Robot-assisted wide-amplitude oscillatory photoacoustic scanning for three-dimensional human peripheral vascular imaging: A preliminary feasibility study

Abstract

Photoacoustic tomography (PAT) is a promising tool for non-invasive vascular imaging, yet conventional linear scanning suffers from “limited-view” artifacts and structural discontinuities due to restricted transducer acceptance angles. To overcome these physical bottlenecks, we propose a robot-assisted wide-amplitude oscillatory (WAO) scanning strategy. By integrating controlled lateral harmonic oscillations into axial linear trajectories via a 6-DoF robotic arm, this method achieves kinematic modulation to physically synthesize a dynamic aperture. This approach effectively captures high-frequency acoustic information typically lost in single-path scans, compensating for hardware-based detection limits. Numerical simulations and a preliminary in vivo feasibility experiment in a healthy participant demonstrate that the WAO strategy expands acoustic spatial coverage by 32% and improves the contrast-to-noise ratio (CNR) by 2.4-fold. This enables high-fidelity 3D reconstruction of complex vascular networks with a high spatial resolution of $215\mathrm{\mu }\mathrm{m}$. The current study is intended to evaluate the technical feasibility of robot-assisted WAO scanning for human peripheral vascular imaging; broader clinical validation, motion tracking, and motion correction remain necessary before claims related to vascular diagnosis or longitudinal monitoring can be made.

Highlights

• •Innovation: This study establishes a robot-enabled kinematic acquisition strategy that uses controlled probe motion and pose recording to reduce hardware-related detection gaps.
• •Practicality: Beyond theoretical modeling, the strategy was evaluated in phantom experiments and in a preliminary in vivo feasibility experiment in a healthy participant.
• •High-Quality Imaging: The method reduces limited-view-related reconstruction artifacts, delivering high-fidelity visualization with more continuous vascular branching.

1. Introduction

Photoacoustic tomography (PAT) combines optical absorption contrast with ultrasound detection and is well suited for vascular imaging, where hemoglobin provides strong endogenous contrast [1], [2], [3]. Compared with purely optical methods, PAT can image vascular structures at greater depths because acoustic scattering in tissue is much weaker than optical scattering. This property is useful for peripheral vascular imaging, where both superficial branching patterns and deeper vessel segments may be relevant to the assessment of vascular morphology and hemodynamic changes [4], [5]. Three-dimensional imaging is especially important in this setting because vessel continuity, tortuosity, and spatial relationships are difficult to interpret from isolated two-dimensional slices. In many practical systems, however, volumetric PAT is reconstructed from sequentially acquired two-dimensional frames. The quality of each frame, the acoustic viewing angle, and the spatial accuracy of frame compounding therefore directly affect the fidelity of the final 3D vascular image.

Several technical routes have been developed to improve vascular PAT. Large-aperture 3D-PACT systems, including hemispherical, semi-circular, and matrix-array configurations, can provide broad acoustic coverage and large fields of view [6], [7], [8], [9], [10]. These systems have shown the value of wide angular detection for volumetric vascular imaging, particularly when the target anatomy can be placed within a fixed detector geometry. High-speed all-optical, MEMS-based, and handheld panoramic systems have further improved acquisition speed, field of view, and volumetric stitching for subcutaneous vascular imaging [11], [12], [13], [14]. In parallel, robotic photoacoustic imaging has been introduced to improve probe positioning, scanning repeatability, and contact stability. For example, force-controlled robotic PA systems have been used for peripheral vascular imaging [15], and vision-servo-based robotic systems have been reported for reproducible long-term monitoring of peripheral arteries [16]. These studies indicate that robotic control can reduce operator dependence and improve spatial repeatability, which is difficult to achieve with fully manual scanning.

Despite these advances, limited-view artifacts remain a central problem for linear-array-based PAT. A linear transducer has a finite acoustic acceptance angle, so wavefronts emitted from boundaries with unfavorable orientations may be weakly detected or missed [17], [18], [19], [20]. In vessel imaging, this limitation can appear as discontinuous sidewalls, lateral smearing, reduced contrast, or incomplete branches after 3D compounding. Hardware-based solutions, such as full-ring or hemispherical arrays, can increase angular coverage, but they may reduce system flexibility, increase system complexity, or complicate access to curved peripheral anatomical surfaces [21], [22]. Reconstruction-side methods, including model-based, iterative, and deep-learning approaches, can suppress limited-view artifacts, but they operate mainly on already acquired data and may remain constrained when certain acoustic views are not physically measured [23], [24], [25], [26]. Multiview and synthetic-aperture acquisition provide a more direct route by changing the detector view before reconstruction. Gateau et al. and Linger et al. demonstrated rotate-translate and multiview linear-array PA imaging schemes [27], [28], showing that complementary views can improve single-side-access imaging. However, these approaches use regular tomographic trajectories rather than anatomy-guided robotic scanning paths. Existing robotic PA studies, on the other hand, have mainly emphasized force regulation, probe repositioning, or visual servoing rather than using the robot trajectory itself to synthesize additional acoustic viewing angles.

These limitations motivate an acquisition-level strategy in which robot motion is used not only for probe positioning, but also for acoustic-view design. The key idea of the present work is to treat the robot trajectory as a controllable kinematic aperture. Instead of relying on a fixed linear scan, we generate a vessel-aware baseline path from an infrared vascular pre-scan and a 3D surface point cloud, and then superimpose a wide-amplitude oscillatory (WAO) motion onto this path. The baseline path follows the superficial vascular roadmap, whereas the oscillatory component introduces lateral displacement and probe-orientation variation around the vessel course. This trajectory allows the same linear-array transducer to sample complementary receive views along tortuous peripheral vessels while recording the 6-DOF probe pose for 3D compounding. Because the additional angular information is physically acquired before reconstruction, the proposed strategy is complementary to model-based or learning-based artifact reduction. In this sense, WAO is not a new photoacoustic signal-generation mechanism; it is a robot-enabled kinematic aperture-synthesis acquisition strategy for mitigating limited-view artifacts.

