction of the desired sound field. By tightly linking the coupling characteristics of amplitude and phase in space through interference and wave equations, the relationship between amplitude and phase can be simplified to:

[0062]

[0063] Direct strong coupling effect of target pixels

[0064] In acoustic holograms, the direct coupling effect between individual pixels is a direct result of the principle of acoustic wave interference and the inhomogeneity of medium propagation. Each pixel can be considered as a source of sound waves, where amplitude and phase jointly determine its contribution to the overall sound field. Based on the phase and amplitude coupling mechanism, the concealment and blood spray strategies in the Lizard Optimization Algorithm (HLOA) are employed to solve for the compensation amplitude of each pixel in the hologram, thereby compensating for amplitude distortion caused by phase encoding and achieving more accurate sound field reconstruction.

[0065] In mathematical notation, a single pixel in a phase hologram can be defined as p(i,j), with its amplitude and phase represented by A(i,j) and φ(i,j), respectively. Therefore, the complex representation of a phase hologram can be written as P(i,j) = A(i,j)e^(-p / p). j φ(i,j) The sound pressure level of a single pixel in the acoustic hologram after amplitude compensation is defined as C(i,j), where C(i,j) is an adjustment factor related to the phase hologram P(i,j), which can be characterized as...

[0066] C(i,j) strong =f(P(i,j))=k1A(i,j)+k2φ(i,j)

[0067] The function f represents the nonlinear mapping between amplitude and phase under ideal conditions. This function depends on the amplitude and phase information in the phase hologram. It adjusts the compensation amplitude according to the specific values ​​of amplitude and phase to achieve accurate reconstruction of the sound field. In this mapping relationship, k1 and k2 are used as adjustment factors for amplitude and phase, respectively, representing the degree of influence of amplitude and phase on the compensation amplitude. By adjusting C(i,j), the problem of insufficient imaging precision caused by the lack of amplitude control can be effectively compensated.

[0068] Global indirect weak coupling effect

[0069] In acoustic holograms, the coupling effect between adjacent pixels and the target pixel is significant. For example... Figure 2 As shown in c1-c8, when the phase holography of the target pixel and the compensation amplitude are coupled, the coupling effect of the surrounding pixels also has a certain impact on the target pixel. Therefore, it is particularly important to study the indirect coupling relationship between the target pixel and its surrounding n layers of pixels. This indirect coupling relationship is affected not only by the distance and phase difference between pixels, but also by the mutual coupling effect of global pixels on the central pixel. By considering the indirect weak coupling effect between global pixels, the imaging precision can be significantly improved, and the system performance in complex acoustic fields and multipath environments can be enhanced. Mathematically, the global weak coupling effect can be characterized as...

[0070]

[0071] Where D d This represents the set of all pixels globally that are at a distance d from the target pixel; Defined as distance attenuation factor; w d φ(x,y)-φ(i,j) is a weighting coefficient related to distance d, reflecting the degree of influence of the coupling effect between pixels in different layers on the coupling effect of the target pixel; φ(x,y)-φ(i,j) represents the phase difference between the target pixel and the surrounding pixels. The threshold value of the influence of the weak coupling layer on the intermediate pixels is defined as e=10. -5 That is, when the weak coupling effect of a weakly coupled layer pixel on the target pixel is less than e, the search for outer layer pixels stops. Utilizing the blood spray strategy in the Hologram Algorithm (HLOA), the direct strong coupling effect of local target pixels in the hologram and the weak coupling effect between global pixels and the target pixel are balanced. Thus, the coupling effect between global pixels, considering both strong and weak coupling effects, can be characterized as...

[0072]

[0073] In the aforementioned study, a mathematical model was employed to describe the weak coupling effect between pixels in acoustic holograms, consistent with the academic research field of acoustic holograms. This model considers the distance and phase difference between pixels, as well as their influence on the central pixel—all crucial factors in acoustic holograms. By setting a threshold 'e', ​​the search range can be effectively limited, thereby optimizing the compensation amplitude of the hologram, improving imaging precision, and enhancing system performance in complex sound fields and multipath environments. Furthermore, the application of the HLOA algorithm, particularly its blood ejection strategy, provides an effective method for balancing local and global coupling effects, which is of great significance for achieving accurate reconstruction of acoustic holograms.

