Dual Illumination and Detection Photoacoustic Tomography of Hollow Metal Cylinders

Abstract

Photoacoustic tomography is an innovative non-ionizing imaging technique that combines optical contrast with ultrasound resolution for 3D object characterization. While promising, its broader adoption is limited by challenges such as shallow penetration depth and strong optical scattering. To address these issues, this study introduces a dual illumination and detection photoacoustic tomography method, specifically designed for symmetrical objects like hollow metallic cylinders. The illumination system plays a critical role in determining the quality of photoacoustic signals and, thus, the final image. This approach enhances spatial resolution and contrast by using complementary light delivery and signal detection. In industrial settings, where accurate and efficient non-destructive testing is essential, traditional techniques often lack the precision required. The dual illumination and detection strategy offers significant improvements in effective resolution, contrast, defect detection, and artifact reduction, surpassing the limitations of unidirectional approaches. This technique not only strengthens the characterization of metal structures but also contributes to a deeper understanding of their physical behavior. Applications extend across various fields, including aerospace and biomedical engineering. This paper explores the underlying principles and potential of this advanced imaging modality, highlighting its value in modern diagnostic and inspection technologies.

1. Introduction

Photoacoustic (PA) tomography is an imaging technique that combines optical and ultrasound information, a hybrid imaging modality that continues to evolve, especially for applications of medicine and biology [1]. The integration of high-resolution optical imaging with the depth penetration of ultrasound represents a major advancement in biomedical imaging. Although Rosencwaig reported the first application of PA imaging in solids in 1973 [2,3], subsequent advances in laser technology and instrumentation have established PA imaging as a powerful tool for diagnosis, monitoring, and therapeutic guidance in medicine [4,5], as well as for industrial non-destructive testing (NDT) [6,7,8].

The technique relies on the PA effect, wherein material absorbs pulsed or modulated light and subsequently emits ultrasound waves, thereby enabling the visualization of its structural and functional characteristics. Efficient PA absorbers convert absorbed light into acoustic waves, and wavelength-dependent absorption properties and the efficiency of light energy deposition determine their performance. The nonradiative decay processes and the mechanism of nonradiative energy transfer that plays an important role in the generation of PA signals from solids are discussed in [9]. Quantitative PA imaging techniques aim to extract quantitative information from PA signals to provide precise measurements of various tissue properties. This approach enhances the diagnostic capabilities of PA imaging beyond mere qualitative assessments. A critical component is the illumination of the experimental PA system, as it directly determines the generation of PA signals and influences image quality. Common techniques employ multispectral imaging and structured illumination strategies [10,11]. Those approaches offer microscale resolution and a wide range of contributions but are still limited in the penetration depth [1]. However, challenges such as object geometry, light fluence attenuation, acoustic heterogeneity, and ill-posed inverse problems on image reconstruction necessitate advanced techniques and regularization strategies to improve the image quality, i.e., accuracy and stability. To address this problem, many regularization techniques have been developed [12]. Other studies [13] use contrast agents to improve the image quality.

Despite significant progress in PA tomography for biomedical and industrial applications, substantial challenges persist, particularly in achieving high-resolution imaging of deep internal structures. These limitations are primarily due to the shallow light penetration, optical scattering, and restricted angular coverage inherent in systems that employ unidirectional illumination and detection, like linear sensors arrays in a fixed line, useful for obtaining two-dimensional images, or circular arrays that partially surround the study object and improve angular coverage. In industrial manufacturing, where ensuring product integrity is critical, NDT is essential for identifying defects, discontinuities, or material degradation without compromising the component's usability or structure [4,14,15]. However, commonly used unidirectional NDT techniques—such as contact ultrasound (pulse-echo), direct transmission ultrasound, and laser-induced ultrasound—often suffer from limited contrast, structural artifacts, and incomplete internal visualization [16,17,18]. These shortcomings hinder the accurate detection of subsurface flaws, internal cavities, and weak joints.

The acoustic coupling medium around the sample is crucial for signal fidelity; common detection mechanisms require water, oil, or gel [19]. Cutting-edge research has developed sophisticated methods to circumvent the acoustic impedance mismatch problem and perform PA imaging in air, broadly categorized by laser-induced ultrasound imaging [17], which may also involve optical detection (e.g., optoacoustic interferometry) [20] or electromagnetic induction [21]. Unfortunately, this imaging flexibility can lead to high energies, reaching an ablation regime that may cause damage to the object of interest; hence, it is not convenient for NDT. Furthermore, many current experimental setups rely on contact-based measurements, which can be inadequate in scenarios where preserving structural integrity or avoiding environmental contamination is crucial. These constraints highlight the need for advanced imaging strategies that can deliver high-quality results while minimizing physical interaction.

To overcome these limitations, dual-illumination and dual-detection PA tomography represent a promising alternative [22,23]. By exploiting the axial symmetry of immersed objects and acquiring signals from opposing directions, dual-illumination and detection enhance angular coverage, improve the signal-to-noise ratio, and reduce spatial ambiguities. This approach enables more accurate and robust reconstruction of internal features, effectively addressing many of the deficiencies associated with traditional unidirectional methods.