In this study, we developed and evaluated a robot-assisted WAO photoacoustic scanning workflow for three-dimensional human peripheral vascular imaging. The system integrates infrared vessel mapping, surface point-cloud registration, vessel-centerline extraction, pre-planned robotic trajectory execution, synchronized laser triggering, and pose-encoded 3D reconstruction. We first analyzed the WAO mechanism using spatial coverage and k-space support to explain how the oscillatory trajectory expands the observable acoustic support of the linear-array probe. We then tested the effect of the trajectory in k-Wave simulations and used Monte Carlo optical fluence simulations to examine whether dynamic illumination variation could act as a confounding factor. Finally, we validated the imaging performance using a wire phantom and a preliminary in vivo dorsal-hand experiment in a healthy participant. The study is intended to assess the technical feasibility of WAO-based acquisition for improving limited-view peripheral vascular PAT, while broader clinical validation, motion tracking, motion correction, and systematic parameter optimization remain future work.

2. Materials and methods

In this Section, we first introduce the custom-developed robot-assisted imaging system in Section 2.1, detailing the hardware integration of the robotic and imaging subsystems. Building upon this foundation, to achieve alignment between the image and physical spaces, we derive a theoretical transformation model from the photoacoustic image to the robot’s end-effector coordinate system and quantitatively evaluate the Target Registration Error (TRE) through experiments. Subsequently, Section 2.2 provides an in-depth mathematical derivation of the WAO scanning mode, establishing the theoretical basis for scanning trajectory optimization. Finally, Section 2.3 integrates the aforementioned hardware and algorithmic frameworks to demonstrate a vision-assisted, pre-planned vessel-guided workflow for robotic trajectory generation, execution, and 3D volumetric reconstruction.

2.1. Roboticized photoacoustic platform: System design and implementation

The robotic-PAT system performs real-time, 2D cross-sectional vascular imaging (Fig. 2A). Comprising robotic and imaging modules (laser, sensors, DAQ, host PC), it employs a multi-wavelength laser (Lasersound OPO-M-10, Tsingpai Technology) providing stable output across 700–960 nm and 1064 nm. A detachable flange connects a Y-shaped bundle ($1200\times 400\mathrm{\mu }\text{m}$ fibers; 11 mm input) delivering a $33\times 1\text{mm}$ rectangular beam ($\sim 65°$ divergence). A 128-channel linear transducer (5 MHz, 80% bandwidth) captures PA signals, using an acoustic lens for elevational focusing. An angle-adjustable mechanism aligns the fiber. Signals are pre-amplified by 60 dB, parallel acquired by DAQ, and reconstructed via CUDA-accelerated back-projection (Visual Studio 2019) at 10 fps [29].

Fig. 2.

Robot-assisted imaging strategy. A. System operation flow chart. B. Schematic diagram of two-dimensional WAO fused imaging. C. Phase-controlled trajectory decomposition. Splitting the scan into ‘Forward’ ($\otimes$) and ‘Return’ ($\odot$) paths with a 180° phase difference ensures precise spatial overlap. This symmetric design guarantees uniform sampling and counteracts mechanical inertia, effectively suppressing imaging artifacts.

To ensure precise co-registration between the spatial coordinates and the photoacoustic signals, we implemented a position-synchronized triggering scheme(refer to Fig. 1.D). To ensure precise co-registration between the spatial coordinates and the photoacoustic signals, we implemented a position-synchronized triggering scheme. The robotic manipulator acts as the master controller, generating a trigger signal at each discrete spatial increment ($d_R$). This signal is transmitted to the laser system to initiate the excitation sequence. Upon receiving the robot’s trigger (after a stabilization delay $t_d$), the laser emits the optical pulses and simultaneously outputs a synchronization signal (Sync Out) to the DAQ card. This “sequential hardware synchronization” triggering logic ensures that the data acquisition is strictly phase-locked to the laser emission, thereby seamlessly integrating the robot’s motion, the laser excitation, and the ultrasonic recording into a unified timeframe.

Fig. 1.

Schematic diagram of robot-assisted tomographic imaging. A. System configuration. B. Conventional linear scanning. C. WAO scanning. D. Timing diagram of the synchronization between robotic movement and laser emission.

3D image generation requires accurate spatial mapping of temporal 2D sequences, making system spatial relationships fundamental. We derived the photoacoustic image-to-robot coordinate transformation and conducted a scenario-based error analysis (Supplemental S1). To validate the accuracy of the calibration, six distinct feature points within the phantom space were used as validation targets. The coordinates of these points were identified in the photoacoustic images and transformed into the phantom coordinate system using the derived calibration matrix. These predicted positions were then compared against the ground truth physical coordinates provided by the phantom design.

The detailed validation results for each target point are presented in Table 1. The Euclidean distance between the predicted position ($P_{pred}$) and the true position ($P_{true}$) is defined as the TRE.

Table 1.

Detailed TRE for six validation points. All units are in millimeters (mm).

Target ID	True position $(x,y,z)$	Predicted position $(x,y,z)$	TRE
1	$(15.00,20.00,5.00)$	$(15.25,20.15,4.80)$	0.354
2	$(15.00,20.00,15.00)$	$(14.65,20.25,15.20)$	0.474
3	$(30.00,20.00,10.00)$	$(30.30,19.65,10.25)$	0.524
4	$(30.00,20.00,20.00)$	$(29.60,20.35,19.75)$	0.587
5	$(45.00,20.00,8.00)$	$(45.15,19.80,8.10)$	0.269
6	$(45.00,20.00,18.00)$	$(44.55,20.30,18.20)$	0.576

A statistical summary of the calibration performance is provided in Table 2. The system achieved a Mean TRE of 0.464 mm with a standard deviation of 0.129 mm.

Table 2.

Statistical summary of the calibration accuracy.

