Acoustic phase holographic imaging method

Abstract

The invention relates to the technical field of acoustic imaging, in particular to an acoustic phase holographic imaging method. The method comprises the following specific steps: S1, dispersing a hologram to be imaged into a sub-wavelength scale image pixel sequence; s2, calculating holographic plane amplitude and phase distribution required for reconstructing the hologram by adopting a time reversal method; s3, solving an optimal coupling compensation amplitude by adopting an angle exid optimization algorithm; and S4, reflecting the incident sound wave by using the holographic plane structure, and transmitting the phase and compensation amplitude information of the image after coding and coupling so as to reconstruct an acoustic hologram matched with the pre-designed image. The invention provides an APH (Acoustical Phase Hologram) method, and aims to meet the requirement of holographic imaging in a complex environment. By pre-designing a phase image and utilizing a time reversal technology, amplitude phase decoupling regulation and control are realized on a holographic plane, so that a phase image with energy attenuation resistance and anti-interference capability is obtained on an image plane.

Description

Technical Field

[0001] The invention relates to the technical field of acoustic imaging, and in particular to an acoustic phase holographic imaging method. Background Art

[0002] Conventional acoustic holograms focus on generating 3D images with an acoustic amplitude or intensity field that indicates the energy distribution that can be perceived by an observer. In previous cases, the phase was an inadvertent physical quantity on the image plane. However, in terms of information communication, the phase is another valuable information carrier, and its distribution contains information equivalent to the amplitude channel. Here, the observation of "acoustic phase holograms" through metamaterials is demonstrated. It is demonstrated that the holograms designed in the phase channel are more robust and anti-interference than traditional amplitude holograms, which may lead to applications in acoustic / optical communications.

[0003] Acoustic holography is an advanced method of acoustic wave manipulation. It records and reconstructs the complete information of the wave field to achieve precise control and imaging of the sound field. In recent years, it has shown great application potential and is of great significance to a variety of applications such as particle manipulation, improved medical imaging, and ultrasound therapy. In the past few years, people have made considerable efforts in studying acoustic holographic control. Holograms are usually set up by active transducer arrays or passive metamaterials to achieve pixel-by-pixel modulation of the phase and amplitude of the sound waves. However, it is still challenging to achieve complete control of sound, which requires completely independent modulation of the amplitude and phase on the two degrees of freedom in acoustic holography, which together determine any signal. Figure 1 Figure 1 is a diagram of the acoustic holographic imaging mechanism; a is amplitude holography by phase modulation (AH by PM); b is amplitude holography by amplitude-phase decoupling modulation (AH by APM); c is phase holography by amplitude-phase decoupling modulation (PH by APM). However, when the incident wave interacts with the complex metasurface, a complex coupling effect must occur between the amplitude and the phase. The previous pure phase holography (PM) method ignores the error caused by the inevitable change of amplitude information during the phase modulation process ( Figure 1 a), although phase modulation can adjust the sound field, it cannot solve the effect of amplitude on the image. In high-resolution imaging, strict reliance on phase control may lead to distortion. To overcome this defect, an amplitude phase holography (APM) method that simultaneously controls amplitude and phase is proposed, which effectively improves the ability to manipulate the holographic sound field ( Figure 1 c), especially for creating complex 3D patterns. Although the APM method increases the freedom of sound field control, its system often introduces computational complexity and causes energy loss due to the inherent amplitude manipulation, thus affecting the overall efficiency of sound propagation. Summary of the invention

[0004] The purpose of the present invention is to propose an acoustic phase holographic imaging method to address the problems existing in the background technology so as to adapt to holographic imaging in complex environments.

[0005] The technical solution of the present invention:

[0006] A first aspect of the present invention provides an acoustic phase holographic imaging method, comprising the following specific steps:

[0007] S1, discretizing the hologram to be imaged into a sub-wavelength scale image pixel sequence and placing it at a phase position;

[0008] In step S1, the amplitude A is encoded on the holographic plane j and phase φ j The sound pressure P j The sound pressure is calculated by superimposing the wave components of all pixels on the image plane. The calculation is represented by the following formula:

[0009]

[0010] Where N is the total number of image pixels, A 0l and φ 0l They are (x l ,y l ,z l ) is the amplitude and initial phase at the lth pixel, A j and φ j They are the amplitude and phase of the jth pixel on the hologram plane, respectively. The image pixel and the hologram pixel are at (x j ,y j ,z j ) is represented by

[0011] S2, using the time reversal method to calculate the amplitude and phase distribution of the holographic plane required to reconstruct the hologram;

[0012] In step 2, the time reversal characteristic is used to directly project the pre-designed acoustic holographic image, and the holographic image is characterized as follows:

[0013]

[0014] Where n is the total number of pixels of the holographic image, is the spatial point (x, y, z) and the hologram pixel (x j ,y j ,z j ) between the two; the scheme for generating pure phase holography assumes that the amplitude is A j =1, the pure phase hologram is characterized as:

[0015]

[0016] S3, using the horned lizard optimization algorithm to solve the optimal coupling compensation amplitude;

[0017] In step S3, before solving the optimal coupling compensation amplitude, it is necessary to determine the coupling relationship between the pixels: including the strong coupling effect between the target pixels and the amplitude-phase indirect weak coupling effect of the global pixels.

