1. Introduction

Photoacoustic imaging (PAI) represents a breakthrough in biomedical imaging by combining optical excitation with ultrasonic detection, enabling high-resolution visualization of deep tissues [1–3]. This hybrid approach overcomes the optical diffusion limit while maintaining optical contrast, allowing label-free monitoring of hemodynamic processes and providing crucial functional and molecular information for disease diagnosis and progression monitoring [4,5]. The imaging quality in PAI fundamentally depends on the detection of laser-induced ultrasound waves, where the sensor’s bandwidth and angular coverage play decisive roles in determining spatial resolution and image fidelity. Despite significant advances in sensor technology, current acoustic detectors face two fundamental limitations. The frequency response of current sensors poses inherent constraints on spatial resolution. While high-frequency detection theoretically enables better spatial resolution, the achievable bandwidth is severely limited by acoustic impedance mismatches between the sensor materials (such as rigid piezoelectric ceramics, lithium niobate, or glass) and soft biological tissues. This impedance mismatch causes significant reflection and transmission losses at the sensor-tissue interface, particularly at higher frequencies, leading to reduced detection sensitivity and compromised axial resolution [6,7]. The fundamental nature of this material property mismatch makes it particularly challenging to overcome through conventional sensor design approaches. Although efforts have been made to address this limitation through the development of specialized sensors, such as PVDF (Polyvinylidene Fluoride) based detectors and optical resonators [8–10]. the trade-off between bandwidth and detection sensitivity remains a fundamental challenge.

These fundamental limitations in bandwidth and angular coverage have motivated extensive exploration of multi-sensor approaches to expand the effective detection capabilities. By incorporating sensors with different frequency responses, researchers combined low-frequency sensors for deep tissue penetration with high-frequency sensors for enhanced resolution of superficial structures [11–16]. While this strategy showed promise in accessing a broader frequency spectrum, most implementations simply selected the “best” signal from each sensor within its optimal frequency range, or directly superimposed the signals without considering their complex interactions. These methods, though intuitively appealing, often resulted in compromised image quality due to several overlooked factors.

The primary challenge lies in the complex phase relationships inherent in acoustic detection. Piezoelectric and optical sensors, being acoustically resonant devices, exhibit frequency-dependent phase responses that vary significantly across their bandwidth [17–19]. When signals from different sensors are combined, these phase variations can lead to destructive interference. Moreover, the spatial-temporal coupling in acoustic wave propagation means that signals detected at different angles and frequencies carry intrinsically different phase information about the source distribution [7]. Direct signal combination without proper phase compensation can therefore result in spatial artifacts and resolution degradation, potentially yielding worse results than single-sensor approaches. This fundamental oversight in previous multi-sensor implementations has limited their effectiveness in achieving truly broadband, high-fidelity photoacoustic imaging.

To address these challenges, we present a comprehensive framework for synthesizing signals from sensors with complementary frequency bands and spatial responses. Our approach integrates three essential steps to achieve optimal signal synthesis. First, we develop a combined theoretical-experimental method for precise characterization of sensor point spread functions (PSF). Second, we implement phase-aware deconvolution algorithms that preserve signal coherence across different frequency bands, ensuring consistent phase relationships throughout the detection bandwidth. Third, we design optimal signal synthesis strategies that maximize the effective bandwidth while maintaining high SNR. This method achieves significant improvements in image contrast and resolution compared to conventional direct addition, demonstrating that proper phase management is more critical than amplitude compensation for high-quality image synthesis. The feasibility of this framework was verified by using two optical sensors with distinct diameters and working bandwidths (peaked at 22 MHz and 31 MHz, respectively). Based on the framework, we achieved enhanced spatial resolution (from 170 μm to 83 μm) and SNR (from 24 dB to 30 dB). While developed for optical fiber sensors, our approach is generalizable to various sensor technologies, including other optical and electrical detection schemes, offering a versatile solution for enhancing PAI system performance.

