A multi-plane acoustic hologram generation method and system based on a phys-GAN framework

Abstract

The application discloses a kind of multi-plane acoustic hologram generation method and system based on Phys-GAN framework. The target acoustic intensity map on different target planes is obtained, and pretreated;Phys-GAN network architecture is constructed, including generator network and discriminator network, the target acoustic intensity map is input into the generator network, and the phase hologram is output;Source plane complex acoustic field is constructed, and the source acoustic field is propagated to each target plane by acoustic propagation operator, to obtain the reconstructed sound intensity distribution map;Fake samples, real samples are input into the discriminator network, and the reconstruction loss is calculated against loss;Generator total loss function is constructed, the parameters of generator network are updated until the preset convergence condition is met, and the trained generator network is obtained;Based on the trained generator network, multi-plane acoustic hologram is generated.The application combines deep convolutional neural network and differentiable physical propagation layer, to realize high-precision acoustic holographic reconstruction of target sound intensity distribution on multiple spatial planes.

Description

Technical Field

[0001] This invention relates to the field of deep learning technology, and more specifically to a method and system for generating multi-plane acoustic holograms based on the Phys-GAN framework. Background Technology

[0002] Currently, acoustic holography, by recording and reconstructing the amplitude and phase distribution of a sound field in space, enables precise control of sound wave energy in three-dimensional space, and has significant application value in human-computer interaction scenarios such as ultrasound therapy, non-invasive neuromodulation, particle manipulation, and haptic feedback. Traditional acoustic hologram generation methods typically rely on iterative optimization algorithms based on physical models, such as the Iterative Angular Spectrum Approach (IASA) and Direct Search (DS). IASA utilizes an angular spectrum propagation model to perform alternating projections and amplitude constraint updates between the source and target planes until the error between the reconstructed and target sound fields meets a preset threshold. DS, on the other hand, minimizes the mean square error of the reconstructed sound field by traversing and adjusting the phase distribution at the pixel level.

[0003] However, the aforementioned traditional iterative algorithms all have significant limitations in practical applications. First, the IASA algorithm exhibits non-monotonic convergence during optimization, making it prone to getting trapped in local optima. This results in a large amount of speckle noise and severe inter-plane crosstalk in the reconstructed sound field, making it difficult to meet the requirements of high-fidelity sound field reconstruction. Second, while the DS algorithm can guarantee a monotonically decreasing objective function, its pixel-by-pixel search strategy has extremely high computational complexity. It cannot fully traverse the solution space within a limited computation time, making it difficult to obtain the globally optimal phase solution. This is particularly true in multi-plane, high-resolution sound field reconstruction tasks, where its practicality is severely limited. More importantly, both IASA and DS are designed algorithms for a single holographic plane, resulting in inherent bottlenecks in information capacity and spatial reconstruction range. They struggle to encode multiple spatially separated target sound field information on the same hologram, failing to meet the demands of large-capacity, multi-region dynamic sound field parallel control in practical applications.

[0004] Therefore, how to achieve high-precision acoustic holographic reconstruction of the target acoustic intensity distribution on multiple spatial planes is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] In view of the above problems, the present invention is proposed to provide a method and system for generating multiplanar acoustic holograms based on the Phys-GAN framework to overcome or at least partially solve the above problems.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, embodiments of the present invention provide a method for generating multiplanar acoustic holograms based on the Phys-GAN framework, specifically including the following steps: S1. Obtain target acoustic intensity maps on different target planes, and preprocess the target acoustic intensity maps; S2. Construct a Phys-GAN network architecture, which includes a generator network and a discriminator network. Input the target acoustic intensity map into the generator network and output a phase hologram corresponding to the source plane through the generator network. S3. Based on the phase hologram and the preset source plane amplitude distribution, construct the source plane complex sound field, and propagate the source sound field to each of the target planes through the acoustic propagation operator to obtain the reconstructed sound intensity distribution map; S4. Input the reconstructed sound intensity distribution map as a fake sample and the target sound intensity distribution map as a real sample into the discriminator network, calculate the adversarial loss, and calculate the reconstruction loss based on the reconstructed sound intensity distribution map and the target sound intensity distribution map. S5. Construct a generator total loss function based on the adversarial loss and the reconstruction loss, and update the parameters of the generator network using the total loss function until a preset convergence condition is met to obtain the trained generator network. S6. Generate a multiplanar acoustic hologram based on the trained generator network.

