Plane Wave Imaging with Large-Scale 2D Sparse Arrays: A Method for Near-Field Enhancement via Aperture Diversity

Abstract

In the context of a medical imaging application for preclinical research, specifically cerebrovascular imaging in small animals, this work addresses the challenges associated with using a large-scale 2D ultrasonic array comprising $32\times 32$ elements ($96\lambda \times 96\lambda$ ). The application imposes stringent requirements: operation in the extreme near field, high spatial resolution, high frequency, high frame rate, and imaging within a highly attenuating medium. These demands, combined with current technological limitations, such as element size and constraints on the number of channels that can be driven in parallel, present significant challenges for system design and implementation. To assess system performance, plane wave imaging is employed as a reference modality due to its ability to meet high acquisition speed requirements. Our analysis reveals limitations in spatial coverage and image quality when operating the full aperture under plane wave transmission constraints. To address these limitations, we propose a sparse aperture strategy. When combined with advanced signal processing techniques, this approach enhances both contrast and resolution while preserving acquisition speed, making it a promising solution for high-performance ultrasonic imaging under the demanding conditions of preclinical research.

1. Introduction

Ultrasound imaging has become an essential tool in preclinical cerebrovascular research due to its ability to provide non-invasive, real-time, and high-resolution visualization of cerebral anatomy and hemodynamics [1,2]. It enables assessment of cerebral blood flow, tissue perfusion, and blood–brain barrier integrity in animal models, supporting studies of ischemic stroke, cerebral hemorrhage, and small vessel disease [3]. Contrast agents enhance sensitivity to microvascular changes and vascular permeability. It is also used to monitor therapeutic responses, including neuroprotective agents and reperfusion strategies. Its affordability and portability enable longitudinal studies without repeated invasive procedures.

When combined with other modalities such as MRI or PET [4], ultrasound supports multimodal analysis, providing a flexible and efficient platform for studying cerebrovascular pathophysiology and developing novel therapies [1,2,5,6].

However, despite these advantages, implementing high-frequency ultrasound imaging in animal research presents several technical challenges [7,8,9,10]. While higher frequencies are essential for resolving small anatomical structures, such as the microvasculature in rodent brains, they are subject to increased acoustic attenuation in biological tissues, which limits penetration depth and degrades signal quality in deeper regions. Anatomical access is further constrained by the skull [11], which attenuates ultrasound waves and often necessitates craniotomies or acoustic windows to maintain image quality [12]. These limitations are especially critical in volumetric imaging with 2D arrays, which enables three-dimensional reconstruction of vascular flow and morphology but is highly sensitive to motion artifacts—such as respiration and cardiac pulsation—and remains restricted to superficial cortical regions.

These limitations highlight the need for optimized imaging protocols, specialized transducer designs, and advanced compensation strategies to improve image quality and enhance the utility of ultrasound in preclinical cerebrovascular studies [8,12,13,14,15].

In this context, plane wave imaging has emerged as a key technique for enabling ultra-fast acquisitions and efficient use of large apertures. By transmitting unfocused waves across the entire array, this method allows for rapid capture of cerebral blood flow dynamics with high temporal resolution [16].

Although plane wave imaging can generate an image from a single transmission, it tends to produce significant sidelobes and reduced image quality compared to focused beam techniques. These artifacts can be mitigated by compounding multiple images acquired at different transmission angles, thereby enhancing overall image fidelity. In linear arrays, typical angle sets range from 3 to 30, while 2D arrays commonly use configurations spanning from $5\times 5$ to $11\times 11$ angles. Determining the optimal number of transmission angles requires experimental validation or simulation to balance image quality and acquisition complexity [9,12,17].

However, volumetric imaging still presents significant technological challenges in terms of aperture design. Achieving apertures large enough to ensure high spatial resolution is difficult, especially at high frequencies. Maintaining half-wavelength element spacing to avoid grating lobes conflicts with the need to transmit sufficient acoustic energy into the medium and to ensure adequate element sensitivity. This constraint forces the use of very small elements, which typically exhibit low radiation efficiency and high electrical impedance, further complicating transducer design and signal transmission. As a result, the number of parallel channels required often exceeds the capabilities of current electronic systems and the system tends to operate with low efficiency.

To address these challenges, there is a growing trend toward the development of transducers with larger elements [13,18]. Most research efforts rely on large-scale 2D ultrasonic arrays with $32\times 32$ elements (15 MHz, BW = 70%), featuring inter-element spacing of approximately $3\lambda$, which represents the largest commercially available aperture (Vermon S.A.). However, due to the element size, these systems have limited steering capabilities and are complex to operate. Moreover, controlling such a large number of elements in parallel is technically demanding. Nowadays, several systems that can manage up to 256 channels simultaneously have emerged, often relying on complex multi-system configurations. Unfortunately, this introduces incompatibilities with the plane wave imaging modality.

This work explores the implementation of a volumetric imaging system based on plane wave transmission using large apertures, while operating with a reduced number of active elements for preclinical imaging in small animal models. Specifically, using a $32\times 32$ array with $3\lambda$ element spacing, we investigate the contribution of individual elements to image formation in the extreme near field, as well as their limitations in beam steering. Based on these findings, we propose a solution that employs 256 active elements to generate plane wave images by leveraging the spatial diversity of the transmit aperture, rather than relying on beam deflection, to enhance image quality. This work focuses on the emission part of the process, particularly on the suppression of artifacts caused by the flat front on the received signals. This approach also enables system-level optimizations that improve data encoding and reduce the data throughput between the acquisition system and the beamforming and processing unit.

2. Materials and Methods

The intended application focuses on stroke research and aims to develop analytical tools for tissue characterization, anatomical structure identification, and cerebrovascular system analysis in rat models (see Figure 1). The project is currently in its early stages, prior to experimental work, during which we are defining the instrumentation, evaluating its operability, and identifying the necessary adaptations for the specific application.

The rat brain has an approximate volume of $1765{\mathrm{mm}}^3$, with a length ranging from 2 to 2.5 cm and a depth between 1 and 1.5 cm. From an ultrasound perspective, it presents several challenges: high-frequency imaging is required to resolve small anatomical structures, the tissue is highly attenuating, and the skull acts as a barrier that is difficult to penetrate [19]. In this context, it is essential to position the transducer as close as possible to the region of interest to minimize attenuation effects. However, this may place the transducer in a region where its performance is suboptimal. Additionally, working with small animals introduces practical constraints. Although several studies address this type of application and describe positioning and coupling mechanisms, few provide details on array operability [20,21]. In anatomical imaging mode, image quality is limited, and large volumes of data combined with complex post-processing are often required to accurately reconstruct cerebrovascular structures.