2. Methodology

Figure 1 illustrates the proposed multi-sensor synthesis framework, which consists of setup of framework and three key steps: precise PSF estimation, phase-aware deconvolution, and multi-sensor synthesis. Each step is designed to address specific technical challenges while maintaining the integrity of acoustic information, ultimately achieving optimal imaging performance. The formula descriptions and detailed implementation steps of the framework are given below.

 

Fig. 1. Schematic representation of the multi-sensor synthesis framework for photoacoustic imaging. The framework is divided into three key modules: (1) Precise PSF Estimation, combining finite element analysis (FEA) calculations and spatial response measurements to derive fine PSF; Here, the sensor pair was linearly scanned for photoacoustic detection. (2) Phase-Aware Deconvolution, which utilizes the characterized PSF to construct phase filter and convolution with different frequency bands; and (3) Multi-Sensor Synthesis, integrating outputs from different sensors with position corrections and intensity matching to achieve phase correction image. The integration of these steps ensures optimal bandwidth utilization and improved image resolution.

Download Full Size | PDF

2.1. Theoretical foundation

In a lossless homogeneous medium, the photoacoustic wave function at generated by thermal expansion can be written as [20]:

Using the Green function of free space, the solution to this photoacoustic wave equation can be written as [17]:

For practical sensors with finite bandwidth and specific impulse responses, the measured pressure can be expressed as:

2.2. Multi-sensor synthesis implementation

2.2.1. Precise PSF estimation

The foundation of our approach lies in the accurate characterization of each sensor’s PSF through a hybrid method combining theoretical calculations and experimental measurements, as illustrated in Fig. 1(top panel). The process consists of two parallel paths that converge to obtain a precise PSF characterization. In the theoretical path, we employ finite element analysis (FEA) to calculate the sensor's impulse response ${D_{1,2}}({\omega ,\theta } )$, where $\omega $ represents the angular frequency, and $\theta $ denotes the incident angle of acoustic waves. Using the acoustic dispersion relation in tissue, we can map the temporal frequencies $\omega $ to spatial frequency with $\omega = {c_0}\sqrt {k_x^2 + k_y^2} $ and $\theta = {\tan ^{ - 1}}({k_y}/{k_x})$, where ${k_x}$ and ${k_y}$ are the spatial frequency components. This interpolation allows us to recover two spatial dimensions transform from the temporal domain signal.

In parallel with the theoretical calculations, we conduct spatial response measurements using a point source configuration, as shown in Fig. 1. A 10 μm-diameter microball phantom, serving as an acoustic point source, is positioned at a fixed distance from the scanning plane where sensor 1 (S1) and sensor 2 (S2) perform linear scanning. This experimental setup enables the measurement of the actual spatial transfer functions under practical conditions. The measured signals are then processed to obtain the experimental PSFs.

The theoretical and experimental results are cross-correlated to optimize the system parameters. We fine-tuned critical parameters including sensor size, acoustic velocity, and orientation angles to maximize the correlation between calculated and measured PSFs. This optimization ensures that our theoretical model accurately reflects the actual sensor behavior. The resulting two-dimensional $PS{F_{1,2}}({{k_x},{k_y}} )$ captures both amplitude and phase responses across the entire frequency spectrum of interest.

Importantly, this PSF estimation process serves as a one-time calibration requirement. Once the PSF is accurately characterized for a specific system configuration, it remains valid for all subsequent imaging scenarios under the same setup, providing a reliable foundation for the phase-aware deconvolution and multi-sensor synthesis.

