# Study of the Impact of Probe Steering Capability on the Performance of Off-Axis Measurements of Backscattered Signals

Lenin Chinchilla, Régine Guillermin, Emilie Franceschini, Alessandro Stuart

Savoia

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Lenin Chinchilla, Régine Guillermin, Emilie Franceschini, Alessandro Stuart Savoia. Study of the Impact of Probe Steering Capability on the Performance of Off-Axis Measurements of Backscattered Signals. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2025, 72 (2), pp.251 - 262. 10.1109/tuffc.2024.3519194 . hal-05204088

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# Study of the Impact of Probe Steering Capability on the Performance of Off-Axis Measurements of Backscattered Signals

Lenin Chinchilla<sup>D</sup>, Member, IEEE, Régine Guillermin<sup>D</sup>, Emilie Franceschini<sup>D</sup>, Member, IEEE, and Alessandro Stuart Savoia<sup>D</sup>, Member, IEEE

**Abstract**—In the field of quantitative ultrasound (QUS), several studies have been conducted to parameterize tissue anisotropy by measuring the angular dependence of the backscatter coefficient (BSC). Early foundational studies utilized a single-element transducer, and more recent ones used ultrasound linear array probes. However, probe features such as directivity and crosstalk can strongly affect both, the transmission of an ultrasound beam and the measurements of the backscattered signals, independent of the imaging strategy used, either the focused beam steering or the plane wave imaging (PWI). In this work, we present a comparative analysis between a capacitive micromachined ultrasonic transducer (CMUT) probe and a commercial piezoelectric probe, in which the BSC is measured using the focused beam steering imaging strategy on isotropic and anisotropic tissue-mimicking phantoms along different insonification angles. The results show how the limited steering capabilities of linear probes can affect the measurement of BSC, and, in general, the anisotropic QUS parameters, bringing into discussion their consideration in the development of experimental strategies for the assessment of tissue anisotropy.

**Index Terms**—Backscatter coefficient (BSC), capacitive micromachined ultrasonic transducer, crosstalk, piezoelectric, quantitative ultrasound (QUS), tissue anisotropy.

<figure><img src="image_2.png" /></figure>

## I. INTRODUCTION

SPECTRAL quantitative ultrasound (QUS) techniques rely on the frequency-based analysis of the signals backscattered from biological tissues to provide insights into tissue

Received 19 November 2024; accepted 9 December 2024. Date of publication 19 December 2024; date of current version 12 February 2025. This work was supported by the Agence Nationale de la Recherche (ANR) under Grant ANR-15-CE19-0017 and Grant ANR-10-LABX-0092 and in part by the Colombian Department of Science and Technology Colciencias. (Corresponding author: Alessandro Stuart Savoia.)

Lenin Chinchilla is with CNRS, Centrale Marseille, LMA, Turing Centre for Living Systems, Aix-Marseille University, 13007 Marseille, France, and also with the Department of Industrial, Electronic, and Mechanical Engineering, Roma Tre University, 00146 Rome, Italy.

Régine Guillermin and Emilie Franceschini are with CNRS, Centrale Marseille, LMA, Turing Centre for Living Systems, Aix-Marseille University, 13007 Marseille, France.

Alessandro Stuart Savoia is with the Department of Industrial, Electronic, and Mechanical Engineering, Roma Tre University, 00146 Rome, Italy (e-mail: alessandro.savoia@uniroma3.it).

Digital Object Identifier 10.1109/TUFFC.2024.3519194

microstructure [1]. These techniques are generally based on the parameterization of the backscatter coefficient (BSC) of a tissue, which is a fundamental property similar to its attenuation and sound speed. Most QUS approaches for describing tissue microstructure assume that the tissue of interest is homogeneous and isotropic. However, some biological tissues, such as flowing aggregating blood [2], [3], [4], [5], skeletal muscles [6], [7], and myocardium [8], [9], [10], show angle-dependent acoustic properties (BSC and/or attenuation coefficient). For clinical applications of these QUS approaches, the use of ultrasound imaging systems with multielement arrays is required, and the reference phantom method [11] is a well-established technique to provide system-independent BSC estimates. This method consists of normalizing the echo signal power spectra from a region of interest in the tissue with the power spectrum from the same depth in a well-characterized reference medium. This normalization method corrects the depth-dependent diffraction and focusing effects of the ultrasound beam and accounts
## Highlights

* A conventional piezoelectric probe and a CMUT probe, with similar array geometry and center frequency, were compared to evaluate the impact of steering capabilities on the characterization of tissue anisotropy.

* The off-axis BSC and beam pattern measurements of both probes showed significant deviations for the larger angular directions.

* The effects of the limited steering capability of linear probes must be considered in the development of experimental strategies for the analysis of tissue anisotropy.

for the electromechanical system response because these factors affect the tissue data and the normalization data in the same way. The practical evaluation and analysis of tissue anisotropy requires off-axis measurements in the medium under examination, that is, measurements along directions other than the direction perpendicular to the probe surface. Garcia-Duitama et al. [3] and Guerrero et al. [7] recently proposed anisotropic QUS parameters by using the reference phantom method to compensate for the system-dependent effects when performing plane wave imaging (PWI) beamforming or conventional focused beam steering with a linear array. In [3], the BSC was measured on flowing blood at different insonification directions and flow conditions using the PWI modality. An isotropic scattering model was fit to the measured BSC data to estimate the mean size of red blood cell aggregates at different insonification directions [3]. It was also demonstrated that fitting the anisotropic scattering model to the off-axis BSC measurements improved the QUS estimation of red blood cell aggregate size [12]. The red blood cell aggregate size is a useful QUS biomarker of systemic inflammation for the monitoring of circulatory disorders, such as diabetes, deep vein thrombosis, and cardiopulmonary bypass [13]. In [7], different QUS parameters based on the backscattered power were defined to quantify the presence and orientation of anisotropic scatterers. These QUS parameters were derived from the normalized power spectral density of the signals backscattered from the investigated medium. The backscattered signals were acquired at different insonification directions using the focused beam steering modality, and QUS parameters were evaluated: the asymmetric backscattered power difference (aBSPD) parameter to assess the presence of aligned scattering structures and the mean backscattered power difference (mBSPD) to quantify the average power loss caused by anisotropy in the scattering medium. In [14] and [15], the anisotropic QUS parameters previously developed in [7] were used to evaluate the anisotropy of the human cervix, suggesting that the mBSPD could be a useful clinical biomarker of cervical remodeling during pregnancy. The works described above show the growing interest in evaluating tissue anisotropy using a linear probe. However, independent of the imaging modality used, either the focused beam steering or the PWI, the steering performance of the probe is determined by the transducer array element directivity and affected by the inter-element crosstalk. Such characteristics, which are related to the array design and the transducer technology, impose a maximal angle to which the backscattered signals can be measured. When the probe is run beyond this maximum angle, the imposed and actual beam angles can differ significantly,

so that the off-axis measurements of BSC (or equivalently backscattered power) are biased. Off-axis measurements and calculations of the BSC should be implemented correctly to provide system-independent imaging QUS biomarkers. Using accurate off-axis BSC measures would provide QUS estimates that better quantify anisotropic tissue microstructure which in turn would enhance the clinical value of such estimates.