In our case, we will be working with the SITAU II ultrasound imaging system (DASEL SISTEMAS S.L., Arganda del Rey, Spain), which supports 256 channels and operates with a two-dimensional aperture at 15 MHz. The array consists of $32\times 32$ elements, with a lateral size of 96 wavelengths and a bandwidth of 70% (manufactured by Vermon S.A., Tours, France). The objective of this work is to analyze the performance of the aperture to determine its applicable range and to adapt it to a configuration of 256 active elements by designing the multiplexing system and evaluating its operability.

This study is conducted in a theoretical framework and is based on simulation models. For this purpose, custom computational tools have been developed using the simulation framework proposed by Piwakowski [22].

3. Large-Scale 2D Array

In a two-dimensional array configuration, using elements larger than ${\displaystyle \frac{\lambda }{2}}\times {\displaystyle \frac{\lambda }{2}}$ introduces significant design challenges, even in the relatively straightforward case of a full matrix array. Beyond balancing system performance with hardware constraints, such as reducing the total number of elements, the design process must also address complex trade-offs between the aperture’s inherent physical characteristics and the specific operational requirements of the application. These requirements typically include penetration depth, beam-steering capability, spatial resolution, dynamic range, and individual element sensitivity.

In this context, a matrix array with elements sized at $3\lambda \times 3\lambda$ (see Figure 2A) clearly prioritizes radiation efficiency and sensitivity over beam-steering capability. Compared to half-wavelength elements, this configuration achieves a $36\times$ increase in both radiation efficiency and sensitivity. However, this improvement introduces diffraction-induced modulation in the array response, resulting in a sensitivity drop of approximately $-6\mathrm{dB}$ at an angle of ${10}^{°}$, thereby limiting the array’s steering range. Figure 2B illustrates the focal behavior at various steering angles and highlights the associated reduction in dynamic range.

This design choice becomes evident when considering the attenuation characteristics of the inspection scenario. At $15\mathrm{MHz}$, the acoustic attenuation within the biological tissue is approximately $7.5\mathrm{dB}/\mathrm{cm}$. Additionally, the use of a coupling medium introduces further attenuation of around $1.8\mathrm{dB}/\mathrm{cm}$. Consequently, maximizing the transmitted energy into the biological tissue is critical, and minimizing the propagation path through the coupling layer is advantageous. Figure 2C shows the impact of attenuation on the acoustic field along the propagation axis for the biological tissue and for the coupling layer.

Based on the attenuation curves and, as an example, assuming that a coupling layer of at least 10 mm is required, the region of interest should not exceed 40 mm. Under these conditions, we would accept an attenuation of 22.5 dB between the beginning and the end of the sample. Considering a pulse–echo process, in 30 mm this results in a total loss of approximately 50 dB. This example illustrates the problem of attenuation and highlights the need for proper insonification of the medium in order to recover the maximum amount of reflected energy. From this point onward, the attenuation effect of the coupling medium will be included in all simulations.

3.1. Plane Wave Generation

Considering the limitations introduced by increasing the element size for conventional beam steering, we must study how this affects the process of deflecting a plane wavefront. In Figure 3, we present the beampatterns for several cases of planar aperture steering (at $0^{°}$, $6^{°}$, and ${12}^{°}$, see Figure 3A,B,D), and we show the cross-section at ($Z=30\mathrm{mm}$, $Y=0\mathrm{mm}$) for steering angles ranging from $0^{°}$ to ${14}^{°}$.

The first observation is that the acoustic field consistently exhibits a ripple of approximately $2\mathrm{dB}$, attributed to the configuration of empty columns required by the connection system. Secondly, the acoustic pressure remains stable along the aperture projection. When analyzing the steering results, increasing the steering angle leads to a reduction in field amplitude compared to the $0^{°}$ case. Additionally, a lobe platform emerges at approximately $-12\mathrm{dB}$, which reduces the dynamic range and introduces out-of-plane reflector signals in that region. For instance, at a steering angle of ${10}^{°}$, a $6\mathrm{dB}$ loss in the main lobe is observed. In such a scenario, a target located outside the wavefront would produce a reflection only $6\mathrm{dB}$ below, further contributing to the presence of undesired signals in that area.

Therefore, it can be concluded that even in the case of plane wave imaging, the beam-steering capability is notably constrained. The ability to generate angular diversity is limited to a narrow range between $-4^{°}$ and $+4^{°}$, resulting in a reduced overlap region within approximately $-2\mathrm{mm}$ to $+2\mathrm{mm}$. This reduction corresponds to nearly 50% of the insonified area, significantly impacting the effective imaging zone. Additionally, this limitation is accompanied by a $6\mathrm{dB}$ decrease in dynamic range. Under these conditions, employing plane wave imaging to exploit angular diversity does not appear to be a recommended approach.

3.2. Aperture Performance

Another challenge of operating in the near field with large elements is their limited beam opening angle (approximately ${19}^{°}$ in this case), which prevents uniform perception of the insonified region across all elements. As a result, some elements may fail to reach certain areas within the region of interest. This issue has a significant impact on the dynamic range. The beamforming process, which assumes that all elements contribute equally to the focal point, yields a theoretical dynamic range of $20log(1/\sqrt{N_e})$, where $N_e$ is the number of elements in the square aperture. In this case, this value corresponds to $30\mathrm{dB}$. However, since the element contributions are not uniform, the dynamic range does not reach this theoretical value. In this context, each element contributes to the dynamic range depending on the relative position of the reflector with respect to the array, and this contribution can be approximated as follows:

$$DR\approx 20log\left({\displaystyle \frac{max\left(P_i\left(\overrightarrow{x}\right)\right)}{\sqrt{{\sum }_i^{N_e}{P}_i\left(\overrightarrow{x}\right)}}}\right)$$

(1)

where $P_i\left(\overrightarrow{x}\right)$ is the reflection detected on the $i^{th}$-element from the position of the reflector $\overrightarrow{x}$. For effective focusing and optimal aperture utilization, it is desirable that the intensity contribution from each element at a given spatial location be of the same order of magnitude. The individual contribution of each element to the image can be assessed by analyzing the intensity with which it perceives each point within the region of interest.

In this study, for each point within the region of interest, we computed the influence applied by the 1024 elements and analyzed how these values are distributed relative to their mean. As an example, we present the distribution of these values, normalized to their mean, at three specific axial positions: Z = 10 mm (Figure 4A), Z = 20 mm (Figure 4B), and Z = 30 mm (Figure 4C). At shallow depths, the differences are notably significant, compromising both the efficient use of electronic resources for certain elements and the overall beamforming efficiency. As depth increases, the intensity distribution becomes more uniform, enhancing the operational balance of the imaging system.

Figure 4D shows the average intensity level across the elements, highlighting that maximum pressure is produced between $Z=10\mathrm{mm}$ and $Z=20\mathrm{mm}$. These curves will be included as reference overlays in all spatial plots. Figure 4E,F illustrate the distribution of values below and above the mean, respectively. Notably, in the region of maximum average intensity, differences of up to $32\mathrm{dB}$ between extreme values can be observed.