[0008] Further, in step S1, the process of preprocessing the target acoustic intensity map includes: The target acoustic intensity maps of N different target planes are stacked in the channel dimension to form an input tensor of size H×W×N; Wherein, H and W are the height and width of the target acoustic intensity map, respectively.

[0009] Furthermore, the generator network described in step S2 adopts a U-Net architecture; The U-Net architecture includes an encoder, a bottleneck layer, and a decoder. The encoder extracts multi-scale sound field features through stepwise downsampling. The decoder restores spatial resolution through transposed convolution and performs channel concatenation between the feature maps of the corresponding layers of the encoder and the upsampled feature maps of the decoder through skip connections. The bottleneck layer is located at the bottom layer of the U-Net architecture network and is used to capture highly abstract features of the sound field distribution.

[0010] Furthermore, in step S3, the acoustic propagation operator is a differentiable propagation operator based on the angular spectrum method. The differentiable propagation operator is used to provide gradient information of the physical propagation of sound waves during the back propagation process of the generator network.

[0011] Furthermore, in step S5, the generator's total loss function further includes a total variation regularization term, which is expressed as:

[0012] in, For the generated phase map, These are the gradient operations for the image in the horizontal and vertical directions, respectively.

[0013] Furthermore, the generator's total loss function is expressed as:

[0014] in, λ rec To reconstruct the loss weights, L rec To rebuild the losses, λ adv To counteract the loss of weight, L adv To combat the losses.

[0015] Secondly, embodiments of the present invention provide a multi-plane acoustic hologram generation system based on the Phys-GAN framework, comprising: A generator for extracting features from a multiplane acoustic intensity map and outputting a phase map of a holographic surface; Discriminator, the discriminator being used to determine the difference between the true sound intensity map and the reconstructed sound intensity map obtained by propagation of the phase map; An angular spectrum propagation layer, which acts as a non-learnable physical propagation module, maps the generated phase map to the reconstructed sound intensity map of each plane. The loss function module jointly considers physical reconstruction error and adversarial loss, guiding the network to generate phase holograms during training.

[0016] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method and system for generating multi-planar acoustic holograms based on the Phys-GAN framework, which has the following beneficial effects: 1. This invention proposes a physics-guided deep learning framework—Phys-GAN—for multi-plane reconstruction tasks and high-capacity dynamic sound field control scenarios. This method is based on a Generative Adversarial Network (GAN) structure, integrating a deep convolutional neural network with a differentiable physical propagation layer to achieve high-precision acoustic holographic reconstruction of target sound intensity distribution across multiple spatial planes. The physical propagation layer introduces a sound wave propagation mechanism, enabling the model to model acoustic physical processes and ensuring consistency between the generated amplitude hologram and the physical model. Phys-GAN requires only one input data point: a set of target images indicating the reconstruction pattern at different heights. The network parameters are automatically optimized through the interaction between the neural network and the physical model, achieving accurate reconstruction of multi-plane acoustic holograms. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0018] Figure 1 This is a flowchart of the multi-plane acoustic hologram generation method provided in this embodiment of the invention; Figure 2 This is a schematic diagram of the multi-plane acoustic hologram generation process provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the generator provided in an embodiment of the present invention; Figure 4 This is a structural diagram of the multi-plane acoustic hologram generation system provided in an embodiment of the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] This invention discloses a method for generating multiplanar acoustic holograms based on the Phys-GAN framework, such as... Figure 1 As shown, the specific steps include: S1. Obtain target acoustic intensity maps on different target planes, and preprocess the target acoustic intensity maps; S2. Construct a Phys-GAN network architecture, which includes a generator network and a discriminator network. Input the target acoustic intensity map into the generator network and output a phase hologram corresponding to the source plane through the generator network. S3. Based on the phase hologram and the preset source plane amplitude distribution, construct the source plane complex sound field, and propagate the source sound field to each of the target planes through the acoustic propagation operator to obtain the reconstructed sound intensity distribution map; S4. Input the reconstructed sound intensity distribution map as a fake sample and the target sound intensity distribution map as a real sample into the discriminator network, calculate the adversarial loss, and calculate the reconstruction loss based on the reconstructed sound intensity distribution map and the target sound intensity distribution map. S5. Construct a generator total loss function based on the adversarial loss and the reconstruction loss, and update the parameters of the generator network using the total loss function until a preset convergence condition is met to obtain the trained generator network. S6. Generate a multiplanar acoustic hologram based on the trained generator network.