[0074] Phase LAM metasurface design for coupled amplitude compensation

[0075] In acoustic holographic imaging, the design of a phase LAM metasurface with coupled amplitude compensation is key to achieving acoustic wave manipulation. Figure 4 The design process of the phase hologram after coded coupling compensation amplitude on the LAM metasurface is shown, where a is the phase hologram; b is the compensation amplitude; c is the phase LAM metasurface with coded coupling compensation amplitude; d is the cell structure of the LAM metasurface; e and f are the responses of cell parameters h1 and w to reflection amplitude and phase under decoupling conditions. Figure 4 d specifically showcases the geometry of the cell. Under frontal sound illumination, the sound wave reaches a decoupling point within the internal structural space of the LAM metasurface, achieving decoupling modulation of the phase and amplitude of the sound wave reflected from the surface by the cell. This decoupling of the amplitude and phase of the sound wave on the LAM metasurface allows modulation of all amplitude and phase combinations on the holographic surface within the full range of [0, 1] and [0, 2π]. Figure 4 As shown in e and 4f.

[0076] The cell in the LAM metasurface consists of three channels: upper (C1), middle (C2), and lower (C3), with heights h1, h2, and h3, respectively. The widths of channels C1 and C3 are d = βD (where the air fill ratio is defined as β = 0.8, D = λ / 4 is the cell width, and λ is the wavelength of the sound wave). In this study, the speed of sound in air is C0 = 340 m / s². -1 The sound wave frequency is chosen to be 1.7kHz, resulting in D = 5mm. The width of the middle cell is w, the channel walls are assumed to be acoustically rigid, and the total height of the cell is h = h1 + h2 + h3, with h2 fixed at 5mm. The cell's sound wave incident channel length h1 and the middle channel width w modulate the sound wave phase and amplitude. Figure 4 e and f show the reflection amplitude and phase response of the cell to parameters h1 and w under decoupling conditions. The relationship between h1 and w and phase and amplitude can be characterized by the following formula.

[0077]

[0078] Taking the acoustic hologram of the letter P as an example, the phase hologram of the letter P can be coupled with the compensation amplitude and encoded into the LAM metasurface. For example... Figure 4 As shown in Figure c, the holographic metasurface encoding the letter P information consists of an 87×87 cell array. Each cell has the same external dimensions, while its internal structural dimensions are determined by the phase and amplitude information of pixels at different locations in the coupled hologram. Because the cell width D has subwavelength properties, the amplitude A and phase φ of the reflected sound wave are independent of the incident direction. By placing the plane wave at a 45° angle, a phase hologram with coupled amplitude compensation can be presented on the image plane. Figure 3 As shown, where a is Figure 2 The local coupling effect of c1, c2, and d1 is shown in the diagram; b represents the coupling effect between the target pixel and surrounding layer pixels in c2; it is worth noting that... Figure 3 The phase hologram in 'a' is obtained by taking the cosine of the phase in the range [0, 2π]. This effectively improves the impact on image quality caused by the same beginning and end values ​​of the period at the connection point of two adjacent periods, making the phase hologram range [-1, 1]. This design method ensures that the amplitude and phase of each pixel in the hologram are accurately encoded, thereby achieving high-quality sound field reconstruction.

[0079] In this embodiment, each cell has the same external dimensions but different internal dimensions; the cells are set as either a fixed structure or an adjustable structure.

[0080] When the cell structure is fixed, the processor calculates the specific parameters of each cell, and then uses additive manufacturing to create an LAM metasurface with the corresponding dimensions. Specifically, based on the input image, the sound pressure (P(x)=A(x)e) at the phase position projected onto the holographic surface is calculated. iφ(x) This determines the amplitude and phase information at the corresponding location. Based on the phase and amplitude, each cell (e.g., ...) can be determined according to the above formula. Figure 4 The dimensions d and h1 in the figure are shown. Each cell modulates the sound wave using d, h1, w and λ in these two formulas (λ is the wavelength of the sound wave).

[0081] When a cell is set to an adjustable structure, the control unit, in conjunction with the motion mechanism, adjusts the position of the internal structure of the cell to meet the specific parameters calculated by the processor. Specifically, the upper channel C1 in the cell can be set as an active structure. A pneumatic or hydraulic drive mechanism can move the upper channel C1 within the cell, adjusting its position relative to the middle channel C2 and the lower channel C3, thereby changing the parameters to meet the requirements and thus controlling the sound waves.