2.2.2. Phase-aware deconvolution

Using precisely characterized PSF, we implement phase-aware deconvolution to address phase misalignment challenges (Fig. 1 middle panel). Following the photoacoustic detection, the signals from sensors S1 and S2 undergo preliminary reconstruction to generate low-frequency and high-frequency images respectively, reflecting their distinct frequency response characteristics. The phase misalignment issue arises from the band-pass nature of sensor frequency responses, particularly near their resonant frequencies (S1: 22 MHz, S2: 31 MHz), as described by the Kramers-Kronig relations. To address this challenge, we construct a phase filter f_1,2(x, y) based on the precisely characterized PSF:

This pure phase filter design ensures that only phase information is modified while preserving the amplitude spectrum. The phase-corrected image can then be obtained through convolution

As evident in Eq. (6), this operation effectively eliminates the phase distortions introduced by different sensor response functions while maintaining the original signal amplitude information.

To evaluate the computational efficiency, we conducted performance testing of the phase-aware deconvolution algorithm. The tests were performed on a personal computer equipped with an Intel Core i9-14900 K processor (base frequency 3.2 GHz) using MATLAB R2021a environment. For a standard test sample (1000 × 1000 pixels single-precision floating-point image, 4 bytes per pixel), the complete processing pipeline, including phase estimation and deconvolution operations, took 0.12 seconds. This processing speed suggests the feasibility of near-real-time implementation in clinical settings, particularly with potential optimization through GPU acceleration and parallel processing in future iterations.

2.2.3. Multi-sensor synthesis

The final stage of our framework, illustrated in Fig. 1(bottom panel), implements an adaptive multi-sensor synthesis strategy that optimally combines the phase-corrected signals from both sensors. The synthesis algorithm incorporates a complex weighting factor w derived from the measured PSFs. The weighting factor is constructed such that its magnitude reflects the ratio of the measured PSF intensities between the two sensors. Meanwhile, its phase component compensates for the spatial offset between the centers of the measured PSF envelopes. This design ensures proper amplitude scaling and spatial alignment of signals from both sensors. Two synthesis approaches are implemented and compared:

Conventional direct addition (DA) method performs a weighted combination of the reconstructed signals [16]:

The phase-corrected (PC) synthesis incorporates the deconvolved signals:

This adaptive synthesis algorithm not only adjusts the contribution of each sensor based on their respective SNR characteristics across different frequency bands, but also compensates for positional differences to maintain high phase coherence. By ensuring in-phase addition, it satisfies the inequality $({|{PS{F_1}} |+ w \cdot |{PS{F_2}} |} )\ge ({|{PS{F_1} + w \cdot PS{F_2}} |} )$. As a result, this scheme is capable of maximizing the system’s bandwidth.

This multi-sensor synthesis framework overcomes the limitations of previous approaches that either ignored phase relationships or relied on direct image fusion without proper signal processing. By maintaining phase coherence throughout the workflow, our method achieves enhanced image resolution and quality. Moreover, it is flexible and adaptable to various sensor technologies, making it suitable for diverse photoacoustic imaging systems.

3. Multi-sensor synthesis

3.1. Sensor response calculation

To validate the multi-sensor synthesis method, we employed two optical fiber sensors with distinct diameters: 125 µm (S1) and 90 µm (S2). These sensors were specifically selected for their complementary frequency responses and significant phase variations, which make them ideal candidates for demonstrating the effectiveness of phase correction in multi-sensor synthesis. Through chemical etching, we precisely engineered their response spectra, with S1 exhibiting a peak response at ∼22 MHz and S2 at ∼31 MHz. Figure 2 presents the calculated amplitude and phase spectra of the sensor responses obtained through finite element analysis (FEA). The FEA simulations incorporated comprehensive material parameters characterizing both the surrounding medium and the fiber structure. For the water medium, we used an acoustic velocity of 1500 m/s and acoustic impedance of 1.5 MRayl. The fiber glass parameters included a longitudinal wave velocity of 3745 m/s, transverse wave velocity of 5950 m/s, and density of 2240 kg/m³. When acoustic waves interact with the fiber, they induce mechanical vibrations that result in birefringence changes, detectable through heterodyne detection as described in our previous works [24]. The induced birefringence changes were calculated using Pockels constants p₁₁ = 0.113 and p₁₂ = 0.252.

