Optical Tracking for Freehand Swept Synthetic Aperture Imaging

Abstract

Achieving higher resolution for deeper tissue structures remains a significant challenge in ultrasound imaging due to the inherent limitations of diffraction. Swept Synthetic Aperture (SSA) techniques, which utilize the motion of a single transducer to effectively increase the imaging aperture, offer a promising solution. Building on SSA, we propose that freehand SSA provides a flexible approach with real-time adaptability to varying patient anatomies. This paper introduces the Optically Tracked SSA (OT-SSA) platform, an approach that integrates external tracking to ensure accurate transducer positioning during freehand sweeps. Key sources of image degradation, such as spatial calibration error, tracking precision, and out-of-plane motion were directly analyzed and addressed within the system. In in vivo quadriceps imaging, OT-SSA reduced average lateral speckle autocorrelation size from 2.33 mm to 0.49 mm compared to a stationary aperture, demonstrating substantial resolution gains. The results establish OT-SSA as a robust and adaptable approach for high-resolution imaging.

Graphical Abstract

I. Introduction

Ultrasound (US) imaging is a widely utilized diagnostic tool due to its non-invasive nature and cost-effectiveness. However, its resolution is fundamentally limited by diffraction, which results in suboptimal image quality when targeting deeper anatomical structures. This limitation is exacerbated in obese patients, where greater imaging depth leads to further degradation of resolution and reduced ability to accurately resolve clinically relevant targets, including pathological findings [1]. This diffraction-limited resolution is a consequence of the relatively small size of the imaging aperture, a physical limitation common to all wave-based imaging modalities. In optics, similar challenges have driven the development of various super-resolution techniques [2]–[5]. While these have revolutionized microscopy, their direct translation to ultrasound is difficult. For example, Ultrasound Localization Microscopy bypasses optical diffraction limits, but it remains restricted to vascular imaging and depends on the use of exogenous contrast agents [6], [7].

One intuitive approach to enhancing the diffraction-limited resolution in ultrasound involves increasing the aperture size [8]. However, the use of physically larger transducers introduces its own set of challenges, including increased complexity, higher costs, limited compatibility with commercial ultrasound systems, and reduced adaptability to patient-specific anatomy [9], [10]. As a result, various approaches have been explored to increase the effective aperture size without enlarging the physical transducer.

For example, the Coherent Multi-Transducer US (CoMTUS) Imaging System extends the imaging aperture through the use of two synchronized, identical linear or volumetric arrays sharing a common FOV. The acquisition sequence involves each transducer sequentially emitting plane waves (PW) into the shared field, while both transducers simultaneously receive the backscattered echoes [11], [12]. Due to the freehand placement of the transducers, the system allows flexible orientations and positions. However, the separation between the independent transducers creates a discontinuous aperture, leading to grating lobes—unwanted secondary beams that occur due to missing spatial frequencies and that reduce image contrast [13], [14]. As a result, the lateral resolution achievable by CoMTUS is constrained by a trade-off: expanding the effective aperture while trying to preserve image quality.

A different approach combines three commercial phased arrays creating a large aperture with 384 elements and a 10 cm lateral size [15]. Here the transducers act as a single aperture with all three arrays simultaneously transmitting PWs angled with respect to the central array. In this case, gaps between the arrays are minimized by using a 3D-printed concave fixture to stack the transducers, and by applying an auto-regressive filter [16] to predict signals received by virtual elements placed in empty spaces between transducers. This method offers several benefits such as full-aperture transmission with all three transducers for quicker data acquisition, and improved ease of use. However, its fixed geometry limits real-time adaptability and the high channel count might hinder its compatibility with commercial systems.

Swept Synthetic Aperture (SSA) utilizes the motion of a single transducer to synthesize a larger, continuous aperture [17]. As the probe sweeps across the imaging field, low-resolution images acquired at different spatial locations are coherently combined to reconstruct a higher-resolution image. This approach parallels methods used in sonar and radar imaging, where the motion of an antenna enhances spatial resolution through similar synthetic aperture techniques [18], [19]. The feasibility of SSA has been demonstrated in controlled settings, such as using a robotic arm to move the transducer while simultaneously recording its position [17], and through a 3D-printed mechanical fixture that restricted the transducer’s motion to one degree of freedom (DOF), with position estimation achieved through data-based methods [20]. While these setups confirm SSA’s potential, they also introduce limitations; robotic arms are impractical in many settings due to their complexity, and constrained one-degree-of-freedom motion limits flexibility in real-world applications. In contrast, freehand SSA would inherently offer significantly more adaptability. The unconstrained motion of a single transducer would allow the system to accommodate patient-specific anatomies and would maintain compatibility with current ultrasound platforms, including compact point-of-care systems. However, the success of this approach hinges on the ability to accurately reconstruct the synthesized aperture from unconstrained probe motion, which requires 6-DOF transducer tracking.