[0082] Characterization of Amplitude-Compensated Phase Acoustic Hologram Fabrication Process

[0083] The accuracy of holograms is crucial to the accuracy of sound field reconstruction. The manufacturing accuracy of holograms is affected by various factors, including errors during the manufacturing process. In the process of fabricating LAM metasurfaces using 3D printing technology, 3D printing errors can lead to distortions and unexpected regions in the hologram projected from the LAM metasurface onto the image plane. For example... Figure 5As shown, a. Scanning experimental platform; b. Phase holograms of the letter P, ginkgo leaf, and rose; c. Amplitude-compensated phase holograms of the letter P, ginkgo leaf, and rose; d. Experimental holograms of the letter P, ginkgo leaf, and rose. To improve the accuracy of the holograms, this study used a 3D printing device with a printing accuracy of 0.2 mm to fabricate the required LAM metasurface (such as...). Figure 5 (as shown in a). The experimental phase of this study was conducted in a sealed anechoic chamber to investigate the holographic fabrication process. Specifically, plane waves emitted from a loudspeaker were obliquely incident on the LAM metasurface, facilitating holographic generation. After interacting with the LAM metasurface, the incident sound waves underwent demodulation, were then remodulated, and reflected at an angle perpendicular to the LAM subsurface. A microphone mounted on a scanning platform was used to scan the modulated sound waves, thereby capturing the necessary holograms. Notably, the LAM metasurface did not impose any angular constraint on the incident sound waves; the angle of the reflected waves was always perpendicular to the LAM surface. To further demonstrate the imaging quality of the phase acoustic holograms after amplitude compensation, more complex target images, such as ginkgo leaves and roses, were selected for holographic fabrication. The printed holographic surfaces were scanned in three dimensions using a confocal microscope with a scanning accuracy of λ / 4, or one-quarter of the wavelength. This high-precision scanning allowed for detailed analysis of the printed holograms and comparison with theoretical holograms to assess errors in the fabrication process and the quality of holographic reconstruction. This method allows for the quantitative evaluation of hologram accuracy and optimization of designs to reduce errors during 3D printing. This is significant for improving the performance of acoustic holograms in sound field reconstruction, particularly in complex sound fields and multipath environments. Furthermore, this high-precision manufacturing and evaluation method opens up new possibilities for the application of acoustic holograms in other fields, such as high-capacity acoustic volumetric displays and dynamic particle manipulation.

[0084] Holographic Correlation Verification

[0085] In this section, the first letter "H" from the word "holography" was selected as the target image to verify the optimization effect of the amplitude compensation method on various phase holograms. For example... Figure 6 As shown, a) is the phase hologram of the letter H.; b) is the optimized hologram after coupling amplitude compensation; c) is the experimental hologram; d) is the three-dimensional deviation between the optimized hologram and the pre-designed image; e) is the correlation between the letter H holograms obtained by APH, PH and AH methods at different imaging distances and the pre-designed image; f) is the amplitude compensation of phase hologram a; g) is the convergence curve during the iterative optimization process of the HLOA algorithm; and experimental verification was performed using an image plane containing a 91×91 pixel array. Figure 6 'a' shows a phase hologram of the letter 'H' for comparison; Figure 6 b shows a phase hologram with coupling amplitude compensation obtained through numerical simulation; Figure 6 c shows the experimental hologram. Figure 6 d shows the 3D deviation between the amplitude-compensated phase hologram and the pre-designed image. Figure 6 The figure shows the correlation curves between holograms obtained by the APH, PM, and APM methods and pre-designed images under different distance conditions. These curves demonstrate the correlation between the fabricated holograms and the pre-designed images, providing an evaluation of the performance of different holographic imaging techniques under the same acoustic parameters. Therefore, when designing holograms, the optimal positional relationship between the image plane and the LAM metasurface must be considered to obtain the best imaging results. Figure 6 f shows the amplitude-compensated phase hologram with optimal coupling to the phase hologram, obtained through iterative calculation using the HLOA (Horned Lizard Optimization Algorithm). Figure 6 g depicts the convergence curve of the HLOA algorithm in 1000 optimization iterations, and the phase holograms with compensated amplitudes at the corresponding positions after various iteration counts. After adjusting the color bar range from [-1, 1] to [-1, 0], the holograms at the corresponding iteration positions show phase holograms with coupling amplitude compensation, which enhances the visual recognizability of the holograms and significantly improves quantitative image quality assessment. In the experiment, the phase information and compensated amplitude information of the coupled holograms were encoded into the structural dimensions of the LAM metasurface sample unit, and the LAM metasurface sample was fabricated using 3D printing technology. The sample size was 12.6 × 12.6 × 2 cm. 3 It consists of a 25×25 unit array, and the image area is 22cm away from the surface of the LAM metasurface.