Additionally, we evaluated the percentage of the aperture that contributes above and below the mean intensity level (Figure 4H and Figure 4I, respectively). The requirement for a balanced aperture allowed operation from depths starting at $15\mathrm{mm}$. However, as observed in Figure 4E,F, this condition may still result in intensity differences of up to $22\mathrm{dB}$, introducing a natural apodization effect across the aperture. These figures indicate that the region of peak pressure is predominantly shaped by the contribution of a limited number of elements.

Finally, to assess the degree of similarity among the elements, we used the Gini coefficient [23,24]. This metric quantifies the level of inequality within a set of values and is particularly useful for analyzing distributions with significant internal variation, as is the case here. Values close to zero indicate high similarity, while values near one reflect high inequality (Figure 4G).

$$G={\displaystyle \frac{{\displaystyle \sum _{i=1}^n\sum _{j=1}^n\left|x_i-x_j\right|}}{2n^2\overline{x}}}$$

(2)

Values below $0.2$ indicate low inequality, values between $0.2$ and $0.3$ indicate moderate inequality, and values above $0.3$ imply high inequality.

The Gini plot shows that below $15\mathrm{mm}$, the acoustic field is mainly determined by a small number of elements, resulting in low resource utilization. For the full aperture, a compromise solution can be found operating from $30\mathrm{mm}$.

From the simulations, we can deduce that the optimal scanning range capable of covering the full aperture can be approximated as a cylinder from $30\mathrm{mm}$ to $40\mathrm{mm}$ with a diameter of $4\mathrm{mm}$. In this case, the pulse–echo attenuation is approximately $25.8\mathrm{dB}$.

The full aperture requires 1024 electronic channels for operation. Outside of highly specialized laboratories, no system currently supports fully integrated control of this configuration. However, commercial solutions allow partial operation by synchronizing up to four 256-channel systems.

An alternative approach involves operating the aperture with a single 256-channel system combined with a column-wise multiplexer, typically activating eight consecutive columns. This configuration is the most commonly reported in the literature, although detailed operational descriptions are limited. Some studies describe dividing the aperture into seven overlapping windows (50% overlap), each capturing blocks of $32\times 8$ elements. Each acquisition is processed independently and later assembled into a unified 3D image.

Structural imaging in preclinical near-field applications generally yields low-quality results, as many signals contribute minimally to the beamforming process, confirmed by our simulations (see Figure 4). Only through advanced temporal image-differencing techniques can the cerebrovascular system be effectively reconstructed.

4. Sparse Aperture

After describing the challenges of angular plane wave emissions, defining the operating conditions for the full aperture, and outlining the limitations of the hardware system, we propose a solution to these issues based on sparse apertures. A sparse aperture can accommodate hardware constraints, and element selection can be optimized to equalize the overall contribution across the array. Additionally, by using multiple sparse apertures in transmission, we can introduce the necessary diversity into the beampattern to enable effective plane wave imaging without steering. This approach helps reduce artifacts typically associated with conventional plane wave methods, ensures efficient use of electronic resources, and improves beamforming performance. It also aims to uniformly cover the entire region of interest with balanced intensity using a single emission angle, $0^{°}$, thereby simplifying the transmission strategy while maintaining image quality.

The objective is not to identify a single optimal aperture, but to define a set of randomly generated apertures within a common framework that exhibit similar main lobe beam pattern characteristics while differing in their sidelobe distributions. This is achieved by keeping the receive aperture constant across transmissions and combining signals directly at the reception channels.

For this study, the aperture is divided into $4\times 4$ element bins arranged on an $8\times 8$ grid. Various apodization modes are applied based on the number of active elements per bin. Within each bin, active elements are randomly selected, introducing diversity while ensuring consistent global behavior across the aperture [9]. Figure 5 shows three representative strategies used in this work.

The goal of the transmission is to achieve uniform insonification within the region of interest while enabling rapid energy dispersion outside it, thereby minimizing the impact of external noise sources. The wavefront should remain planar and temporally compact and span the widest possible coverage area, free from secondary fronts that could degrade dynamic range.

To optimize aperture performance, we propose dividing it into two zones: an inner and an outer region. Within each zone, the objective is to homogenize the contribution of active elements while spatially segmenting the insonified area, thus reducing mutual interference between regions.

4.1. Sparse Emission Aperture: Inner Region

We aim to design an aperture capable of generating a wide, flat beam with low sidelobe levels, effectively insonifying the central projection of the aperture. This can be achieved through aggressive windowing, which suppresses the contribution of peripheral elements and enhances main lobe uniformity.

This window must be adapted to the available resources [10,20]. In addition to the spatial discretization already employed (a matrix grid with spacing of $3\lambda \times 3\lambda$), we consider the limitation that the emission amplitude cannot be controlled and is assumed to be fixed for all elements. Consequently, the windowing effect is achieved by adjusting the density of active elements within each bin (see Figure 5).

Ultimately, the resulting aperture should be regarded not as an exact realization of the theoretical model, but as a practical approximation. In Figure 6, we show an example comparing the desired apodization (a Taylor window) with the one actually achieved. The resulting shape is significantly distorted due to the grid structure, which favors alignment in the projection of the elements. The contrast in the obtained field is 10 times lower than desired, although both patterns match along the axis within a range of $\pm 5^{°}$ (see Figure 6B).

An aperture designed with a Taylor window was analyzed (see Figure 7), and the contribution of its elements to insonifying the region of interest was evaluated. Balanced participation occurs at depths beyond 10 mm. Although edge and outer elements show lower participation, especially near the aperture, the number of channels with above-average intensity exceeds those with low intensity. This behavior remains consistent with the intended apodization. From 20 mm onwards, the difference between the elements forming the aperture is below 3 dB.

If we observe the acoustic field generated between $Z=3\mathrm{mm}$ and $40\mathrm{mm}$ in another particular case of this strategy, we see that it has an irregular structure (see Figure 8). However, it drops rapidly—by nearly 25 dB—for X values close to $\pm 2.2\mathrm{mm}$. The distribution of secondary lobes is highly irregular, and as in the case of the full aperture, deflection severely penalizes the dynamic range. It is not possible to go beyond $4^{°}$, preventing efficient overlap between deflected images.

The proposed strategy enables the generation of multiple apertures under a common apodization scheme, resulting in similar main lobe behavior while exhibiting distinct sidelobe distributions. Using this approach, we compare the performance of several apertures in Figure 9. For each configuration, the acoustic field was computed at $Z=30\mathrm{mm}$, spanning the lateral range from $X=-5\mathrm{mm}$ to $5\mathrm{mm}$, under flat emission conditions. The corresponding wavefront shapes were extracted, and both the similarities and differences among these profiles are relevant to the intended application.