A similar requirement exists in freehand 3D ultrasound, where 6-DOF tracking has been widely adopted to reconstruct volumetric datasets from a series of 2D slices acquired along the elevational axis [21]. Over the past two decades, several tracking systems have been explored for this purpose, with the most common categories being electromagnetic (EM) and optical tracking. While EM tracking can achieve submillimeter accuracy in ideal conditions, its performance is highly sensitive to magnetic field distortions, metallic interference, and sensor alignment, making it unreliable in many real-world environments [22]. Optical tracking offers a more stable alternative. One recent low-cost implementation uses ArUco markers arranged on a dodecahedron affixed to the transducer. This setup requires only a standard video camera and is robust to occlusion. However, such systems typically achieve only moderate spatial accuracy—around 2.9 mm ± 5.5 mm [23].

While these tracking modalities all support full 6-DOF pose estimation and are viable for standard 3D ultrasound reconstruction, SSA imaging imposes far more stringent accuracy requirements. In 3D ultrasound, small tracking errors result in minor spatial misalignments that can be visually tolerated or smoothed during rendering. In contrast, SSA relies on coherent compounding of radiofrequency (RF) data across transducer positions. Even sub-millimeter deviations can lead to phase misalignment, destructive interference, and loss of resolution. As a result, sub-wavelength accuracy (0.25λ) is essential for robust SSA image formation [24].

To meet the spatial fidelity required for coherent reconstruction, our OT-SSA platform employs infrared (IR) based optical tracking. This more precise class of optical systems uses active or passive IR markers tracked by specialized cameras, achieving spatial fidelities on the order of ±0.2 mm while remaining robust to ambient lighting and environmental conditions [25]. These IR systems have already been employed in freehand 3D ultrasound—for example, enabling accurate fetal phantom volume reconstruction with sub-millimeter translation accuracy [26].

This paper extends our previous conference proceedings on the Optically Tracked SSA (OT-SSA) imaging platform [27], [28], which demonstrated the feasibility of using IR tracking for freehand SSA and showed improved resolution compared to a stationary multistatic aperture. While our prior work focused on demonstrating improved image quality, this study provides a comprehensive system-level evaluation of OT-SSA. We introduce a component-wise analysis of factors affecting image formation, including spatial calibration, tracking precision, frame spacing, and sweep extent. We assess sensitivity to out-of-plane motion using both simulations and real freehand trajectories, and adopt a beamforming method that better models off-axis points relative to the fixed elevation focus.

We further expand image-based validation through a larger set of phantom sweeps to assess repeatability, and conclude with a new in vivo demonstration to highlight clinical potential. Collectively, these findings establish that the OT-SSA platform can consistently achieve high-resolution imaging under realistic scanning conditions and provide a robust framework for future studies aimed at tackling the more complex physical dynamics of freehand transducer motion in vivo.

II. Theory

This section offers a brief review of the theoretical basis for SSA imaging established in prior work [10]. SSA improves lateral resolution by expanding the system’s spatial frequency coverage through transducer motion. In the spatial frequency domain, or k-space, each transmit-receive event samples a portion of the image’s frequency content [29]. As the transducer sweeps across different positions and orientations, it accesses new spatial frequencies, broadening overall k-space coverage. By the Fourier relationship, this results in a narrower point spread function (PSF) and thus improved lateral resolution. To fully benefit from this, signals acquired from different positions must be coherently combined. This is possible under the assumption that the imaging system behaves approximately as a linear shift-invariant (LSI) system. Under this assumption, spatial shifts in transmit-receive geometry result in predictable time delays in the received signals [30], which are compensated via delay-and-sum (DAS) beamforming.

In SSA, each acquisition obtained throughout the sweep is beamformed onto a fixed output grid using the known pose of the transducer. This can be achieved either by updating the transmit and receive element positions or by transforming the beamforming grid into the transducer’s local frame. The resulting low-resolution subimages, each aligned to the same spatial grid, are then coherently summed, preserving phase, to yield a high-resolution image with enhanced spatial frequency coverage. Importantly, subimage overlap is necessary to achieve the theoretical gains of SSA. The effective aperture is limited not only by sweep length but by the extent to which transmitted beams insonify common spatial locations. Diverging waves facilitate this overlap by increasing angular coverage with depth, particularly when transmitted from small elements with wide acceptance angles.

In freehand SSA, the lack of controlled probe motion means that the sweep trajectory often deviates from a strictly planar path. As a result, acquired frames may not lie on a common 2D imaging plane—violating a core assumption of conventional SSA. Although 6-DOF tracking enables retrospective alignment to a reference plane, physical limitations of the transducer still apply. Most 1D arrays use a fixed mechanical lens to focus energy in the elevation direction, confining the transmitted beam to a narrow slice around the elevational focal depth. This introduces two key challenges. First, because the beam is not truly divergent in elevation, conventional delay models become inaccurate when beamforming points that lie away from the elevational focal plane—leading to time-of-flight errors. Second, targets outside the main elevational beam receive minimal acoustic energy, and the resulting signals are often dominated by edge waves. In such regions, the assumed beam geometry no longer holds, making accurate reconstruction difficult and reducing image quality.

Finally, non-uniform lateral sampling—caused by variable sweep speed typical of freehand motion—leads to irregular spacing between acquisitions and uneven k-space coverage. This can distort the system’s frequency response, producing sidelobes, PSF broadening, or anisotropic resolution. Together, these challenges highlight the sensitivity of SSA to uncontrolled motion, emphasizing the need not only for robust validation and characterization, but also for the adoption of novel strategies that address the unique demands of freehand coherent imaging.