[0021] This invention proposes a physics-guided deep learning framework—Phys-GAN—for multi-plane reconstruction tasks and high-capacity dynamic sound field control scenarios. Based on a generative adversarial network (GAN) structure, this method integrates a deep convolutional neural network with a differentiable physical propagation layer to achieve high-precision acoustic holographic reconstruction of target sound intensity distribution across multiple spatial planes. The physical propagation layer introduces a sound wave propagation mechanism, enabling the model to model acoustic physics processes and ensuring consistency between the generated amplitude hologram and the physical model. Phys-GAN requires only one input data set—a set of target images indicating the reconstruction pattern at different heights. The network parameters are automatically optimized through the interaction between the neural network and the physical model, achieving accurate reconstruction of multi-plane acoustic holograms.

[0022] The following is a detailed description of each of the above steps: In step S1, firstly, the data at different heights on different target planes are obtained. Z 1 ，Z 2 ，……，Z N ) target acoustic intensity map I target { I 1 ，I 2 ，……，I N}, initialize the propagator and preprocess the acquired target acoustic intensity map; In this embodiment, the target acoustic intensity maps obtained for training are derived from publicly available datasets, including the EMNIST dataset and the QuickDraw dataset. These datasets are all publicly available data resources, providing diverse image samples for model training.

[0023] During model training, the dataset is divided into training, validation, and test sets in a ratio of 8:1:1 to ensure the objectivity and generalization ability of the model evaluation.

[0024] In terms of data preprocessing, the original images were first uniformly resized, with all input images scaled to 50×50 pixels to match the physical size requirements of the phased array (PTA) system. Subsequently, the image data was normalized, linearly mapping pixel values ​​to the [0,1] interval to improve the stability and convergence performance of model training.

[0025] In step S2, the Phys-GAN network architecture is constructed, as follows: Figure 2 As shown, the Phys-GAN network architecture consists of a generator network and a discriminator network, and incorporates a physical model of sound wave propagation to construct a training feedback mechanism. The core objective of Phys-GAN is to learn and generate source phase holograms from the sound intensity distributions on multiple target planes, propagate the angular spectrum to each target plane, reconstruct its sound intensity distribution, and achieve high-fidelity reconstruction of multi-plane sound fields.

[0026] During network training, the generator aims to generate the source phase distribution corresponding to the multi-planar target sound field, while the discriminator is responsible for distinguishing the real target sound intensity pattern from the sound intensity pattern reconstructed after angular spectrum propagation of the source phase output by the generator. The generator ensures point-by-point physical accuracy by minimizing the mean square error (MSE) between the reconstructed sound field and the target sound field; it utilizes adversarial loss to drive the generated sound field to approximate the real sound field in statistical distribution and spatial characteristics, effectively mitigating the over-smoothing problem that might be caused by a single MSE loss. The discriminator receives the real sound intensity map and the generated sound intensity map, outputting the probability of whether a sample is real or fake. Its training objective is to maximize the probability of discriminating against real samples and minimize the probability of misclassifying generated samples, continuously improving its discriminative ability. The generator, based on the gradient signal fed back from the discriminator, adjusts its own parameters through backpropagation and optimizes them in conjunction with the MSE loss to achieve accurate generation of the multi-planar sound field.

[0027] The generator network uses an improved U-Net architecture as its backbone. U-Net's unique "U"-shaped structure comprises an encoder, a bottleneck layer, and a decoder, which can effectively extract deep semantic features while preserving shallow spatial details, making it suitable for pixel-level phase prediction tasks.