Metric	Value (mm)
Mean TRE	0.464
Standard Deviation	0.129
RMS Error	0.481
Maximum TRE	0.587

As shown in the results, the maximum recorded error was 0.587 mm, which is strictly within the pre-defined tolerance threshold of 0.6 mm. This confirms that the proposed calibration method satisfies the accuracy requirements for precise robotic imaging.

2.2. Principles of WAO scanning operation

Fig. 2B illustrates the WAO scanning trajectory optimized for vascular interfaces. By superimposing a lateral harmonic component onto the traditional axial linear scan, this method significantly expands the effective 2D lateral field of view without altering the probe’s feed direction. Mathematically, The definitions of all parameters are provided in Table 3. The WAO trajectory is defined by an axial feed $s\left(t\right)=v_{axial}t$ along the vessel centerline and a lateral oscillation $q\left(t\right)=Asin\left(2\pi f_{osc}t\right)$. In our in vivo experiments, we set the axial speed $v_{axial}=4.2\text{mm/s}$, the amplitude $A=5\text{mm}$, and the frequency $f_{osc}=2\text{Hz}$. The speed of 4.2 mm/s was chosen to provide a spatial sampling pitch of 0.42 mm given the 10 Hz laser rate, ensuring high-resolution sampling along the tortuous vascular paths. The 5 mm amplitude was optimized to fully cover the vessel width and maximize the acceptance angle for limited-view correction. Although the instantaneous detection angle relative to the vessel varies due to the oscillation, this high-density spatial sampling ensures that each vascular segment is interrogated from multiple complementary perspectives. This multi-view accumulation effectively homogenizes the sensitivity distribution along the vascular cross-section. For 3D volumetric imaging, we implemented a phase-controlled trajectory decomposition (Fig. 2.C) to eliminate inertial impacts caused by abrupt directional changes. The oscillatory scan is split into two smooth unidirectional motions with a 180° phase shift. This design ensures precise spatial overlap between forward “$⨂$” and return ”$\odot$” paths, guaranteeing imaging symmetry and registration accuracy.

Table 3.

Implemented parameters for WAO scanning.

Parameter	Symbol	Value	Implementation rationale
Axial Speed	$v_{axial}$	4.2 mm/s	Provides $\sim$0.4  mm sampling pitch (matched to 10  Hz laser).
Oscillation Amp.	$A$	5 mm	Covers vessel width and expands detection angle.
Oscillation Freq.	$f_{osc}$	2 Hz	Ensures mechanical stability and sufficient sampling density.

Because the oscillation frequency was 2 Hz and the laser repetition rate was 10 Hz, each WAO cycle contained five laser-triggered acquisitions. The temporal sampling interval was $0.1\mathrm{s}$, corresponding to an axial sampling interval of approximately 0.42 mm at the axial speed of 4.2 mm/s. The five laser shots within each oscillation cycle therefore corresponded to a phase interval of 72° along the prescribed harmonic trajectory. The lateral sampling position of each frame was determined by $q\left(t\right)=Asin\left(2\pi f_{\mathrm{osc}}t\right)$, with $A=5\mathrm{mm}$ and $f_{\mathrm{osc}}=2\mathrm{Hz}$. In the present implementation, the probe orientation also varied during WAO scanning within an angular range of approximately $\pm 10°$. Each acquired 2D PA frame was paired with the robot-recorded 6-DOF probe pose, including both position and orientation, at the corresponding trigger time. Based on the calibration between the robot coordinate system and the probe imaging coordinate system described in Section 2.1 and Supplemental S1, each frame was then mapped into the common 3D reconstruction coordinate system according to its measured spatial pose.

2.3. High-fidelity robotic 3D imaging via WAO-synthesized aperture

Fig. 2.A shows our 3D imaging workflow, which is integrated into a cohesive multi-modal process. Initially, an 800 nm infrared (IR) camera captures images of the target area; since blood vessels are highly sensitive to this wavelength, these IR images are used to extract the general vascular trajectory, which serves as the preliminary path planning for the robot. It is important to note that while infrared imaging provides a reliable 2D roadmap, its limited penetration depth necessitates the use of photoacoustic imaging for true 3D visualization. To bridge this gap, a depth camera mounted on the robotic end-effector captures the 3D point cloud of the skin surface. By fusing the data from the two pre-aligned cameras, we map the 2D vascular paths extracted from the IR images onto the 3D surface point cloud, resulting in a pre-planned robotic scanning trajectory. Finally, by superimposing the WAO scanning strategy onto this trajectory, the robot executes precise movements based on 6-DOF positional information to acquire a sequence of 2D photoacoustic images for high-fidelity reconstruction.

The parameters in Table 3 should be interpreted as representative implementation settings for this feasibility study rather than globally optimized values. Oscillation amplitude primarily determines the lateral excursion of the probe and therefore the range of complementary receive views. A larger amplitude can increase angular diversity and k-space support, but it also increases the trajectory length, acquisition time, and sensitivity to pose-registration or motion errors. Oscillation frequency controls the temporal phase sampling of the harmonic trajectory. At a fixed laser repetition rate, increasing the frequency reduces the number of laser shots per oscillation cycle and may degrade angular sampling, whereas a lower frequency improves phase sampling at the cost of longer scan time. The axial scanning speed determines the frame spacing along the vessel centerline; slower speeds increase sampling density and spatial averaging, whereas faster speeds reduce acquisition time but may undersample tortuous vascular segments. Thus, the current setting of $A=5\mathrm{mm}$, $f_{\mathrm{osc}}=2\mathrm{Hz}$, and $v_{\mathrm{axial}}=4.2\mathrm{mm/s}$ was selected as a practical balance among vessel coverage, mechanical stability, laser-triggered sampling density, and scan duration.