III. Methods

A. System integration

The experimental framework includes three main components: the Verasonics Vantage ultrasound scanner (Verasonics Inc., Washington) equipped with a P4–2 transducer (3 MHz, 64 elements), and the NDI Polaris Vega^® XT optical tracking system (Northern Digital Inc., Ontario) as shown in Fig. 1. The tracking system consists of a camera unit and a specialized NDI tool equipped with a pattern of four Passive Sphere^™ reflectors. By tracking the relative position of these markers in real time, the camera accurately identifies the tool’s position and orientation within 3D space with a reported volumetric accuracy of 0.12 mm RMS within the main capture volume and 0.15 mm RMS in the extended volume. The transducer is securely mounted within a custom, handheld-sized 3D-printed fixture providing rigid physical connection between the imaging array and the NDI tool housing the passive infrared reflectors. In practice, the camera reliably tracks the tool as long as all markers remain visible within the capture volume. Since the primary motion during sweeps occurs laterally, the maximum sweep length is effectively constrained by the width of the tracking volume. However, this does not pose a practical limitation: all sweeps in this study were under 20 cm, well within the effective tracking range (see Fig. 1d) [31].

Fig. 1.

Physical setup and coordinate systems for OT-SSA imaging. (a) Key hardware components and their associated coordinate frames, with transformation matrices indicating the spatial relationships between them. (b) Schematic of the transducer’s primary sweep direction, including matrices describing relative motion. (c) Experimental setup for an OT-SSA acquisition using the CIRS phantom. (d) Optical tracking system working volume, illustrating the line-of-sight coverage from three viewpoints. Images in (d) are adapted directly from NDI Polaris Vega XT documentation, which defines the volume within which tool tracking is maintained.

Acoustic and optical acquisition in the Verasonics platform are managed by separate sequencers operating asynchronously. To align their start times, a ‘sync’ command halts acoustic acquisition until optical tracking begins, ensuring the first acoustic and optical frames correspond. Both systems then acquire at 400 Hz, enabling frame-by-frame pose matching. Synchronization was verified by performing abrupt sweeps over a point target in a phantom; inflection points in the tracked trajectory coincided with changes in RF data, indicating no detectable lag across trials at this acquisition rate.

B. Data acquisition

During the sweep, each frame was acquired at 400 Hz using a single divergent wave transmission, firing 12 elements from a virtual source located at (0, 0, –2.88) mm relative to the array center, with full aperture reception. This transmit configuration improves signal-to-noise ratio over single-element firing while maintaining wide field coverage per frame [32].

Because SSA combines multiple spatially distinct acquisitions into a single compounded image, the effective frame rate of the final OT-SSA image is not determined by the acquisition rate of the Verasonics system. Instead, each compounded image corresponds to a complete sweep, making the frame rate dependent on sweep duration. For example, a 1s sweep yields an effective frame rate of 1Hz. In this study, sweep durations ranged from sub-second to approximately 3s.

We imaged three targets to evaluate the system’s performance: (1) the ATS 539 phantom (Sun Nuclear, Melbourne), which contains cylindrical lesions and wire targets embedded in a speckled background; (2) the CIRS 3D abdominal phantom (CIRS, Norfolk, VA), which includes a curved surface and embedded 3D targets; and (3) the quadriceps muscle of 5 healthy volunteers, scanned under IRB approval.

All OT-SSA sweeps were acquired using the ATL P4–2 transducer. A multistatic reference acquisition was also performed with the same transducer, serving as the baseline for comparison across all image quality experiments.

In vivo scans were performed along the inner thigh to avoid bone-induced acoustic shadowing, with the sweep direction aligned longitudinally to the quadriceps muscle. For in vivo scans, an additional focused beam acquisition was performed with the ATL L12–5 linear array (7.8 MHz, 256 elements, 50 mm aperture size) to provide a high-resolution reference from a larger, higher-frequency array.

Each SSA sweep was completed using freehand motion. For the in vivo scans, sweep durations ranged from 1.2s to 1.7s, corresponding to effective frame rates of approximately 0.6–0.8Hz. Phantom sweeps exhibited a wider range of durations, as illustrated in Fig. 2, which shows examples of both a fast and a slow sweep. No acquisitions were excluded based on out-of-plane motion or sweep duration.

Fig. 2.

Phantoms and representative motion profiles for flat (top) and curved (bottom) sweeps. Red dots show the selected transducer positions evenly spaced in the lateral dimension, the rest of the frames are discarded. The insets show the resampled motion profiles used for beamforming.