[0028] The encoder consists of a series of stacked convolutional modules; each module contains a convolutional layer, a batch normalization layer, and a LeakyReLU activation function; the encoder extracts multi-scale sound field features from the input multi-planar sound intensity map by compressing the spatial size of the feature map through progressive downsampling and increasing the number of channels, from local texture to global structure.

[0029] The bottleneck layer is located at the bottom layer of the network and is used to capture highly abstract features of the sound field distribution. To enhance gradient propagation and prevent network degradation, residual connections are introduced in the bottleneck layer and deep convolutional blocks, enabling the network to learn identity mappings more easily.

[0030] The decoder gradually restores the spatial resolution of the feature maps through transposed convolutions. At each layer of decoding, the network performs channel-by-channel concatenation between the feature map of the corresponding encoder layer and the currently upsampled feature map through skip connections. This mechanism effectively compensates for the high-frequency spatial information lost during downsampling, which is crucial for high-fidelity reconstruction of sound field details.

[0031] Physical prior constraints are introduced into the generator network to improve the performance of the generated phase map in terms of physical realizability and spatial smoothness. In addition to applying reasonable numerical constraints to the phase values ​​during the output stage, a total variational regularization term is introduced during network training to effectively suppress high-frequency noise components in the phase distribution, enhancing its spatial continuity and structural stability. The phase map output by the generator is directly used as input to the angular spectrum propagation layer. The sound field reconstruction effect is evaluated through forward computation of the physical propagation model, thus constructing a closed-loop constraint and feedback mechanism based on the physical model. This end-to-end deep learning architecture, as shown... Figure 3 As shown, the generator can automatically learn the complex physical laws of sound wave back propagation and achieve high-precision inversion from sparse sound intensity sampling to holographic phase map.

[0032] Figure 3 The network architecture of the generator shown is divided into three parts: the input part, the backbone network, and the output part.

[0033] 1. The input section is used to input data, i.e., a schematic diagram of the expected multi-plane sound field. The left side of the image shows the sound intensity distribution maps of two different target planes as the input tensor, as illustrated in the example of the sound field distribution for numbers "1" and "2". The input size is 2×50×50. Here, "2" represents the number of channels (corresponding to two sound intensity maps of the target planes), and "50×50" represents the spatial resolution of the sound field. By integrating the spatial information of different planes into a three-dimensional tensor, the convolution kernel can simultaneously observe the intensity contrast of the two planes during scanning, thereby learning the physical correlations (interference, diffraction relationships) between them.

[0034] 2. The backbone network consists of three parts: the encoder path, the bottleneck layer, and the decoder path.

[0035] (1) Encoder path (left-side down) The encoder is responsible for feature extraction and spatial compression. During this process, the number of channels doubles progressively with depth, from 16 to 32 to 64 to 128. 3×3 convolutions (orange arrows) are used to extract local spatial features. 2×2 max pooling (yellow down arrows) downsamples at the end of each stage, halving the spatial size while increasing the receptive field. Feature blocks are represented by green vertical bars in the diagram, with numbers indicating the current number of channels. In this stage, the original digital image disappears, transforming into a high-dimensional feature vector containing highly generalized information.

[0036] (2) Bottleneck layer (bottom center) This is the lowest layer of the network, used to capture sound field features. At this point, the feature map reaches its minimum resolution and maximum channel depth (256 channels). Dropout (dark green square) with a probability of 0.3 is introduced at the bottom to prevent overfitting and improve generalization ability.

[0037] (3) Decoder path (upper right side) The decoder is responsible for restoring abstract features to their original spatial resolution. Upsampling (yellow upward arrow) uses 2×2 upsampling to progressively restore the feature map size. Channel fusion uses skip connections (red long arrow) to concatenate the feature maps of the corresponding layers of the encoder (yellow blocks, block copied) with the current feature map of the decoder. For example, the annotations 128+256, 64+128, 32+64, and 16+32 in the figure represent the combination of deep semantic information and shallow spatial details, which is crucial for high-fidelity sound field reconstruction. Dropout is applied at different stages of the decoding process, with 0.1 (purple square) and 0.2 (blue square) dropout values ​​introduced to enhance network stability.