At the algorithmic level, to accurately extract vascular structures from the 2D IR images, we employ a convolutional neural network (CNN) based on the U-Net architecture [30]. This network utilizes an encoder–decoder design with skip connections to preserve high-resolution spatial information. Let the input infrared image be denoted as $\mathbf{X}\in {\mathbb{R}}^{H\times W\times 1}$, and the predicted probability map as $\hat{\mathbf{Y}}\in {\left[\mathrm{0,1}\right]}^{H\times W}$. During the encoding stage, the feature map ${\mathbf{x}}_l$ is downsampled through consecutive convolutions and max-pooling operations at the $l$th level ($l=1,\dots ,4$): ${\mathbf{x}}_l={\text{Pool}}_{max}\left(\sigma \left({\mathcal{C}}_3^2\left({\mathbf{x}}_{l-1}\right)\right)\right)$ where ${\mathcal{C}}_3^2\left(\cdot \right)$ denotes two consecutive 3 × 3 convolutions and $\sigma \left(\cdot \right)$ is the ReLU activation function. Subsequently, the decoder recovers spatial resolution via bilinear upsampling and channel-wise concatenation: ${\mathbf{y}}_l={\mathcal{C}}_3^2\left(\left[{\mathcal{U}}_{up}\left({\mathbf{y}}_{l+1}\right);{\mathbf{x}}_l\right]\right)$ where ${\mathcal{U}}_{up}\left(\cdot \right)$ denotes the upsampling operation and $[\cdot ;\cdot ]$ represents the skip connection fusion. The final segmentation map $\hat{\mathbf{Y}}$ is generated via a Sigmoid activation: $\hat{\mathbf{Y}}=\frac{1}{1+exp(-{\mathcal{C}}_1\left({\mathbf{y}}_1\right))}$ To derive the vessel centerlines required for robotic path planning, a morphological skeletonization algorithm $\mathcal{S}\left(\cdot \right)$ is applied to the binarized mask: ${\mathbf{C}}_{vessel}=\mathcal{S}\left(\mathbb{I}(\hat{\mathbf{Y}}>\tau )\right)$ where $\mathbb{I}\left(\cdot \right)$ is the indicator function with a threshold $\tau =0.5$. The dataset employed in this study comprises nearly 1000 self-collected infrared images of the back of the hand, encompassing subjects across different genders and age groups. For model development, 800 high-quality images were selected and partitioned into training, validation, and testing sets with a ratio of 80%, 10%, and 10%, respectively. The network was optimized using the Adam optimizer with a predefined learning rate of $1e^{-4}$. The training process was conducted over 100 epochs to achieve stable convergence. In the present study, the U-Net module was used to generate an initial superficial-vessel roadmap for robotic path planning. Because a systematic pixel-level segmentation benchmark was not performed, we do not claim that the network has been fully validated for general vascular segmentation. Quantitative evaluation using manually annotated test sets, including Dice coefficient, precision, recall, centerline localization error, and path-planning success rate, will be required in future work.

To ensure efficient coverage of the complex vasculature, we prioritized major superficial vessels (typically $>1$ mm in diameter) which serve as the topological backbone. Since the PA transducer possesses a finite effective field of view, navigating along these primary trunks allows the WAO scan to naturally encompass surrounding secondary vessels. Serving as spatial indices within the point cloud, these centerlines underpin our “Image-Guided Path Planning Module”, which generates a sequence of scanning waypoints along the vessel. Upon execution by the robotic controller, this sequence constitutes the ”vessel-aware baseline scanning path”. The final WAO scanning trajectory is then generated by superimposing a modulation pattern onto this baseline. To ensure reconstruction accuracy, the imaging system was rigorously synchronized with the robotic kinematics, enabling the acquisition of spatially correlated 2D photoacoustic images. Finally, a 3D volumetric image was reconstructed based on the precise trajectory and the corresponding image sequence (The detailed scanning process is demonstrated in video 1).

3. Experimental validation

3.1. Simulation results

To evaluate the efficacy and physical consistency of the WAO strategy, we conducted a series of dual-domain numerical investigations encompassing both acoustic and optical characteristics. Specifically, we first performed comparative simulations to assess scanning performance and image fidelity, thereby validating the significant advantages of the proposed method in terms of both spat-physical coverage and reconstructed image quality. Furthermore, to ensure that the observed signal enhancements are strictly attributable to the synthesized acoustic aperture rather than local fluctuations in light delivery — which could otherwise act as a confounding variable — we conducted a rigorous 3D Monte Carlo analysis. This secondary investigation quantitatively verifies the stability of optical fluence within deep tissue during dynamic probe oscillation, effectively isolating the acoustic contribution from potential optical artifacts.

3.1.1. Comparative simulation of scanning performance and image fidelity

In this section, we systematically validated the advantages of the proposed WAO scanning trajectory over traditional linear scanning strategies through both multi-angle simulations. To elucidate the performance enhancement mechanism of WAO, we established a 2D simulation framework comprising spatial coverage analysis, photoacoustic sensitivity field distribution, and k-Wave image reconstruction. The experimental design and corresponding analyses are detailed as follows:

To provide a more quantitative interpretation of the proposed “kinematic synthesized aperture”, we further analyzed the WAO scanning process in the spatial-frequency domain. Conceptually, WAO should be regarded as a robot-enabled kinematic aperture-synthesis acquisition strategy, rather than as a fundamentally new photoacoustic signal-generation mechanism. It does not change the photoacoustic effect, acoustic propagation physics, transducer bandwidth, or reconstruction model; instead, it changes the set of receive-view directions sampled by the same linear-array hardware through controlled probe motion and pose recording. In linear-array photoacoustic imaging, the visibility of a boundary depends on whether the acoustic wavefronts generated by its spatial-frequency components can be received within the finite angular acceptance of the transducer. Let $\mathbf{k}=(k_x,k_z)$ denote a 2D spatial-frequency vector and let ${\mathbf{n}}_i$ denote the receive-axis direction of the probe at the $i$th sampled robot pose. For a transducer with an effective receive half-angle $\alpha$, the pose-dependent observable k-space support can be approximated as

$$C_i\left(\mathbf{k}\right)=\mathcal{B}\left(\left|\mathbf{k}\right|\right)H\left[\alpha -{cos}^{-1}\left(\frac{\mathbf{k}\cdot {\mathbf{n}}_i}{\left|\mathbf{k}\right|}\right)\right],$$ (1)

where $H\left(\cdot \right)$ is the Heaviside function and $\mathcal{B}\left(\left|\mathbf{k}\right|\right)$ represents the radial frequency band determined by the acoustic bandwidth of the imaging system. This formulation separates the radial bandwidth limit from the angular receive-view limit. The WAO strategy does not change $\mathcal{B}\left(\left|\mathbf{k}\right|\right)$; instead, it changes the set of receive directions $\left\{{\mathbf{n}}_i\right\}$ through robot-controlled lateral oscillation and probe-orientation variation.