[0018] In step S3, the amplitude A(x) and phase φ(x) are coupled in space through the wave equation of the sound wave, and the sound pressure is described by the wave equation or its propagation complex form, and the sound pressure is expressed as a complex form P(x)=A(x)e iφ(x) ;

[0019] The coupling relationship between the amplitude A(x) and the phase φ(x) is described by the derivative of the complex sound pressure;

[0020] In sound wave propagation, the rate of change of amplitude and the rate of change of phase are related to each other through the propagation equation. and phase change The coupling relationship between them is characterized as follows:

[0021]

[0022] The coupling characteristics of amplitude and phase in space are closely linked through interference and wave equations. In the ideal case without attenuation and scattering, the relationship between amplitude and phase is simplified to:

[0023]

[0024] Strong coupling effect between target pixels:

[0025] A single pixel in a phase hologram is defined as P(i,j), and its amplitude and phase are represented by A(i,j) and φ(i,j) respectively; the complex representation of the phase hologram is: P(i,j)=A(i,j)e iφ(i,j)

[0026] The sound pressure of a single pixel in the acoustic hologram after the corresponding compensation amplitude is defined as C(i,j);

[0027] Where C(i,j) is the adjustment factor related to the phase hologram P(i,j) and can be represented as:

[0028] C(i,j) strong =f(P(i,j))=k 1 A(i,j)+k 2 φ(i,j)

[0029] The f function is the nonlinear mapping relationship between amplitude and phase under ideal conditions; k1 and k 2 They are respectively used as adjustment factors for amplitude and phase, characterizing the influence of amplitude and phase on the compensation amplitude; by adjusting C(i,j), the imaging fineness is compensated.

[0030] Global indirect weak coupling effect

[0031] Characterized by:

[0032]

[0033] Where D d Represents the set of all global pixels whose distance from the target pixel is d; Defined as the distance attenuation factor; w d is the weight coefficient related to the distance d, which reflects the 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 peripheral pixels;

[0034] The threshold value of the weak coupling layer's influence on the middle pixel is defined as e=10 -5 , that is, when the weak coupling effect of the weak coupling layer pixel on the target pixel is less than e, the search for the outer layer pixel point is stopped;

[0035] By using the blood jet strategy in the horned lizard optimization algorithm, the direct strong coupling effect of local target pixels in the hologram and the indirect weak coupling effect of global pixels on target pixels are balanced, and the coupling effect between global pixels of strong coupling and weak coupling effects is characterized as follows:

[0036]

[0037] S4. Using the holographic plane to reflect the incident sound wave, encoding the phase and compensation amplitude information of the image transmitted after coupling, so as to reconstruct an acoustic hologram matching the pre-designed image and realize phase imaging; the reconstructed phase hologram is obtained by taking the cosine of the measured phase in the range of [0, 2π], so that the range of the phase hologram changes from [0, 2π] to [-1, 1], specifically including:

[0038] Linearization: Phase information itself is nonlinear because it changes from 0 to 2π in one cycle. By taking the cosine, this nonlinear relationship can be converted into a linear relationship. The cosine function is periodic in the interval [0, 2π] and its value range is [-1, 1]. This linearization helps to simplify subsequent mathematical operations and signal processing.

[0039] Enhance contrast: In image processing, converting phase information to the range of [-1, 1] can enhance the contrast of the image. The output value of the cosine function is between -1 and 1. This range expansion makes the details of the image more obvious and easier to observe and analyze.

[0040] The decoupled modulation of the phase and amplitude of the reflected sound wave in step S4 is achieved by adjusting the geometric shape and structural parameters of the holographic plane unit cell.

[0041] Preferably, under the irradiation of frontal sound, the sound wave reaches a decoupling point in the internal structural space of the holographic plane unit cell, realizing decoupled modulation of the phase and amplitude of the reflected sound wave; the decoupled modulation of the amplitude and phase of the sound wave on the holographic plane realizes that all combinations of amplitude and phase on the holographic plane can be modulated in the full range of [0,1] and [0,2π].

[0042] A second aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program implements the steps of the above-mentioned acoustic phase holographic imaging method when executed by a processor.

[0043] Compared with the prior art, the present invention has the following beneficial technical effects:

[0044] 1. The present invention proposes an acoustic phase hologram (APH) method, which is designed to meet the needs of holographic imaging in complex environments. By pre-designing the phase image and using the time reversal technology, the amplitude-phase decoupling control is realized on the holographic plane, and then a phase image with the ability to resist energy attenuation and interference is obtained on the image plane.

[0045] 2. The present invention deeply studies the coupling mechanism of phase and amplitude between global pixels in the hologram, introduces the Horned Lizard Optimization Algorithm (HLOA) to iteratively optimize the optimal coupling compensation amplitude of the phase image in a complex environment, and uses the time reversal method to calculate the metasurface amplitude and phase distribution required to reconstruct the hologram. The Lossy Acoustic Metamaterial (LAM) structure is used to encode the phase and compensation amplitude information of the transmitted image after coupling; the present invention relies on the compensation amplitude of the corresponding phase hologram in a complex environment by coupling the phase hologram, and finally obtains a phase hologram that has both the ability to finely control the sound field and the anti-interference ability.

[0046] 3. The method of the present invention has the advantage that phase modulation in the traditional pure phase modulation (PM) method does not directly cause energy loss, and integrates the characteristics of the amplitude-phase decoupling control (APM) method that simultaneously controls phase and amplitude to increase the freedom of sound field control. It solves the problem of insufficient imaging fineness due to lack of amplitude control in PM in complex sound fields and multi-path environments, and the problem of unnecessary energy loss caused by direct amplitude control by the APM method, which affects system efficiency. Compared with PM and APM of traditional acoustic metasurfaces, the APH method can obtain high-fidelity and high-quality acoustic holograms in complex sound fields with energy loss, which is of great significance for the practical application of acoustic holography technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a diagram of the acoustic holographic imaging mechanism;

[0048] Figure 2 Diagram of iterative optimization process of HLOA algorithm for solving optimal amplitude compensation;

[0049] Figure 3 It is the relationship diagram between the strong coupling layer and the weak coupling layer;

[0050] Figure 4 A design diagram of a phase holographic plane with coupled compensation amplitude;

