An acoustic phase holographic imaging method

Abstract

This invention relates to the field of acoustic imaging technology, and in particular to an acoustic phase hologram imaging method. It includes the following specific steps: S1, discretizing the hologram to be imaged into a subwavelength scale image pixel sequence; S2, calculating the holographic plane amplitude and phase distribution required for holographic reconstruction using a time-reversal method; S3, solving for the optimal coupling compensation amplitude using a cornerstone optimization algorithm; S4, reflecting the incident sound wave using a holographic plane structure, encoding the phase and compensation amplitude information of the coupled image, to reconstruct an acoustic hologram matching a pre-designed image. This invention proposes an acoustic phase hologram (APH) method, aiming to adapt to the holographic imaging requirements in complex environments. By pre-designing a phase image and utilizing time-reversal technology, amplitude and phase decoupling control is achieved on the holographic plane, thereby obtaining a phase image on the image plane with resistance to energy attenuation and interference.

Description

Technical Field

[0001] This invention relates to the field of acoustic imaging technology, and in particular to an acoustic phase holographic imaging method. Background Technology

[0002] Traditional acoustic holograms focus on generating 3D images with acoustic amplitude or intensity fields, which indicate the energy distribution perceptible to the observer. In the past, phase was a neglected physical quantity on the image plane. However, in information communication, phase is another valuable information carrier, its distribution containing information equivalent to the amplitude channel. Here, we present observations of “acoustic phase holograms” using metamaterials. It is demonstrated that holograms designed in the phase channel are more robust and resistant to interference than traditional amplitude holograms, potentially leading to applications in acoustic / optical communication.

[0003] 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 represents phase-modulated amplitude holography (AH by PM); b represents amplitude holography with decoupled amplitude and phase modulation (AH by APM); and c represents phase holography with decoupled amplitude and phase 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 c), 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. Summary of the Invention

[0004] The purpose of this invention is to address the problems existing in the background technology by proposing an acoustic phase holographic imaging method to adapt to holographic imaging in complex environments.

[0005] The technical solution of the present invention:

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

[0007] S1. Discretize the hologram to be imaged into a subwavelength scale image pixel sequence and place it at the phase position;

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

[0009]

[0010] Where N is the total number of pixels in the image, A 0l 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 ) is represented as

[0011] S2. Calculate the amplitude and phase distribution of the holographic plane required for holographic reconstruction using the time reversal method;

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

[0013]

[0014] 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; the scheme for generating pure phase holography assumes that the amplitude is A. j =1, pure phase holography is characterized as:

[0015]

[0016] S3. The optimal coupling compensation amplitude is solved using the horned lizard optimization algorithm;

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

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

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

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

[0021]

[0022] By tightly linking the coupling properties of amplitude and phase in space through interference and wave equations, the relationship between amplitude and phase simplifies 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 a phase hologram is: P(i,j) = A(i,j)e iφ(i,j)

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

[0027] Where C(i,j) is a regulation factor related to the phase hologram P(i,j), which can be characterized as:

[0028] C(i,j) strong =f(P(i,j))=k1A(i,j)+k2φ(i,j)

[0029] The f function represents the nonlinear mapping relationship between amplitude and phase under ideal conditions; k1 and k2 are adjustment factors for amplitude and phase, respectively, characterizing the degree of influence of amplitude and phase on the compensation amplitude; and the imaging fineness is compensated by adjusting C(i,j).

[0030] Global indirect weak coupling effect

[0031] Characterized as:

[0032]

[0033] 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, 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 surrounding pixels;

[0034] The threshold value for the influence of the weakly coupled layer on the intermediate pixel is defined as e = 10. -5 That is, when the weak coupling effect of the weakly coupled layer pixel on the target pixel is less than e, the search for the outer layer pixel is stopped.

[0035] By utilizing the blood spraying strategy in the horned lizard optimization algorithm, the direct strong coupling effect of local target pixels and the weak coupling effect between global pixels and target pixels in the hologram are balanced. The coupling effect between global pixels with strong and weak coupling effects is characterized as follows:

[0036]

[0037] S4. The incident sound wave is reflected using a holographic plane, and the phase and compensation amplitude information of the coupled image are encoded to reconstruct an acoustic hologram that matches the pre-designed image, thus achieving phase imaging. The reconstructed phase hologram is obtained by taking the cosine of the measured phase in the range of [0, 2π], changing the range of the phase hologram from [0, 2π] to [-1, 1]. Specifically, this includes:

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

[0039] Enhancing Contrast: In image processing, converting phase information to the range of [-1, 1] can enhance image contrast. The output value of the cosine function is between -1 and 1; this extended range makes image details more apparent, facilitating observation and analysis.