[0038] 3. Output Part: 1×1 Convolution (Green Arrow) In the final stage, a 1×1 convolution is used to map the multi-channel features into a single-channel phase map. Activation Function: The Tanh activation function is applied here to restrict the output to... The right side of the image shows the predicted source plane phase hologram, with a size of [insert size here]. It contains the phase information needed to reconstruct the sound field of multiple targets.

[0039] Legend: The legend in the upper right corner of the image clearly defines each component: Convolutional layers: 3×3 (orange arrow) and 1×1 (green arrow).

[0040] Sampling layers: Max Pooling (downward) and Up Sampling (upward).

[0041] Connections: Skip connection (red arrow) and Block copied (yellow block).

[0042] Dropout: Three levels (0.1 Purple, 0.2 Blue, 0.3 Green).

[0043] This network balances the depth and spatial accuracy of features through a U-shaped symmetric structure. By inputting multi-plane acoustic intensity data, utilizing the detail information preserved by skip connections, and combining the robustness of Dropout and residual connections, the generator can efficiently and in real-time calculate physically realizable source plane phase holograms, providing accurate initial phases for subsequent physical propagation simulations (angular spectrum propagation layers).

[0044] The expression for the total variational regularization term is:

[0045] in, This represents the generated phase map. These are the gradient operations for the image in the horizontal and vertical directions, respectively. This regularization term significantly enhances the spatial continuity and structural stability of the phase map by suppressing high-frequency noise components in the phase distribution.

[0046] The main function of the discriminator network is to distinguish between the real target acoustic hologram and the acoustic hologram predicted by the generator and reconstructed after physical propagation, thereby providing the generator with an effective adversarial feedback signal.

[0047] In this embodiment, the real sample is defined as the desired target acoustic hologram. The fake sample, on the other hand, is a reconstructed acoustic hologram obtained by propagating the source phase hologram output by the generator through a linear acoustic model (LAM). .

[0048] The above describes the components of the Phys-GAN network architecture; the following describes the image input and output process: The generator network takes as input a set of normalized acoustic intensity images of N target planes. To fully utilize the spatial correlation across multiple planes, these N acoustic intensity images are stacked along the channel dimension to form an input tensor of size H×W, where H and W are the height and width of the image, respectively. The network output is a phase hologram of the source plane. Considering the periodicity and physical meaning of the phase, the output layer uses the Tanh activation function to strictly constrain the output values ​​within a certain range. This not only avoids phase value overflow but also accelerates network convergence.

[0049] The discriminator takes the sound intensity distribution map as input and outputs the probability that the sample belongs to the acoustic hologram of a real target. For real samples... The discriminator aims to output a probability close to 1; however, for counterfeit samples... Its goal is to output a probability close to 0. In this way, the discriminator can progressively learn the discriminative features of the real acoustic hologram in terms of spatial distribution and statistical properties.

[0050] During training, the optimization objective of the discriminator can be formally expressed as:

[0051] The goal is to maximize the probability of correctly classifying real samples while minimizing the probability of misclassifying generated samples. To achieve this objective, this paper uses a binary cross-entropy loss function to supervise the discriminator, with the overall loss function defined as the sum of the loss for real samples and the loss for fake samples:

[0052] The BCE loss for real samples and the BCE loss for fake samples are respectively expressed as:

[0053]

[0054] in Indicates the labels of real samples. This indicates that the sample label was forged. It represents logarithmic operations.

[0055] By minimizing the aforementioned loss function, the discriminator can continuously improve its ability to distinguish between the real target acoustic hologram and the reconstructed acoustic hologram. During adversarial training with the generator, the discriminator provides the generator with stable and effective gradient feedback, thereby promoting the generator to gradually generate reconstructed results that are closer to the real target acoustic hologram in terms of spatial structure and energy distribution.