[0051] Figure 5 This is the experimental diagram of the amplitude compensated phase acoustic holographic scanning field;

[0052] Figure 6 This is the holographic correlation verification diagram;

[0053] Figure 7 This is a verification diagram of the anti-interference ability of the amplitude compensated phase acoustic hologram;

[0054] Figure 8 Schematic diagram of the process of the imaging method in an embodiment of the present invention. DETAILED DESCRIPTION

[0055] In this paper, an acoustic phase hologram (APH) method is proposed through analytical derivation, numerical simulation, algorithm optimization and experimental demonstration to adapt to holographic imaging in complex environments. The coupling mechanism of phase and amplitude between global pixels in the hologram is deeply studied, and the horned lizard optimization algorithm (HLOA) is introduced to iteratively optimize the optimal coupling compensation amplitude in complex environments. The time reversal method is used to calculate the metasurface amplitude and phase distribution required for reconstructing the hologram. The design idea is realized by using the Lossy Acoustic Metamaterial (LAM) structure to encode the phase and compensation amplitude information of the transmitted image after coupling. This design idea is based on an inherent mechanism different from the previous design and relies on the compensation amplitude of the corresponding phase hologram coupled in complex environments using phase holography. This method not only has the advantage of phase modulation in the traditional pure phase modulation (PM) method that does not directly cause energy loss, but also integrates the characteristics of the amplitude-phase decoupling modulation (APM) method that simultaneously regulates phase and amplitude to increase the degree of freedom of sound field control. The problem of insufficient imaging precision due to lack of amplitude control in PM in complex sound fields and multipath environments is solved, as well as the problem of unnecessary energy loss caused by direct amplitude control by the APM method, which affects system efficiency. Compared with PM and APM of traditional acoustic metasurfaces, the APH method can obtain high-fidelity and high-quality acoustic holograms in complex sound fields with energy loss, which is of great significance for the practical application of acoustic holography technology.

[0056] The proposed mechanism enables the phase holographic imaging method after coupling compensation amplitude to achieve fine control of the three-dimensional acoustic field, while having the advantages of simple design, low manufacturing cost, flat 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 in complex environments. Similar to optical holograms, acoustic holography provides new capabilities for particle manipulation and application improvement. However, due to the lack of the ability to modulate amplitude and phase simultaneously, the current production of acoustic holograms has to rely on phase modulation methods and complex decoupled amplitude phase modulation. This paper numerically and experimentally proves that high-fidelity acoustic holograms can be stably generated using phase modulation with coupled compensation amplitude.

[0057] The following uses a specific case to introduce this solution in detail:

[0058] Example 1

[0059] The present invention proposes an acoustic phase holographic imaging method, such as Figure 2As shown, a1 is the phase hologram; a2-a8 are the phase holograms after coupling compensation amplitude; b1 is the initial random amplitude; b2-b8 are 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 the letter P in the phase hologram of a1; d2-d8 are the local pixels at the position of the letter P in the phase hologram after coupling amplitude compensation; e is the iterative convergence curve; f is the metasurface model encoding the amplitude and phase information at different positions; g is a schematic diagram of the holographic plane; Figure 2 g shows the holographic plane of the coded phase hologram; Figure 2 f shows the holographic plane model after the coded phase holographic coupling compensated amplitude. Considering the general principle of acoustic holographic reconstruction, the hologram is discretized into a sub-wavelength scale image pixel sequence. The coded amplitude A on the holographic plane j and phase φ j The sound pressure P j The sound pressure can be calculated by superimposing the wave components of all pixels on the image plane. The calculation of the sound pressure is represented by the following formula. j and phase φ j The information is pre-designed in the unit structure of the corresponding holographic plane. Under the irradiation of a plane wave with a fixed frequency of f = 17000 Hz, the unit cell of the holographic plane performs an amplitude A on the incident sound wave. j and phase φ j The reflected sound waves are modulated to reconstruct a holographic image that matches the pre-designed image.

[0060]

[0061] Where N is the total number of image pixels, A 0l and φ 0l They are (x l ,y l ,z l ) is the amplitude and initial phase at the lth pixel, A j and φ j They are the amplitude and phase of the jth pixel on the hologram plane, respectively. The image pixel and the hologram pixel are at (x j ,y j ,z j ) can be represented as Due to the time reversal symmetry, the pre-designed acoustic holographic image can be directly projected, and the holographic image can be characterized as

[0062]

[0063] Where n is the total number of pixels of the holographic image, is the spatial point (x, y, z) and the hologram pixel (x j ,yj ,z j ). However, previous schemes for generating pure phase holograms assumed that the amplitudes were all A j =1, so the pure phase hologram can be characterized as

[0064]

[0065] HLOA algorithm solves the amplitude mechanism of phase holographic compensation

[0066] In the study of solving the coupling compensation amplitude problem, this paper introduces a new swarm-based intelligent optimization algorithm - the Horned Lizard Optimization Algorithm (HLOA). The HLOA algorithm is inspired by the defense strategies of horned lizards when attacked, including concealment, skin color change, blood spray and escape strategies, which help horned lizards avoid attacks from predators. Compared with traditional intelligent optimization algorithms, such as genetic algorithms and particle swarm algorithms, the HLOA algorithm shows significant advantages in dealing with high-dimensional optimization problems. By simulating the five defense strategies of horned lizards, the algorithm achieves a good balance between global search and local search strategies, and is particularly suitable for solving optimization problems in high-dimensional solution spaces.

[0067] Strategy 1: Crypsis behavior Crypsis behavior strategy.

