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The total focusing method (TFM) is often considered to be the ‘gold standard’ for ultrasonic imaging in the field of nondestructive testing. The use of matrix phased arrays as probes allows for high-resolution volumetric TFM imaging. Conventional TFM imaging involves the use of full matrix capture (FMC) for ultrasonic signals acquisition, but in the case of a matrix phased array, this approach is associated with a huge volume of data to be acquired and processed. This severely limits the frame rate of volumetric imaging with 2D probes and necessitates the use of high-end equipment. Thus, the aim of this research was to develop a novel design method for determining the optimal sparse 2D probe configuration for specific conditions of ultrasonic imaging. The developed approach is based on simulated annealing and involves implementing the solution of the sparse matrix phased array layout optimization problem. In order to implement simulated annealing for the aforementioned task, its parameters were set, the acceptance function was introduced, and the approaches were proposed to compute beam directivity diagrams of sparse matrix phased arrays in TFM imaging. Experimental studies have shown that the proposed approach provides high-quality volumetric imaging with a decrease in data volume of up to 84% compared to that obtained using the FMC data acquisition method.

This paper introduces the subarray partition based on the sparse array weighted K‐means clustering method, which extends the conventional K‐means clustering method through the inclusion of a weight matrix approach. This matrix is derived by recording the frequency of each element's occurrence across multiple independent sparse arrays, thereby generating a frequency matrix. The performance of SWKCM is demonstrated through simulations and comparisons with four similar methods. To assess the effectiveness and superiority of the SWKCM, it is applied to the subarray partition of a 40×40 uniform planar phased array and compared with the other four methods. The simulation results show that the proposed SWKCM method maintains comparable sidelobe suppression capabilities to those of KCM, achieving a normalized peak sidelobe level of ‐43.1076 dB. Furthermore, compared to the K‐means clustering method, the sparse array weighted K‐means clustering method significantly enhances the stability of subarray partition outcomes, as evidenced by a reduction in the peak sidelobe level standard deviation from 1.0991 to 0.8104, resulting in a 26.3% decrease in variability.

Sparse arrays have grating lobes in the far field pattern due to the large spacing of elements residing in a rectangular or triangular grid. Random element spacing removes the grating lobes but produces large variations in element density across the aperture. In fact, some areas are so dense that the elements overlap. This paper introduces a low discrepancy sequence (LDS) for generating the element locations in sparse planar arrays without grating lobes. This nonrandom alternative finds an element layout that reduces the grating lobes while keeping the elements far enough apart for practical construction. Our studies consider uniform sparse LDS arrays with 86% less elements than a fully populated array, and numerical results are presented that show these sampling techniques are capable of completely removing the grating lobes of sparse arrays. We present the mathematical formulation for implementing an LDS generated element lattice for sparse planar arrays, and present numerical results on their performance. Multiple array configurations are studied, and we show that these LDS techniques are not impacted by the type/shape of the planar array. Moreover, in comparison between the LDS techniques, we show that the Poisson disk sampling technique outperforms all other approaches and is the recommended LDS technique for sparse arrays.

An optical phased array (OPA) with 2-D circular sparse array aperture has been proposed and demonstrated in the silicon integrated photonic platform. The sparse distribution of the antenna array can realize no grating lobes in 2-D full field of view (FOV). To achieve fast and accurate phase calibration for OPA, an improved rotating element electric field vector algorithm based on golden section search method (GSS-REV) has also been proposed and verified. The 32-element antenna sparse distribution of the proposed OPA is designed and fabricated. A far-field beam steering measurement across 20° × 20° range features the side lobe suppression ratio (SLSR) of larger than 4.81 dB and a full width at half-maximum (FWHM) of approximately 0.63° × 0.59°. The resolvable points are derived to be ∼1076. The OPA chip has also been demonstrated on range measurement with frequency-modulated continuous-wave (FMCW) system.

The ultrasonic phased array total focusing method (TFM) has the advantages of full-range dynamic focusing and high imaging resolution, but the problem of long imaging time limits its practically industrial applications. To reduce the imaging calculation demand of TFM, the locations of active array elements in the sparse array are optimized by combining almost different sets with the genetic algorithm (ADSGA), and corrected based on the consistency of the effective aperture with the equivalent point diffusion function. At the same time, to further increase the imaging efficiency, a sparse-TFM image with lower resolution is obtained by reducing the number of focus points and then interpolated by the new edge-directed interpolation algorithm (NEDI) to obtain a high quality sparse-TFM image. Compared with TFM, the experimental results show that the quantitative accuracy of the proposed method is only decreased by 1.09% when the number of sparse transmitting elements reaches 8 for a 32-element transducer, and the imaging speed is improved by about 16 times with the same final pixel resolution.