C. Spatial information processing

A set of transformation matrices were utilized to convert the camera’s tracking data into the spatial position and orientation of the imaging array and compute the image reconstruction grid. The translation and rotation data recorded by the camera (expressed as a vector and quaternion respectively) were structured as a set of homogeneous transformation matrices $A_f$, each frame $f$ corresponding to a distinct camera measurement. First, a subset of evenly spaced frames $A_{f_s}$ were identified based on 0.5 mm intervals (explored further in the results section) along the lateral (x-axis) dimension of the reconstruction plane. For a 10 cm sweep, this process would result in 200 frames. To identify these frames, array poses $B_f$ relative to the reconstruction plane were calculated using the fixed tool-to-transducer calibration matrix $X$ (described below) and an initial guess at the reconstruction plane defined by a transformation matrix ${\tilde{A}}_0$:

$$B_f=X^{-1}{A}_f^{\prime }X$$ (1)

using the recorded tracking data expressed relative to the reconstruction plane:

$$A_f^{\prime }={\tilde{A}}_0^{-1}{A}_f$$ (2)

The initial reconstruction plane ${\tilde{A}}_0$ was based on the median value of all tool poses $A_f$, computed using the translation vectors and Euler angles. While any choice of reconstruction grid is allowable, a plane aligned with the direction and orientation of the sweep will be best supported by the acquired data. Subsequently, the reconstruction plane $A_0$ was updated using the median value of the equally spaced subset of frames $A_{f_s}$ and new relative tool poses were calculated:

$$A_{f_s}^{\prime }=A_0^{-1}{A}_{f_s}$$ (3)

Using the updated relative tool poses, the final set of calibrated array positions relative to the reconstruction grid (red markers in Fig. 2) was computed as:

$$B_{f_s}=X^{-1}{A}_{f_s}^{\prime }X$$ (4)

For easier calculation of time delays and spatial masks for beamforming, this relationship was inverted to express the common reconstruction grid $\overrightarrow{r}=(x,y,z)$ relative to the array position in each selected frame:

$${\overrightarrow{r}}_{f_s}=B_{f_s}^{-1}\overrightarrow{r}$$ (5)

To estimate the rigid transformation $X$ between the tracking tool and the transducer, we parameterized the DAS beamforming algorithm as a differentiable function of the six DOFs in $X$ (three rotations and three translations) [33]. Each calibration run used four freehand sweeps of the same 3D abdominal phantom, acquired with varied trajectories. During optimization in PyTorch (Adam optimizer), the sweeps were cycled sequentially—iteration 1 used sweep 1, iteration 2 used sweep 2, and so on—returning to sweep 1 after every four iterations. This cycle was repeated for a total of 400 iterations, corresponding to 100 iterations per sweep. At each iteration (Fig. 3), the current transformation estimate $X$ was used to convert the optical tracking data into a transducer pose $B$.

Fig. 3.

Calibration optimization workflow. Optical tracking data and raw ultrasound channel data from freehand sweeps are used to iteratively optimize the calibration parameters.

Beamforming was always performed on the same fixed reconstruction grid: a 2 cm × 2 cm patch in the xz plane, positioned at an 8 cm depth. This location ensured sufficient elevational overlap between frames, even in sweeps with substantial out-of-plane motion, while limiting computational load. The fixed beamforming grid, defined in the global coordinate system, was transformed into the transducer’s local coordinate frame. This transformed grid was then used for beamforming and the loss was computed as the mean of $1-r$, where $r$ is the Pearson correlation between the normalized envelopes of temporally adjacent acquired frames, encouraging spatial consistency among the reconstructed images. The initial value of $X$ was derived from a geometric estimate based on the known physical dimensions of the 3D-printed fixture.

D. Image reconstruction

In freehand SSA, transformed reconstruction points ${\overrightarrow{r}}_{f_s}$ generally fall outside the imaging plane $\text{y}=0$, requiring a beamforming method capable of handling out-of-plane reconstruction. To address this, we adopted the dual virtual source method described in [34], which models transmit and receive delays using two virtual sources: one for lateral focusing and another for elevation focusing. Each grid point ${\overrightarrow{r}}_{f_s}=(x,y,z)$ was projected onto the imaging plane to create a virtual point ${\overrightarrow{r}}_{f{v}_s}=\left(x,0,z_{proj}\right)$, where $z_{proj}$ accounts for the radial distance from the elevation focus caused by the lens. The projected point ${\overrightarrow{r}}_{f{v}_s}$ was then used to compute time of flight from the lateral virtual source to the receiver elements using a spherical wave propagation model. We modified this method such that points falling outside the defined angular acceptance of the elevation beam were approximated using a plane wave steered from the edge of the mask, maintaining continuity in the delay field across the entire grid. This is consistent with prior work [35], which showed that in these regions – where the signal is primarily due to edge waves rather than focused transmission – modeling a smooth delay transition helps avoid artifacts from abrupt time of flight changes.

E. System validation and benchmarking

A set of targeted experiments and simulations was conducted to evaluate individual components of the OT-SSA system and to isolate specific sources of image degradation attributed to the role of each component in the image formation process.

1). Simulations:

Simulations were performed using Field II software [36], [37] to quantify the effects of out-of-plane motion and sweep extent on image quality. The simulated medium consisted of four point targets positioned at depths [4, 6, 8, 10] cm, with aperture parameters set to match the characteristics of the P4–2 transducer, including its elevation focus at 6 cm.

To assess sensitivity to out-of-plane motion, lateral sweeps spanning 8 cm were simulated under varying motion conditions. Elevational translation was varied by setting maximum out-of-plane displacements from 0 to 3 cm, applied linearly across the sweep. Similarly, elevation tilt was varied up to ±15°, simulating linear changes in angular deviation over the sweep. For more realistic out-of-plane deviations, we preserved the simulated medium and substituted the controlled motion profiles with five real 6-DOF trajectories taken from the same sweeps used for the in vivo imaging experiments.