[0040] In step S4, the decoupling modulation of the phase and amplitude of the reflected sound wave is achieved by adjusting the geometry and structural parameters of the holographic plane cell.

[0041] Preferably, under the illumination of the frontal sound, the sound wave reaches the decoupling point in the internal structural space of the holographic plane 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 enables all combinations of amplitude and phase on the holographic plane to 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, which, when executed by a processor, implements the steps of the acoustic phase holographic imaging method described above.

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

[0044] 1. This invention proposes an Acoustic Phase Hologram (APH) method, designed to meet the holographic imaging requirements in complex environments. By pre-designing a phase image and utilizing time reversal technology, amplitude and phase decoupling modulation is achieved on the holographic plane, thereby obtaining a phase image on the image plane that resists energy attenuation and interference.

[0045] 2. This invention delves into the coupling mechanism of phase and amplitude between global pixels in a hologram. It introduces the Holodomon Optimization Algorithm (HLOA) to iteratively optimize the coupling compensation amplitude of the phase image under complex environments, and employs a time-reversal method to calculate the metasurface amplitude and phase distribution required for hologram reconstruction. By utilizing the Lossy Acoustic Metamaterial (LAM) structure to encode the phase and compensation amplitude information of the coupled transmitted image, this invention relies on utilizing the compensation amplitude of the corresponding phase hologram under complex environments to ultimately obtain a phase hologram that simultaneously possesses the ability for fine-tuning the sound field and anti-interference capabilities.

[0046] 3. The method of this invention 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 regulates phase and amplitude to increase the degrees of freedom in sound field control. It solves the problem of insufficient imaging precision caused by the lack of amplitude regulation in PM in complex sound fields and multipath environments, as well as the problem of unnecessary energy loss caused by direct amplitude regulation in APM methods, which affects system efficiency. Compared with traditional acoustic metasurface PM and APM, the APH method can obtain high-fidelity and high-quality acoustic holograms in complex sound fields despite energy loss, which is of great significance for the practical application of acoustic holography technology. Attached Figure Description

[0047] Figure 1 Diagram of acoustic holographic imaging mechanism;

[0048] Figure 2 The diagram illustrates the iterative optimization process of the HLOA algorithm for finding the optimal amplitude compensation.

[0049] Figure 3 This diagram illustrates the relationship between strongly coupled and weakly coupled layers.

[0050] Figure 4 Design drawing of a phase holographic plane with coupling compensation amplitude;

[0051] Figure 5 Experimental diagram of phase acoustic holographic scanning field with amplitude compensation;

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

[0053] Figure 7 This is a verification diagram of the anti-interference capability of amplitude-compensated phase acoustic holograms.

[0054] Figure 8 This is a schematic flowchart of the imaging method in an embodiment of the present invention. Detailed Implementation

[0055] 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 Lossy Acoustic 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 regulate 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.

[0056] 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.

[0057] The following specific case study will be used to provide a detailed introduction to this solution:

[0058] Example 1

[0059] This 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 is the iterative solution process for 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 a1 phase hologram; 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 amplitude and phase information at different positions; g is a schematic diagram of the holographic plane. Figure 2 g represents the holographic plane encoding phase holography; Figure 2 f illustrates the holographic plane 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, and the coded amplitude A on the holographic plane 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 within the unit structure of the corresponding holographic plane. Under illumination by a plane wave with a fixed frequency of f = 17000 Hz, the unit cells of the holographic plane 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.

[0060]

[0061] Where N is the total number of pixels in the image, A 0l 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...

[0062]

[0063] 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 ,yj ,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

[0064]

[0065] HLOA algorithm for solving phase holographic compensation amplitude mechanism

[0066] 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 the horned lizard's five defense strategies, the algorithm achieves a good balance between global and local search strategies, making it particularly suitable for solving optimization problems with high-dimensional solution spaces.

[0067] Strategy 1: Crypsis behavior (covert behavior strategy).

[0068] Based on color theory, a stealth behavior strategy 1 for the horned lizard in the HLOA algorithm is established. Strategy 1 can be characterized as follows:

[0069]

[0070] Where in the formula Let this be the new search agent position in the solution search space for the (t+1)th iteration; It is the best search agent for generation t; r1, r2, r3, and r4 are random integers generated between 1 and the maximum number of search agents, where r1≠r2≠r3≠r4; These are the r1, r2, r3, and r4th search proxies selected, respectively; Max iter This represents the maximum number of iterations, where σ is a random binary value of 0 or 1. Let c1 and c2 be 2, where c1 ≠ c2 and contain random numbers generated by the normalized palette.

[0071] Strategy 2: Skin darkening or lightening

[0072] By replacing the worst search agent with skin brightening and darkening strategies, the simulated skin brightening and darkening strategies of the horned lizard can be characterized by Equations 5 and 6, respectively.