Conventional ultrasound imaging systems for clinical purposes are usually equipped with linear ultrasound probes based on piezoelectric lead zirconate titanate (PZT) transducer arrays, which may suffer from a high level of inter-element crosstalk that considerably affects their steering ability, as demonstrated in several studies [16], [17], [18], [19]. To overcome the limitations imposed by crosstalk effects on the steering capabilities of the probe, some solutions have been reported in the literature, for example, based on the use of appropriate transmit apodization [19] or on the manipulation of the transmit excitation signals [18], [20]. However, these techniques have been proposed to improve the B-mode image quality and could affect important characteristics for spectral analysis (such as the frequency content of the data) and beam properties (such as depth of focus and beamwidth). In addition, these techniques only consider the effects of crosstalk in transmit, but not in receive, which also degrades off-axis measurements. Another solution is to intervene in the manufacturing process to reduce the mechanical and acoustic coupling between the individual piezoelectric elements that make up the ultrasound probe [21].

In recent years, MEMS-based electrostatic ultrasonic transducers have emerged as an alternative technology for manufacturing ultrasonic probes, which has shown some advantages over conventional piezoelectric probes. For example, several works in the field of photoacoustic imaging [22], [23] showed that capacitive micromachined ultrasonic transducer (CMUT)-based probes outperformed conventional piezoelectric probes, in terms of bandwidth and angular sensitivity (directivity). The probe performance in terms of steering capability can affect the accuracy in the measurement and evaluation of the ultrasonic backscatter anisotropy in biological tissues. However, little attention has been paid to evaluating the accuracy of measuring the backscatter anisotropy.

This article aims to study the impact of the limited steering ability of linear probes on the evaluation of backscatter anisotropy. This study has been carried out by comparing the performance of a CMUT probe and a commercial piezoelectric probe for off-axis measurements of the BSC using the focused beam steering imaging modality. The two probes present a similar array design in terms of center frequency, pitch,
and elevation focus, allowing a fair comparison in terms of steering capability, which is strictly related to the transducer technology, in this case standard PZT ceramic technology versus CMUT sacrificial-release-based [24] reverse fabrication process [25], [26], [27] technology. The steering ability of the two probes was first evaluated by measuring the TX beam patterns in the azimuth plane and by computing the deviation of the estimated beam directions with respect to the steering angles imposed by the delay profiles programmed in the scanner. Then, the BSC measurements obtained with the PZT and CMUT probes were compared on isotropic and anisotropic tissue-mimicking phantoms using the same imposed steering angles.

This article is organized as follows. Section II describes the experimental setups used to measure the TX beam pattern, as well as the BSC of isotropic and anisotropic tissue-mimicking phantoms. Section III reports the comparative analysis between the TX beam pattern and BSC measurement results obtained with the two probes. The discussion and conclusion are given in Sections IV and V, respectively.

## II. MATERIALS AND METHODS

### A. Piezoelectric and CMUT Probes, and the US Scanner

The two probes used in this study, the piezoelectric LA435 (ESAOTE, Florence, Italy) and the HF3 CMUT prototype [27], feature both 192-element arrays with a 0.2-mm pitch and an elevation of 3.5 and 3 mm, respectively. The two-way center frequency averaged over all the 192-array elements was 10.9 and 10.8 MHz for the piezoelectric and CMUT probes, respectively. In terms of the fabrication process, the piezoelectric array is based on a conventional acoustic stack configuration, with a PZT ceramic operating in thickness vibration mode supported by a polymeric composite backing material and coupled to a silicon lens through matching layers. In contrast, the CMUT array is microfabricated on silicon through a surface micromachining process, during which the silicon substrate is removed after having applied a polymeric composite backing, and directly coupled to a silicon lens. The profoundly different fabrication and packaging process, along with the distinct materials used in the array integration, result in notable differences in terms of electro-acoustic response characteristics and different mechanical crosstalk levels, which is a key factor in their differing steering performance. For the electrical interconnection, the piezoelectric probe uses an in-probe flex circuit to route the element signals to a multicoaxial cable, while the CMUT probe contains additional in-probe circuit boards with low-noise amplifiers, which also connect to a multicoaxial cable. Although both probes share the same cable type, the CMUT's in-probe electronics introduce a higher potential for electrical crosstalk due to more complex signal routing. Table I reports the two-way -6-dB center frequency, $f_c$, the pitch, and the elevation aperture of the two probes, and Fig. 1(a) shows pictures of the probes used.

The ULtrAsound OPen scanner ULA-OP [28] was used to drive the ultrasound probes and collect ultrasound radio frequency (RF) data with a sampling frequency of 50 MHz.

<table><caption>TABLE I
PIEZOELECTRIC AND CMUT PROBE SPECIFICATIONS</caption><thead><tr><th></th><th>f<sub>c</sub> (MHz)*</th><th>pitch (mm)</th><th>elevation aperture (mm)</th></tr></thead><tbody><tr><td>LA435</td><td>10.9</td><td>0.2</td><td>3.5</td></tr><tr><td>HF3</td><td>10.8</td><td>0.2</td><td>3.0</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>Fig. 1. (a) Photographs of the CMUT and piezoelectric probes. (b) Schematic of the experimental configuration used to measure the transmitted beam patterns with a hydrophone, and representation of the reference systems for the scanning area $(x-y)$ and the probe $(x_p-y_p)$.</figcaption></figure>

The ULA-OP analog front-end featured linear transmitters specifically consisting of 64 arbitrary waveform generators with a maximum output voltage of 12-V peak amplitude, and low-noise receivers with a bandpass frequency response ranging from 1 to 16 MHz. The raw RF data were acquired using the ULA-OP and postprocessed using MATLAB (MathWorks, Natick, MA, USA).

### B. TX Beam Pattern Measurements

The TX 2-D beam pattern in the azimuth plane was measured for each beam direction with a pressure measurement system composed of a 0.5-mm-diameter needle hydrophone (Model NH0500, Precision Acoustics, U.K.), a preamplifier, and a DC coupler. The output signal of the DC coupler was connected to a digitizer (PCI digitizer CS11G8, Gauge, Montreal, QC, Canada), for the acquisition of the hydrophone signal at a sampling frequency $F_s = 250$ MHz. The hydrophone was fixed onto a three-axis translation stage. A two-axis motorized translation stage (Physik Instrumente, model M-403.4PD, Karlsruhe, Germany) was used to control the hydrophone position in the $xy$ plane with a spatial resolution of 0.018 mm, and a manual translation table (Thorlabs, PT1, Le Mesnil-le-Roi, France) to control the $z$-direction. The $x, y$ and $z$ coordinates refer to the lateral, axial, and elevation directions, respectively [Fig. 1(b)]. The pulse repetition frequency (PRF) signal from the ULA-OP was

<footnote>* -6 dB two-way center frequency averaged over 192 elements.</footnote>
used as a trigger signal to synchronize the acquisition of the hydrophone signals with the TX excitation signals. The sound speed in the ULA-OP was set to 1486 m/s, corresponding to the sound speed in pure water at $T = 21$ °C, that is, the temperature at which the experiments were performed. The probes were excited with a one-cycle sinusoidal burst at 10 MHz. This frequency was selected as it closely matches the central frequency of the probes, ensuring that the −20-dB response spectrum of both probes remains within the system bandwidth. The beam steering angle $\beta$ (also referred to as the insonification direction) was varied from −30° to 0° in steps of 5°, keeping the focus at a depth of 15 mm and using an aperture of 32 elements.