[0068] The color theory is used to establish the secret behavior strategy 1 of the horned lizard in the HLOA algorithm. Strategy 1 can be characterized as follows:

[0069]

[0070] In the formula is the new search agent position in the solution search space at the t+1th iteration; is the best search agent of the tth generation; r1, r2, r3, r4 are integer random numbers generated between 1 and the maximum number of search agents, r1≠r2≠r3≠r4; are the selected search agents r1, r2, r3, and r4 respectively; Max iter represents the maximum number of iterations, σ is a random binary value of 0 or 1, Let 2, c1, c2, where c1≠c2 contains random numbers generated by the normalized palette.

[0071] Strategy 2: Skin darkening or lightening

[0072] The skin brightening and darkening strategies are used to replace the worst search agent. The skin brightening and darkening strategies of the simulated horned lizard can be represented by Equation 5 and Equation 6, respectively.

[0073]

[0074] Where Light1 and Light2 are random numbers generated between the palette normalization values ​​Lightening1 (0 value) and Lighthening2 (0.4046661 value). Similarly, Dark1 and Dark2 are random numbers generated between Darkening1 (0.5440510 value) and Darkening2 (1 value). In addition, in both equations and denote the worst and best search agents, respectively. Note that the worst search agent in iteration t is replaced by a new search agent obtained by the skin-darkening or skin-lightening strategy.

[0075] Strategy 3: blood-squirting

[0076] Characterizing the defense mechanism of the blood shot by the horned lizard as projectile motion, the trajectory equation can be represented by the horizontal motion in the horizontal direction and the free fall motion in the vertical direction using the vector equation as

[0077]

[0078] in is the current search agent; t is the current iteration, v0 is set to 1seg, and α is set to ε is set to 1E-6, g is the gravity of the earth, 0.009807km / s2

[0079] Strategy 4: move-to-escape

[0080] In order to balance the global and local search strategies, the random fast movement avoidance strategy of the horned lizard in the environment was simulated and mathematically modeled. The mobile escape strategy can be characterized as

[0081]

[0082] in is the best search agent of generation T, walk is a random number generated between -1 and 1, ε is a random number generated from a standard Cauchy distribution with mean σ set to 0 and 1 respectively. is the current i-th search agent in generation T. In this equation It is around Then add Generate displacements (global moves) through the solution search space.

[0083] Strategy 5: α-melanophore stimulating hormone (α-MSH) rate

[0084] By simulating the stimulation of temperature on α-melanocytes in the skin of horned lizards, selecting the best fitness value, and normalizing the melanophore(i) value vector in the interval [0,1], the α-melanocyte rate value of the horned lizard can be defined as

[0085]

[0086] Fitness max and Fitness min are the best and worst fitness values ​​in the current T generation, respectively, and Fitness(i) is the current fitness value of the i-th search agent. When the α-MSH rate is less than 0.3, the search agent is replaced, which can be represented by the following formula:

[0087]

[0088] in Is the current search agent is the best search agent found, r1 and r2 are integer random numbers generated between 1 and the maximum number of search agents, where r1≠r2, and Is r1, r2 search agent selected

[0089] The following uses the acoustic hologram of the first letter P of "Phase" as an example. The pre-designed letter P image is composed of 87×87 pixels, that is, it is necessary to solve the global optimal coupling compensation amplitude matrix based on the 87×87-dimensional phase hologram. In the process of solving the compensation amplitude, it is necessary to simultaneously consider the search strategy of the global 7569 pixel points of the balanced hologram and the local position of the letter P in the image to ensure that the loss values ​​of the global and local positions of the compensation amplitude obtained by each iterative optimization are in the direction of decreasing. Finally, the phase hologram with the optimal coupling compensation amplitude is obtained, as shown in Figure 2 As shown in a8.

[0090] In the process of reconstructing the acoustic hologram, the horned lizard's defense strategy is introduced into the phase holographic calculation to calculate the optimal compensation amplitude of the hologram to improve the accuracy and efficiency of the sound field reconstruction. After the compensation amplitude is introduced, a complex coupling relationship will appear between the amplitude and phase in the hologram. This coupling relationship is not a simple linear superposition of a single pixel. This coupling relationship involves direct and indirect interactions, which are reflected in each pixel of the hologram.

[0091] by Figure 2 Taking the middle pixel in d1 as an example, when the amplitude compensation is performed on this pixel, a direct strong coupling effect is observed between the pixel and its phase and compensation amplitude. In addition, the 8 pixels around the middle pixel also have an indirect weak coupling effect on the coupling of the middle pixel. Furthermore, the 8n pixels in the outer layer also have a smaller indirect weak coupling effect on the middle pixel. This complex coupling effect requires that when designing the hologram, the interaction between each pixel and its surrounding pixels must be taken into account to ensure that the hologram can accurately reconstruct the expected sound field.

[0092] From the perspective of the mechanism of acoustic holographic imaging, this paper deeply studies the strong coupling effect between imaging pixels and the weak coupling effect of the peripheral pixels on the central pixel when a certain pixel is used as the radiation source. In an acoustic hologram, each pixel not only serves as the emission source of sound waves, but also interacts with other pixels. This interaction manifests itself as a direct strong coupling effect and an indirect weak coupling effect, which together determine the reconstruction quality and efficiency of the acoustic hologram.