[0073]

[0074] Light1 and Light2 are random numbers generated between the palette normalization values ​​Lightening1 (0) and Lightening2 (0.4046661). Similarly, Dark1 and Dark2 are random numbers generated between Darkening1 (0.5440510) and Darkening2 (1). Furthermore, in both equations... and and represent the worst and best search agents, respectively. Note that the worst search agent in iteration t is replaced by a new search agent obtained through the skin-darkening or skin-lightening strategy.

[0075] Strategy 3: Blood-squirting

[0076] The defensive mechanism of the blood shot by the horned lizard can be characterized as projectile motion. The horizontal motion in the horizontal direction and the free fall motion in the vertical direction can be represented by vector equations to form the trajectory equation.

[0077]

[0078] in This 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, and g is Earth's gravity, 0.009807 km / s².

[0079] Strategy 4: Move-to-Escape

[0080] To balance global and local search strategies, a mathematical model is used to simulate the horned lizard's random, rapid movement and evasion strategies in its environment. This movement escape strategy can be characterized as...

[0081]

[0082] in It is the best search agent for generation T, walk is a random number generated between -1 and 1, ε is a random number generated from the standard Cauchy distribution with average value σ set to 0 and 1 respectively. It is the current i-th search agent in generation T. In this equation... It revolves around Then add Displacement (global movement) is generated by solving the search space.

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

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

[0085]

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

[0087]

[0088] in It is the current search agent The best search agent is found, and r1 and r2 are random integers generated between 1 and the maximum number of search agents, where r1 ≠ r2. and The search proxies r1 and r2 were selected.

[0089] The following example uses the acoustic hologram of the initial letter "P" of "Phase". 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 balancing 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, the phase hologram with the optimal coupling compensation amplitude is obtained, as shown below. Figure 2 As shown in a8.

[0090] 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.

[0091] 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.

[0092] 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.

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

[0094] 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:

[0095]

[0096] 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:

[0097]

[0098] Direct strong coupling effect of target pixels

[0099] 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.

[0100] 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...

[0101] C(i,j) strong =f(P(i,j))=k1A(i,j)+k2φ(i,j)

[0102] 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.

[0103] Global indirect weak coupling effect

[0104] 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...

[0105]

[0106] 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...

[0107]

[0108] 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.

[0109] Phase holographic planar design for coupling compensation amplitude

[0110] In acoustic holographic imaging, the design of the phase holographic plane with coupled amplitude compensation is the key to achieving acoustic wave manipulation. Figure 4 The design process of the phase hologram after coded coupling compensation amplitude on the holographic plane is shown, where a is the phase hologram; b is the compensation amplitude; c is the phase holographic plane with coded coupling compensation amplitude; d is the cell structure of the holographic plane; e and f are the responses of cell parameters h1 and w to reflection amplitude and phase under decoupling conditions; Figure 4d specifically showcases the geometry of the cell. Under the illumination of the frontal sound, the sound wave reaches the decoupling point within the holographic plane's internal structural space, 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 holographic plane allows modulation of all combinations of amplitude and phase on the holographic surface within the full range of [0, 1] and [0, 2π]. Figure 4 As shown in e and 4f.

[0111] A cell in the holographic plane consists of three channels: top (C1), middle (C2), and bottom (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.

[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 compensated amplitude and encoded onto the holographic plane. 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 4 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.

[0114] Characterization of Amplitude-Compensated Phase Acoustic Hologram Fabrication Process

[0115] 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 manufacturing holographic planes using 3D printing technology, 3D printing errors can lead to distortions and unexpected areas in the hologram projected from the holographic plane onto the image plane. For example... Figure 5 As shown, a. the scanning experimental platform; b. phase holograms of the letter P, ginkgo leaves, and roses; c. amplitude-compensated phase holograms of the letter P, ginkgo leaves, and roses; d. experimental holograms of the letter P, ginkgo leaves, and roses. To improve the accuracy of the holograms, this study used a 3D printing device with a printing accuracy of 0.2 mm to manufacture the required holographic plane (e.g., 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 onto the holographic plane to facilitate holographic generation. After interacting with the holographic plane, 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 holographic plane 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 surface was three-dimensionally scanned using a confocal microscope with a scanning accuracy of λ / 4, i.e., 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 quantitative evaluation of the hologram accuracy and optimization of the design to reduce errors in the 3D printing process. This is significant for improving the performance of acoustic holograms in sound field reconstruction, especially in complex sound fields and multipath environments. Furthermore, this high-precision fabrication 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.

[0116] Holographic Correlation Verification

[0117] 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 6As 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 holographic plane 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 amplitude 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 holographic image were encoded into the structural dimensions of the holographic planar sample unit, and the holographic planar 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, with the image area 22cm away from the holographic plane surface.