For a conventional linear scan, the receive direction is nearly fixed, and the total observable support is therefore

$$C_{\mathrm{linear}}\left(\mathbf{k}\right)=1-\prod _i\left[1-C_i^{\mathrm{linear}}\left(\mathbf{k}\right)\right].$$ (2)

Because the probe orientation changes little during linear scanning, $C_{\mathrm{linear}}\left(\mathbf{k}\right)$ occupies a limited angular sector in k-space. Spatial-frequency components outside this sector are weakly sampled, which corresponds to the well-known limited-view loss. These missing components are especially relevant to vessel sidewalls, whose boundary normals generate oblique acoustic wavefronts relative to the primary receive direction.

In WAO scanning, each laser-triggered PA frame is associated with a different robot-recorded pose. The corresponding synthesized k-space support is given by the union of the pose-dependent supports

$$C_{\mathrm{WAO}}\left(\mathbf{k}\right)=1-\prod _i\left[1-C_i^{\mathrm{WAO}}\left(\mathbf{k}\right)\right].$$ (3)

The lateral oscillation and the approximately $\pm 10°$ probe-orientation variation generate multiple complementary receive directions within one oscillation cycle. As shown in Fig. 4, this broadens the angular support in k-space while preserving the same radial bandwidth. The additional support appears mainly at oblique spatial-frequency directions, indicating that WAO preferentially improves the sampling of sidewall-related acoustic information rather than uniformly increasing all frequency components.

Fig. 4.

K-space analysis of the WAO kinematic synthesized aperture. (A) Observable k-space support of conventional linear scanning. (B) Expanded k-space support of WAO scanning. (C) Additional oblique spatial-frequency components recovered by WAO compared with linear scanning. Gray denotes the support already covered by linear scanning, whereas red denotes the additional support introduced by WAO. (D) Angular support comparison showing an approximately 31.9% increase in observable k-space angular coverage. The blue markers indicate the five laser-triggered probe poses within one WAO cycle.

We quantified this effect using the normalized angular-support gain

$$\eta =\frac{{\int }_{\Omega }{C}_{\mathrm{WAO}}\left(\mathbf{k}\right)d\mathbf{k}-{\int }_{\Omega }{C}_{\mathrm{linear}}\left(\mathbf{k}\right)d\mathbf{k}}{{\int }_{\Omega }{C}_{\mathrm{linear}}\left(\mathbf{k}\right)d\mathbf{k}}\times 100\text{\%},$$ (4)

where $\Omega$ denotes the analyzed 2D k-space domain within the same radial frequency band. In this study, acoustic coverage was defined as the normalized observable support within the analyzed spatial or k-space domain under identical transducer bandwidth, receive half-angle, and imaging ROI. For the k-space analysis, $C\left(\mathbf{k}\right)$ was treated as a binary support function, where $C\left(\mathbf{k}\right)=1$ indicates that the spatial-frequency component $\mathbf{k}$ falls within the receive-view support of at least one sampled probe pose, and $C\left(\mathbf{k}\right)=0$ otherwise. The WAO trajectory increased the observable k-space angular support by approximately 31.9%, consistent with the acoustic coverage gain reported in the spatial-domain simulation. Thus, the reported 32% improvement represents the relative increase in observable angular/spatial support introduced by the WAO trajectory; it does not indicate an increase in the intrinsic acoustic bandwidth, optical fluence, laser pulse energy, or pulse number. This k-space result explains why WAO reduces sidewall degradation and improves vessel-boundary continuity in the subsequent k-Wave simulation and phantom validation.

Initially, in the spatial coverage simulation, we simulated the probe scanning along preset spatial curves to quantify its acoustic detection range. As illustrated in Figs. 3A and.B, the WAO scanning strategy incorporates a specific lateral oscillation mechanism, enabling the probe to capture target signals from a broader range of angles. The video demonstrating the dynamic spatial coverage simulation is available in the Video 1. Quantitative analysis reveals that, compared to the traditional scanning method, the effective acoustic field coverage of the WAO scanning trajectory is increased by 32%. This geometric advantage provides a fundamental solution to the limited-view problem inherent in linear scanning. Subsequently, to evaluate the detection capability, we analyzed the photoacoustic field distribution (Figs. 3.C and.D). The system’s sensitivity was defined through the coupling of optical and acoustic fields. The photoacoustic sensitivity distribution was generated by calculating the product of two normalized fields: the optical fluence distribution within the tissue, modeled via Monte Carlo simulations based on actual fiber parameters, and the probe’s acoustic reception sensitivity field, simulated using the k-Wave toolbox [31]. Analysis of this coupled field indicates that at a critical imaging depth of $10\text{mm}$, the WAO scanning strategy yields a sensitivity distribution that is not only higher in intensity but also more spatially uniform laterally, effectively mitigating the attenuation typically observed at the edges of traditional scans. Furthermore, vessel imaging validation was performed using k-Wave simulations, as illustrated in Figs. 3.E and.F.

Fig. 3.

Spatial coverage and simulation results. (A, B) Spatial coverage projection views of the acoustic field for linear scanning and WAO scanning, respectively. (C, D) Acoustic field coverage maps of the 2D transducer. (E, F) Corresponding simulated vessel images for the respective scanning methods.