[0086] Image quality analysis

[0087] Figure 6 Figures b and c show the sound pressure distribution of the sound field in the image plane of the numerical simulation and experimental holograms, respectively. These results demonstrate good agreement between the numerical simulation and experimental results. To quantitatively evaluate the quality of the phase hologram after amplitude compensation, a precise comparison was performed between the optimized hologram and the pre-designed image. For this purpose, an image correlation parameter was introduced to measure the similarity between the holograms obtained by the APH, PH, and AH methods and the pre-designed image. A correlation value approaching 1 indicates a higher similarity between the generated hologram and the target image. Unit correlation is achieved only when the generated hologram is completely identical to the pre-designed image.

[0088] Considering the distance between the image plane and the LAM metasurface is between 15-25 cm, the influence of different imaging distances on image correlation was analyzed. The correlation between the holographic image and the pre-designed original image can be characterized by the following formula.

[0089]

[0090] Where P represents the target image, H represents the holographic image, and PR and HG represent the average values ​​of each image.

[0091] Figure 6 The study depicted the relationship between image correlation and imaging distance. The results showed that amplitude compensation enhanced the design of phase holograms. Specifically, holograms designed using the amplitude-phase holography (APH) method exhibited higher correlation. Compared to pure phase holography (PH) and pure amplitude holography (AH) methods, the APH method showed a significant advantage in hologram correlation. Within an imaging distance range of 15 to 25 cm, the correlation of holograms designed using the APH method consistently remained above 92%. Notably, the maximum image correlation reached 94.542%, while the lowest correlation was 92.006%, significantly higher than that of holograms designed using the PH and AH methods.

[0092] Furthermore, it was observed that, under the same imaging conditions, the correlation of holograms designed using both the PH and AH methods decreased with increasing imaging distance. Notably, compared to the AH method, the correlation of holograms designed using the PH method decreased more slowly. In contrast, the correlation change of holograms designed using the APH method was more gradual. The experimental results confirm the effectiveness and flexibility of the method in reconstructing complex holograms under complex conditions.

[0093] Verification of the anti-interference capability of amplitude-compensated phase acoustic holograms

[0094] This section will explore in depth the application capabilities of the acoustic phase holography (APH) method in complex environments. For example... Figure 7 As shown, 7a is a phase hologram with different noise intensities; b is a phase hologram with different noise intensities and an amplitude compensation optimization algorithm; c is an amplitude hologram with different noise intensities; d is a pre-designed image with different noise intensities; e is the distribution of correlation curves between the three holograms and the pre-designed image; f is the distribution of deviation curves between the three holograms and the pre-designed image. The letter "H," representing "holography," was selected as the pre-designed image to systematically study the imaging effects of phase holography (PH), acoustic phase holography (APH), and amplitude holography under random noise of different intensities. By introducing random noise of different amplitudes (such as...) into the pre-designed image... Figure 7 As shown in d), the aim is to verify the adaptability of various holographic imaging methods to environmental noise.

[0095] Experiments were conducted to determine the holographic imaging performance of the PH method under different noise backgrounds. Figure 7a). Subsequently, phase holograms with optimal compensation amplitude under various noise backgrounds were presented ( Figure 7 b), and amplitude holograms under different noise conditions (see Figure 7 c). These results provide a visual understanding of the performance of different holographic imaging methods under the influence of noise.

[0096] To quantitatively evaluate the performance of the holographic imaging method, correlation verification was performed. Figure 7 e) This study compares the correlation between holograms obtained by various holographic imaging methods and pre-designed images under different environmental noise intensities. This comprehensive analysis not only highlights the adaptability of the APH method in complex environments but also provides new insights into the performance of various holographic imaging methods in the presence of noise. These findings contribute to advancing the practical application of holographic imaging technology in noise control and image quality enhancement.