The usable imaging area is limited to a region of $4\times 4\mathrm{mm}$, where the apertures still show small differences, and the behavior of the tails of the wavefront varies in each case. The goal is to leverage the technical limitations that prevent perfect apodization as a tool to generate diversity.

To introduce and exploit signal diversity, the reception aperture must remain fixed. Under this condition, a series of consecutive transmissions can be averaged when received through the same aperture, potentially even directly within the acquisition system. If the transmission aperture remains constant, this averaging primarily reduces electronic noise, thereby improving contrast. However, if the transmission aperture varies between shots, part of the acoustic noise it generates can also be mitigated, further enhancing contrast.

Let the set of signals $N_w$, corresponding to $N_w$ shots, received in the channel-i be defined as follows:

$$S=\{s_{i1}\left(t\right),s_{i2}\left(t\right),\dots ,s_{i{N}_w}\left(t\right)\}$$

(3)

We can consider different approaches for combining these signals. We define the signal ${\widehat{s}}_i\left(t\right)$ as the mean value:

$${\widehat{s}}_i\left(t\right)={\displaystyle \frac{1}{N_w}}\sum _j^{N_w}{s}_{ij}\left(t\right)$$

(4)

We define the signal ${\widehat{s}}_i\left(t\right)$ as the one with the minimum absolute value at each time t:

$${\widehat{s}}_i\left(t\right)=arg\underset{s_{ij}\left(t\right)\in S}{min}\left|s_{ij}\left(t\right)\right|$$

(5)

We define ${\widehat{s}}_i\left(t\right)$ as the average of the L signals with the smallest absolute values at each time t:

$${\widehat{s}}_i\left(t\right)={\displaystyle \frac{1}{L}}\sum _{j\in {\mathcal{I}}_L\left(t\right)}{s}_{ij}\left(t\right)$$

(6)

where ${\mathcal{I}}_L\left(t\right)\subset \{1,2,\dots ,N\}$ is the index set corresponding to the L signals with the smallest $|s_{ij}\left(t\right)|$ values at time t.

As an illustrative example, we consider the 1024 received signals corresponding to a single receive element for a scene containing a single reflector, with no added noise, insonified using $N_w=1024$ different transmit apertures (see Figure 10). For these signals, a histogram of the values at each time instant was computed and visualized as an image, where color indicates the number of coincident values. Over each histogram, the result of combining the signals according to each proposed criterion is shown in red. Below each histogram, the corresponding image of the simulated point is presented, obtained after processing the 256 signals per channel for each data combination strategy.

In Figure 10A, we show a randomly selected case from the 1024 acquisitions, displaying the signal corresponding to a central element of the aperture. In Figure 10B, we present the average of all 1024 acquisitions, again showing the signal from a central element. In Figure 10C, we display the average of the 10 acquisitions with the lowest amplitude among the 1024, focusing on the same central element. Finally, in Figure 10D, we show the individual acquisition with the lowest amplitude, also corresponding to the central element.

What we observe in Figure 10 is that the sequence of signals obtained from multiple transmissions using different apertures enables processing of the raw data prior to beamforming. This processing effectively suppresses acoustic noise generated by the plane wave while preserving the echoes from the main reflectors. When selecting the signals with the lowest amplitudes, we observe a narrowing of the pulse, which leads to an improvement in bandwidth. The improvement is more drastic in this case, but it can also cause a loss in peak value. In the resulting image, this translates into a significant reduction in sidelobes, particularly in their spatial extent, and a noticeable suppression of reverberation artifacts associated with plane wave transmission. It is important to highlight that some of these techniques are compatible with current technology.

To globally assess the performance of the different methods, we calculated, for a reflector located at $(0,0,21.22)\mathrm{mm}$, the image generated along the Z-axis for various values of $N_w=8,32,64,128$. For reception the full aperture was used, and 300 cases were evaluated for configuration. For each point along the axis, Figure 11 shows the maximum value (black line), the minimum (green line), and the mean (red line). As a reference, and to visualize the improvement, a single-shot case $N_w=1$ has also been included. In all cases, an SNR of 20 dB was applied. Additionally, a line at −25 dB from the main peak is used as a reference for measuring axial resolution ($\Delta z$, see

Table 1. Data extracted from Figure 11 used to evaluate the performance of each configuration (dynamic range at three points, variance, and axial resolution).

${\mathit{N}}_{\mathit{w}}$	Method	$21.22$ mm	$21.27$ mm	$21.35$ mm	$21.22$ mm	$21.27$ mm	$21.35$ mm	$\mathbf{\Delta }\mathit{z}$ ($\mathsf{\mu }$m)
		Mean (dB)			Std (dB)
8	min	0.71	16.47	43.9	0.032	3.05	5.72	100
	average-min(4)	0.34	13.58	34.69	0.018	1.5	4.99	110
	average	0.0	11.37	26.67	0.0	0.91	3.55	123
32	min	1.0	20.46	53.47	0.026	2.85	2.88	97
	average-min(4)	0.75	17.23	45.29	0.019	1.41	2.37	104
	average	0.0	11.35	25.87	0.0	0.38	1.11	123
64	min	1.12	23.37	59.28	0.023	3.64	2.6	97
	average-min(4)	0.9	19.43	51.62	0.015	1.62	1.67	103
	average	0.0	11.34	26.39	0.0	0.37	0.9	123
128	min	1.69	26.31	64.75	0.021	3.75	3.12	58
	average-min(4)	1.49	21.99	57.58	0.016	2.01	1.54	97
	average	0.47	11.37	26.26	0.0	0.25	0.67	123

).

Finally, on the curve, in addition to the main peak, two additional points corresponding to other relevant positions on the curve are indicated: $Z=21.22\left(\mathrm{main}\right),21.27,21.35\mathrm{mm}$. For these points, we calculated their variance and the amplitude difference with respect to the main echo value (see Table 1).

For all cases, the main peak exhibits an axial resolution close to $\lambda =100\mathsf{\mu }$m, with very low variance in amplitude. The primary differences among the various results are observed in the secondary peaks that follow the main one. Averaging, regardless of the value of $N_w$, does not provide a significant improvement in the results. The minimum criterion behaves very aggressively, resulting in a loss in amplitude of approximately 1.6 dB at the reflector position, but it also yields the greatest improvement in dynamic range and can even achieve an axial resolution below $\lambda$. However, it shows high variance in the secondary peaks, as a consequence of the inherent randomness of the procedure. The mean of minima method, limited to the four lowest values, provides a more balanced result as $N_w$ increases. Good-quality results are obtained from $N_w=64$ onwards; from $N_w=32$, the results offer adequate quality with a reasonable number of shots. Below this value, for high-speed imaging, the minimum criterion appears to be more suitable.

4.2. Sparse Emission Aperture: Outer Region

The scanning area can be extended by employing a ring-shaped emission configuration. Since we are operating in the very near field, this approach enables sonification of regions beyond the lateral range of $\pm 2.5$ mm, complementing the coverage provided by the Taylor emission.