 

Fig. 2. Acoustic response characteristics of dual optical fiber sensors with different diameters. The two-dimensional impulse response ${D_1}({{k_x},{k_y}} )$ and ${D_2}({{k_x},{k_y}} )$ show amplitude (a, b) and phase (d, e) responses for 125-µm and 90-µm diameter sensors, respectively. The frequency-dependent amplitude and phase spectra (c, f) under θ = 0° incidence demonstrate distinct resonant behaviors at 0.0146 and 0.02 1/μm (corresponding to ∼22 MHz and ∼31 MHz), with significant phase variations near these frequencies. The distinct resonant frequencies and phase variations highlight the need for phase correction in multi-sensor synthesis.

Download Full Size | PDF

To comprehensively characterize the sensors’ spatial-frequency responses, we performed systematic calculations across an angular range from 0° to 360° with 1° intervals, while the frequency range spanned from 0.1 to 100 MHz with 0.1 MHz steps. The calculated two-dimensional impulse response ${D_{1,2}}({{k_x},{k_y}} )$ in Fig. 2(a, b, d, and e) reveal a characteristic cos(2θ) angular dependence, indicating that the sensors can exhibit significantly different responses and may even experience destructive summation at different angles. As shown in Fig. 2(c) and 2(f), both sensors exhibit pronounced phase variations at their resonant peaks, which are critical for understanding their behavior in multi-sensor systems. This angular-dependent behavior further emphasizes the importance of proper phase alignment in multi-sensor synthesis for optimal performance.

3.2. Point spread function (PSF) calculation

Figure 3 demonstrates our PSF characterization results. The experimental setup follows the configuration shown in Fig. 1, maintaining consistent geometric parameters between theoretical calculations, where a point source is positioned 2.5 mm from the sensor scanning plane. Two sensors (S1 and S2) are arranged parallel with 0.5 mm spacing, oriented perpendicular to the imaging plane. The sensors perform synchronized linear scanning across a 40 mm range with 10 μm sampling intervals, corresponding to a spatial Nyquist frequency of 0.05 1/μm, well above our system's maximum spatial frequency response (approximately 0.02 1/μm for the high-frequency sensor). At each scanning position, the acoustic signal characteristics are determined by the source-to-sensor distance and incident angle, which define the system's spatial impulse response.

 

Fig. 3. Point Spread Function (PSF) characterization and validation. (a) Calculated and (e) experimentally measured PSF for S1 and S2. (b) Calculated and (f) measured PSF envelopes. (c) Calculated and (g) measured lateral line profiles. (d) Calculated and (h) measured tilted line profiles. The fiber diameter and principal axis orientation were optimized to maximize the correlation between calculated and measured PSF, establishing the reference for phase-coherent synthesis. Scale bars: 100 µm.

Download Full Size | PDF

Through optimization of the theoretical model parameters, specifically the fiber diameter and the orientation angle of the principal axes, we achieved maximum correlation between calculated and measured PSFs. Figure 3(a) present the optimized calculated PSF for the S1 and S2, respectively, while Fig. 3(e) show their experimental counterparts. The surrounding ripple patterns in both calculated and measured PSF arise from the finite detection bandwidth of each sensor. Regarding the discrepancies between calculated and measured results in Fig. 3(c)(i) and Fig. 3 g(i), primarily arise from frequency-dependent ultrasound attenuation in the propagation medium, which was not incorporated in our theoretical calculations. This frequency-dependent attenuation is an inherent characteristic of real-world measurements, resulting in a narrower sensor bandwidth and higher sidelobes in the time domain. Nevertheless, the calculated and measured results still maintain good consistency. This optimized PSF characterization, achieved through careful parameter matching, serves as the foundation for subsequent phase correction in the multi-sensor synthesis process, ensuring accurate acoustic field reconstruction.