[0093] Study on the coupling mechanism of amplitude and phase

[0094] In the reconstruction process of the acoustic hologram, the spatial variation of the amplitude A(x) and the phase φ(x) can be coupled through the wave equation of the acoustic wave, and the sound pressure can be described by the wave equation or its propagation complex form, expressing the sound pressure in the complex form P(x) = A(x)e iφ(x) The coupling relationship between amplitude A(x) and phase φ(x) can be studied by taking the derivative of the 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 related to each other through the propagation equation, and the amplitude change can be and phase change The coupling relationship between them is characterized as follows:

[0095]

[0096] This coupling relationship reflects how amplitude and phase affect each other during sound wave propagation. When the phase changes rapidly, the amplitude may decrease, and vice versa. This complex coupling effect requires that when designing a hologram, the interaction between each pixel and its surrounding pixels must be considered to ensure that the hologram can accurately reconstruct the expected sound field. The coupling characteristics of amplitude and phase in space are closely linked through interference and wave equations. In the ideal case without attenuation and scattering, the relationship between amplitude and phase can be simplified to:

[0097]

[0098] Direct strong coupling effect of target pixel

[0099] In acoustic holograms, the direct coupling effect between individual pixels is a direct result of the principle of acoustic interference and the inhomogeneity of medium propagation. Each pixel can be regarded as the emission source of the sound wave, where the amplitude and phase jointly determine the contribution of the point to the overall sound field. According to the phase and amplitude coupling mechanism, the concealment and blood jet strategies in the Horned Lizard Optimization Algorithm (HLOA) are used to solve the compensation amplitude of each pixel in the hologram to compensate for the amplitude distortion caused by phase encoding and achieve more accurate sound field reconstruction.

[0100] In mathematical expression, a single pixel in a phase hologram can be defined as p(i,j), and its amplitude and phase are represented by A(i,j) and φ(i,j), respectively. Therefore, the complex representation of the phase hologram can be written as P(i,j)=A(i,j)e j φ(i,j) The sound pressure of a single pixel in the acoustic hologram after the corresponding compensation amplitude is defined as C(i,j), where C(i,j) is the adjustment factor related to the phase hologram P(i,j), which can be expressed as

[0101] C(i,j) strong =f(P(i,j))=k 1 A(i,j)+k 2 φ(i,j)

[0102] The f function is the nonlinear mapping relationship between amplitude and phase in an ideal situation. This function depends on the amplitude and phase information in the phase hologram. It adjusts the compensation amplitude according to the specific values ​​of the amplitude and phase to achieve accurate reconstruction of the sound field. In this mapping relationship, k 1 and k 2 As the adjustment factors of amplitude and phase respectively, they characterize the influence of amplitude and phase on the compensation amplitude; by adjusting C(i,j), the problem of insufficient imaging fineness caused by the lack of amplitude regulation can be effectively compensated.

[0103] Global indirect weak coupling

[0104] In acoustic holograms, the coupling effect of adjacent pixels on the target pixel cannot be ignored. Figure 2As shown in c1-c8, when the phase hologram and compensation amplitude of the target pixel are coupled with each other, the coupling effect of the surrounding pixels will also have a certain impact on the target pixel. Therefore, it is particularly important to study the indirect coupling relationship between the target pixel and the n layers of pixels around it. This indirect coupling relationship is not only affected by the distance and phase difference between the pixels, but also by the mutual coupling effect of the global pixel on the central pixel. By considering the indirect weak coupling effect between global pixels, the fineness of imaging can be significantly improved, and the performance of the system in complex sound fields and multipath environments can be improved. In mathematical expression, the global weak coupling effect can be represented as

[0105]

[0106] Where D d Represents the set of all global pixels whose distance from the target pixel is d; Defined as the distance attenuation factor; w d is the weight coefficient related to the distance d, which reflects 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 peripheral pixels. The threshold value of the influence of the weak coupling layer on the intermediate pixel is defined as e=10 -5 , that is, when the weak coupling effect of the weak coupling layer pixel on the target pixel is less than e, the search for the outer layer pixel is stopped. The blood jet strategy in the Horned Lizard Optimization Algorithm (HLOA) is used to balance the direct strong coupling effect of the local target pixel in the hologram and the indirect weak coupling effect of the global pixel on the target pixel, so that the coupling effect between the global pixels that considers both strong coupling and weak coupling effects can be characterized as

[0107]

[0108] In the above study, a mathematical model was used to describe the weak coupling effect between pixels in the acoustic hologram, which is consistent with the academic research field of acoustic holograms. The model takes into account the distance and phase difference between pixels, as well as their influence on the central pixel, which are important factors in the acoustic hologram. By setting the threshold e, the search range can be effectively limited, thereby optimizing the compensation amplitude of the hologram, improving the fineness of the imaging, and improving the performance of the system in complex sound fields and multipath environments. In addition, the application of the HLOA algorithm, especially its blood jet strategy, provides an effective method for balancing the solution of local and global coupling effects, which is of great significance for achieving accurate reconstruction of acoustic holograms.

[0109] Design of Phase Holographic Plane with Coupling Compensation Amplitude

[0110] In the process of acoustic holographic imaging, the design of phase holographic plane with coupled compensation amplitude is the key to achieve the control of acoustic waves. Figure 4 The design process of the phase hologram after the encoding coupling compensation amplitude on the holographic plane is demonstrated, where a is the phase hologram; b is the compensation amplitude; c is the phase holographic plane with the encoding coupling compensation amplitude; d is the unit cell structure of the holographic plane; e and f are the responses of the unit cell parameters h1 and w to the reflection amplitude and phase under decoupling conditions; Figure 4 d shows the geometry of the unit cell. Under the irradiation of positive sound, the sound wave reaches the decoupling point in the internal structure space of the holographic plane, realizing the decoupled modulation of the phase and amplitude of the unit cell to the surface reflected sound wave. The decoupling of the amplitude and phase of the sound wave on the holographic plane realizes that all combinations of amplitude and phase on the holographic plane can be modulated in the full range of [0, 1] and [0, 2π], such as Figure 4 e and 4f.