To implement this, the aperture is structured into concentric rings derived from bin segmentation. The dispersion strategy must be carefully designed to suppress edge effects and must account for the distortion caused by central elements, which can radiate several decibels more than the outer elements (see Figure 4). These factors can lead to elevated secondary lobe levels. At the same time, the strategy should ensure coverage over a broad spatial domain to promote diversity in field distributions. Accordingly, the secondary ring is selected within the bin structure, maintaining one element per bin in both the outermost ring and the immediately adjacent inner ring (see Figure 5).

This configuration is analyzed in Figure 12. The ring-based arrangement ensures uniform participation across array elements. However it emits lower energy than the Taylor apodization. The average participation distribution spans a wide area, including the projected footprint of the elements. The Gini coefficient rapidly converges toward an equilibrium state, indicating that element participation becomes balanced from a radial distance of 15 mm onwards. It is observed that, despite the uniform weighting, this configuration involves a portion of the aperture in which the maximum element contribution is 5 dB lower than in the Taylor configuration (see Figure 7).

Based on this strategy, four aperture configurations were designed, and the resulting fields and corresponding planar wavefronts were computed (Figure 13). All configurations exhibit a planar wavefront formed within the region between 2.5 mm and 5 mm, leaving the central zone ($\pm 2.5$ mm) with a decay margin ranging from 6 dB to 12 dB and a disordered distribution. This behavior helps reduce the presence of imaging artifacts originating from the central region.

For demonstration purposes, we consider another example with a different number of emission apertures. Using a line of reflectors distributed along the Z-axis every 250 $\mathsf{\mu }$m as a reference, we simulated $N_w=128,64,32$ and observed (see Figure 14) the acquisition at a specific element located at position $(-4.2,-2.25)$. For these signals, knowing that they all correspond to the same scene and share common elements, we applied three different processing methods to reduce noise.

The first method, averaging, reduces electronic noise but is insufficient to eliminate all secondary oscillations characteristic of a flat wavefront (B, E, H). The second method, minimum selection, is a more aggressive approach that yields high contrast without secondary lobes; however, it is highly sensitive to the random configuration of apertures and introduces high-frequency noise typical of nonlinear systems (C, F, I). The third method, averaging a subset of the lowest-amplitude acquisitions, provides a smoother response with a significant reduction in secondary lobes, though not as pronounced as with minimum selection. The number of acquisitions used in the subset depends on the desired level of smoothness; in this case, we averaged the four lowest values (D, G, J).

The original signal is shown in Figure 14A. In the simulation, additive noise was introduced at a level of 20 dB relative to the maximum peak amplitude across all acquisitions. Figure 14B–D correspond to 128 emissions; Figure 14E–G to 64 emissions; and Figure 14H–J to 32 emissions. Disregarding the arithmetic mean—which does not yield a significant improvement—the most favorable results are obtained using either the minimum value or the mean of the minimums. Clearly, as the number of acquisitions increases, the likelihood of achieving a more accurate reconstruction also improves. When the acquisition count is high, the mean of the minimums produces highly satisfactory results. However, under constraints on the number of shots, using the minimum value in combination with appropriate filtering techniques offers a robust and efficient compromise.

Finally, Figure 15A,B show the diffraction pattern of the two emission apertures within the plane of interest. To assess how they complement each other, a combined representation of the mean field from both configurations is also included (see Figure 15C). The Taylor emission is approximately 6 dB stronger than that of the ring. It should also be noted that the insonification strategy for the outer region is 10 dB lower than that of the inner region, and similarly, the reflectors in the outer zone are 20 dB weaker when insonifying the inner region. This creates a degree of isolation between the two zones, which can help reduce interference in complex scenes.

One aspect to consider is that, if the same reception aperture is used for both emissions, it is possible to combine the results from both acquisitions on the same signals:

$${\widehat{s}}_i\left(t\right)={\widehat{s}}_{iR}\left(t\right)+K{\widehat{s}}_{iT}\left(t\right)$$

(7)

where ${\widehat{s}}_{iT}\left(t\right)$ is the signal processed from the Taylor-apodized emission, ${\widehat{s}}_{iR}\left(t\right)$ is the signal processed from the ring-shaped emission, and K is a weighting factor, empirically determined in this case as $K=0.4$.

In Figure 16, we can see how this process works. In this case, the full aperture was used for reception. First, for a value of $Z=20.9\mathrm{mm}$, the curve defining the viewing area was calculated (blue line in Figure 16A). The combination of both excitations allows coverage of a region of $\pm 4.5\mathrm{mm}$ with a ripple of approximately $1\mathrm{dB}$ and a drop of 9 dB at 5 mm from the center of the aperture. To test how the regions perform, four targets were placed at the same depth at positions $X=\{-6,-4,0,6\}$. The outermost values fall outside the field of view, while the other two belong, respectively, to the ring and the inner zone. Figure 16B shows the beamforming results using ${\widehat{s}}_{iR}\left(t\right)$ (orange line), ${\widehat{s}}_{iT}\left(t\right)$ (blue line), and the combined signal ${\widehat{s}}_i\left(t\right)$ (green line); see also Figure 16A. All signals were generated using the criterion of the average of the four lowest-amplitude acquisitions over 64 emissions. Finally, Figure 16C shows the resulting image.

One of the most relevant outcomes is the effective separation between the inner and outer regions, which minimizes cross-interference and reduces the influence of elements outside the imaging area, including grating lobes generated from outside the field. The combination of signals ${\widehat{s}}_{iT}\left(t\right)$ and ${\widehat{s}}_{iR}\left(t\right)$ enables reconstruction of the complete image. In this sense, everything in Figure 16C that lies beyond the marked boundaries consists of lobes caused by reflectors within the region of interest and therefore should not be considered part of the image.

From a system design perspective, the ability to construct ${\widehat{s}}_i\left(t\right)$ directly within the acquisition system contributes to improved signal acquisition and compression capabilities. However, it can also reduce the dynamic range and should therefore be implemented with appropriate control. If each emission is processed independently, it has the advantage of reducing cross-interference between the two regions.

The use of multiple transmit apertures during reception, in conjunction with nonlinear processing operators such as the minimum function, facilitates the acquisition of echo signals with enhanced bandwidth. As a consequence, axial resolution is improved, approaching the order of one wavelength. Additionally, by inherently suppressing grating lobes, this methodology simplifies the design constraints of the receive aperture and enhances overall image fidelity.

4.3. Sparse Reception Aperture

The proposed processing approach for plane wave imaging contributes to enhancing both dynamic range and axial resolution. Additionally, by centering the imaging region over the aperture projection, it helps mitigate external interference. However, lateral resolution is primarily determined by the receive aperture. The increased bandwidth, combined with the narrow steering angle within the region of interest, ensures that grating lobes do not constitute a design constraint.