The experiment was performed as follows: first, the probe was aligned and positioned so that the $x_p y_p$ plane of the probe matched the xy plane of the scanning area when $\beta = 0°$. In the z-direction (still at $\beta = 0°$), the hydrophone needle was positioned, thanks to the manual translation table by searching the best locations in the xz plane that maximize the signal amplitudes at two different positions (separated by 6 mm) in the y-direction. We then checked that these two best locations were in the same xy plane of the scanning area. Finally, to mitigate the effects of the limited angular sensitivity of the hydrophone [29], the hydrophone itself was tilted along the beam direction using a manual rotation stage [Fig. 1(b)]. This adjustment allows the hydrophone to operate within the central region of its angular response, where sensitivity remains optimal and consistent. The mechanical stage was programmed to automatically scan an area in the xy plane of $3 \times 6$ mm with steps of 0.05 mm in x and 0.1 mm in y. This scan area was chosen to take into account the −6 dB, two-way depth of focus, which was estimated to be approximately 6 mm, using the approximated formula $7.08\lambda f_{\#}^2$ [30]. Although the pressure wavefronts may not always be perfectly perpendicular to the hydrophone surface when scanned away from the beam axis, for all the steering angles considered, the maximum angle deviation in the array beam pattern region within −6 dB of the peak amplitude is negligible. As a result, hydrophone sensitivity remains stable, ensuring reliable measurements across this region.

For each point of the scanned area, the pulse intensity integral $\text{PII}(x, y)$ was computed from the conversion of the hydrophone signal $v(t)$ (in volts) into a pressure signal using the frequency-dependent calibration data. $\text{PII}(x, y)$, which represents the energy of the pressure $p(t)$ per unit area, was computed as

$$ \text{PII}(x, y) = \frac{1}{\rho c} \int_{\Delta t} p(t, x, y)^2 dt \quad (1) $$

where $\rho$ and $c$ are the mass density and sound speed in water, respectively, and $\Delta t$ is the time duration of the signal.

The estimated steering angle $\beta_{\text{meas}}$ was obtained by fitting a linear function $x_i = f(y_i) \approx my_i + b$ with the positions of the maximum values of $\text{PII}(x, y)$, denoted $(x_i, y_i)$. The resulting slope value $m$ allowed obtaining the steering angle as $\beta_{\text{meas}} = \arctan(m)$.

For each probe, acquisitions were performed for imposed steering angles in the range from −30° to 0° with a step of

<figure><img src="image_4.png" /><figcaption>Fig. 2. Examples of B-mode images and the analyzed ROI at $\beta = 0°$ for both (a) isotropic phantom and (b) anisotropic phantom. The red shadow represents the common area between the different orientations of the analyzed beams (i.e., $\pm 20°$ for the isotropic phantom and from −20° to 0° for the anisotropic phantom).</figcaption></figure>

$5°$. The uncertainty of $\beta_{\text{meas}}$ was achieved from the maximal absolute difference between two estimated values obtained by different acquisitions at −15° and −20°, resulting to be 0.4°.

### C. BSCs of Isotropic and Anisotropic Tissue-Mimicking Phantoms

BSC measurements were performed on tissue-mimicking phantoms by using the reference phantom technique to account for the electromechanical system response and the depth-dependent diffraction and focusing effects of the ultra-sound beam [11]. The reference phantom is an isotropic homogeneous phantom consisting of distilled water, 2% (w/w) agar powder (A9799, Sigma Aldrich, France), and 1% (w/w) polyamide microparticles with a mean diameter of 7 µm (Orgasol 2001 UD NAT 1, Arkema, France). The performance of the CMUT and piezoelectric probes for off-axis BSC measurements has been evaluated on isotropic and anisotropic phantoms (Fig. 2). The isotropic homogeneous phantom was composed of distilled water, 2% (w/w) agar powder, and 1% (w/w) polyamide microparticles with a mean diameter of 11 µm (Orgasol 2001 EXD NAT 1, Arkema, France). The polyamide microparticles had a sound speed of 2300 m/s, a density of 1030 kg/m³, and a Poisson's ratio of 0.42, as provided in [31]. The anisotropic phantom was composed of two layers: a top layer of 4 mm thickness made of two isolated glass beads of 0.5 mm diameter embedded in an agar-agar gel, and a bottom layer made of rod-like fibers with a mean diameter of 246 µm obtained from a dialysis filter (Dialyser FX100, Fresenius Medical Care, Bad Homburg, Germany) embedded in an agar-agar gel background, as shown in Fig. 2(b). The glass beads were used as references to position the probes in a repeatable way between different series of acquisitions. The fibers were mainly made of polysulfone with a sound speed of 2240 m/s and a density of 1240 kg/m³ [32].

For the three phantoms (reference, isotropic, and anisotropic), the longitudinal sound speed $c_l$ and attenuation were measured at $\beta = 0°$ by using an unfocused circular single-element transducer of center frequency 7.5 MHz in the pulse-echo mode. The attenuation was determined using an insertion-loss broadband technique [32] and was obtained from ten different locations in the phantoms. The measured attenuation (expressed in dB/cm) was fit in the frequency range 3.5–9-MHz bandwidth with the linear function $\alpha_s f$, where $f$ is the frequency in MHz and $\alpha_s$ is the attenuation coefficient in dB/cm/MHz. Table II summarizes
<caption>TABLE II</caption>

SOUND SPEED $c_l$ AND ATTENUATION COEFFICIENT $\alpha_s$ MEASURED AT $\beta = 0^\circ$ FOR THE THREE PHANTOMS (REFERENCE, ISOTROPIC, AND ANISOTROPIC)

<table><thead><tr><th>Phantom</th><th>c<sub>l</sub> (m/s)</th><th>α<sub>s</sub> (dB/cm/MHz)</th></tr></thead><tbody><tr><td>Isotropic</td><td>1505.6 ± 0.8</td><td>0.054 ± 0.015</td></tr><tr><td>Anisotropic</td><td>1520.2 ± 0.8</td><td>0.513 ± 0.061</td></tr><tr><td>Reference</td><td>1504.5 ± 0.2</td><td>0.065 ± 0.005</td></tr></tbody></table>

the longitudinal sound speed $c_l$ and attenuation coefficient $\alpha_s$ measured from the reference, isotropic, and anisotropic phantoms.