To evaluate the influence of sweep extent, ideal lateral sweeps ranging from 2 to 20 cm were simulated, isolating the effect of aperture growth without confounding factors.

Cystic contrast [38] was used to evaluate beam distortion from point target images in all simulations. This metric, defined as the ratio of total signal energy within a radius around the point to the full image energy, is well-suited for noiseless simulations. In this setting, energy outside the 0.6 mm radius target region arises solely from PSF distortion and not from speckle or acoustic clutter and would contribute to off-axis scattering.

2). Experiments:

To evaluate the impact of system parameters on reconstruction accuracy, a series of experiments were conducted targeting three key factors: (1) lateral frame spacing, (2) optical tracking precision, and (3) calibration accuracy. Image quality in phantom and in vivo scenarios was also assessed as a comprehensive validation of the system’s performance.

To asses the effect of lateral frame spacing on compounding performance, we acquired data from the ATS 539 phantom, targeting lesions at various depths. The primary form of degradation expected from increased frame spacing is contrast-reducing grating lobes. Consequently, generalized Contrast-to-Noise-Ratio (gCNR) [39], a metric of lesion detectability in terms of contrast, was utilized to evaluate the impact of frame spacing on image quality.

The fidelity of the camera’s motion tracking was assessed to determine its precision in capturing the subtleties of freehand motion. Specifically, we investigated whether the apparent jitter observed in the tracking data reflected actual motion dynamics. Gaussian smoothing was applied to the optical tracking data using temporal window sizes of 0.05, 0.125, 0.25, and 0.5 seconds (20, 50, 100, and 200 samples respectively). Experiments were conducted with the ATS 539 and CIRS phantoms, representing flat and curved motion profiles, respectively. In each experiment, smoothing was applied independently to each motion dimension to isolate and analyze their individual effects on the 1D PSF.

To evaluate the impact of calibration accuracy, image reconstructions were performed using both the initial geometric estimate and the optimized calibration matrix. These reconstructions were performed on data acquired from the ATS 539 and CIRS phantoms. Analysis focused on relevant regions such as point targets and high-contrast tissue boundaries, where geometric alignment is critical. Additionally, calibration robustness was evaluated by analyzing convergence behavior across multiple optimization runs, assessing repeatability, and verifying pose accuracy via tracking of a static point target under transducer motion.

Finally, the resolution improvements achieved with OT-SSA were validated experimentally. For quantitative analysis, we utilized the ATS 539 phantom, which contains cylindrical lesions and wire targets embedded in a background speckle. This setup allowed us to evaluate image quality enhancements specifically in terms of Full Width at Half Maximum (FWHM) resolution and gCNR. We also conducted additional experiments using the CIRS 3D abdominal phantom and in vivo volunteer scans. These were intended primarily for visual assessment of image quality in settings more representative of clinical use.

IV. Results

A. Out-of-plane motion

Simulations assessing elevational translation and tilt shown in Fig. 4 revealed that the OT-SSA system maintains high image quality for moderate levels of out-of-plane deviation. Specifically, idealized motion profiles with up to 1 cm of translation or 5° of rotation still yielded improved image quality over multistatic acquisitions using the same transducer. These results suggest that, within these bounds, the system can tolerate elevational deviations without significantly compromising signal coherence. When a representative freehand trajectory was applied, image degradation remained limited, exhibiting better performance than predicted by translation or rotation alone, despite the presence of more complex motion. However, the freehand sweeps demonstrate that translational and angular deviations can interact in either compensatory or compounding ways, making their combined impact difficult to predict. Moreover, freehand motion varies considerably across sweeps; even if two sweeps share similar maximum translation or rotation values, they can differ substantially in the overall shape of their motion trajectories. Therefore, tolerance is best assessed on a per-sweep basis by verifying that the beamforming grid remains within the transducer’s elevational beam throughout the acquisition, rather than relying solely on maximum translation or rotation metrics.

Fig. 4.

Impact of out-of-plane motion on cystic contrast. Top: B-mode SSA images for selected out-of-plane translation, rotation, and one representative freehand sweep (pentagon marker; also indicated in bottom panels by an arrow). Bottom left: Cystic contrast versus maximum out-of-plane rotation or translation. Dashed lines indicate multistatic reference levels from a stationary aperture. Scattered markers show results for five freehand sweeps, with marker type identifying each sweep. Bottom right: Out-of-plane translation and tilt profiles extracted from the same freehand trajectories, with marker types matching those in the contrast plot.

B. Sweep extent

Simulations examining sweep extent shown in Fig. 5 revealed that resolution improves with increasing aperture up to a threshold, beyond which additional lateral translation yields no further benefit. This threshold occurs when new transducer positions no longer generate wavefronts that overlap at the imaging depth, a limitation governed by element width and transducer angle. When beamforming grid points fall outside the lateral support of the current transducer position, they are excluded by the beamforming mask and contribute nothing to synthetic aperture summation. For flat sweeps, a plateau in cystic contrast was observed beyond a 12 cm sweep for the deepest target (10 cm depth). Shallower targets reached their plateau earlier, consistent with the angular coverage limits of the diverging wavefront. This plateau indicates that no additional energy was being concentrated within the fixed radius used for evaluation. This is also reflected in the B-mode images, where improvements between 2 cm and 12 cm sweeps were substantial, but changes from 12 cm to 20 cm appeared minimal. However, this does not imply true resolution saturation. FWHM measurements revealed that the lateral PSF continued to narrow at the deepest target up to a sweep extent of 14 cm, indicating that resolution improvements persisted beyond the point where changes became less visually apparent. Curved sweeps, in which rotation angles the beam toward a common imaging region, could partially mitigate this effect by maintaining greater overlap at depth.