Design choices must meet the requirements of providing optimal resolution and enhancing contrast. Under ideal conditions, an isolated target imaged with a full $32\times 32$ narrowband aperture would theoretically yield a dynamic range of approximately $-30$ dB. For a sparse aperture with 256 elements, the theoric dynamic range varies between $-30$ and $-18$ dB depending on the spatial distribution of the elements. If the design is not appropriate, and considering that the system operates in the very near field, these values may be even lower (see Equation (1)). In scenarios with multiple targets, the interaction of various secondary wavefront patterns reduces these margins.

It becomes feasible to reconstruct the full aperture in reception using four acquisitions of 256 elements (see Figure 17(A-1–A-4)). For this reception configuration, we have simulated the image generated by the full aperture for a series of targets distributed along the axis Z $(X=0,Y=0)$ and present a detailed view. Additionally, we show the signal received at the element located at (0.3, –0.15) for this image. Two emission cases have been simulated: (B) the full aperture and (C) the Taylor emission-based dispersion strategy ($N_w=8$, min-method). As observed, in the case of full emission, the secondary wavefronts from the plane wave introduce oscillations that elevate the background amplitude, thereby reducing the dynamic range. In Figure 17C, the dispersion strategy achieves a higher dynamic range. In Figure 17D, we present the signal received at the element located at (0.3, –0.15) for both emissions. Although our approach incurs some loss in reflectivity in certain targets, the resulting image exhibits an increased dynamic range and reveals the underlying interference structure between the secondary lobes of each reflector.

At this stage, the design of the receive aperture becomes a more classical problem, primarily focused on ensuring both contrast and lateral resolution. This is constrained by technical factors such as the number of elements and their sensitivity, as illustrated in Figure 4. In this context, it remains a priority to maintain balanced energy across the receive channels. The Taylor and ring-shaped aperture designs proposed for transmission meet this requirement but exhibit two very different operational patterns: the Taylor aperture achieves low sidelobes and low resolution, while the ring aperture results in high sidelobes and high resolution. In Figure 18, we repeat—under the same conditions as in Figure 17—the simulation for reception based on Taylor apodization and ring apodization. Additionally, we compare these with the full aperture reconstruction and the conventional plane wave approach from Figure 17, evaluating the lateral resolution $\Delta x$ at −6 dB over the target at $(0,0,20.5)$ achieved by each configuration.

In Figure 18A,C, we show an aperture following Taylor apodization and its corresponding generated image. This configuration emphasizes the suppression of sidelobes but results in poor lateral resolution. In Figure 18B,D, we present an aperture arranged in a ring distribution, selected to enhance lateral resolution, along with its corresponding image. This setup improves resolution but exhibits elevated sidelobes, which reduce the dynamic range.

If we examine the lateral profiles in Figure 18E, ranked from worst to best, we have conventional plane wave (FULL), $\Delta x=500\mathsf{\mu }\mathrm{m}$, with a dynamic range of −7.4 dB; Taylor (TAYLOR), $\Delta x=500\mathsf{\mu }\mathrm{m}$, with a dynamic range of −7.4 dB; sparse–full (SP_FULL), $\Delta x=326\mathsf{\mu }\mathrm{m}$, with a dynamic range of −16.4 dB; and ring (RING), $\Delta x=214\mathsf{\mu }\mathrm{m}$, with a dynamic range of −17 dB and a sidelobe level of −11 dB.

While for axial resolution we have been able to achieve values on the order of $\lambda$ or even smaller, the lateral resolution is determined by the behavior of the apodization window. Theoretically, the resolution for this aperture is around $400\mathsf{\mu }\mathrm{m}$, which is four times greater than the axial resolution. The values obtained for the different implementations range between $500\mathsf{\mu }\mathrm{m}$ and $200\mathsf{\mu }\mathrm{m}$, with a trade-off associated with increased sidelobe levels. Our conclusion is that, once the challenge of grating lobes has been avoided, the design of the receive aperture should be primarily guided by the application’s requirements for contrast and resolution. The most versatile option is to acquire the full aperture and then apply digital signal processing techniques to achieve the desired objectives. However, this solution increases the acquisition time by four.

As an example, one solution is to compose the image using the geometric mean of the Taylor apodization and the ring apodization. In Figure 19, we show the result of this combination for the same scenario as in Figure 17 and Figure 18. The outcome is similar to that obtained with SP_FULL, featuring a slightly lower dynamic range and slightly higher lateral resolution, but with practically equivalent performance.

5. Imaging System

The technological implementation of the presented solution involves addressing several key challenges. First, depending on the selected operational mode, the system requires the development of two to three independent multiplexing structures: two for transmission (potentially shared with reception) and one specifically for reception. The first structure uses a Taylor apodization scheme; the second employs a ring-shaped scheme; and the third, dedicated to reception, is designed to cover the full aperture in a maximum of four firings.

Second, since beamforming does not require knowledge of the position of the emission elements, the system could incorporate a mechanism to autonomously and randomly select transmitting apertures within the constraints of each transmission strategy. Additionally, a processing stage could be implemented in the receiving channels to apply a nonlinear, minimum-based filter functioning as an EMI-like filtering stage [25].

A final example has been developed to evaluate a more complex scenario: three double-point curves were designed, spaced 125 $\mathsf{\mu }$m apart in the Z-axis and 500 $\mathsf{\mu }$m in the X-axis. This configuration is illustrated in Figure 20, which shows the image obtained using the full aperture. In the image, the targets are visible but exhibit a very low dynamic range, close to 3 dB.

For the same scenario, we computed the image using our double-emission scheme. First, the full aperture reconstructed from the four complementary acquisitions was used, and second, a ring-shaped aperture combined with a Taylor-tapered apodization aperture was used, integrated geometrically after beamforming.

In the first case (see Figure 21), the two regions are presented separately. For the inner region, the image displays only the central part of the scene, which is reconstructed with good resolution and a dynamic range close to 15 dB. In contrast, the image of the outer region, while maintaining resolution, shows a reduction of approximately 50% in dynamic range.

In Figure 21C, both images are combined by merging the data during the beamforming process (which can also be performed in the reception channels). To preserve balance in the final image, the central region was attenuated by 6 dB.

Finally, Figure 22 shows the result of combining the Taylor and ring strategies in reception. In these two cases, the two regions are already presented as combined by Equation (7) (Figure 22A,B), and the following image displays the result of applying the geometric mean between both apertures. The outcome is similar to that presented in Figure 21, with two reception apertures instead of four.

System Performance

After analyzing the results and considering the necessary trade-off between application requirements and system performance, we propose that, based on the described operating method, the aperture can be effectively set between 20 mm and 30 mm. In pulse–echo mode, this results in 15 dB of attenuation within the sample and 7.2 dB in the coupling material (a total attenuation of 22.2 dB), compared to the 31 dB caused by increasing the radiating surface. If necessary, we can move the acquisition forward to $15\mathrm{mm}$ at the expense of reducing the homogeneity of the element contributions within the ring configuration.