To measure the BSCs of phantoms, the probe was excited with a one-cycle sinusoidal burst at 10 MHz. As performed previously in the hydrophone measurements, a beam focused at 15 mm was transmitted using an aperture of 32 elements. Dynamic focusing was performed in RX by using a maximum aperture of 64 elements with an *f*-number of 1.56. No apodization was applied in either TX or RX. For both the reference and isotropic phantoms, the beam steering angles were varied in the TX from -20° to 20° in steps of 5°, placing the probe at a distance of 10 mm from the water/phantom interface. Then, raw RF data for all the beam steering angles were acquired from 20 uncorrelated frames by translating the probe every 500 µm. For the anisotropic phantom, the beam steering angles were varied in transmission from -20° to 0° in steps of 5°. The anisotropic phantom was heterogeneous, with varying fiber alignments and fiber concentrations across different regions. To ensure both the CMUT and piezoelectric probes were positioned consistently, the probes were aligned using the two glass beads as reference points. [Fig. 2(b)], and only 2 uncorrelated frames of RF echo signals separated by 300 µm in elevation were acquired. The acquisition of raw RF data was repeated ten times to evaluate the repeatability of the experiments. Note that only 80 echo lines were uncorrelated among the 160 echo lines in the center of one frame obtained using the full-aperture transmission.

The power spectral densities (PSD) of the RF signal echoes were measured from regions of interest (ROI) centered at a depth of 15 mm from the probe face (corresponding approximately to the elevation focus for both probes), that is, 5 mm from the water/phantom interface (Fig. 2). The size of ROIs corresponded to 80 uncorrelated echo lines laterally and at least 15 pulse lengths axially, gated with a rectangular window. The ROI for the homogeneous isotropic phantom was placed in the center of the image. The ROI for the heterogeneous anisotropic phantom was located on the left side of the image, corresponding to the most homogeneous region of the phantom for the two uncorrelated frames separated by 300 µm in elevation. The average power spectral density of the isotropic or anisotropic phantom $S_{\text{sample}}$ (and the average power spectral density of the reference phantom $S_{\text{ref}}$, respectively) was calculated as the average of the PSD measured from the echo lines within the ROI of one frame (and from the echo lines within the ROIs of the 20 acquired frames, respectively). For each beam steering angle $\beta$, the BSC is given by

$$BSC_{\text{meas}}(\beta, f) = BSC_{\text{ref}}(f) \frac{S_{\text{sample}}(\beta, f)}{S_{\text{ref}}(\beta, f)} e^{4z_d f (\alpha_s - \alpha_{\text{ref}})} \quad (2)$$

<caption>TABLE III</caption>

MEASURED BEAM STEERING ANGLE $\beta_{\text{meas}}$. THE GOODNESS-OF-FIT COEFFICIENT $R^2$ OF THE LINEAR FITTING USED TO COMPUTE $\beta_{\text{meas}}$ AND THE MAXIMUM AMPLITUDE OF PII (DENOTED $A_{\text{max}}$) ARE ALSO REPORTED FOR EACH BEAM DIRECTION

<table><thead><tr><th rowspan="2">β<sub>set</sub></th><th colspan="3">Piezoelectric probe</th><th colspan="3">CMUT probe</th></tr><tr><th>β<sub>meas</sub></th><th>R<sup>2</sup></th><th>A<sub>max</sub></th><th>β<sub>meas</sub></th><th>R<sup>2</sup></th><th>A<sub>max</sub></th></tr></thead><tbody><tr><td>0°</td><td>-0.4°</td><td>0.72</td><td>1925.4</td><td>0°</td><td>0.551</td><td>314.9</td></tr><tr><td>-5°</td><td>-5.6°</td><td>0.98</td><td>1996.4</td><td>-4.9°</td><td>0.992</td><td>310.0</td></tr><tr><td>-10°</td><td>-7.7°</td><td>0.99</td><td>1986.8</td><td>-9.4°</td><td>0.998</td><td>284.2</td></tr><tr><td>-15°</td><td>-11.4°</td><td>0.99</td><td>1607.4</td><td>-14.1°</td><td>0.999</td><td>239.6</td></tr><tr><td>-20°</td><td>-17.0°</td><td>0.99</td><td>1308.9</td><td>-18.1°</td><td>0.999</td><td>214.4</td></tr><tr><td>-25°</td><td>-20.7°</td><td>0.99</td><td>918.5</td><td>-22.3°</td><td>0.999</td><td>163.8</td></tr><tr><td>-30°</td><td>-24.8°</td><td>0.99</td><td>411.2</td><td>-27°</td><td>0.999</td><td>114.2</td></tr></tbody></table>

where $BSC_{\text{ref}}$ is the known reference phantom BSC given by (2) in [31] using the Faran model [33], $\alpha_s$ and $\alpha_{\text{ref}}$ are the attenuation coefficients of the investigated and reference phantoms, respectively, and $z_d$ is the distance from the water/phantom interface to the center of the ROI. The last term (i.e., the exponential function) compensates for attenuation effects.

Finally, the integrated backscatter coefficient (iBSC) was computed as

$$iBSC(\Delta f, \beta) = \frac{1}{(f_2 - f_1)} \int_{f_1}^{f_2} 10 \log_{10}(BSC_{\text{meas}}(\beta, f)) df \quad (3)$$

where $[f_1, f_2]$ is the analyzed frequency bandwidth, for which the PSD $S_{\text{sample}}$ at $\beta = 0^\circ$ of both probes are within the -6-dB bandwidth (to compare fairly the CMUT and piezoelectric probe performance).

### III. RESULTS

#### A. Estimation of the Actual Beam Steering Angles

Fig. 3(a) shows, as an example, the result of beam pattern measurements for the case of $\beta = -15^\circ$ for the two probes, where the actual and set beam directions are represented. Table III reports the estimated beam steering angles and the goodness-of-fit coefficient $R^2$ of the linear regression for all studied cases. Also noted in Table III is the maximum amplitude of PII, denoted $A_{\text{max}}$. For all cases studied, a difference was observed between the measured and set angles. The absolute difference between $\beta_{\text{set}}$ and $\beta_{\text{meas}}$ is less than 1° up to $\beta_{\text{set}} = -15^\circ$ for the CMUT probe (against up to $\beta_{\text{set}} = -5^\circ$ for the piezoelectric probe). Fig. 3(b) shows the maximum pressure (normalized to the maximum pressure at $\beta_{\text{set}} = 0^\circ$) as a function of $\beta_{\text{meas}}$ measured with the two probes. At $\beta_{\text{meas}} = -25^\circ$, the normalized maximum pressure measured with the CMUT probe was 6 dB higher than the piezoelectric probe. Concerning the beam direction and the maximum pressure estimations, the piezoelectric probe exhibited a worse steering capability with a more pronounced deviation between the set and the measured steering angle compared to the CMUT probe. This phenomenon is related to the higher crosstalk, as highlighted in [19], where similar effects are experimentally demonstrated on several linear piezoelectric probes fabricated using a similar transducer technology to the piezoelectric
<figure><img src="image_5.png" /><figcaption>Fig. 3. (a) Transmitted beam pattern measurements at $β_{set} = -15°$ for both piezoelectric and CMUT probes. The black cross represents the point where PII is maximum, and the line in black represents the expected beam direction. (b) Maximum pressure (normalized to the maximum pressure at $β_{set} = 0°$) as a function of $β_{meas}$ measured with the two probes. The symbols represent the measured pressures, and the solid lines are the corresponding fit curves.</figcaption></figure>

probe used in this work. For this reason, the maximum value of $|β_{set}|$ for computing BSC\_meas has been fixed to 20°, which corresponds to the angular range for which the normalized PII\_max is greater than -6 dB for both probes [Fig. 3(b)].