[0097] In summary, this study not only confirms the applicability of phase acoustic holography (APH) in complex environments but also provides new insights and methods for noise control and image quality enhancement in the field of acoustic holography. These findings are of great significance for the practical application of acoustic holography in engineering. To quantify the difference between holograms obtained by different methods and pre-designed holograms, this study introduces the concept of normalized mean square error (NMSE). A lower NMSE value indicates a smaller overall difference between holograms obtained by different methods and pre-designed holograms, thus indicating higher holographic image quality obtained by this method. Figure 7 f shows the deviation between the holograms obtained by the APH, PH, and AH methods and the pre-designed image, which further evaluates the performance of different holographic imaging techniques under the same acoustic parameters. NMSE can be expressed as

[0098]

[0099] Where P represents the theoretical hologram, H represents the fabricated hologram, and ∥"∥_2 represents the Euclidean norm. Furthermore, the relative position between the image plane and the LAM metasurface also affects image quality.

[0100] in conclusion:

[0101] It has been demonstrated that by coupling a phase hologram with an optimally compensated amplitude hologram calculated for the corresponding complex imaging environment, the resulting hologram not only resists the inherent energy attenuation of the phase hologram but also integrates the performance of the APM method in controlling phase and amplitude, thereby improving the accuracy of sound field manipulation. This embodiment delves into the direct strong coupling effect and indirect weak coupling interaction of pixels within the image plane in holographic imaging, calculates the dynamic coupling relationship between pixels at different locations, and introduces an intelligent optimization algorithm to calculate the dynamic coupling compensation amplitude for various application scenarios. This method achieves dynamic and precise coupling modulation of sound waves, thereby generating high-quality holographic images. To verify the performance of the phase holography method after optimal amplitude compensation, not only are numerical simulations and experimental implementations of high-fidelity acoustic holograms demonstrated, but the application of the novel phase holographic imaging mechanism based on optimal amplitude compensation in generating arbitrarily complex holograms is also shown. Furthermore, it is demonstrated that holograms generated by combining phase holograms with optimal compensation amplitudes for various imaging environments effectively address the problem of insufficient imaging accuracy in complex acoustic fields and multipath environments caused by the lack of amplitude control in traditional phase modulation (PM) methods, as well as the unnecessary energy loss caused by direct amplitude control in APM methods. This significantly improves the imaging quality of acoustic holograms in complex acoustic fields.

[0102] In this embodiment, by coupling the phase hologram with the optimal compensation amplitude hologram calculated for the corresponding complex imaging environment, the resulting hologram not only has the characteristic of resisting the inherent energy decay of the phase hologram, but also integrates the performance of the APM method in controlling phase and amplitude, thereby improving the accuracy of sound field manipulation.

[0103] Example 2

[0104] This invention provides a design method for a phase holographic imaging device based on acoustic metamaterials, comprising:

[0105] The acoustic holographic image to be encoded is discretized into a subwavelength scale pixel sequence;

[0106] The cell structure of the LAM metasurface is designed based on the phase and compensation amplitude information of the acoustic holographic image to be encoded;

[0107] The LAM metasurface cell includes three channels: upper, middle, and lower, each with different heights and widths to ensure its subwavelength characteristics.

[0108] The amplitude and phase information corresponding to the holographic image are encoded on the LAM metasurface to achieve decoupled modulation of the acoustic wave.

[0109] In this embodiment, the designed LAM metasurface ensures that the amplitude and phase of each pixel in the hologram are precisely encoded, thereby achieving high-quality acoustic field reconstruction. The printed holographic surface is scanned in three dimensions using a confocal microscope with a scanning accuracy of λ / 4, or one-quarter of the wavelength. This high-precision scanning allows for detailed analysis of the printed hologram and comparison with theoretical holograms to assess manufacturing errors and the quality of holographic reconstruction. This method enables quantitative evaluation of holographic accuracy and optimization of the design to reduce errors during 3D printing. This is significant for improving the performance of acoustic holograms in acoustic field reconstruction, especially in complex acoustic fields and multipath environments. Furthermore, this high-precision manufacturing and evaluation method also opens up new possibilities for the application of acoustic holograms in other fields, such as high-capacity acoustic volumetric displays and dynamic particle manipulation.

[0110] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited thereto. Various changes can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of the present invention.