3.3. Phase-corrected synthesis

We then performed both theoretical calculations and experimental measurements using point sources to validate the effectiveness of phase-corrected synthesis. Figure 4 presents a comprehensive comparison between direct addition and phase-corrected synthesis methods. The calculated complex-field distributions (Fig. 4(a)) and their experimental counterparts (Fig. 4(f)) clearly demonstrate that direct addition of two PSF yields limited improvement due to phase misalignment between sensors, resulting in destructive interference across certain frequency bands. After applying phase correction, however, the imaging quality shows significant enhancement, as evidenced by the shape of the envelope (Fig. 4(b) for calculated, Fig. 4 g for measured results).

 

Fig. 4. Comparison of direct addition and phase-corrected synthesis for point source imaging. (a) Calculated complex-field distributions and (f) corresponding experimental results using direct addition and phase correction methods, respectively. (b) Calculated and (g) measured envelope patterns. (c, d) Calculated lateral and tilted line profiles with (h, i) their experimental counterparts. (e) Full Width at Half Maximum (FWHM) analysis of calculated results and (j) experimental measurements, quantifying spatial resolution improvements in both lateral and tilted directions. Phase-corrected synthesis demonstrates superior performance over direct addition in terms of both signal-to-noise ratio and spatial resolution. Scale bar: 100 μm. S1: Sensor 1, S2: Sensor 2, DA: Direct Addition, PC: Phase Correction.

Download Full Size | PDF

The effectiveness of phase-corrected synthesis is quantitatively analyzed through lateral and tilted line profiles. The calculated profiles (Fig. 4(c) for lateral, Fig. 4(d) for tilted) reveal that the phase-corrected PSF exhibits a sharper main lobe and reduced side lobes compared to direct addition. This improvement is consistently observed in the experimental measurements (Fig. 4(h) for lateral, Fig. 4(i) for tilted). The enhancement in spatial resolution is quantified using full-width at half-maximum (FWHM) analysis, as shown in the bar graphs (Fig. 4(e) for calculated, Fig. 4(j) for measured results). Theoretically, the two-dimensional resolutions are optimized from 90 µm to 56 µm in the lateral direction and from 104 µm to 62 µm in the tilted direction (Fig. 4(e)). Experimental validation using 10 µm microspheres as point sources demonstrates comparable improvements, with measured FWHMs optimized from 170 µm to 83 µm laterally and from 153 µm to 105 µm in the tilted direction (Fig. 4(j)). These results confirm that phase-corrected synthesis effectively preserves signal integrity while maximizing the usable bandwidth, leading to substantially enhanced imaging performance. Note that the resolution in the axial direction was not quantified due to the dual-lobe profile of the PSF, which complicates the measurement.

4. Enhanced photoacoustic imaging

4.1. Phantom imaging

To evaluate the dual-sensor synthesis performance, we conducted imaging experiments using an ink-stained, dried leaf phantom, which provides diverse vascular structures for resolution assessment. The phantom was fabricated by first attaching the flattened leaf to a pre-solidified agar substrate, followed by applying a second layer of liquid agar to fully encapsulate the structure. For photoacoustic imaging, excitation was achieved using a 532 nm pulsed laser, which was expanded through a beam expander to provide uniform illumination with an energy density of 3.4 mJ/cm². Two fiber-optic ultrasound sensors, arranged parallel with a 0.5 mm spacing, were mounted on a motorized stage to perform simultaneous scanning for parallel photoacoustic detection.