[0056]

[0057] Table 1. Phys-GAN Network Framework In one embodiment, the algorithm flow for physical reinforcement self-supervised learning is as follows: Initialize the generator network G and the discriminator network D; A uniform amplitude distribution A is set on the source plane. U ; Constructing a differentiable acoustic wave propagation operator based on the angular spectrum method (ASM) , used to describe the acoustic propagation relationship between the source plane and each target plane; do for each training epoch; Discriminator Update phase; Sample real multiplane sound intensity maps from the target dataset. and assign a real label 1; Input the actual sound intensity map into the discriminator to obtain the discrimination result; Calculate the loss of the real sample based on the binary cross-entropy loss function. ; target acoustic intensity map Input generator to generate source plane phase hologram;

[0058] By combining a uniform amplitude distribution, a complex sound field is constructed in the source plane.

[0059] The source sound field is propagated to each target plane using an acoustic propagation operator to obtain the reconstructed sound intensity distribution.

[0060] The reconstructed acoustic intensity map is used as input to the fake sample discriminator, and a fake label of 0 is assigned. Calculate the loss of fake samples ; Update the discriminator parameters so that minimize; Generator G update phase: Calculate the adversarial loss of the generated sound intensity map in the discriminator;

[0061] Calculate the multi-plane reconstruction error (mean square error);

[0062] Construct the generator's total loss function;

[0063] Backpropagation and updating of generator parameters; end for; Return the trained generator G and discriminator D.

[0064] In step S3, the reconstructed sound intensity distribution map is obtained; After constructing the network, in each training iteration, a set of target acoustic intensity distribution maps (representing the desired acoustic intensity patterns at different altitudes) are input into the generator network G. The generator network G outputs the corresponding source plane phase hologram. φBased on the phase hologram φ and the preset source plane amplitude distribution A, a source plane complex sound field is constructed. The source plane complex sound field is propagated to each target plane using a differentiable acoustic propagation operator to obtain the reconstructed complex sound field on each target plane. The reconstructed sound intensity distribution map on each target plane is calculated. The reconstructed sound intensity distribution maps of all target planes together constitute a multi-plane reconstructed sound intensity distribution map set.

[0065] In step S4, the reconstructed acoustic intensity distribution map obtained by forward propagation of the acoustic propagation operator is defined as a fake sample, and the preprocessed target acoustic intensity map is defined as a real sample; the real sample and the fake sample are simultaneously input into the discriminator network to complete the adversarial loss calculation; at the same time, the reconstruction loss is calculated based on the pixel-level numerical difference between the reconstructed acoustic intensity distribution map and the target acoustic intensity map. Real samples are assigned a label value of 1, representing real target sound field data; fake samples are assigned a label value of 0, representing simulated data generated by the model. Real and fake samples are input into the discriminator network in batches. The discriminator network distinguishes between the two types of samples based on their spatial distribution and statistical characteristics, and outputs the probability value corresponding to the real sample.

[0066] The adversarial loss is calculated using a binary cross-entropy loss function, which is the sum of the discriminant loss of the discriminator for real samples and the discriminant loss for fake samples. By minimizing this adversarial loss, the discriminator's ability to distinguish between real and reconstructed sound fields is optimized, while adversarial gradient feedback is provided to the generator network, driving the generator to output a phase hologram that is more physically realistic.

[0067] Using the mean square error as the basis for calculating the reconstruction loss, the mean square error between the reconstructed sound intensity distribution map and the target acoustic intensity map is calculated pixel by pixel to obtain the reconstruction loss. The reconstruction loss is used to constrain the phase hologram output by the generator to maintain a high degree of physical consistency with the target sound field after physical propagation, so as to avoid problems such as excessive smoothing and loss of details in the reconstruction results.

[0068] In step S5, the generator total loss function is constructed and the network parameters are updated. The generator total loss function consists of two parts: adversarial loss and reconstruction loss. The expression for the generator total loss function is as follows:

[0069] in, λ rec To reconstruct the loss weights, L rec To rebuild the losses, λ adv To counteract the loss of weight, L adv To combat the losses.

[0070] Using the generator's total loss function, the parameters of the generator network G are updated using gradient descent; simultaneously, the parameters of the discriminator network D are updated according to a preset discriminator loss function; steps S3 to S5 are iteratively executed until a preset convergence condition is met. The convergence condition may be reaching a preset maximum number of iterations, such as 3000, or the generator's total loss function value decreasing below a preset threshold.