Claims

1. A phase holographic imaging device based on acoustic metamaterials, characterized in that, It includes a sound wave generator, a LAM metasurface, and at least one control unit; Among them, the sound wave generator is used to generate plane sound waves; The LAM metasurface is used to receive sound waves and modulate their phase and amplitude. The LAM metasurface consists of multiple independent cells arranged in a rectangular array. Each cell of the LAM metasurface is composed of three channels: upper, middle, and lower, numbered C1, C2, and C3 respectively, with heights of h1, h2, and h3 respectively. The widths of channels C1 and C3 are ; The air channel fill ratio is defined as follows: , For cell width, The wavelength of the sound wave; The width of the middle cell is w; the channel walls are acoustically rigid, and the total height of the cells is [value missing]. ,fixed The cell's acoustic wave incident channel length h1 and intermediate channel width w modulate the acoustic wave phase and amplitude. The relationship between h1 and w and the phase and amplitude can be represented by the following formula: ； The control unit controls the structure and geometry of the internal cells of the LAM metasurface, enabling sound waves to reach a decoupling point within the internal structure of the LAM metasurface under frontal sound illumination, and achieving decoupling modulation of the phase and amplitude of the sound waves reflected from the surface by the cells. The control unit also includes a processor that calculates the sound pressure at the phase position projected onto the holographic surface based on the input image, and adjusts the dimensional parameters of the internal cells of the LAM metasurface through the controller.

2. The phase holographic imaging device based on acoustic metamaterials according to claim 1, characterized in that, Each cell has the same external dimensions but different internal dimensions; cells can be set to a fixed or adjustable structure. When the cell has a fixed structure, the specific parameters of each cell are calculated by the processor, and the corresponding LAM metasurface with the specified size parameters is produced by additive manufacturing. When a cell is set to an adjustable structure, the position of the internal structure of the cell is adjusted by the control unit in conjunction with the action structure so that it meets the specific parameters of each cell obtained by the processor.

3. The phase holographic imaging device based on acoustic metamaterials according to claim 2, characterized in that, The cell width D has subwavelength properties, and the amplitude A and phase of the reflected sound wave... It is independent of the incident direction.

4. The phase holographic imaging device based on acoustic metamaterials according to claim 2, characterized in that, The incident sound wave on the LAM metasurface can be at any angle; the angle of the reflected wave is always perpendicular to the LAM surface.

5. The phase holographic imaging device based on acoustic metamaterials according to claim 2, characterized in that, The LAM metasurface is manufactured using 3D printing equipment with a precision of 0.2 mm.

6. The phase holographic imaging device based on acoustic metamaterials according to claim 5, characterized in that, The fabricated LAM metasurface was three-dimensionally scanned using a confocal microscope, with a scanning accuracy of [missing information]. To assess errors in the manufacturing process and the quality of holographic reconstruction, and to optimize the design to reduce errors in the 3D printing process.

7. The phase holographic imaging device based on acoustic metamaterials according to claim 1, characterized in that, The control unit controls the imaging device to achieve acoustic phase holographic imaging according to the following steps: S1. Discretize the hologram to be imaged into a subwavelength scale image pixel sequence and place it at the phase position; S2. The amplitude and phase distribution of the LAM metasurface required for holographic reconstruction are calculated using the time reversal method; S3. The optimal coupling compensation amplitude is solved using the horned lizard optimization algorithm to optimize the calculation of the compensation amplitude and improve the accuracy of sound field reconstruction. S4. The incident sound wave is reflected by the LAM metasurface, and the phase and compensation amplitude information of the coupled image are encoded to reconstruct an acoustic hologram that matches the pre-designed image, thereby realizing phase imaging.

8. A design method for a phase holographic imaging device based on acoustic metamaterials, comprising the phase holographic imaging device according to any one of claims 1-7, characterized in that, include: The acoustic holographic image to be encoded is discretized into a subwavelength scale pixel sequence; The cell structure of the LAM metasurface is designed based on the phase and compensation amplitude information of the acoustic holographic image to be encoded; The LAM metasurface cell includes three channels: upper, middle, and lower, each with different heights and widths to ensure its subwavelength characteristics. The amplitude and phase information corresponding to the holographic image are encoded on the LAM metasurface to achieve decoupled modulation of the acoustic wave.

Images