In Section III-B, special attention will be paid to the influence of this beam steering angle bias on the BSC measurements. Indeed, when the dynamic focusing in RX is carried out, the delays applied to the elements are calculated according to the receiving angle. To compute the BSC, this angle must be the same as in transmission. If the difference between the measured and set angles is neglected, a scattering angle between the transmitting and receiving beams exists, so the measurement procedure given in (2) will result in a differential scattering cross section per unit volume (and not a differential backscattering cross section per unit volume = BSC). In the following, the BSC results are reported in two ways: 1) by considering the imposed steering angles $β_{set}$ for dynamic focusing in RX, named uncorrected BSC\_meas (for which the difference between the measured and set angles is not taken into account); and 2) by considering the measured steering angles $β_{meas}$ for dynamic focusing in RX, named corrected BSC\_meas.

## B. Measurements of the Spectral BSC Parameters

1) *Isotropic Phantom*: Fig. 4 shows the average PSD in the -6-dB bandwidth measured with the two probes and normalized

<figure><img src="image_6.png" /><figcaption>Fig. 4. Average PSD measured with the two probes on the isotropic phantom for different beam steering angles. Each power spectral density was normalized to its maximum value.</figcaption></figure>

to its maximum value, which exhibits symmetrical results with reference to the beam steering angle. Both probes exhibit bandwidths that are independent of the beam steering angle. For the PSD obtained from the piezoelectric probe, the -6-dB bandwidth was equal to 7–15 MHz (73% fractional bandwidth centered at $f_c = 11$ MHz). For the CMUT probe, the -6-dB bandwidth was equal to 5.5–13 MHz (81% fractional bandwidth centered at $f_c = 9.3$ MHz). It can be observed that the PSD for the piezoelectric probe exhibited a distortion that increases with the beam steering angle, whereas the shape of the PSDs for the CMUT probe was always preserved. Possible reasons for the observed distortion are further discussed in Section IV-C.

Fig. 5(a) gives examples of frequency-dependent BSCs from the isotropic phantom measured with the two probes. For both probes, the standard deviation of frequency-dependent BSC obtained from the ten measurements is around 0.5 dB for all the studied beam steering angles. For each beam steering angle $β$, the absolute error in dB for the measured BSCs was evaluated as $ε(f, β) = |10 \log_{10}(\overline{\text{BSC}_{\text{meas}}(f, β)})/\overline{\text{BSC}_{\text{iso}}(f)})|$, where $\overline{\text{BSC}_{\text{meas}}}$ is the average value over the 10 BSC measurements and $\overline{\text{BSC}_{\text{iso}}}$ is the BSC theoretical prediction using the Faran model [31], [33] assumed to be the expected BSC value. The $\overline{\text{BSC}_{\text{meas}}}$ curves were in good agreement with the theoretical $\overline{\text{BSC}_{\text{iso}}}$ curves, whatever the probe used and the dynamic focusing considered in RX (corrected or uncorrected), with absolute errors less than 1.3 dB within the -6 dB bandwidth. Fig. 5(b) shows the iBSC results for the bandwidth of 7–13 MHz, for which the PSD at $β = 0°$ of both probes are within the -6-dB bandwidth. For both probes, a satisfactory agreement was obtained between the measured and predicted iBSCs with an absolute relative error of less than 0.4 dB for all the considered beam steering angles.

2) *Anisotropic Phantom*: Fig. 6(a) and (b), respectively, represents the uncorrected BSC\_meas considering $β_{set}$ for the dynamic focusing in RX (and the corrected BSC\_meas considering $β_{meas}$ for the dynamic focusing in RX, respectively) for all the studied beam steering angles. Note that the -6-dB bandwidths of the PSD were equal to 7–12 MHz for the piezoelectric probe and 4–11 MHz for the CMUT probe. However, the BSCs were calculated over a wide frequency bandwidth of 3.5–15 MHz to qualitatively compare the measurements
<figure><img src="image_7.png" /><figcaption>Fig. 5. (a) Uncorrected and corrected BSCmeas measured with both piezoelectric and CMUT probes at βset = 0° and -20° for the isotropic phantom. The plotted BSCs correspond to the mean value ± standard deviation computed from 10 BSC measurements. The dashed lines correspond to the predicted BSC by using the Faran model. (b) Corresponding iBSCs. The plotted iBSCs correspond to the mean value and standard deviation computed from 10 iBSC measurements.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 6. (a) Uncorrected BSCmeas measured with the piezoelectric and CMUT probes for the anisotropic phantom. The plotted BSCmeas corresponds to the mean value computed from 10 BSC measurements. The vertical dotted lines represent the 7–11-MHz frequency range, which is within the -6-dB bandwidths of the two probes. (b) Same as (a) for the corrected BSCmeas. (c) Corresponding iBSCs as a function of βmeas and the dashed lines are the corresponding fit curves for the uncorrected and corrected iBSCs.</figcaption></figure>

with the theoretical backscattering of a single finite cylinder, as discussed in Section IV-D. For both probes, the standard deviation of BSCmeas obtained from the ten measurements was approximately 0.5 dB, whatever the considered beam steering angles, which means that the repositioning of both probes for the ten measurements was quite good. It can be noticed that the BSC amplitude increases as β approaches 0°, as expected. Indeed, this beam steering angle corresponds to the direction perpendicular to the aligned fiber structure, for which the BSC amplitude is maximum [8], [34].

Fig. 6(c) shows the iBSC within the 7–11-MHz bandwidth as a function of βmeas. Good agreement between iBSCs measured with the CMUT and piezoelectric probes is obtained for βmeas less than 6°, whereas the uncorrected iBSCs have smaller values than the corrected iBSCs for βmeas greater than 6°, whatever the considered probe.