[0111] The unit cell in the holographic plane consists of three channels: upper (C1), middle (C2), and lower (C3), with heights h1, h2, and h3, respectively. The width of channels C1 and C3 is d = βD (where the filling ratio of the air channel is defined as β = 0.8, D = λ / 4 is the unit cell width, and λ is the wavelength of the sound wave). In this study, the speed of sound in air is C 0 =340ms -1 , the sound wave frequency is selected as 1.7kHz, and D = 5mm is obtained. The width of the middle cell is w, the channel wall is assumed to be acoustically rigid, the total height of the cell is h = h1 + h2 + h3, and h2 is fixed to 5mm. The cell acoustic wave incident channel length h1 and the middle channel width w have a modulation effect on the acoustic wave phase and amplitude. Figure 4 e, f show the reflection amplitude and phase response of the cell to the parameters h1 and w under decoupling conditions. The relationship between h1 and w and phase and amplitude can be represented by the following formula

[0112]

[0113] 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 then encoded into the holographic plane. Figure 4 As shown in Figure c, the holographic metasurface encoding the letter P is composed of an 87×87 cell array. The outer dimensions of each cell are the same, while the internal structure dimensions are determined by the phase and amplitude information of the pixels at different positions of the coupled hologram. Since the cell width D has a subwavelength nature, the amplitude A and phase φ of the reflected sound wave are independent of the incident direction. By setting the plane wave at an angle of 45°, a phase hologram after coupling compensation amplitude can be presented on the image plane. Figure 3 As shown, where a is Figure 2The local coupling effects of c1, c2, and d1 in the figure; b is the coupling effect between the target pixel in c2 and the pixels in the surrounding layers; it is worth noting that Figure 4 The phase hologram in a is obtained by taking the cosine of the phase in the range of [0, 2π], which effectively improves the impact of the same beginning and end values ​​of the period at the connection position of two adjacent periods on the imaging quality, making the phase hologram range become [-1, 1]. This design method can ensure that the amplitude and phase of each pixel in the hologram are accurately encoded, thereby achieving high-quality sound field reconstruction.

[0114] Characterization of the fabrication process of amplitude compensated phase acoustic hologram

[0115] The accuracy of the hologram is crucial to the accuracy of the sound field reconstruction. The manufacturing accuracy of the hologram is affected by various factors, including errors in the manufacturing process. In the process of using 3D printing technology to manufacture the holographic plane, 3D printing errors may cause distortion and unexpected areas in the hologram projected from the holographic plane to the image plane. Figure 5 As shown, a. Scanning experimental platform; b. Phase hologram of letter P, ginkgo leaf and rose; c. Amplitude compensated phase hologram of letter P, ginkgo leaf and rose; d. Experimental hologram of letter P, ginkgo leaf and rose; In order to improve the accuracy of the hologram, this study used a 3D printing device with a printing accuracy of 0.2mm to manufacture the required holographic plane (such as Figure 5 a). The experimental phase of this study was conducted in a sealed anechoic chamber to investigate the process of holographic fabrication. Specifically, the oblique incidence of plane waves emitted from a loudspeaker onto the holographic plane facilitated holographic generation. After the incident sound waves interacted with the holographic plane, they underwent demodulation, then remodulated and reflected at an angle perpendicular to the LAM metasurface. A microphone mounted on a scanning platform was used to scan the modulated sound waves, thereby capturing the necessary holograms. It is worth noting that the holographic plane did not impose any angle constraints on the incident sound waves; the angle of the reflected wave was always perpendicular to the LAM metasurface. To further demonstrate the imaging quality of the phase acoustic hologram after amplitude compensation, more complex target images, such as ginkgo leaves and rose flowers, were selected for holographic fabrication. The printed holographic surface was scanned in three dimensions using a confocal microscope with a scanning accuracy of λ / 4, i.e., one quarter of the wavelength. This high-precision scan allowed the printed holograms to be analyzed in detail and compared with theoretical holograms to evaluate the errors in the manufacturing process and the reconstruction quality of the holograms. In this way, the accuracy of the holograms can be quantitatively evaluated and the design can be optimized to reduce errors in the 3D printing process. This is of great significance for improving the performance of acoustic holograms in sound field reconstruction, especially in complex sound fields and multipath environments. In addition, this high-precision fabrication and evaluation method also provides new possibilities for the application of acoustic holograms in other fields, such as high-capacity acoustic volume display and dynamic particle manipulation.

[0116] Holographic correlation verification

[0117] In this section, the initials “H” from the word “hologram” are selected as the target image to verify the compensation optimization effect of the amplitude compensation method on various phase holograms. 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 hologram obtained at different imaging distances by the APH, PH and AH methods and the pre-designed image; f is the amplitude compensation of the phase hologram a; g is the convergence curve during the iterative optimization process of the HLOA algorithm; experimental verification was carried out using an image plane containing a 91×91 pixel array. Figure 6 a shows the phase hologram of the letter “H” for comparison; Figure 6 b shows the phase hologram with coupled amplitude compensation obtained by 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 e shows the correlation curves between the holograms obtained by the APH, PM, and APM methods and the pre-designed images under different distance conditions. These curves show 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 a hologram, the optimal positional relationship between the image plane and the holographic plane must be considered to obtain the best imaging results. Figure 6 f shows the amplitude compensated phase hologram with the best coupling to the phase hologram calculated iteratively using the HLOA (Horned Lizard Optimization Algorithm) algorithm. Figure 6 g depicts the convergence curve of the HLOA algorithm in 1000 optimization iterations, as well as the phase hologram with compensated amplitude at the corresponding position after various iteration counts. After adjusting the color bar range from [-1, 1] to [-1, 0], the hologram at the corresponding iteration position shows a phase hologram with coupled amplitude compensation, which enhances the recognizability of the hologram to the naked eye and significantly improves the quantitative image quality assessment. In the experiment, the phase information and compensated amplitude information of the coupled holographic image are encoded into the structural dimensions of the holographic plane sample unit, and the holographic plane sample is manufactured using 3D printing technology. The sample size is 12.6×12.6×2cm 3 , consisting of a 25×25 unit array, and the image area is 22cm away from the holographic plane surface.