[0071] In this embodiment, Set to 10, Setting it to 1, due to the significant difference between adversarial loss and reconstruction loss, a weighting coefficient is introduced to balance the various loss terms to avoid one loss term dominating the optimization process during training. Considering the high requirements for physical consistency in acoustic holographic reconstruction tasks, the weight of the reconstruction loss is appropriately increased so that the model prioritizes sound field reconstruction accuracy while ensuring adversarial generation capability. After repeated determination, when... Set to 10, Setting it to 1 yields the best results, allowing for both objectives to be met simultaneously.

[0072] In step S6, a multi-plane acoustic hologram is generated. After training, the trained generator network is used for the actual multi-plane acoustic hologram generation task. Specifically, the desired multi-plane target acoustic intensity distribution map is input into the trained generator network, and its output is the corresponding source plane phase hologram. This phase hologram can be combined with a preset uniform amplitude distribution to form a complete source plane complex sound field, which in turn drives the phased array transducer array to achieve high-precision, high-fidelity reconstruction of a specified acoustic intensity mode on multiple target planes.

[0073] Example: In this embodiment, the training dataset used is derived from publicly available datasets, including the EMNIST dataset and the QuickDraw dataset. These datasets are all publicly available data resources, providing diverse image samples for model training. The development environment used is PyCharm, and the entire process is completed using Python. All work was performed on a workstation equipped with an Intel® Xeon® Gold 5218 CPU (2.3GHz), 128GB of RAM, and an NVIDIA RTX 2080Ti GPU.

[0074] In the Phys-GAN framework, the generator network predicts the phase distribution on the holographic plane, while the discriminator and physical constraints work together in the optimization process through an embedded acoustic wave propagation model. Network parameters are updated using the Adam optimizer with a learning rate of 0.001. The optimization process is a gradient descent-based physically consistent optimization process for a given target amplitude distribution.

[0075] Before optimization begins, the weight parameters in the generator network are randomly initialized using a truncated normal distribution with a standard deviation of 0.1, and the bias term is initialized to 1. To improve the stability of the optimization process and mitigate the risk of getting trapped in local optima, uniformly distributed random noise with an amplitude range of 0–0.05 is superimposed onto the input target amplitude hologram during each iteration. This noise is introduced only during the optimization phase and removed after optimization is complete.

[0076] In each iteration, the phase distribution output by the generator is first propagated forward through a differentiable physical propagation layer. This propagation process is based on the angular spectrum method and is used to simulate the propagation behavior of sound waves from the holographic plane to the target plane. Subsequently, the reconstructed sound intensity distribution is compared with the target amplitude mode, and a loss function is constructed based on the reconstruction error and physical consistency constraints, thereby updating the network parameters in reverse.

[0077] After the optimization process is complete, input noise is removed, and the corresponding phase hologram is obtained based on the network output in the final converged state. It should be noted that when the input target amplitude mode changes, in order to ensure the quality of the reconstructed sound field, Phys-GAN needs to re-execute the optimization process from the same random initial state.

[0078] In this embodiment, the size of the input target amplitude image is 50×50. In both dual-plane and multi-plane acoustic holographic design tasks, the Phys-GAN method converges to a stable solution within approximately 3000 iterations, and the computation time for a single optimization on a GPU is on the order of hundreds of seconds, verifying that the method has acceptable computational efficiency while ensuring reconstruction quality.

[0079] Based on the same inventive concept, embodiments of the present invention also provide a multi-planar acoustic hologram generation system based on the Phys-GAN framework, such as... Figure 4 As shown, it includes: A generator for extracting features from a multiplane acoustic intensity map and outputting a phase map of a holographic surface; Discriminator, the discriminator being used to determine the difference between the true sound intensity map and the reconstructed sound intensity map obtained by propagation of the phase map; An angular spectrum propagation layer, which acts as a non-learnable physical propagation module, maps the generated phase map to the reconstructed sound intensity map of each plane. The loss function module jointly considers physical reconstruction error and adversarial loss, guiding the network to generate phase holograms during training.