Finally, we modeled a blood vessel with a diameter of $2\text{mm}$ and moved the probe according to the WAO scanning lateral configuration to acquire signals in 2D cross-sectional plane, which were then reconstructed and fused via linear superposition. To quantitatively evaluate the morphological fidelity of the reconstructed images, we performed a continuous radial resolution analysis as illustrated in Fig. 5.A. We calculated the FWHM of the vessel wall profile along 360° directions. As shown in Fig. 5.B, the Linear scan (red dashed line) exhibits severe anisotropy: while the resolution is high at 0° and 180° (0.2 mm), it degrades significantly at the side walls (90° and 270°), with FWHM broadening to over 1.0 mm due to the limited-view problem. In contrast, the WAO scan (blue solid line) maintains a consistent FWHM of approximately 0.35 mm across the analyzed angular range, indicating improved angular uniformity of the reconstructed vessel-wall profile rather than a complete isotropic volumetric resolution characterization.

Fig. 5.

Quantitative analysis of directional FWHM uniformity. (A) Schematic of the radial FWHM measurement. (B) Comparison of resolution uniformity. The Linear scan (red dashed line) shows severe resolution degradation at the side walls (90°/270°), while the WAO scan (blue solid line) reduces the angular variation of the reconstructed vessel-wall profile.

3.1.2. Monte Carlo simulation of optical fluence stability in deep tissue

To evaluate whether dynamic illumination variations could act as a confounding factor in the WAO experiment, we performed 3D Monte Carlo (MC) simulations of photon transport [32]. A potential concern is that the dynamic lateral oscillation of the probe might induce local fluctuations in light delivery, referred to here as dynamic illumination effects. To address this, we modeled the optical fluence distribution under varying probe incidence angles to evaluate illumination stability at the target depth. The simulation was implemented using a standard 3D MC framework for photon transport in a homogeneous tissue volume ($50\times 50\times 30{\text{mm}}^3$) with optical properties representative of generic biological soft tissue within the near-infrared window (Table 4). To accurately replicate our experimental setup, the illumination source was modeled as a rectangular surface beam ($33\times 1{\text{mm}}^2$) with an initial divergence angle of $\sim 65°$. To simulate the WAO scanning process, the incident angle of the light source relative to the tissue surface was dynamically varied across multiple orientations, including 0°, $\pm 5°$, and the maximum deflection of $\pm 10°$, with $10^8$ photon packets launched per configuration to ensure a high signal-to-noise ratio.

Table 4.

Optical properties used in the Monte Carlo simulation.

Parameter	Symbol	Value
Absorption coefficient	${\mu }_a$	$0.1{\text{cm}}^{-1}$
Scattering coefficient	${\mu }_s$	$100{\text{cm}}^{-1}$
Anisotropy factor	$g$	0.9
Reduced scattering coefficient	${\mu }_s^{\prime }={\mu }_s(1-g)$	$10{\text{cm}}^{-1}$
Refractive index	$n$	1.4

The optical parameters were selected to represent a scattering-dominant soft-tissue condition in the near-infrared window rather than a subject-specific hand model. In this model, the absorption coefficient was set to ${\mu }_a=0.1{\mathrm{cm}}^{-1}$, the scattering coefficient to ${\mu }_s=100{\mathrm{cm}}^{-1}$, the anisotropy factor to $g=0.9$, and the refractive index to $n=1.4$, giving a reduced scattering coefficient of ${\mu }_s^{\prime }={\mu }_s(1-g)=10{\mathrm{cm}}^{-1}$. These values describe a weakly absorbing but strongly scattering medium, in which the initial illumination-angle difference is expected to be progressively smoothed with depth. The purpose of this MC analysis was therefore not to reproduce all layered and heterogeneous structures of the human dorsal hand, but to test whether the WAO-induced angular variation of the incident beam could produce a large fluence fluctuation at the analyzed depth of 10 mm under a representative soft-tissue condition.

The resulting optical fluence $\Phi$ (${\text{J/cm}}^2$) was recorded within a 3D voxel grid, from which normalized values were extracted at a central region of interest at $z=10\text{mm}$. As illustrated in Fig. 6, the continuous dynamic fluence profile reconstructed based on the probe’s harmonic oscillation ($2\text{Hz}$, $\pm 10°$) demonstrates that the optical fluence at this depth exhibits negligible fluctuations (variance $<2\text{\%}$) and remains strictly confined within a stable $\pm 5\text{\%}$ envelope throughout the entire cycle. This stability is consistent with the broad-beam geometry and the scattering-dominant tissue assumption: after several scattering events, the local fluence at depth becomes less sensitive to small changes in the initial incidence angle. These MC results support the interpretation that dynamic illumination variation is unlikely to be the dominant source of the observed image-quality improvement under the modeled conditions. However, they do not fully exclude optical effects in all tissue settings or subject-specific anatomies.

Fig. 6.

Monte Carlo simulation results evaluating optical fluence stability at a depth of $10\text{mm}$ during WAO scanning. The red line represents the dynamic oscillation angle of the probe ($\pm 10°$ at $2\text{Hz}$), while the blue line indicates the simulated normalized optical fluence at the target depth. The fluence fluctuations are small ($<2\text{\%}$) and remain within a $\pm 5\text{\%}$ stability zone (shaded gray area), supporting the interpretation that WAO-induced illumination-angle variation is unlikely to be the dominant source of image-quality changes under the modeled scattering-dominant condition.

3.2. Phantom validation of imaging performance

To benchmark artifact suppression and morphological fidelity, we imaged a $150\mathrm{\mu }\mathrm{m}$ metal wire phantom, which serves as a high-contrast proxy for microvasculature. By comparing conventional linear scanning with the proposed WAO strategy under identical experimental configurations, we evaluated the 3D reconstructed volumes through two rigorous metrics: CNR and FWHM-based dimensional accuracy.