[0118] Image quality analysis

[0119] Figure 6b and 6c show the sound pressure distribution of the acoustic field in the image plane of the numerically simulated and experimental holograms, respectively. These results show that there is good agreement between the numerical simulation results and the experimental results. In order to quantitatively evaluate the quality of the phase hologram after amplitude compensation, an accurate comparison is performed between the optimized hologram and the pre-designed image. For this purpose, an image correlation parameter is introduced to measure the similarity between the holograms obtained by the APH, PH and AH methods and the pre-designed image. Correlation values ​​tending to 1 indicate a higher similarity between the generated hologram and the target image. Unit correlation can only be achieved when the generated hologram is completely consistent with the pre-designed image.

[0120] Considering that the distance between the image plane and the holographic plane is between 15-25cm, the influence of different imaging distances on image correlation is analyzed. The correlation between the holographic image and the pre-designed original image can be characterized by the following formula

[0121]

[0122] Where P represents the target image, H represents the holographic image, and PR and HG represent the average values ​​of each image.

[0123] Figure 6 e depicts the relationship between image correlation and imaging distance. The results show that amplitude compensation enhances the design of phase holograms. Specifically, holograms designed using the amplitude phase holography (APH) method exhibit higher correlation. Compared with pure phase holography (PH) and pure amplitude holography (AH) methods, the APH method shows significant advantages in hologram correlation. Within the imaging distance range of 15 to 25 cm, the correlation of holograms designed by the APH method always remains above 92%. It is worth noting that the maximum image correlation reaches 94.542%, while the correlation at the lowest position is 92.006%, which is significantly higher than the correlation of holograms designed by the PH and AH methods.

[0124] It is also observed that, under the same imaging conditions, the correlation of the holographic images designed by the PH and AH methods decreases with increasing imaging distance. It is noteworthy that the correlation of the holograms designed by the PH method decreases more slowly than that of the AH method. In contrast, the correlation of the holograms designed by the APH method changes more gradually. The experimental results confirm the effectiveness and flexibility of our method in reconstructing complex holograms under complex conditions.

[0125] Verification of the anti-interference capability of amplitude-compensated phase acoustic hologram

[0126] In this section, we will explore the application capabilities of the acoustic phase holography (APH) method in complex environments. Figure 7As shown in 7a, phase hologram with different noise intensities added; b. phase hologram with amplitude compensation optimization algorithm after adding different noise intensities; c. amplitude hologram after adding different noise intensities; d. pre-designed images under different noise intensities; e. correlation curve distribution between the three holograms and the pre-designed images; f. deviation curve distribution between the three holograms and the pre-designed images. The letter "H" representing "holography" is selected as the pre-designed image, and the imaging effects of phase holography (PH), acoustic phase holography (APH) and amplitude holography under random noise of different intensities are systematically studied. By introducing random noise of different amplitudes into the pre-designed image (such as Figure 7 d), aiming to verify the adaptability of various holographic imaging methods to environmental noise.

[0127] Experiments were conducted to determine the holographic imaging performance of the PH method under different noise backgrounds ( Figure 7 a). Subsequently, the phase hologram with the best compensation amplitude under various noise backgrounds is shown ( Figure 7 b), and amplitude holograms under different noise conditions (see Figure 7 c). These results provide an intuitive understanding of the performance of different holographic imaging methods under the influence of noise.

[0128] In order to quantitatively evaluate the performance of the holographic imaging method, a correlation validation was performed ( Figure 7 e), the correlation between the holograms obtained by various holographic imaging methods and the pre-designed images under different environmental noise intensities was compared. 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 are helpful to advance the practical application of holographic imaging technology in noise control and image quality enhancement.

[0129] In conclusion, the study not only confirms the applicability of acoustic phase 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 applications. In order to quantify the difference between the holograms obtained by different methods and the pre-designed holograms, this study introduced the concept of normalized mean square error (NMSE). A lower NMSE value indicates a smaller overall difference between the holograms obtained by different methods and the pre-designed holograms, thereby indicating that the holographic image quality obtained by this method is higher. Figure 7 f shows the deviation between the holograms obtained by the APH, PH, and AH methods and the pre-designed images, which further evaluates the performance of different holographic imaging techniques under the same acoustic parameters. NMSE can be expressed as

[0130]

[0131] Where P represents the theoretical hologram, H represents the manufactured hologram, and ∥"∥_2 represents the Euclidean norm. In addition, the relative position between the image plane and the holographic plane will also affect the image quality.

[0132] in conclusion:

[0133] It has been demonstrated that by coupling a phase hologram with an optimal compensation amplitude hologram calculated for a corresponding complex imaging environment, the resulting hologram not only has the characteristics of resisting 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 deeply studies the direct strong coupling effect and indirect weak coupling interaction of pixels in the image plane in holographic imaging, calculates the dynamic coupling relationship between pixels at different positions, and introduces an intelligent optimization algorithm to calculate the dynamic coupling compensation amplitude for various application scenarios. This method realizes dynamic and precise coupling modulation of sound waves, thereby producing high-quality holographic images. In order to verify the performance of the phase holographic method after optimal amplitude compensation, not only the numerical simulation and experimental realization of high-fidelity acoustic holograms are demonstrated, but also the application of the new mechanism of phase holographic imaging based on coupled optimal amplitude compensation in the generation of arbitrarily complex holograms is demonstrated. In addition, it is clarified that the hologram generated by combining the phase hologram with the optimal compensation amplitude for each imaging environment effectively solves the problem of insufficient imaging accuracy in complex sound fields and multipath environments due to the lack of amplitude control in the traditional phase modulation PM method, as well as the unnecessary energy loss caused by direct amplitude control in the APM method. This significantly improves the imaging quality of acoustic holograms in complex sound fields.