The imaging results demonstrate significant improvements through our phase-corrected synthesis approach. As shown in Fig. 5(a)–(d), while individual sensors (S1 and S2) could detect the leaf vein structures, their images exhibit limitations in either resolution or sensitivity. The direct addition synthesis shows moderate enhancement but still suffers from phase misalignment artifacts. In contrast, the phase-corrected synthesis achieves superior image quality with enhanced contrast and resolution. To quantitatively assess the improvement, we analyzed four representative regions containing vessels of different sizes and orientations (Fig. 5(e)–(h)). The normalized amplitude profiles (Fig. 5(i)–(l)) clearly demonstrate that phase-corrected synthesis achieves sharper vessel boundaries and higher contrast-to-noise ratio compared to both single-sensor imaging and direct addition. The suppression of sidelobe artifacts is also significant, as can be seen in the areas indicated by the red arrows in the Fig. 5(j) and (k) and detailed regions R2 and R3. The performance under low SNR condition (R4) also has been into consideration, as shown in Fig. 5(h) and Fig. 5 l. Specifically, the measured vein widths (Fig. 5 m) show consistent improvement of spatial resolution across all four areas with phase-corrected synthesis. The enhancement is particularly pronounced in region R1, where the vein width measurement improved from approximately 150 μm to 100 μm.

 

Fig. 5. Comparative analysis of leaf vasculature imaging using different sensor configurations and synthesis methods. (a-d) Photoacoustic images of the same leaf area acquired using: (a) S1, (b) S2, (c) DA, and (d) PC. (e-h) Detailed visualization of four selected regions (R1-R4) demonstrating vascular structures (red arrows) under different imaging conditions. (i-l) Corresponding normalized amplitude profiles across the vessels in R1-R4, showing enhanced contrast and resolution with phase-corrected synthesis. (m) Quantitative comparison of measured vein widths across the four regions, demonstrating improved spatial resolution with phase-corrected synthesis. (n) Signal-to-noise ratio (SNR) analysis showing consistent enhancement using phase-corrected synthesis compared to direct addition across all four areas. Scale bar: 1 mm for Fig. (a-d), 200 μm for Fig. (e-h). S1: Senor1, S2: Sensor 2, DA: Direct addition, PC: Phase Correction.

Download Full Size | PDF

For vein width measurements, we analyze the normalized envelope curves perpendicular to the target vessels. The full width at half maximum (FWHM) is defined as the horizontal distance from the left side to the right side of the envelope curve at half the peak height after Gaussian fitting. For SNR calculations, we define signal amplitude as the peak value of the normalized envelope curve, while noise amplitude is determined by the root mean square (RMS) value from background regions without photoacoustic absorber. The SNR is then calculated as 20log10(signal amplitude /noise amplitude).

Furthermore, the SNR analysis (Fig. 5(n)) reveals substantial improvements with phase-corrected synthesis across all regions. The most significant improvement was observed in region R1, with an SNR improvement of approximately 6 dB. Regions R2 and R3 exhibited consistent SNR gains of 4-6 dB compared to direct addition synthesis. Even in region R4, where the signal conditions were challenging, the phase-corrected method (Fig. 5(h)) still achieved a resolution enhancement from 125 μm to 99 μm while attaining a 3 dB SNR gain compared to direct addition. These results validate that our phase-corrected synthesis method effectively combines the advantages of both sensors while minimizing their individual limitations, resulting in enhanced imaging performance for complex biological structures.

4.2. Human subject imaging

By using the dual-sensor synthesis approach, we conducted in vivo imaging experiments on palm microvasculature from two volunteers (Fig. 6). The palm region was selected for its rich vascular network containing vessels of various diameters, which presents an ideal test case for evaluating the enhancement of imaging capabilities. Prior to imaging, standard preparation procedures were followed: the palmar surface was cleaned with alcohol swabs, and the hand was positioned firmly against the imaging window of a water tank containing the two fiber-optic sensors. The sensors were positioned 6 mm from the skin surface, and linear scanning was performed using a motorized stage. Photoacoustic excitation was achieved using a 1064 nm pulsed laser, expanded through a beam expander to form a uniform spot on the human skin with an illumination energy of 15 mJ/cm², well below the safety limit. The laser illumination used during the experiments complied with the safety standards for human use outlined by the American National Standards Institute (ANSI Z136.1-2014), ensuring participant safety throughout the process. The Ethics Committee of Jinan University granted ethical approval for these human imaging experiments (JNUKY-2023-0151). The imaging results from both volunteers (V1 and V2) revealed distinct characteristics across different sensor configurations. When using the S1 alone (Fig. 6(a), e), we observed superior contrast for larger vessels but limited resolution for fine vascular structures, particularly evident in regions R1 and R4 with the red arrows indicated. In comparison, S2 (Fig. 6(b), f) demonstrated enhanced capability in resolving finer vessels, though with reduced contrast for larger vessels, as clearly visible in the magnified views, showed by the red arrows in regions R2 and R5.