[0118] Image quality analysis

[0119] Figure 6Figures 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.

[0120] Considering the distance between the image plane and the holographic plane 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.

[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 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.

[0124] 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.

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

[0126] This section will explore in depth the application capabilities of the acoustic phase holography (APH) method in complex environments. For example... Figure 7As 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.

[0127] Experiments were conducted to determine the holographic imaging performance of the PH method under different noise backgrounds. Figure 7 a). 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.

[0128] 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.

[0129] 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

[0130]

[0131] 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 holographic plane also affects the image quality.

[0132] in conclusion:

[0133] 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.

[0134] 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.

[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, it implements the steps of the acoustic phase holographic imaging method described in Embodiment 1.

[0137] 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. An acoustic phase holographic imaging method, characterized in that, The specific steps include the following: S1. Discretize the hologram to be imaged into a subwavelength scale image pixel sequence and place it at the phase position; S2. Calculate the amplitude and phase distribution of the holographic plane required for holographic reconstruction using the time reversal method; S3. The optimal coupling compensation amplitude is solved using the horned lizard optimization algorithm. Before solving the optimal coupling compensation amplitude in step S3, it is necessary to determine the coupling relationship between pixels: including the strong coupling effect between target pixels and the global indirect weak coupling effect. The amplitude A(x) and phase φ(x) are coupled through the wave equation of sound waves in spatial variation. The strong coupling effect and the global indirect weak coupling effect between target pixels are characterized. The blood spray strategy in the horned lizard optimization algorithm is used to balance the strong coupling and weak coupling effects. S4. The incident sound wave is reflected by the holographic plane, 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. 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 sound pressure P j The sound pressure level is calculated by superimposing the wave components of all pixels on the image plane, and is characterized by the following formula: Where N is the total number of pixels in the image, A 0l and φ 0l They are respectively (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 ) is represented as 3. The acoustic phase holographic imaging method according to claim 2, characterized in that, In step 2, the time reversal property is used to directly project the pre-designed acoustic holographic image, which is represented as follows: 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; the scheme for generating pure phase holography assumes that the amplitude is A. j =1, pure phase holography is characterized as:

4. The acoustic phase holographic imaging method according to claim 1, characterized in that, In step S3, the spatial variations of amplitude A(x) and phase φ(x) are coupled through the wave equation of sound waves. The sound pressure is 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) is described by the derivative of complex sound pressure; In sound wave propagation, the rate of change of amplitude and the rate of change of phase are related through the propagation equation, which states that the change in amplitude... and phase change The coupling relationship between them is characterized as follows: By tightly linking the coupling properties of amplitude and phase in space through interference and wave equations, the relationship between amplitude and phase simplifies to:

5. The acoustic phase holographic imaging method according to claim 4, 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 by A(i,j) and φ(i,j), respectively; the complex representation of a phase hologram is: P(i,j) = A(i,j)e iφ(i,j) The sound pressure level of a single pixel in the acoustic hologram after compensation is defined as C(i,j); Where C(i,j) is a regulation factor related to the phase hologram P(i,j), which can be characterized as: C(i,j) strong =f(P(i,j))=k1A(i,j)+k2φ(i,j) The f function represents the nonlinear mapping relationship between amplitude and phase under ideal conditions; k1 and k2 are adjustment factors for amplitude and phase, respectively, characterizing the degree of influence of amplitude and phase on the compensation amplitude; and the imaging fineness is compensated by adjusting C(i,j).

6. The acoustic phase holographic imaging method according to claim 5, characterized in that, The global indirect weak coupling effect is characterized as follows: 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, 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 surrounding pixels; The threshold value for the influence of the weakly coupled layer on the intermediate pixel is defined as e = 10. -5 That is, when the weak coupling effect of the weakly coupled layer pixel on the target pixel is less than e, the search for the outer layer pixel is stopped. By utilizing the blood spray strategy in the horned lizard optimization algorithm, the direct strong coupling effect of local target pixels and the indirect weak coupling effect of global pixels to target pixels in the hologram are balanced. The coupling effect between global pixels with strong and weak coupling effects is characterized as follows:

7. The acoustic phase holographic imaging method according to claim 1, characterized in that, In step S4, the decoupling modulation of the phase and amplitude of the reflected sound wave is achieved by adjusting the geometry and structural parameters of the holographic plane cell.

8. The acoustic phase holographic imaging method according to claim 7, characterized in that, Under the illumination of the frontal sound, the sound wave reaches the decoupling point in the internal structural space of the holographic plane 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 enables all combinations of amplitude and phase on the holographic plane to be modulated in the full range of [0,1] and [0,2π].

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the steps of the acoustic phase holographic imaging method according to any one of claims 1 to 8.

Images