The WAO strategy demonstrated a clear quantitative and qualitative superiority over the conventional linear approach. Specifically, WAO achieved a significantly higher CNR ($20.42\text{dB}$ vs. $16.76\text{dB}$; Figs. 7A, D). This enhancement confirms that the synthesized wide-angle aperture effectively captures a broader range of high-frequency spatial components, thereby boosting the signal intensity while simultaneously suppressing background noise through improved spatial averaging. Furthermore, the WAO strategy successfully mitigated the morphological distortions typically associated with limited-view imaging. The measured FWHM of $164\mathrm{\mu }\mathrm{m}$ under WAO closely approximated the $150\mathrm{\mu }\mathrm{m}$ ground truth, representing a substantial improvement over the $189\mathrm{\mu }\mathrm{m}$ broadened profile observed in the linear scan (Figs. 7B, E).

Fig. 7.

Quantitative evaluation using a $150\mathrm{\mu }\mathrm{m}$ metal wire phantom. (A, B) Conventional linear scan: 3D reconstruction (CNR: 16.76 dB), enlarged line profile (FWHM: $189\mathrm{\mu }\mathrm{m}$). (C, D) Proposed WAO scan: 3D reconstruction with enhanced CNR (20.42 dB), line profile with improved FWHM ($164\mathrm{\mu }\mathrm{m}$).

A detailed analysis of the cross-sectional views (Figs. 7C, F) further elucidates these findings: while the linear scan suffers from pronounced lateral blurring and “smearing” due to the restricted detection angle, the WAO strategy improves vessel-boundary continuity by providing broader coverage of the object’s Fourier space. These results indicate that WAO can enhance signal sensitivity and reduce limited-view-induced structural distortion under the tested phantom conditions, while complete volumetric quantification will require further directional resolution characterization.

3.3. In vivo experimental results

To ensure consistent acoustic coupling and prevent contact artifacts, all scanning experiments were performed with the sample and transducer submerged in a water tank. All human experiments were approved by the Ethics Committee of The Hong Kong Polytechnic University (Approval No. HSEARS20260528003), covering all methodologies, durations, and instrument validations. The 1064 nm laser fluence was maintained at $15{\text{mJ/cm}}^2$, strictly complying with ANSI safety guidelines [33].

To validate the imaging performance of the system, we conducted two robot-assisted imaging experiments on the dorsum of the hand of the same subject. The experimental group utilized the WAO trajectory for scanning, with a scan time of 189 s; as a comparison, the control group performed a conventional linear scan from the same starting position, taking 124 s. Due to the more complex path planning involved in the WAO scanning strategy, its scan time was approximately 1.5 times that of the simple linear scan. Subsequently, we performed 3D reconstruction on the acquired photoacoustic signals, and the results are shown in Fig. 8.A (experimental group) and Fig. 8.F (control group). In terms of overall visual quality, compared to the control group, the experimental group (WAO) images exhibited higher contrast and superior visualization of the vascular network. To further analyze imaging details, we selected the blood vessels at the base of the index finger as the region of interest (zoom area, as indicated by the gray region in the figure). Figs. 8.B and D display the $z-x$ and $z-y$ planar cross-sectional images of the control group in this focused area, while Figs. 8.C and E present the corresponding planar images of the WAO scan. It can be clearly observed from the comparison that the images of the focused area optimized by the WAO trajectory demonstrate better uniformity in spatial distribution. This advantage is mainly attributed to the multi-angle compound imaging provided by the WAO strategy, which significantly increased the effective numerical aperture of the system, thereby reducing the anisotropy. The projected vessel profile measured from the maximum-intensity-projection (MIP) image yielded an apparent in-plane resolution of approximately $215\mathrm{\mu }\mathrm{m}$. This value should be interpreted as a MIP-derived in-plane apparent resolution of the reconstructed vascular projection, rather than an axial, lateral, elevational, or isotropic volumetric resolution.

Fig. 8.

Comparative in vivo imaging of blood vessels in the dorsal hand. (A) Vascular reconstruction using the WAO scanning trajectory. (F) Reconstruction using a conventional linear scan. (B, D) Projection images of the zoom area in the $z-x$ and $z-y$ planes, respectively, obtained from the linear scan. (C, E) Corresponding projection images of the zoom area reconstructed using the WAO scan.

The in vivo experiment was performed over a 189-second WAO acquisition window, during which hand tremor, arterial pulsation, and subject motion could not be fully excluded. No independent motion tracking or motion correction was implemented in the present feasibility experiment. Therefore, the lateral shadowing or ghosting visible around the vessel in Fig. 8A should be interpreted with caution. This artifact may arise from involuntary hand tremor, arterial pulsation, residual probe–image co-registration error, or frame-to-frame mismatch during multiview compounding. Accordingly, the in vivo result supports the preliminary feasibility of WAO-based 3D peripheral vascular imaging, but it should not be regarded as evidence of motion robustness.

4. Discussion and conclusion

This study investigated robot-assisted wide-amplitude oscillatory (WAO) scanning as an acquisition-level strategy for mitigating limited-view artifacts in linear-array photoacoustic imaging of peripheral vasculature. By superimposing a lateral oscillatory motion onto a vessel-guided baseline trajectory, the robot acquires complementary receive views while recording the 6-DOF pose of each photoacoustic frame. This design expanded the observable acoustic support by approximately 32% and increased the k-space angular support by 31.9%, without changing the transducer hardware. The method should therefore be interpreted as a robot-enabled kinematic aperture-synthesis strategy, rather than as a new photoacoustic signal-generation mechanism or a fully optimized scanning protocol.

The main benefit of WAO is that it increases the amount of physically acquired multiview information before reconstruction. This distinguishes it from reconstruction-side limited-view correction methods, such as model-based, iterative, or learning-based compensation, which mainly operate on already acquired data. At the same time, WAO is complementary to these approaches: pose-encoded multiview data generated by robot-controlled scanning could provide richer input for model-based reconstruction or learning-based artifact suppression in future implementations.