With the wide application of additive manufacturing components and composite materials, it is of great significance to detect defects with non-destructive testing methods in the material manufacturing process and in service. Due to the strong attenuation and inhomogeneity characteristics, it is inefficient and poor imaging results to detect its internal defects by conventional ultrasonic testing methods. To improve the detection accuracy, this paper proposes an improved imaging algorithm with time reversal-total focusing method (TR-TFM) imaging technology to improve the defects detection in strongly attenuating materials. The experimental results show that the amplitude of the defect signal is increased by 8.30 dB, and compared with total focusing method (TFM), the diameter of the detected defect with TR-TFM imaging is increased from 1.20 mm to 1.60 mm, which is more adjacent to the accurate size. Meanwhile, with the sparse matrix based on FMC data, TR-TFM could obtain the same image quality with the approximate time of TFM imaging.

The design of conical frustum phased array antennas for air traffic control (ATC) radar systems is addressed. The array architecture, which is controlled by a fully digital beam-forming (DBF) network, is composed by a set of equal vertical modules. Each module consists of a linear sparse array that generates on receive multiple instantaneous beams pointing along different directions in elevation. To reach the best trade-off between the antenna complexity (i.e., minimum number of array elements and/or radio frequency components) and radiation performance (i.e., matching a set of reference patterns), the synthesis problem is formulated in the Compressive Sampling (CS) framework. Then, the positions of the array elements and the complex excitations for generating each single beam are jointly determined through a customized version of the Bayesian CS (BCS) tool. Representative numerical results, concerned with ideal as well as real antenna models, are reported both to validate the proposed design strategy and to assess the effectiveness of the synthesized modular sparse array architecture also in comparison with conventional arrays with uniformly-spaced elements.

The use of sparse matrix phased arrays can increase the speed of 3D-imaging of the internal structure of objects in ultrasonic nondestructive testing using the Total Focusing Method. The sparse transducer configuration determines the quality of the results. An application of Simulated Annealing for determining the configurations of sparse matrix phased arrays is discussed in terms of the restoration of high quality images of the internal structure of test objects. The performance of the configuration obtained by Simulated Annealing is verified by computer modeling.

The utilization of efficient digital self-interference cancellation technology enables the simultaneous transmit and receive (STAR) phased array system to meet most application requirements through STAR capabilities. However, the development of application scenario requirements makes array configuration technology for STAR phased arrays increasingly important. Thus, this paper proposes a sparse shared aperture STAR reconfigurable phased array design based on beam constraints which are achieved by a genetic algorithm. Firstly, a design scheme for transmit and receive arrays with symmetrical shared apertures is adopted to improve the aperture efficiency of both transmit and receive arrays. Then, on the basis of shared aperture, sparse array design is introduced to further reduce system complexity and hardware costs. Finally, the shape of the transmit and receive arrays is determined by constraining the side lobe level (SLL), main lobe gain, and beam width. The simulated results indicate that the SLL of the transmit and receive patterns under beam-constrained design have been reduced by 4.1 dBi and 7.1 dBi, respectively. The cost of SLL improvement is a reduction in transmit gain, receive gain, and EII of 1.9 dBi, 2.1 dBi, and 3.9 dB, respectively. When the sparsity ratio is greater than 0.78, the SLL suppression effect is also significant, and the attenuation of EII, transmit, and receive gains do not exceed 3 dB and 2 dB, respectively. Overall, the results demonstrate the effectiveness of a sparse shared aperture design based on beam constraints in producing high gain, low SLL, and low-cost transmit and receive arrays.

Three-dimensional (3-D) imaging sonar systems require large planar arrays, which incur hardware costs. In contrast, a cross array consisting of two perpendicular linear arrays can also support 3-D imaging while dramatically reducing the number of sensors. Moreover, the use of an aperiodic sparse array can further reduce the number of sensors efficiently. In this paper, an optimized method for sparse cross array synthesis is proposed. First, the beamforming of a cross array based on a multi-frequency algorithm is simplified for both near-field and far-field. Next, a perturbed convex optimization algorithm is proposed for sparse cross array synthesis. The method based on convex optimization utilizes a first-order Taylor expansion to create position perturbations that can optimize the beam pattern and minimize the number of active sensors. Finally, a cross array with 100 + 100 sensors is employed from which a sparse cross array with 45 + 45 sensors is obtained via the proposed method. The experimental results show that the proposed method is more effective than existing methods for obtaining optimum results for sparse cross array synthesis in both the near-field and far-field.