Fig. 5.

Impact of sweep extent on FWHM and cystic contrast. Left: FWHM and Cystic contrast as functions of sweep length for targets at varying depths. Right: Corresponding B-mode images for selected sweep extents.

C. Frame spacing

Experimental analysis of frame spacing in Fig. 6 shows that image quality begins to degrade beyond 1 mm frame spacing, confirming 0.5 mm as a conservative choice and establishing 1 mm as a practical upper limit for this imaging configuration. Notably, gCNR fluctuations increase past this threshold, likely due to greater influence from individual out-of-plane frames. Since fewer frames are used, any with poor coupling or degraded quality would disproportionately affect reconstruction.

Fig. 6.

gCNR variation with frame spacing. Experiments demonstrate the dependency of gCNR on frame spacing, with lesion detectability decreasing for spacings greater than 1 mm. The effect is consistently observed across various depths within the phantom

D. Tracking fidelity

Fig. 7 presents the impact tracking fidelity, modeled by post-processing smoothing of the recorded trajectories to reduce tracking precision. Even sub-millimeter deviations from the original motion trajectory led to noticeable broadening and distortion of the PSF. This confirms that the high-frequency variations captured by the optical system are not noise but represent essential features of freehand motion that preserve coherence during SSA reconstruction. Two key observations emerged from comparing the flat and curved profiles. First, the magnitude of motion in each degree of freedom determined the extent to which smoothing could meaningfully perturb the trajectory. In the flat sweep, axial motion was negligible, so smoothing produced only minimal deviations in that direction resulting in no appreciable PSF degradation. In contrast, the curved sweep exhibited greater axial motion, allowing smoothing to introduce deviations that visibly distorted the PSF shape. Second, distortions resulting from out-of-plane motion were minimal, even when induced deviations were comparable in magnitude (i.e., sub-millimeter) to those that caused visible PSF degradation in lateral and axial directions. This suggests a reduced sensitivity of OT-SSA to elevational tracking error—likely due to the beamforming process occurring in the xz-plane making it less susceptible to errors orthogonal to the beamforming grid. However, this observation is limited to the modest range of elevational motion present in the tested profiles.

Fig. 7.

Effect of temporal smoothing on motion precision and PSF quality. Top: Normalized PSFs reconstructed using motion profiles smoothed with Gaussian filters of increasing window sizes (see legend, in seconds). Smoothing is applied to a single dimension at a time. Bottom: Deviations in motion trajectories introduced by each smoothing level, relative to the unsmoothed reference (flat line), illustrate the impact of temporal filtering on motion profile.

C. Calibration matrix

The accuracy and robustness of the optimized calibration matrix were evaluated through repeatability analysis, convergence behavior, and reconstruction quality. Fig. 8 shows the individual loss curves for the four training sweeps from one representative optimization run. For each run, the optimization process alternated loss computation between sweeps – using a single sweep per iteration – so that all four sweeps contributed independently to parameter updates. This strategy ensured that the resulting calibration matrix was not overfit to any single sweep, but instead generalized to reduce loss consistently across all four. The curves show that loss decreased rapidly for each sweep, indicating both stable convergence and broad applicability of the optimized calibration parameters. The precision of the resulting calibration matrix was also confirmed in a separate testing case by tracking a fixed point target during motion, which exhibited less than 0.5 mm of frame-to-frame variation and no systematic bias. Finally, SSA reconstruction using the optimized calibration matrix yielded visibly improved image quality compared to reconstructions using the initial geometric estimate. This difference is evident in Fig. 8c, especially below 10 cm depth, where the optimized reconstruction reveals sharper boundaries and better-defined point targets.

Fig. 8.

Evaluation of a single calibration optimization run. (a) Convergence of the loss function across the four independent training sweeps used in the second calibration run (X₂), demonstrating consistent reduction over iterations. (b) Tracked position of a stationary point target across frames, showing sub-millimeter residual motion and no systematic bias. (c) SSA image reconstructions using the initial geometric estimate versus the optimized calibration matrix for a curved sweep. All images displayed with a 60 dB dynamic range.

Fig. 9 shows that three independent calibrations (each using a different set of four sweeps) yielded highly consistent transducer trajectories when applied to the same test sweep (not used in optimization), confirming the repeatability of the calibration process. The greatest variation is observed in the out-of-plane translation—likely due to the loss function being computed over beamformed images in the xz-plane, making elevational parameters less observable during optimization. All three calibrations yielded similarly shaped PSFs, showing narrow profiles with reduced off-axis energy compared to the initial geometric estimate.

Fig. 9.

