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This paper presents a method for generating dynamic caustic patterns by utilising dual-optimised holographic fields with Phased Array Transducer (PAT). Building on previous research in static caustic optimisation and ultrasonic manipulation, this approach employs computational techniques to dynamically shape fluid surfaces, thereby creating controllable and real-time caustic images. The system employs a Digital Twin framework, which enables iterative feedback and refinement, thereby improving the accuracy and quality of the caustic patterns produced. This paper extends the foundational work in caustic generation by integrating liquid surfaces as refractive media. This concept has previously been explored in simulations but not fully realised in practical applications. The utilisation of ultrasound to directly manipulate these surfaces enables the generation of dynamic caustics with a high degree of flexibility. The Digital Twin approach further enhances this process by allowing for precise adjustments and optimisation based on real-time feedback. Experimental results demonstrate the technique’s capacity to generate continuous animations and complex caustic patterns at high frequencies. Although there are limitations in contrast and resolution compared to solid-surface methods, this approach offers advantages in terms of real-time adaptability and scalability. This technique has the potential to be applied in a number of areas, including interactive displays, artistic installations and educational tools. This research builds upon the work of previous researchers in the fields of caustics optimisation, ultrasonic manipulation, and computational displays. Future research will concentrate on enhancing the resolution and intricacy of the generated patterns.

For near-field acoustic holography, sparse array measurement for cost reduction can result in inaccuracy due to aliasing error. To attenuate it, there are data-driven methods based on artificial intelligence theories. Among these, the JTCSA-NAH method has not adopted measures for robustness enhancement despite its high accuracy in practice. In this work, the influence of measuring noise on JTCSA-NAH is analyzed followed by the principle of adding Gaussian noise for robustness improvement. Based on the relevant prior conditions, the ICCSA-NAH method, which relies on self-identity constraint data working as the Kalman gain is proposed. Subsequently, numerical example and experiment are carried out, and the results show that compared with JTCSA-NAH method, the mean errors of near-field vibration velocity reconstruction are theoretically and experimentally reduced from 15.19% and 23.64% to 6.03% and 12.45%, respectively, by the ICCSA-NAH method, which verifies the feasibility and superiority of the proposed method.

In this manuscript, we describe a novel methodology for nearfield acoustic holography (NAH). The proposed technique is based on convolutional neural networks, with autoencoder architecture, to reconstruct the pressure and velocity fields on the surface of the vibrating structure using the sampled pressure soundfield on the holographic plane as input. The loss function used for training the network is based on a combination of two components. The first component is the error in the reconstructed velocity. The second component is the error between the sound pressure on the holographic plane and its estimate obtained from forward propagating the pressure and velocity fields on the structure through the Kirchhoff–Helmholtz integral; thus, bringing some knowledge about the physics of the process under study into the estimation algorithm. Due to the explicit presence of the Kirchhoff–Helmholtz integral in the loss function, we name the proposed technique the Kirchhoff–Helmholtz-based convolutional neural network, KHCNN. KHCNN has been tested on two large datasets of rectangular plates and violin shells. Results show that it attains very good accuracy, with a gain in the NMSE of the estimated velocity field that can top 10 dB, with respect to state-of-the-art techniques. The same trend is observed if the normalized cross correlation is used as a metric.

The performance of near-field acoustic holography (NAH) with a sparse sampling rate will be affected by spatial aliasing or inverse ill-posed equations. Through a 3D convolution neural network (CNN) and stacked autoencoder framework (CSA), the data-driven CSA-NAH method can solve this problem by utilizing the information from data in each dimension. In this paper, the cylindrical translation window (CTW) is introduced to truncate and roll out the cylindrical image to compensate for the loss of circumferential features at the truncation edge. Combined with the CSA-NAH method, a cylindrical NAH method based on stacked 3D-CNN layers (CS3C) for sparse sampling is proposed, and its feasibility is verified numerically. In addition, the planar NAH method based on the Paulis–Gerchberg extrapolation interpolation algorithm (PGa) is introduced into the cylindrical coordinate system, and compared with the proposed method. The results show that, under the same conditions, the reconstruction error rate of the CS3C-NAH method is reduced by nearly 50%, and the effect is significant.

While conventional Bayesian compressive sensing exploits signal sparsity for accurate sound field reconstruction from under-sampled measurements, its practicality is limited by high computational complexity and slow convergence. To address these limitations, this paper proposes a variational Bayesian compressive sensing framework integrated with equivalent source modeling for sound field reconstruction. The approach first establishes a sparse representation of the sound field using the equivalent source method, and then assigns hierarchical prior distributions to the equivalent source strengths and the noise precision within this Bayesian model. Mean-field variational inference is adopted to derive an analytically tractable approximation to the true posterior distribution by minimizing the Kullback–Leibler divergence, thus enabling efficient estimation of the equivalent source strengths and subsequent high-accuracy sound field reconstruction. This proposed method retains the desirable statistical advantages of Bayesian modeling while enhancing computational efficiency. Numerical simulations and experiments validate that the proposed method achieves superior reconstruction accuracy compared with conventional Bayesian compressive sensing and orthogonal matching pursuit algorithm, with significantly reduced computational burden and enhanced robustness in low signal-to-noise ratio scenarios.