 

Fig. 6. In vivo photoacoustic imaging of human palm microvasculature demonstrating the enhanced imaging capability of phase-corrected synthesis. Results from two volunteers (V1 and V2) are presented. (a-d) V1 imaging results using: (a) S1, (b) S2, (c) DA, and (d) PC. Detailed views of three selected regions (R1-R3) show distinct vascular patterns. (e-h) V2 imaging results following the same imaging configurations, with detailed visualization of regions 4-6. In both groups, phase-corrected synthesis demonstrates superior vessel definition and contrast compared to single-sensor imaging or direct addition synthesis. The normalized grayscale images (-1 to 1) highlight the enhanced visibility of fine vascular structures. Scale bar: 1 mm for Fig. 6(a-h), 200 μm for detailed R1-R6. S1: Sensor1, S2: Sensor2, DA: Direct Addition, PC: Phase Correction.

Download Full Size | PDF

Direct addition synthesis (Fig. 6(c), g) showed moderate improvements in overall vessel visibility but introduced phase mismatch artifacts, particularly noticeable in regions R3 and R6. In contrast, phase-corrected synthesis (Fig. 6(d), h) achieved optimal performance by effectively combining the detection capabilities of both sensors while minimizing their individual limitations, indicated by the red arrows. This superiority is particularly evident in the detailed views, where regions R1-R3 in volunteer V1 showcase enhanced vessel definition compared to single-sensor imaging. Similarly, regions R4-R6 in volunteer V2 demonstrate improved contrast-to-noise ratio and clearer delineation of vessel boundaries.

Our phase-corrected synthesis method successfully addresses several critical imaging challenges. Fine vascular structures previously indistinguishable in single-sensor images become clearly visible, while the tailing effects and oscillatory artifacts common in single-sensor imaging are significantly suppressed. The method enables simultaneous visualization of vessels of varying sizes with high fidelity, achieving an optimal balance between resolution and imaging depth. These results demonstrate that our phase-corrected synthesis approach effectively combines the complementary information from both sensors, providing comprehensive visualization of the complex vascular network in human tissue. By maintaining high contrast for larger vessels while preserving the resolution necessary for imaging microvasculature, this method shows considerable potential for clinical applications requiring detailed vascular imaging.

5. Discussion and conclusion

In this work, we developed and implemented a multi-sensor synthesis strategy for enhanced photoacoustic imaging. Through calibration of their transfer functions combined with phase correction and spatial alignment techniques, we achieved precise phase synchronization between each sensor’s imaging results. The system employs an adaptive weighing algorithm to compensate for intensity variations between sensors, further enhancing image quality. Quantitative analysis demonstrates that our approach yields a 6 dB improvement in signal-to-noise ratio (SNR) and a 2-fold enhancement in spatial resolution. In human subject experiments by using a dual-optical-sensor system, we achieved an optimal balance between spatial resolution and imaging depth while capturing comprehensive vascular network information.