Each emission cycle lasts 40 $\mathsf{\mu }$s, with data acquisition occurring over 13.3 $\mathsf{\mu }$s. With a sampling rate of 62.5 MHz (14 bits) across 256 channels, each acquisition generates 560,000 bytes. For a communication channel of 3 GB/s, the transfer time is 186.6 $\mathsf{\mu }$s, while for a Gigabit Ethernet system, it is 2.797 ms. This means that, depending on the communication technology, it is possible to parallelize the transmission of one acquisition with either 3 or up to 74 firings.

Based on these timings and assuming maximum transfer speed, different operating modes can be selected depending on the desired image speed and/or quality. For example, using a minimum-based method with $N_w=9$ and two acquisitions, the fastest imaging rate is achieved, with 893 volumes per second (approximately $9\times 9\times 10{\mathrm{mm}}^3$). To increase image quality, using a reception based on four subapertures (SP_FULL) and an emphaverage-min criterion with $N_w=32$, a rate of 62 volumes per second can be obtained. In the case of using the combination of the Taylor aperture with the ring in reception, a rate of 124 volumes per second can be achieved.

Disregarding the computational cost of beamforming, we can state that, depending on the configuration used, the system is capable of providing a spatial resolution of between ($200\times 200\times 100\mathsf{\mu }{\mathrm{m}}^3$) and ($300\times 300\times 100\mathsf{\mu }{\mathrm{m}}^3$) and a temporal resolution ranging from 893 to 62 Hz. In the literature, the only example that provides relevant data with the same aperture reports a spatial resolution of ($200\times 280\times 175\mathsf{\mu }{\mathrm{m}}^3$) and a temporal resolution of 6 Hz [20]. In another work [21], for a 7 MHz ($32\times 32$) aperture based on the same four-region multiplexing system, configurations are presented that enable the generation of volumes with 4, 10, and 16 aperture pairs (with five plane waves per pair), achieving temporal resolutions of 750 Hz, 300 Hz, and 187 Hz, respectively.

6. Experimental Results

In order to experimentally verify the feasibility of using spatial diversity from sparse apertures to improve image quality in plane wave imaging as an alternative to beam steering, we employed a $16\times 16$ element array with a center frequency of $5 \mathrm{MHz}\pm 10\%$ (60% bandwidth), manufactured for non-destructive testing (NDT) (Doppler S.L., Guangzhou, China https://www.cndoppler.com/ (accessed on 9 October 2025)). A SITAU 1 system (DASEL S.L, https://www.daselsistemas.com, (accessed on 9 October 2025)) with up to 128 parallel channels multiplexed to 256 was used as the working platform.

The inter-element spacing is $0.9\times 0.9$ mm, with each element measuring $0.7\times 0.7$ mm. Operating in water, this corresponds to an inter-element distance of approximately $3\lambda \times 3\lambda$ ($\lambda =300\mathsf{\mu }$m). This aperture is similar to the one we have proposed for our application, although it operates at a lower frequency and contains fewer elements, thus offering reduced spatial diversity. To make the problem equivalent, we propose reducing the number of active elements from 256 to 64. The experimentation is limited to resolving the inner region.

Unfortunately, the $16\times 16$ configuration offers fewer opportunities to exploit spatial diversity compared to the $32\times 32$ aperture, and it does not easily conform to the dispersion schemes proposed in the previous sections. To preserve discretization capability across the aperture, we opted to organize it into $2\times 2$ bins, with a maximum of four active elements per bin. This scheme yields a total of 84 active transducers.

Since it is desirable for the central bins of the aperture to maintain a high level of participation, in order to reduce the number of channels to 64, the remaining bins must undergo a random selection (purging) process. Figure 23 shows (A) the desired apodization strategy, (B) its adaptation to the available aperture and resources, and (C) several resulting dispersion strategies, from which the emission apertures are randomly selected.

For simplicity, reception is performed using the full aperture, constructed from four complementary subapertures. For each experiment, three images were obtained: the full plane wave image, generated by transmitting a single plane wave using the entire aperture and receiving with the full aperture, and our proposed solution in two configurations for $N_w=32$, the minimum criterion (min) and the average of the four lowest signals (average-min(4)).

A total of four experiments were designed. Figure 24 shows several images of the experimental setup. The experiments conducted include the following: imaging the head of a pin; imaging two filaments at different depths; imaging seven parallel wires at the same depth; and volumetric imaging of a rat skull. Due to the reduced aperture size, the imaging region is limited to $X=[-2,2]$, $Y=[-2,2]$ and depths between 10 mm and 20 mm. All the reconstructed images include contour lines at $-6$ dB and $-12$ dB, used to assess spatial resolution and energy spread.

The first experiment (see Figure 25) is designed to demonstrate the improvements achieved in the received ultrasonic signals. In the top row, the signal from element 106 shows a clear reduction in interference caused by secondary wavefronts. This improvement is consistently observed across all channels. Since the target is the head of a pin, the echo naturally includes contributions from surrounding structures, which remain visible in the final image despite signal processing—especially in channels located near the edges of the aperture. When comparing the reconstructed images, the average-min(4) technique yields the highest image quality, combining the benefits of the min approach with significantly reduced high-frequency noise. The enhancement is particularly evident in axial resolution and in the suppression of noise along the axial direction.

Table 2. Resolution data measured in the pinhead experiment.

	$\mathbf{\Delta }{\mathit{z}}_{-6\mathbf{dB}}$	$\mathbf{\Delta }{\mathit{z}}_{-12\mathbf{dB}}$	$\mathbf{\Delta }\mathit{z}$	$\mathbf{\Delta }{\mathit{x}}_{-6\mathbf{dB}}$	$\mathbf{\Delta }{\mathit{x}}_{-12\mathbf{dB}}$
full plane wave	270 $\mathsf{\mu }$m	573 $\mathsf{\mu }$m	1000 $\mathsf{\mu }$m	800 $\mathsf{\mu }$m	1600 $\mathsf{\mu }$m
min	210 $\mathsf{\mu }$m	300 $\mathsf{\mu }$m	800 $\mathsf{\mu }$m	565 $\mathsf{\mu }$m	1480 $\mathsf{\mu }$m
average-min(4)	210 $\mathsf{\mu }$m	300 $\mathsf{\mu }$m	565 $\mathsf{\mu }$m	800 $\mathsf{\mu }$m	1480 $\mathsf{\mu }$m

presents the resolution data for Figure 25. The two proposed techniques yield similar results, both outperforming the full plane wave method. However, the pinhead produces a complex echo response, and the entire pulse cannot be attributed solely to plane wave reverberation. If we consider the total pulse length $\Delta z$ (it is produced at −20 dB), it exceeds the wavelength, and at this depth, a small grating lobe ($-20$ dB) is generated at 4.1 mm from the target. With the target located at 1.33 mm, this results in a displacement of 2.67 mm, which falls outside the valid imaging zone defined between $-2$ mm and 2 mm.