Evaluation of calibration matrix repeatability. Top: Deviation in estimated transducer motion for a test sweep, computed using three independently optimized calibration matrices, each derived from a unique set of four training sweeps. Deviations are shown relative to the initial geometric estimate (black dashed line). All three matrices yield consistent deviations in the same direction, with inter-matrix differences remaining below 1 mm. Bottom: PSFs of the circled point target on the B-mode image of the flat phantom, reconstructed using each calibration matrix. All three PSFs are similar and narrower than that obtained using the initial geometric estimate (black), confirming consistent and improved image reconstruction across runs.

F. Image quality

Our final system evaluation focused on the image quality achieved using SSA. Across all phantom imaging targets, SSA images demonstrated substantial improvements in target detectability and resolution compared to reference images obtained from a stationary aperture with multistatic acquisition. This improvement became more pronounced in deeper regions, where the large effective aperture of SSA maintains a low f-number and thus preserves high lateral resolution. Table I presents a quantitative comparison between SSA and multistatic images of the ATS 539 phantom across five independent 10 cm sweeps. Qualitatively, improvements in lateral resolution are evident in the CIRS phantom images in Fig. 10, where SSA enhances lesion boundary definition and structural visibility – especially at depth. It is important to note that this phantom is three-dimensional, so minor differences between the SSA and multistatic images may be present due to small variations in the imaging plane. Although fields of view were matched to the best of our ability, direct one-to-one visual comparisons are not possible. Despite this, the enhanced resolution and clarity achieved with SSA are consistently observed at greater depths.

TABLE I.

Quantitative comparison between ATS 539 phantom images. Values are presented as mean ± standard deviation.

Depth (cm)	gCNR		Lateral FWHM (mm)
	Multistatic	SSA	Multistatic	SSA
2	0.89 ± 0.08	0.98 ± 0.01	0.70 ± 0.10	0.60 ± 0.21
4	0.88 ± 0.08	0.96 ± 0.01	1.10 ± 0.11	0.70 ± 0.30
6	0.82 ± 0.13	0.93 ± 0.00	1.60 ± 0.16	0.90 ± 0.26
8	0.76 ± 0.11	0.91 ± 0.02	2.30 ± 0.23	1.10 ± 0.29
10	0.65 ± 0.09	0.93 ± 0.04	2.80 ± 0.28	1.10 ± 0.29
12	0.71 ± 0.17	0.94 ± 0.02	3.90 ± 0.39	1.00 ± 0.39

Fig. 10.

Comparison of B-mode images obtained using a multistatic acquisition with a stationary aperture and the SSA technique, both utilizing the same transducer. The images depict approximately the same region and plane of the CIRS phantom. Note that the fields of view are not exactly matched due to variations in acquisition approaches and the challenges in aligning the exact transducer positions between multistatic and SSA experiments.

Finally, we present a proof of concept validating the potential of freehand SSA in vivo, using scans from five healthy volunteers. Fig. 11 shows a representative comparison, where SSA demonstrates improved structural definition – muscle groups are more clearly delineated, and speckle size is visibly reduced. A focused image acquired with the linear transducer is also shown for reference. While the linear image provides superior axial resolution due to the transducer’s higher center frequency, it suffers from severely limited penetration. Even with depth-dependent gain, deeper structures are not visible, highlighting a key tradeoff between resolution and penetration. Additionally, its wider elements result in a narrower lateral field of view, further restricting anatomical coverage. It is important to recognize that while SSA produces marked improvement in deep imaging, it does not enhance axial resolution, which is not a function of aperture size.

Fig. 11.

Comparison among SSA, multistatic, and linear images of the quadriceps muscle with dynamic range of 50 dB. The reconstruction grid for the linear image differs is narrower, with data only acquired 5 cm wide consistent with the width of the transducer. The SSA image outperforms the multistatic image across all depths, demonstrating clearer visualization of muscle striations.

Fig. 12 presents four additional in vivo comparisons, showing both the multistatic and OT-SSA images using the same transducer. Across the four volunteers, OT-SSA consistently improved resolution, reducing the average size of the lateral speckle autocorrelation from 2.33 mm to 0.49 mm for image patches at depths greater than 10 cm. The standard deviation of the speckle autocorrelation also decreased from 0.33 mm to 0.06 mm, reflecting consistent image quality across sweeps. As expected from a reconstruction process based solely on linear operations, the speckle statistics remained consistent with a Rayleigh distribution—indicating that the fundamental properties of fully developed speckle were preserved. These results support the utility of SSA for high-quality freehand imaging in vivo, offering enhanced resolution without sacrificing imaging depth.

Fig. 12.

Comparison of Multistatic and OT-SSA reconstructions of the quadriceps muscle across four volunteers. Dynamic range is 50 dB. Fields of view are matched as closely as possible between acquisitions. OT-SSA images demonstrate improved resolution and tissue boundary definition.

V. Discussion

The development of the OT-SSA platform addresses key system-level challenges required for enabling freehand synthetic aperture ultrasound imaging. With all critical system components now functioning robustly and in an optimized manner, future efforts can confidently shift toward addressing medium-related challenges such as tissue heterogeneity, variable acoustic coupling, and physiological motion. These factors are particularly important when imaging organs like the liver or kidneys, where medium characteristics significantly influence wave propagation and the resulting image quality. Our current proof-of-concept focused on the quadriceps, which presents relatively homogeneous tissue, minimal physiological motion, and a favorable acoustic window. However, our long-term goal is to extend this approach to more complex imaging scenarios such as abdominal imaging. Note that due to the inherently sequential and frame-dependent nature of SSA, applications involving rapid motion, such as cardiac imaging, remain outside of what is currently practical with this technique.