[0134] In this embodiment, by coupling the phase hologram with the optimal compensated amplitude hologram calculated for the corresponding complex imaging environment, the resulting hologram not only has the characteristic of resisting 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.

[0135] Example 2

[0136] The present invention provides a computer-readable storage medium having a computer program stored thereon: when the computer program is executed by a processor, the steps of the acoustic phase holographic imaging method described in Example 1 are implemented.

[0137] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited thereto, and various changes can be made within the knowledge scope of technicians in the relevant technical field without departing from the purpose of the present invention.

Claims

1. An acoustic phase holographic imaging method, characterized in that: The specific steps include: S1, discretizing the hologram to be imaged into a sub-wavelength scale image pixel sequence and placing it at a phase position; S2, using the time reversal method to calculate the amplitude and phase distribution of the holographic plane required to reconstruct the hologram; S3, using the horned lizard optimization algorithm to solve the optimal coupling compensation amplitude; S4. Use the holographic plane to reflect the incident sound wave, encode the phase and compensation amplitude information of the transmitted image after coupling, so as to reconstruct an acoustic hologram that matches the pre-designed image and realize phase imaging; the reconstructed phase hologram is obtained by taking the cosine of the measured phase in the range of [0, 2π], so that the range of the phase hologram changes from [0, 2π] to [-1, 1].

2. The acoustic phase holographic imaging method according to claim 1, characterized in that: In step S1, the amplitude A is encoded on the holographic plane j and phase φ j The sound pressure P j The sound pressure is calculated by superimposing the wave components of all pixels on the image plane. The calculation is represented by the following formula: Where N is the total number of image pixels, A 0l and φ 0l They are (x l ,y l ,z l ) is the amplitude and initial phase at the lth pixel, A j and φ j They are the amplitude and phase of the jth pixel on the hologram plane, respectively. The image pixel and the hologram pixel are at (x j ,y j ,z j ) is represented by 3. The acoustic phase holographic imaging method according to claim 2, characterized in that: In step 2, the time reversal characteristic is used to directly project the pre-designed acoustic holographic image, and the holographic image is characterized as follows: Where n is the total number of pixels of the holographic image, is the spatial point (x, y, z) and the hologram pixel (x j ,y j ,z j ) between the two; the scheme for generating pure phase holography assumes that the amplitude is A j =1, the pure phase hologram is characterized as:

4. The acoustic phase holographic imaging method according to claim 1, characterized in that: In step S3, before solving the optimal coupling compensation amplitude, it is necessary to determine the coupling relationship between the pixels: including the strong coupling effect between the target pixels and the global indirect weak coupling effect.

5. The acoustic phase holographic imaging method according to claim 4, characterized in that: In step S3, the amplitude A(x) and phase φ(x) are coupled in space through the wave equation of the sound wave, and the sound pressure is described by the wave equation or its propagation complex form, and the sound pressure is expressed as a complex form P(x)=A(x)e iφ(x) ; The coupling relationship between the amplitude A(x) and the phase φ(x) is described by the derivative of the complex sound pressure; In sound wave propagation, the rate of change of amplitude and the rate of change of phase are related to each other through the propagation equation. and phase change The coupling relationship between them is characterized as follows: The coupling characteristics of amplitude and phase in space are closely linked through interference and wave equations. In the ideal case without attenuation and scattering, the relationship between amplitude and phase is simplified to:

6. The acoustic phase holographic imaging method according to claim 5, characterized in that: Strong coupling effect between target pixels: A single pixel in a phase hologram is defined as p(i,j), and its amplitude and phase are represented as A(i,j) and φ(i,j) respectively; the complex representation of the phase hologram is: P(i,j) = A(i,j)e iφ(i,j) The sound pressure of a single pixel in the acoustic hologram after the corresponding compensation amplitude is defined as C(i,j); Where C(i,j) is the adjustment factor related to the phase hologram P(i,j) and can be represented as: C(i,j) strong =f(P(i,j))=k1A(i,j)+k2φ(i,j) The f function is the nonlinear mapping relationship between amplitude and phase under ideal conditions; k1 and k2 are the adjustment factors of amplitude and phase, respectively, which characterize the influence of amplitude and phase on the compensation amplitude; and the imaging fineness is compensated by adjusting C(i,j).

7. The acoustic phase holographic imaging method according to claim 6, characterized in that: The global indirect weak coupling effect is characterized by: Where D d Represents the set of all global pixels whose distance from the target pixel is d; Defined as the distance attenuation factor; w d is the weight coefficient related to the distance d, which reflects the 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 peripheral pixels; The threshold value of the weak coupling layer's influence on the middle pixel is defined as e=10 -5 , that is, when the weak coupling effect of the weak coupling layer pixel on the target pixel is less than e, the search for the outer layer pixel point is stopped; By using the blood jet strategy in the horned lizard optimization algorithm, the direct strong coupling effect of local target pixels in the hologram and the indirect weak coupling effect of global pixels on target pixels are balanced, and the coupling effect between global pixels of strong coupling and weak coupling effects is characterized as follows:

8. The acoustic phase holographic imaging method according to claim 1, characterized in that: The decoupled modulation of the phase and amplitude of the reflected sound wave in step S4 is achieved by adjusting the geometric shape and structural parameters of the holographic plane unit cell.

9. The acoustic phase holographic imaging method according to claim 8, characterized in that: Under the irradiation of frontal sound, the sound wave reaches the decoupling point in the internal structural space of the holographic plane unit cell, realizing the decoupling modulation of the phase and amplitude of the reflected sound wave; the decoupling modulation of the amplitude and phase of the sound wave on the holographic plane realizes that all combinations of amplitude and phase on the holographic plane can be modulated in the full range of [0,1] and [0,2π].

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the acoustic phase holographic imaging method according to any one of claims 1 to 9 are implemented.

Images