## IV. DISCUSSION

### A. Limitations in Hydrophone Measurements

A primary limitation pertains to potential misalignment between the scanning area and the 2-D beam profile, since the positioning of the hydrophone in elevation (direction perpendicular to the xy plane in Fig. 1) was done by searching the point with the maximum amplitude in the focusing area using a mechanical axis to which was coupled the motorized two-axis

translation stage. Then, two different points were selected, at greater and shallower depths, to search for the maximum amplitude at those locations and verify that they were in the same plane as the 2-D acquisitions. This 2-D acquisition plane was maintained for the other insonification angles. This procedure did not allow for verifying and evaluating the possible misalignment in elevation for all the points, which could be done by carrying out 3-D acquisitions at least for one of the acquisitions to better evaluate this type of misalignment.

Another limitation in the hydrophone measurements is related to the criterion used to sample the acoustic field of an imaging transducer with enough spatial resolution. A possible criterion for “enough resolution” relies on the condition for the maximum effective hydrophone radius ($b_{max}$) to be [35, eq. (13.4)]

$$b_{max} = \frac{\lambda}{4} \left[ (l/2a)^2 + 0.25 \right]^{1/2} \quad (4)$$

in which a is the transducer radius or equivalent dimension, λ is the wavelength in water, and l is the axial distance between the transducer and hydrophone. In the experiments here presented, the recommended $b_{max}$ at a frequency of 10 MHz should be around 0.06 mm (making 2a equal to the aperture A used in transmission, 6.4 mm, and l equal to the elevation focus, 15 mm, and using a sound speed in water of 1500 m/s), whereas the actual effective radius of the
hydrophone at 10 MHz is about 0.28 mm (value taken from the hydrophone data sheet). As a consequence, based on this criterion, the pressure field measurements reported in this study are characterized by limited spatial resolution, meaning that each measurement corresponds to the average value across the effective area of the hydrophone rather than a punctual spatial sample. However, this issue significantly affects only the pressure amplitudes and not the estimates of the beam steering angle based on PII. This issue may be more related to the increasing uncertainty in the amplitude of the pressure as the frequency increases, as indicated in the hydrophone data sheet.

## B. Estimation of the Beam Steering Direction

Different published works have shown that crosstalk degrades the steering capability of linear array probes, and consequently their angular response [17], [18], [19], [36], [37].

Theoretically, the element directivity depends on the element width (with an upper limit defined by the pitch) and on the frequency of the excitation signal. In the case of the probes used here, the two probes have the same pitch and very similar element widths and have been excited under the same conditions, so a similar directivity should be expected. Since the measurements were made in the near field in pulse-echo mode and using a broadband excitation signal, a prediction of the angular response under these conditions should be performed by numerical simulations including very accurate information on the transducers' transmit and receive electromechanical responses. For this article, a first-order approximation of the spatial response of a linear probe has been calculated considering the far-field approximation and continuous-wave operation as the product of the element factor and the array factor [16], [38], [39]. Considering an operating frequency of 10 MHz, the computed radiation pattern shows that the effect of directivity starts to become important at ±20°, where the magnitude of the main lobe is attenuated by 6 dB and the difference between the main lobe and first grating lobe magnitudes is 1.6 dB.

It is recalled that, in the experiments, the probes were excited with a one-cycle pulse at 10 MHz, which corresponds to a wide-band signal with a -6-dB transmit frequency band approximately in the 4–16-MHz range. Thus, the excitation signal bandwidth exceeded the -6-dB transmit bandwidth of the two probes. Since the two probes are characterized by different bandwidths, the fact that the full bandwidth was excited could have potentially impacted the steered beam response. Therefore, to better identify the effect of the bandwidth on the probe steering capabilities, a further experiment was carried out by exciting the piezoelectric probe with a narrow-band signal consisting of ten-cycle Hanning-tapered pulses at 10 MHz, for the case of $\beta = -15°$. This beam direction was selected because it corresponds to the maximal measured off-axis direction at which the grating lobe is expected to be sufficiently attenuated as compared to the main lobe. Fig. 7 shows the comparison between the measured beam pattern and estimated beam direction when the narrow and wide-band excitation is used. No effect of the bandwidth on the estimated beam direction was observed.

<figure><img src="image_9.png" /><figcaption>Fig. 7. (a) Transmitted beam pattern measurements for the piezoelectric probe at $\beta_{set} = -15°$, using one-cycle rectangle window tapered pulse (TXN = 1), and ten-cycle Hanning-tapered pulse (TXN = 10) in transmission. (b) Measured pressure signal in time and frequency for the maximum value of PII, for both cases.</figcaption></figure>

One can note in Table III that the maximum pressure $A_{max}$ at $\beta_{set} = 0°$ for the CMUT probe was 13 dB lower than that of the piezoelectric probe. Such a lower transmit pressure was not solely due to the lower transmit sensitivity of the CMUT probe, which, in normal operation, is known to be only 4.2 dB less than that of the piezoelectric probe. Instead, it was primarily caused by the suboptimal operation of the automatic transmit/receive switches in the low-noise amplifiers (LNAs, MAX4805A, Analog Devices, Wilmington, MI, USA) integrated into the probe [27]. Due to the time required for the control circuits to detect the arrival of the excitation signal and switch from receive to transmit, these switches are known to introduce a high attenuation of the excitation signals, particularly for high frequencies (≥10 MHz), large bandwidths (>100%), and low voltages (≤15 V).

From the bibliography and the results obtained in this work, it can be deduced that the crosstalk effects explain the observed deviations between the setup and the measured directions for the piezoelectric probe for the cases of -10° and -15°. On the other hand, no important deviation was observed for the angular range from 0° to -15° for the CMUT probe, which allows interpreting that crosstalk does not play an important role in the steering capabilities of the specific CMUT probe used in this work. For the cases of -20° to -30°, the results reported a loss of performance for both probes, being the deviation with respect to the expected beam direction smaller for the CMUT probe as compared to the piezoelectric probe. The loss of performance for large steering angles is directly
related to the element directivity and, for the piezoelectric
probe only, also to the high interelement crosstalk. It is worth
emphasizing that, as reported in Ramalli et al. [19], transmit
apodization can improve the beam directivity at the cost of
other beam properties, such as beamwidth and, therefore,
lateral resolution, but it was decided not to use it as the
objective of this paper was to investigate the performance with
a focus on probe directivity.

Regarding the lower pressure generated by the CMUT
probe, potential limitations in terms of the signal-to-noise ratio
(SNR) could arise if the transducer is not optimally driven
and if the received signals are not optimally conditioned.
To address this, if the probe and scanner permit, driving the
CMUT with high-amplitude excitation signals can maximize
the transmit pressure. For instance, the CMUT probe used in
this study can be driven with signals up to a 100-V peak, which
is higher than the LA435 piezoelectric probe, which, according
to the manufacturer's specifications, is limited to about 50 V.
This compensates for the lower transmit sensitivity of the
CMUT. Complementing this, Mattesini et al. [40] compared
the performance of a 7-MHz CMUT probe based on the same
technology used in this article with a state-of-the-art single-
crystal piezoelectric probe that was characterized by higher
transmit sensitivity. They demonstrated that by appropriately
exciting the probes to achieve equal transmit pressure, the
CMUT probe outperformed the piezoelectric probe in terms
of signal power by approximately 9 dB. Therefore, we can
confidently conclude that the results achieved in this article
with the CMUT probe are representative of a linear probe with
lower crosstalk, compared to a standard piezoelectric probe
typically characterized by higher crosstalk.