The simulation and phantom results support this interpretation. The k-space analysis indicates that WAO primarily adds oblique spatial-frequency components associated with vessel sidewalls, while preserving the same bandwidth-limited radial frequency range of the transducer. The Monte Carlo analysis suggests that WAO-induced illumination-angle variation is unlikely to dominate the observed image-quality changes under the modeled scattering-dominant condition. In the wire phantom experiment, WAO increased the CNR from 16.76 dB to 20.42 dB and reduced the measured FWHM from $189\mathrm{\mu }\mathrm{m}$ to $164\mathrm{\mu }\mathrm{m}$. In the preliminary human experiment, WAO improved the visual continuity of the dorsal-hand vascular reconstruction and yielded a MIP-derived in-plane apparent resolution of approximately $215\mathrm{\mu }\mathrm{m}$. These results indicate technical feasibility, but they should not be read as evidence of isotropic 3D resolution, motion robustness, or clinical diagnostic performance.

Several limitations define the current scope of the study. First, the in vivo WAO scan required $189\mathrm{s}$, whereas the conventional linear scan required $124\mathrm{s}$; therefore, the comparison was not matched in acquisition time or pulse number, and the WAO data inevitably included more laser pulses and greater spatial averaging. Second, the reported performance was obtained under one representative parameter setting, rather than through a full optimization of oscillation amplitude, oscillation frequency, and axial scanning speed. Third, the directional resolution of the current linear-array-based system remains anisotropic, and the reported $215\mathrm{\mu }\mathrm{m}$ value should be interpreted only as a MIP-derived in-plane apparent resolution. Fourth, the Monte Carlo model used homogeneous optical properties and did not include layered skin, heterogeneous vascular absorption, subject-specific parameters, or sensitivity sweeps.

The robotic and path-planning components also require further validation. In the present implementation, the robot served primarily as a pose-controlled trajectory execution and acquisition-synchronization platform; closed-loop force control, real-time adaptive navigation, visual servoing, and force-feedback-based probe regulation were not implemented. The U-Net module was used to generate an initial superficial-vessel roadmap, but its independent contribution was not quantified by Dice coefficient, precision, recall, centerline localization error, path-planning success rate, or ablation against manual or threshold-based path generation. Because the workflow depends on an infrared pre-scan, its robustness may decrease for deep, weakly visible, highly branched, or diseased vessels. The WAO trajectory provides a volumetric detection corridor that can tolerate some mismatch between the superficial roadmap and deeper vessel trajectory, but it does not perform real-time dynamic tracking.

Future work should therefore include matched acquisition comparisons, systematic parameter optimization, full axial–lateral–elevational resolution characterization, segmentation and path-planning benchmarks, and layered or subject-specific optical simulations. For in vivo use, motion sensitivity should be evaluated under controlled displacement, tremor-like perturbation, and physiological pulsation conditions. Photoacoustic-feedback-based trajectory updating, external optical motion tracking, fiducial-based registration, physiological gating, and image-based non-rigid correction may help reduce dependence on superficial infrared visibility and improve multiview compounding over longer scans. In its current form, the study supports WAO as a feasible acquisition-level strategy for improving limited-view peripheral vascular photoacoustic imaging, while broader multi-subject and disease-relevant validation will be required before claims of clinical robustness, standardized diagnosis, or longitudinal monitoring can be made.

CRediT authorship contribution statement

Yongjian Zhao: Writing – original draft, Software, Methodology, Conceptualization. Li Shen: Formal analysis, Data curation. Hengrong Lan: Software, Methodology. Yanting Liang: Resources, Project administration. Fei Gao: Supervision, Funding acquisition, Conceptualization. Nanguang Chen: Supervision, Funding acquisition, Conceptualization.

Ethics declaration

Written informed consent to take part in the study and to publish the article has been obtained from all participants or their legal representatives. The privacy rights of participants have been observed.

This study was performed in compliance with relevant laws, regulatory frameworks and guidelines where the research took place. This study was approved by The Hong Kong Polytechnic University. (Approval No. HSEARS20260528003)

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Biographies

Yongjian Zhao received his M.S. degree in Microelectronics and Solid-State Electronics from the University of Chinese Academy of Sciences in 2021, and his Ph.D. in Electronic Engineering from The Chinese University of Hong Kong in 2025. His research focuses on the development of multi-modal and multi-dimensional imaging systems.

Li Shen received his bachelor’s degree from Nanjing University of Science and Technology in 2024. He is currently pursuing a master’s degree at Southeast University in Jiangsu Province, with a research interest in multi-modal data fusion.

Hengrong Lan is special-Appointment Associate Researcher, Suzhou Institute for Advanced Research, University of Science and Technology of China (USTC). His/Her main research interests include photoacoustic/ultrasound super-resolution imaging techniques and their applications in image reconstruction, as well as AI-based image reconstruction methods.

Yanting Liang, M.D. She is a physician specialized in internal medicine. Her primary work focuses on clinical practice and fundamental research covering cardiovascular diseases, acute kidney injury, and chronic kidney diseases. She has conducted a series of systematic studies concerning the pathogenesis and progression mechanisms of related diseases as well as clinical intervention strategies, accumulating extensive clinical experience and solid scientific research achievements.

Fei Gao is a Special-Appointment Researcher and Ph.D. Supervisor at the University of Science and Technology of China (USTC), and has been selected for the CAS Youth Innovation Promotion Association (Merit Selection). In 2017, he established the Hybrid Imaging System Laboratory (HISLab) as an independent Principal Investigator (PI). His work is dedicated to the frontier fundamental research of photoacoustic imaging technology, the development of equipment and algorithms, as well as clinical translational applications.

Nanguang Chen received his BEng in Electromagnetic Measurement and Instrumentation from Hunan University in 1988, M.Sc. in Theoretical Physic from Peking University in 1994, and Ph.D. in Biomedical Engineering from Tsinghua University in 2000. He joined the University of Connecticut in 2000, firstly as a postdoctoral research fellow and subsequentially as an Assistant Research Professor in the Department of Electrical and Computer Engineering. Prof. Chen became an Assistant Professor of Biomedical Engineering at the National University of Singapore in 2004. He was promoted to Associate Professor with tenure in 2011.

Appendix A. Supplementary data

The following is the Supplementary material related to this article.

MMC S1

.

Data availability

Data will be made available on request.