The importance of sensor phase information in multi-sensor synthesis is fundamental to achieving high-quality imaging. Without proper phase correction, imaging quality deteriorates due to the inherent characteristics of sensors, which typically exhibit almost opposite phase responses at high and low frequencies when modeled as resonators. In photoacoustic imaging, this challenge is further complicated by two-dimensional reconstruction, where phase responses vary with angular position. To address these challenges, we developed an integrated approach combining physical modeling with empirical measurements for accurate point spread function (PSF) determination. Our reconstruction algorithm implements phase-aware image fusion, specifically designed to handle sensors with distinct spatial-frequency responses while maintaining signal coherence.

Our approach demonstrates benefits over traditional deconvolution methods for bandwidth or angular expansion [17,19,25,26]. The key innovation lies in the physical synthesis of complementary transfer functions, and our approach focuses specifically on phase correction while maintaining the original amplitude characteristics. Precise PSF estimation process only needs one-time to be characterized for a specific system configuration. Once the PSF is accurately characterized completely, it will also remain valid for all subsequent imaging scenarios under the same setup. Then the phase-aware deconvolution algorithm, implemented through linear filtering, achieves millisecond-level (0.12 s) computational speeds for processing images at the 10⁶ pixels level on a personal computer, while avoiding the computational complexity and potential instabilities associated with iterative deconvolution methods. We developed a comprehensive workflow incorporating system phase calibration, data acquisition, and phase compensation that effectively preserves signal fidelity. However, several aspects warrant further investigation. When SNR conditions are sufficiently high, amplitude correction could be implemented using methods such as Wiener filtering to potentially enhance performance further [25,27]. Additionally, machine learning techniques could be explored for optimal sensor information integration, particularly in handling complex spatial-frequency relationships [28,29]. Furthermore, future research could address the spatially variant nature of transfer functions to enhance imaging performance while maintaining computational efficiency [30,31].

The methodology developed here extends beyond fiber optic sensors to a broader range of sensing technologies. It shows particular promise for microscale and nanoscale silicon-based devices and Fabry-Pérot cavity sensors [32–34], where diverse angular and frequency responses can be effectively synthesized. This approach significantly reduces fabrication precision requirements while maintaining high imaging quality. Furthermore, the technique is readily adaptable to electrically focused transducers and dual-probe ultrasound systems with different frequency characteristics. By enabling the integration of sensors with complementary frequency responses, our method addresses fundamental limitations in angular coverage and bandwidth in photoacoustic imaging, potentially accelerating its clinical adoption across various medical applications.

While this work demonstrates the effectiveness of dual-sensor synthesis, our framework inherently supports extension to multiple sensors for further performance enhancement. The selection of current sensor parameters (125 μm and 90 μm diameters, corresponding to 22 MHz and 31 MHz resonant frequencies respectively) was optimized for bandwidth complementarity while maintaining practical robustness. Through controlled chemical etching, fiber diameter can be reduced to tune the resonant frequency, theoretically allowing coverage up to ∼90 MHz (with 30 μm diameter fiber). However, this upper limit is constrained by both waveguiding requirements and mechanical stability considerations.

The extension to multiple sensors presents both opportunities and challenges. On the technical side, parallel detection of multiple sensor signals could be achieved through time-delay multiplexing schemes, where optical delay lines enable sequential signal acquisition without information loss. More importantly, expanding the sensor array offers two significant advantages: First, strategic distribution of resonant frequencies across a broader bandwidth could further enhance spatial resolution through more complete coverage of the system's frequency response. Second, multi-angle sensor arrangements could improve the angular coverage of the 2D PSF spectrum, potentially enhancing both resolution and imaging isotropy. These improvements align with our core strategy of optimizing the coverage of the system’s spatial-frequency response through phase-coherent synthesis.

Such extensibility does introduce additional complexity in system implementation, particularly in terms of sensor multiplexing and signal processing overhead. Nevertheless, the demonstrated success of phase-aware synthesis with dual sensors provides a solid foundation for these future developments, suggesting that the benefits of enhanced bandwidth and angular coverage could outweigh the increased system complexity.