C. Power Spectral Densities

Comparing the PSD of both probes shows that the CMUT
probe presents a broader bandwidth than the piezoelectric
probe, which was already evidenced in previous studies,
for example, [27]. Distortion in the PSD was observed for
$\beta_{set} = \pm 20^\circ$ with the piezoelectric probe for the reference
and isotropic phantoms (Fig. 4). This distortion could be
due to the effect of nonlinear beam propagation caused by
the higher amplitude pressure generated by the piezoelectric
probe as compared with the CMUT probe in our experimental
conditions (Table III), or/and to the crosstalk effects. The
hypothesis of nonlinear beam propagation was tested by per-
forming complementary experiments with lower amplitudes
for the excitation signal, and the same distortion was obtained
in all cases (data not shown). Therefore, it can be concluded
that this distortion is mainly caused by the crosstalk effects,
which produce deviations in the beam steering angles for
$|\beta_{set}| \ge 10^\circ$.

D. Spectral BSC Parameters

The results presented in Fig. 6 demonstrate that the cali-
bration technique using a reference phantom is not sufficient
to compute accurately the BSC from anisotropic phantoms.
Particular attention should be paid to the limited beam steer-
ing performance of ultrasonic probes, which influences the

accuracy of the off-axis BSC measurements. Indeed, as the
imposed steering angles increase, the actual beam steering
angles deviate from the expected value. A significant error in
the off-axis BSC amplitude could be obtained on anisotropic
phantoms if the actual beam steering angle is not measured and
corrected appropriately, as shown by the difference obtained
between the uncorrected and corrected BSCs in Fig. 6. This
error is more pronounced as the imposed steering angles
increase, especially for the piezoelectric probe in the case of
a similar CMUT/piezoelectric array design. When computing
the corrected BSC for the off-axis measurements, a bias in
beam steering angle measurements can lead to a bias in
BSC estimates. Since a satisfactory match between imposed
and measured beam steering angles was obtained for 0° ≤
$|\beta_{set}| ≤ 15°$ for the CMUT probe (against 0° ≤ $|\beta_{set}| ≤
5°$ for the piezoelectric probe), the calculation of off-axis
BSC measurements with CMUT requires less correction and
thus produces more accurate BSC estimates. To conclude, the
added value of the proposed CMUT probe is a better steering
capability to access a wider range of steering angles and to
produce more accurate BSC estimates.

For the isotropic phantom, the absolute error when com-
pared to the theoretical prediction was less than 1 dB for the
BSC<sub>meas</sub> measured within the 7–13-MHz bandwidth, and less
than 0.5 dB for the iBSC measurements, whatever the beam
steering angle or probe used and whatever the dynamic focus-
ing considered in RX (i.e., corrected or uncorrected BSC<sub>meas</sub>).
Note that there is no significant difference between the uncor-
rected and corrected BSC<sub>meas</sub> for the isotropic phantom (Fig. 5)
since the scattering pattern for Rayleigh scatterers is nearly
isotropic. Indeed, the *kr* product (being *k* the wavenumber
and *r* the characteristic scatterer radius) is equal to 0.23 for
the isotropic phantom with 5.5-μm scatterer radius.

For the anisotropic phantom, a quantitative comparison
between the theoretical and measured BSCs is not as straight-
forward as the comparison made for the isotropic phantom,
because all fibers are not perfectly aligned, and the fiber
concentration is heterogeneous in elevation and uncontrolled.
So, the BSC<sub>meas</sub> at β = 0° was qualitatively compared with the
theoretical predictions of an ensemble of aligned finite fluid
cylinders of radius *r* and length *L* (with acoustic properties of
polysulfone) embedded in a fluid surrounding medium (with
acoustic properties of water) and insonified by a normally
incident plane wave. The length *L* of finite cylinders was set
considering that the fibers are limited in the lateral dimension
by the beamwidth, that is, *L* = 0.3 mm. The differential
backscattering cross section of a finite fluid cylinder σ<sub>c</sub>(*k*, *r*)
is related to the form factor of the finite fluid cylinder given
in [41]. Fig. 8 compares the normalized BSC<sub>meas</sub> measured
at β = 0°, the normalized BSC from monodisperse finite
cylinders σ<sub>c</sub>(*k*, *r*) of radius *r* = 123 μm, and the normalized
BSC from polydisperse finite cylinders (∫*p*(*r*)σ<sub>c</sub>(*k*, *r*)*d*r*) for
which the radii vary from 113 to 133 μm following a uniform
distribution. The normalized response means that each curve
was normalized by its maximum. Both normalized BSC<sub>meas</sub>
and theoretical BSC prediction from polydisperse aligned
finite cylinders follow the same trends with several peaks
and dips. The mismatch between the frequency occurrence
<figure><img src="image_10.png" /><figcaption>Fig. 8. Comparison between the normalized BSC<sub>meas</sub> measured at β = 0° from the anisotropic phantom and the normalized theoretical BSC from monodisperse finite cylinders and polydisperse finite cylinders.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 9. Example of simple ray theory for a single fiber perfectly aligned to the probe placed at the focal depth of 15 mm.</figcaption></figure>

for the peaks and dips can be attributed to errors in size variation and/or acoustic properties of polysulfone, and/or to the approximation of incoherent scattering, since at high volume fractions, the coherent scattering can also influence the frequency dependence of BSC [31], [42].

As observed in Fig. 6, the BSC amplitude (and therefore the iBSC) decreases as the angle between the beam direction and the fiber orientation decreases. These observations are in line with the results obtained by Guerrero et al. [7], for which the backscattered power difference (BSPD) spectral parameter comparable to the iBSC was measured as a function of the beam direction for an anisotropic phantom consisting of aligned fibers (similar to the anisotropic phantom studied here). The BSPD had a maximum amplitude for the beam direction perpendicular to the fiber orientation [7]. Note that the scattering regime for the anisotropic phantom is around kr ≈ 5.15, so a part of the scattering may come from the specular reflection of the fibers. Considering a single fiber perfectly aligned to the probe placed at the focal depth of 15 mm and utilizing simple ray theory (Fig. 9), the distances D between the emitted and received rays at the probe are equal to 2.9, 4.1, 6.0, and 9.2 mm for β<sub>meas</sub> = 5.6°, 7.7°, 11.4°, and 17° with the piezoelectric probe (and equal to 2.6, 5.0, 7.5, and 9.8 mm for β<sub>meas</sub> = 4.9°, 9.4°, 14.1°, and 18.1° with the

CMUT probe). When this distance is of the same order of magnitude or greater than the active half-length of the probe of 6.4 mm, a part of specular reflection cannot be captured by the probe and may explain the significant decrease in the iBSC for the largest β<sub>meas</sub>.