The second experiment (see Figure 26) features two wire reflectors positioned at different depths, enabling a direct evaluation of axial resolution and dynamic range. In addition to the reconstructed images, the figure includes maximum intensity projections along the principal axes (depth and lateral), comparing the average-min(4) technique (red line) with the full plane wave approach (blue line).

The results demonstrate a consistent improvement in both dynamic range and axial resolution with the proposed method. Specifically, the axial resolution is enhanced ($\Delta z_{-6\mathrm{dB}}=200\mathsf{\mu }\mathrm{m}$, $\Delta z_{-12\mathrm{dB}}=280\mathsf{\mu }\mathrm{m}$), allowing for clearer separation between closely spaced reflectors. In this case, no grating lobes are present; only secondary lobes are produced.

Furthermore, the image processed with our technique exhibits a significant reduction in background noise, which enhances the visibility of secondary lobes. Although these lobes appear more pronounced due to the lower noise floor, they remain well-contained, indicating that the method preserves spatial fidelity without introducing artifacts.

The third experiment (see Figure 27) evaluates the imaging of four wires (acupuncture needles, $250\mathsf{\mu }$m diameter) spaced 1 mm apart, positioned at slightly different depths. The average-min(4) technique shows the clearest separation within the $-6$ dB contours and the lowest background noise, while also preserving the geometric arrangement. Compared to min and full plane wave, it minimizes overlap and secondary lobes, confirming its effectiveness for resolving closely spaced reflectors with axial misalignment. We would like to highlight the difficulty of resolving an image of this type using full plane wave, where reverberations are stronger than the actual echoes from the reflectors.

The fourth experiment (see Figure 28) assesses the ability of each technique to image through bone tissue using a rat skull. A reflector placed behind the skull serves to evaluate wave penetration. The figure includes a photograph of the skull and 3D reconstructions using full plane wave, min, and average-min(4). Full plane wave shows poor localization and high dispersion. The min technique improves focus and reduces noise. Average-min(4) yields the clearest result, with a well-defined reflector and minimal background interference, confirming its superior performance in imaging through bone.

Across all experiments, the proposed average-min(4) technique consistently outperforms both the full plane wave and min approaches in terms of image quality, spatial resolution, and noise suppression. In both single-channel and multi-element signal analysis, it demonstrates improved clarity and reduced interference. When imaging closely spaced reflectors and structures at varying depths, it achieves superior axial and lateral resolution, as confirmed by contour analysis at $-6$ dB and $-12$ dB. The method also proves effective in challenging scenarios, such as imaging through bone tissue, where it maintains spatial fidelity and accurately reconstructs reflectors behind complex media. These results validate the robustness and versatility of planar wave imaging based on spatial sparse diversity for high-resolution ultrasonic applications. Additionally, the reception process can benefit from beamforming-based processing techniques that enhance image contrast by suppressing secondary lobes [26,27,28,29,30].

7. Discussion and Conclusions

This study analyzes the performance of a two-dimensional array with large elements for very near-field imaging, specifically targeting applications in preclinical cerebrovascular research. Under these conditions, our interest lies in ensuring that the aperture operates effectively and uniformly, supports high-speed acquisition modes, and remains adaptable to systems with a limited number of active channels.

Metrics were obtained to evaluate the contribution of individual elements to image formation, and optimal operating conditions were proposed to maximize resource efficiency. Based on the results, and considering certain trade-offs, a viable working range is defined from 20 mm and up to 30 mm, with no more than 20 mm of coupling material.

Using region-specific sparsity strategies, a novel methodology was developed to exploit transmit aperture diversity and significantly suppress sidelobes generated by plane wave transmission. Unlike conventional approaches that rely on a single optimized solution, the proposed method employs multiple transmit apertures randomly selected within the constraints of each strategy, while maintaining a common receive aperture.

Simulations demonstrate that applying minimization criteria to samples corresponding to the same receive elements but different transmissions effectively reduces noise, suppresses secondary oscillation patterns, and enhances echo bandwidth, thereby improving axial resolution. This approach eliminates the need for transmit beam steering and enables full operation in plane wave mode without introducing transmit delays. Additionally, it offers substantial design flexibility for the receive aperture, which is no longer constrained by grating lobe generation.

Image quality, particularly in terms of lateral resolution and contrast enhancement, depends on the design of the receive aperture and the beamforming techniques employed. A technique combining two complementary apodizations has been proposed, yielding results comparable to those obtained with a full aperture. The core concept of this work has been experimentally validated using a smaller aperture with a similar design across various scenarios, including volumetric imaging of a rat skull.

The experimental figures reviewed confirm the practical feasibility of the proposed methodology, demonstrating consistent improvements in image contrast across different conditions and validating the theoretical predictions regarding axial resolution and overall image quality.

The analysis indicates that dividing the image area into two regions and adapting the transmission accordingly yields improved performance. However, performance varies between regions due to modulation effects introduced by the elements. The central region achieves the best results, exhibiting a contrast 6dB higher than that of the outer region. These differences can be compensated during acquisition so that both regions are combined in the pre-beamforming stage, providing a more natural image and reducing data volume. However, this also transfers secondary lobe patterns between regions and may reduce the overall dynamic range. Independent processing of both regions minimizes mutual interference, but a dedicated processing technique is required to effectively merge them.

The technological implementation of this solution involves addressing several key challenges. First, depending on the selected operational mode, the system requires the development of two to three independent multiplexing structures: two for transmission (potentially shared with reception) and one specifically for reception. The first structure uses a Taylor apodization scheme; the second employs a ring-distribution scheme; and the third, dedicated to reception, is designed to cover the full aperture in a maximum of four firings.

Second, since beamforming does not require knowledge of the positions of the transmitting elements, the system could incorporate a mechanism to autonomously and randomly select transmit apertures within the constraints of each transmission strategy. Additionally, a processing stage could be implemented in the receiving channels to apply a nonlinear, minimum-based filter functioning as an EMI-like filtering stage [25].

In summary, this work provides solutions to the low-contrast issue in plane wave imaging without requiring wavefront deflection. It optimizes acquisition processes, improves data flow efficiency, and reduces computational cost by enabling full image reconstruction using the same data volume as a single acquisition. Furthermore, the proposed approach simplifies the design of sparse apertures involved in the process, particularly by avoiding the need to optimize specific transmission solutions and, by minimizing grating lobe generation, facilitating the design of the receive aperture.

The development of specialized instrumentation based on this operational approach opens new possibilities for designing portable and low-cost imaging systems, especially in preclinical research environments where flexibility and efficiency are essential.