While this study demonstrates the performance of the OT-SSA system, its validation and benchmarking are subject to several limitations. A primary constraint lies in the evaluation of the calibration matrix, which cannot be validated against a known ground truth due to the absence of a higher-accuracy reference system. Instead, calibration fidelity was assessed through repeatability across independently acquired sweeps, convergence behavior during optimization, and improvements observed in resolution-critical image regions. While these indicators provide strong indirect evidence of robustness, they ultimately remain approximations. A similar limitation applies to the evaluation of the optical tracking system. As demonstrated in Fig. 7, even minor deviations in the tracked motion profile—induced through jitter reduction—led to significant losses in image coherence. Conversely, the improved image quality of OT-SSA relative to multistatic reference images indicates that coherent compounding was successfully achieved, suggesting submillimeter-level tracking precision. These findings support the conclusion that optical tracking is both necessary and sufficient for enabling effective freehand SSA. However, in the absence of a more precise ground-truth reference, tracking accuracy is still inferred through indirect observations. Moreover, while efforts were made to evaluate calibration and tracking separately, complete decoupling of these components is challenging, as most practical assessments inherently involve both operating simultaneously. Another key challenge is scan-to-scan variability. Because SSA and multistatic acquisitions were performed separately, precise replication of the imaging plane is practically unachievable—particularly when relying on freehand transducer motion. Although efforts were made to match fields of view for qualitative comparisons, even small differences in probe position or orientation can result in different beamforming planes, especially when imaging 3D targets. As a result, direct one-to-one comparison between SSA and multistatic images is inherently limited by the inability to exactly reproduce the imaging geometry across independent acquisitions.

Alternative calibration strategies, particularly those using known-geometry phantoms such as cross-wire and N-wire configurations, have demonstrated high accuracy and precision in freehand ultrasound systems [40]–[42]. These methods benefit from well-characterized fiducials and structured acquisition protocols, enabling reconstruction errors near 1 mm under ideal conditions. In contrast, our approach does not rely on a phantom with known geometry, allowing calibration to be performed on arbitrary targets. Our optimization framework also permits the sweep trajectory and beamforming plane to be tailored to specific applications or to enhance sensitivity in the most relevant degrees of freedom. However, this flexibility introduces new questions regarding the optimal conditions for accurate calibration. The influence of sweep geometry and imaging plane selection on calibration precision has yet to be fully characterized. Additionally, while our current evaluation emphasizes robustness and repeatability, future work will directly benchmark this method against established phantom-based techniques to quantify its accuracy and identify potential trade-offs.

According to the findings in this study, less accurate tracking systems alone would likely be insufficient to achieve the required reconstruction precision. However, they could still be leveraged by integrating complementary motion data from multiple sources through sensor fusion or by refining the pose information via post-processing optimization. In addition, in application-specific scenarios where certain degrees of freedom are constrained, such as guided sweeps limited to a fixed elevation plane or anatomical boundaries that restrict axial motion, the tracking accuracy requirements can be relaxed for those constrained dimensions. In such cases, lower-precision tracking for minimally varying axes may still be acceptable, provided the more variable and coherence-critical dimensions are measured with sufficient precision.

OT-SSA also enables future extensions through combined acquisition strategies. While lateral resolution is ultimately limited by the transducer acceptance angle, the field of view can continue to expand proportionally with sweep length, provided the acoustic window remains adequate. Longer sweeps, however, may introduce increased susceptibility to motion artifacts and compounding inaccuracies, particularly in dynamic in vivo settings. These trade-offs will require further investigation and system-level optimization. Another approach may be to move towards volumetric reconstruction, using multiple, relatively parallel sweeps where each slice benefits from the enhanced resolution of OT-SSA. If spatial continuity between sweeps is preserved, post hoc beamforming along arbitrary planes may become feasible, enabling anatomically adaptive image reconstruction with high spatial precision. While non-trivial, these directions highlight the flexibility and potential of OT-SSA to support extended field-of-view and volumetric imaging paradigms in future applications.

VI. Conclusion

We have successfully developed the OT-SSA system and demonstrated its efficacy in resolving anticipated system challenges. This success is evidenced by significant improvements in image quality (e.g., resolution, penetration depth, field of view) across various phantom and in vivo tests. With these system challenges addressed, we are now well-positioned to tackle the next phase of SSA research—addressing medium-related challenges in in vivo imaging. These advancements made with the OT-SSA platform also lay a strong foundation for future developments towards achieving untracked freehand SSA, removing the need for external position sensing. Our goal is to refine this technology to the point where it can be seamlessly integrated into clinical settings, enhancing the diagnostic capabilities of ultrasound.

Highlights.

• This study introduces the Optically Tracked Swept Synthetic Aperture (OT-SSA) system, synchronizing optical tracking with ultrasound acquisition to precisely monitor freehand transducer motion during imaging.

• Experimental results demonstrate that OT-SSA significantly enhances image resolution and quality, especially at depth.

• By providing accurate transducer tracking, OT-SSA enables the study of the complex dynamics of freehand motion in vivo, allowing future research to focus on medium-related challenges.