[0080] This invention embeds a differentiable acoustic propagation operator based on the angular spectrum method after the generator network, explicitly incorporating the forward propagation process of sound waves into the backward propagation gradient link. This ensures that the phase hologram output by the generator strictly adheres to the constraints of the wave equation. Compared to purely data-driven "black box" deep learning methods, the phase distribution generated by this invention is physically realizable, avoiding sound field distortion caused by violating physical laws when applied to actual transducer arrays. This significantly improves the reliability of the transfer from digital design to physical experiments.

[0081] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0082] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for generating multiplanar acoustic holograms based on the Phys-GAN framework, characterized in that, Includes the following steps: S1. Obtain target acoustic intensity maps on different target planes, and preprocess the target acoustic intensity maps; S2. Construct a Phys-GAN network architecture, which includes a generator network and a discriminator network. Input the target acoustic intensity map into the generator network and output a phase hologram corresponding to the source plane through the generator network. S3. Based on the phase hologram and the preset source plane amplitude distribution, construct the source plane complex sound field, and propagate the source sound field to each of the target planes through the acoustic propagation operator to obtain the reconstructed sound intensity distribution map; S4. Input the reconstructed sound intensity distribution map as a fake sample and the target sound intensity distribution map as a real sample into the discriminator network, calculate the adversarial loss, and calculate the reconstruction loss based on the reconstructed sound intensity distribution map and the target sound intensity distribution map. S5. Construct a generator total loss function based on the adversarial loss and the reconstruction loss, and update the parameters of the generator network using the total loss function until a preset convergence condition is met to obtain the trained generator network. S6. Generate a multiplanar acoustic hologram based on the trained generator network.

2. The method for generating multiplanar acoustic holograms based on the Phys-GAN framework as described in claim 1, characterized in that, In step S1, the process of preprocessing the target acoustic intensity map includes: The target acoustic intensity maps of N different target planes are stacked in the channel dimension to form an input tensor of size H×W×N; Wherein, H and W are the height and width of the target acoustic intensity map, respectively.

3. The method for generating multiplanar acoustic holograms based on the Phys-GAN framework as described in claim 1, characterized in that, The generator network described in step S2 adopts a U-Net architecture; The U-Net architecture includes an encoder, a bottleneck layer, and a decoder. The encoder extracts multi-scale sound field features through stepwise downsampling. The decoder restores spatial resolution through transposed convolution and performs channel concatenation between the feature maps of the corresponding layers of the encoder and the upsampled feature maps of the decoder through skip connections. The bottleneck layer is located at the bottom layer of the U-Net architecture network and is used to capture highly abstract features of the sound field distribution.

4. The method for generating multiplanar acoustic holograms based on the Phys-GAN framework as described in claim 1, characterized in that, In step S3, the acoustic propagation operator is a differentiable propagation operator based on the angular spectrum method. The differentiable propagation operator is used to provide gradient information of the physical propagation of sound waves during the back propagation process of the generator network.

5. The method for generating multiplanar acoustic holograms based on the Phys-GAN framework as described in claim 1, characterized in that, In step S5, the generator's total loss function further includes a total variation regularization term, which is expressed as: in, For the generated phase map, These are the gradient operations for the image in the horizontal and vertical directions, respectively.

6. The method for generating multiplanar acoustic holograms based on the Phys-GAN framework as described in claim 5, characterized in that, The generator's total loss function is expressed as: in, λ rec To reconstruct the loss weights, L rec To rebuild the losses, λ adv To counteract the loss of weight, L adv To combat the losses.

7. A multi-planar acoustic hologram generation system based on the Phys-GAN framework, characterized in that, include: A generator for extracting features from a multiplane acoustic intensity map and outputting a phase map of a holographic surface; Discriminator, the discriminator being used to determine the difference between the true sound intensity map and the reconstructed sound intensity map obtained by propagation of the phase map; An angular spectrum propagation layer, which acts as a non-learnable physical propagation module, maps the generated phase map to the reconstructed sound intensity map of each plane. The loss function module jointly considers physical reconstruction error and adversarial loss, guiding the network to generate phase holograms during training.

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