Significant differences can be noticed between the uncorrected and corrected BSC<sub>meas</sub> for the anisotropic phantom (Fig. 6), which is caused by the differences between the scattering and backscattering cross sections, or in other words, by the changes in the directional signal reception. Indeed, this difference increases as the scattering angle increases for both probes. With the piezoelectric probe (and the CMUT probe, respectively), the largest difference is equal to 15.7 dB corresponding to the scattering angle of 3.6° (and is equal to 9.8 dB with the CMUT probe corresponding to the scattering angle of 1.9°, respectively).

V. CONCLUSION

The experimental strategy to measure the anisotropy of the BSC using conventional focused beam steering with a linear probe was evaluated by comparing two probes with similar characteristics in terms of array geometry and operating frequencies: one based on conventional piezoelectric technology and the other on CMUT technology. This study demonstrated that limited probe steering capability plays an important role in developing experimental strategies for analyzing tissue anisotropy, specifically through off-axis measurements of backscattered signals or transmission of an off-axis ultrasound beam. These effects should be routinely characterized in any experimental approach aimed at measuring tissue anisotropy using a linear probe to ensure measurement validity. In this study, the CMUT probe proved advantageous in extending the angular range due to its lower crosstalk compared to a traditional piezoelectric probe with similar nominal frequencies, pitches, and elevation apertures. Thus, CMUT technology can be considered a possible alternative to standard piezoelectric transducer technology to overcome the limitations of conventional piezoelectric probes when performing off-axis measurements, particularly when the steering capability is not predetermined. Nonetheless, attention must be paid to the potentially lower SNR, due to the generally reduced transmit sensitivity of CMUT probes compared to state-of-the-art piezoelectric probes. This reduced sensitivity can be mitigated by using high-voltage excitation signals, though this option may be limited by the maximum voltage capabilities of the scanner. Overall, this work underscores the significant impact of steering capabilities on BSC anisotropy measurements. By using probes with enhanced steering capability, a broader range of steering angles can be accessed, resulting in more accurate BSC estimates. Such improved off-axis BSC measurements provide QUS estimates that more accurately quantify tissue anisotropy, which may hold substantial clinical relevance. Although this study used a CMUT probe, the insights gained are broadly applicable to other transducer technologies with improved steering performance, highlighting the value of advanced transducer designs for accurate tissue anisotropy assessments in clinical settings. Future studies could build on these findings by investigating the clinical
benefits of enhanced steering capabilities for off-axis BSC measurements and anisotropic QUS estimates, particularly in contexts such as monitoring of blood circulatory disorders [13] or assessing cervical remodeling [14], [15].

## ACKNOWLEDGMENT

The authors would like to thank Guy Rabau, Olivier Pot, and Vincent Long from the Laboratory of Mechanics and Acoustics (LMA) for their technical assistance. They authors are also grateful to Barbara Mauti for her support in the packaging of the CMUT probe used in the experiments.

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<figure><img src="image_12.png" /></figure>

**Emilie Franceschini** (Member, IEEE) received the M.S. degree in acoustics from the University of Méditérannée, Marseille, France, in 2003, and the Ph.D. degree in acoustics from the University of Provence, Marseille, 2006.

In 2007, she was a Postdoctoral Fellow at the Laboratory of Biorheology and Medical Ultrasonics, Research Center of the University of Montreal Hospital, Montreal, QC, Canada, conducting research in ultrasonic blood characterization. Since 2008, she has been a Researcher at the French National Center for Scientific Research (CNRS), University of Aix-Marseille, Marseille. Her research interests include ultrasound tissue characterization, ultrasound tomography, quantitative ultrasound techniques, and ultrasonic neurostimulation.

Dr. Franceschini is a member of the French Acoustical Society (SFA) and IEEE UFFC.

<figure><img src="image_13.png" /></figure>

**Lenin Chinchilla** (Member, IEEE) was born in Bucaramanga, Colombia, in 1986. He received the Electronic Engineer and Physicist degrees and the master's degree in electronic engineering from Universidad Industrial de Santander, Bucaramanga, in 2011, 2012, and 2015, respectively, and the Ph.D. degree in engineering sciences, specialty acoustics from AIX-Marseille University, Marseille, France, in co-tutelle with Roma Tre University, Marseille, Italy, in 2020.

He was a Research Engineer at the Multimodal Biomedical Imaging Research Laboratory, Biomaps, Université Paris-Saclay, Orsay, France, from 2020 to 2023, working mainly on the development of new imaging modalities based on ultrafast ultrasound imaging approach. Since 2023, he has held the position of ultrasound scientist at Verasonics, Kirkland, WA, USA. His current research interests include quantitative ultrasound techniques, ultrasound tissue characterization, ultrafast ultrasound imaging, therapeutic ultrasound, and signal processing.

<figure><img src="image_14.png" /></figure>

**Alessandro Stuart Savoia** (Member, IEEE) received the Laurea degree (M.S.) and the Ph.D. degree in electronic engineering from Roma Tre University, Italy, in 2003 and 2007, respectively. Since 2007, he has held a Postdoctoral Research position at the Department of Electronics Engineering, Roma Tre University. In the years 2008 to 2010, he participated as a co-founder and Research and Development Manager in an academic spin-off company of Roma Tre University, focused on the industrial

exploitation of MEMS-based ultrasonic transducers (CMUTs), leveraging scientific results achieved during his Ph.D. and Postdoctoral Research. In 2014, he became an Assistant Professor in electronics at the Department of Engineering, Roma Tre University. In 2020, he obtained the National Scientific Qualification (ASN) for Full Professor in electronics.

He leads research activities at the Acousto-Electronics Laboratory, Department of Industrial, Electronic, and Mechanical Engineering, Roma Tre University, in the field of ultrasonic transducers. His research interests are mainly focused on the development and system integration of MEMS ultrasonic transducers (CMUT and PMUT). He has authored and co-authored more than 120 papers in international journals and conferences, most of them published in IEEE TRANSACTIONS and IEEE Conference Proceedings, and five book chapters. He holds seven international patents.

Dr. Savoia serves the IEEE UFFC Society as an Associate Editor for the IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, as a Guest Editor for the IEEE OPEN JOURNAL ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, as a Chair of the TPC Group 5 "Transducers and Transducer Materials" of the International Ultrasonics Symposium, and as Elected Member of AdCom.

**Régine Guillermin** graduated from the Ecole Nationale Supérieure de Physique de Marseille, France, in 1996, and the Ph.D. degree in physics from the Université de la Méditerranée, Aix-Marseille II, in 2000.

Since 2001, she has been a Research Engineer at the Laboratory of Mechanics and Acoustics, French National Center for Scientific Research (CNRS), UPR, Marseille. Her work is focused on ultrasonic imaging and ultrasonic quantitative characterization for biomedical and underwater applications.