In this study, a sound source modelling method using near-field acoustic holography was proposed as a method to preserve the acoustic radiation characteristics of acoustic heritage, and a series of processes to archive and reproduce the radiation characteristics of the Sacred Bell of King Seongdeok were realized by the proposed approach. The most important essence of an object that produces sound, such as a musical instrument, is the sound itself. Therefore, it is more important to preserve the sound so that future generations can hear it, rather than information such as the appearance, e.g., photo or drawing. However, it cannot be said that all information of sounds is preserved simply by recording well at one point. The sound field radiating from an object also contains spatial radiation characteristics, and it is necessary to preserve information about this. In this study, an actual measurement and reconstruction process based on sound source modeling techniques was proposed to record and reproduce the spatial acoustic radiation characteristics of the Sacred Bell of King Seongdeok. Throughout the process, it was confirmed that the sound field reproduced well represents the unique characteristics of the actual sound heritage and through this, it is expected that a more faithful level of preservation of cultural heritage in the form of intangible sound will be possible.

To solve the problem of sound field reconstruction with fewer measurement points, a sound field reconstruction method based on Bayesian compressive sensing is proposed. In this method, a sound field reconstruction model based on a combination of the equivalent source method and sparse Bayesian compressive sensing is established. The MacKay iteration of the relevant vector machine is used to infer the hyperparameters and estimate the maximum a posteriori probability of both the sound source strength and noise variance. The optimal solution for sparse coefficients with an equivalent sound source is determined to achieve the sparse reconstruction of the sound field. The numerical simulation results demonstrate that the proposed method has higher accuracy over the entire frequency range compared to the equivalent source method, indicating a better reconstruction performance and wider frequency applicability with undersampling. Moreover, in environments with low signal-to-noise ratios, the proposed method exhibits significantly lower reconstruction errors than the equivalent source method, indicating a superior anti-noise performance and greater robustness in sound field reconstruction. The experimental results further verify the superiority and reliability of the proposed method for sound field reconstruction with limited measurement points.

The acoustic holography method was used to characterize a therapeutic focused fully populated 256-element ultrasonic transducer array. Elements of the array with the shape of equal area polygons are densely arranged in an irregular pattern on a spherically concave surface with a radius of curvature of 150 mm and a diameter of 200 mm. The array has a central frequency of 1.2 MHz and is designed to operate in water. The performance of individual array elements was studied based on the holographically reconstructed normal velocity distribution over the array surface. It was shown that with the same electrical signals applied to the elements, their acoustic responses had a phase deviation relative to the nominal values, which can be caused either by the asphericity of the array surface, or by the introduction of additional phase delays by the electrical matching network. To compensate for the detected parasitic phase shifts of the elements and restore the effective sphericity of the radiating surface, the Verasonics V-1 control system was used. The hologram measured after making the correction, as well as the shape of the focal region and acoustic pressure magnitude at the focus, separately measured by a hydrophone, showed that the proposed method reconstructed the nominal operating parameters of the array with high accuracy .

Near-field acoustic holography (NAH) based on compressing sensing (CS) theory enables accurate reconstruction of sound fields using a limited number of sampling points. However, the successful implementation of this technique depends on two crucial factors: (1) the appropriate selection or construction of the spatial basis and (2) an effective sparse regularization process. To enhance reconstruction performance for elongated sound sources, this paper proposes a novel sound field reconstruction method that combines prolate spheroidal wave functions (PSWFs) with the orthogonal matching pursuit (OMP) algorithm. In this method, PSWFs serve as a sparse spatial basis for representing the radiated sound field. The sparse coefficients are determined by the OMP algorithm in a linear subspace composed of basic functions that best match the residual error. The OMP algorithm effectively identifies significant components before potentially selecting incorrect ones by setting an appropriate stopping rule. Numerical simulations are conducted using a line-array source model. The results show that the proposed method can accurately reconstruct the sound pressures of the elongated source model using a relatively small number of samplings. In addition, the proposed method exhibits robustness across a wide frequency range, diverse array configurations and various sampling numbers. The experimental results further validate the feasibility and reliability of the proposed method.

Acoustic holography technology is widely used in the field of ultrasound due to its capability to achieve complex acoustic fields. The traditional acoustic holography method based on single-phase holograms is limited due to its inability to complete acoustic field control with high dynamics and accuracy. Here, we propose a method for constructing an acoustic holographic model, introducing an ultrasonic array to provide dynamic amplitude control degrees of freedom, and combining the dynamically controllable ultrasonic array and high-precision acoustic hologram to achieve the highest acoustic field accuracy and dynamic range. This simulation method has been proven to be applicable to both simple linear patterns and complex surface patterns. Moreover, it is possible to reconstruct the degree of freedom of the target plane amplitude effectively and achieve a breakthrough in high information content. This high-efficiency acoustic field control capability has potential applications in ultrasound imaging, acoustic tweezers, and neuromodulation.