In PA tomography, image reconstruction plays a crucial role in transforming time-resolved pressure signals into spatially resolved images. Reconstruction algorithms can be broadly categorized into analytical, geometric, and model-based approaches. Among them, geometric algorithms stand out for their simplicity, computational efficiency, and ease of implementation, especially when the speed of sound is assumed to be homogeneous. Commonly used geometric methods include back projection (BP), filtered back projection (FBP), time reversal (TR), and Delay-And-Sum (DAS). These algorithms estimate the location of the initial pressure sources by summing time-shifted signals based on the calculated time-of-flight between each detector and image pixel. To overcome resolution and spatial limitations, the evolution of geometric algorithms follows the trend in the development of adaptive beamforming that dynamically weights signals based on their coherence [24,25] or adopts the superior sidelobe suppression to further enforce the signal-to-noise ratio [26,27,28]. Recent research has also focused on deep learning approaches to emulate or enhance these geometric principles, where convolutional neural networks are trained to learn optimal weighting functions from simulated or experimental data, achieving state-of-the-art results in speed and quality for real-time applications [29,30].

The present work explores how dual illumination and detection of the object of interest can overcome some depth limitations and scattering of PA tomography and offers a special emphasis on industrial applications. In the realm of dual illumination PA tomography, inspired by the progress of Fukutani et al. [11], the mechanisms underpinning signal enhancement are integral to optimizing imaging performance, particularly when applied to metal cylinders. The regularization problem is attained by improving the illumination and extending the amount of data with respect to noise. By exploiting the PA effect, which generates ultrasonic and thermal waves after energy absorption, research can significantly improve an image's spatial resolution and contrast in general. This research is motivated by the need to enhance spatial resolution, improve contrast, and reduce artifacts, thereby enabling more accurate and reliable non-destructive evaluation in 2D photoacoustic tomography of hollow metallic cylinders through a dual illumination and detection approach. In Section 2, we address the relationship between the optical and thermoelastic properties of materials and the generation of the PA signal. In Section 2.1, we resume the theoretical impact of the PA effect on metals. On this background, the studied materials are characterized in Section 2.2. Then, Section 2.3 offers an overview of the experimental setup. The essential reference for validation represents the PATLAB simulation in Section 2.4. Finally, Section 2.5 compares the classic primal approach with the proposed dual PA signal processing on a time sequence detector level. The 2D tomographic reconstruction results are presented and analyzed in Section 3. Here, we employed the basic DAS algorithm due to its widespread use in circular acquisition geometries and its proven ability to reconstruct high-contrast features with relatively low computational cost [21]. We discuss our findings in Section 4 and conclude our work and open problems in Section 5.

2. Materials and Methods

This study employs an integrated experimental and computational approach to develop and validate a dual illumination and detection strategy for PA tomography of hollow metallic cylinders. The methodology encompasses the characterization of material properties, a custom experimental setup for sequential laser illumination and acoustic detection, and a comprehensive simulation framework using the PATLAB toolbox version 1.0. Signal processing techniques were developed to align primal signals and synthesize dual signals, which were subsequently reconstructed into 2D tomographic images using the Delay-and-Sum (DAS) algorithm. The following sections detail the physical principles, the materials under evaluation, the experimental setup, simulation parameters, and the computational processing workflows that form the basis of this investigation.

2.1. Physical Transport Considerations

We describe PA signal formation in three steps: (i) optical energy deposition and thermoelastic pressure build-up, (ii) heat diffusion and confinement criteria, and (iii) acoustic propagation and linear detection by the sensor.

2.1.1. Optical Deposition and Initial Pressure

For a short pulse, the absorbed power density $H$ decays exponentially with depth $x$,

$$H(x,t)=H_0{e}^{-{\alpha }_{o}x}f\left(t\right),$$

(1)

with ${\alpha }_o$ [1/cm] as the optical absorption coefficient, H₀ as the power density of the pulse and $f\left(t\right)$ as the pulse profile. Under stress and thermal confinement, the initial pressure $p$ measured in Pascals (1 Pa = 1 N/m²) generated by a PA wave is expressed as

$$p\propto \Gamma {\alpha }_{o}F,$$

(2)

where $\Gamma$ is the temperature-dependent Grüneisen parameter, $\epsilon (1/\mathrm{c}\mathrm{m})$ the absorption coefficient, and F(J/cm²) the optical fluence [31,32]. The Grüneisen parameter contains, in turn, the thermoelastic parameters, as Γ = βK_TV/C_V; with $\beta$ as the thermal expansivity, K_T as the bulk modulus, and C_V as the specific heat, with respect to constant temperature $T$ and volume $V$ [33]. All of these parameters are directly proportional to PA amplitude. The PA effect relies on the photothermal effect to produce sound, although not all photothermal processes necessarily lead to PA signals.

2.1.2. Heat Diffusion and Confinement

The theory of Rosencwaig and Gersho in 1975 predicts the dependence of the PA signal of a solid on the thermal absorption coefficient $\alpha$_T of the solid for a specific wavelength [2]. The main source of the acoustic signal of a solid arises from the heat flow. The thermal diffusion equation in the solid can be written in terms of the temperature

$${\displaystyle \frac{d^{2}T}{d{x}^2}}={\displaystyle \frac{1}{k}}{\displaystyle \frac{dT}{dt}}-A{e}^{{\alpha }_{T}x}{[1+e}^{i\omega t}],$$

(3)

where κ = k/ρC_V is the thermal diffusivity of the material with thermal conductivity $k$ and density $\rho$; A = $\alpha$_TI₀/2k with the incident monochromatic light flux I₀, assuming full efficiency of the light to heat conversion.

The incremental pressure of a metal piece under chopped light is

$$dp=\gamma {\displaystyle \frac{p_0}{V_0}}dV,$$

(4)

where p₀, V₀ are the pressure and the volume of the metal piece at ambient temperature, and $\gamma$ is the ratio of specific heats; $dp$ is proportional to the envelope of the sinusoidal pressure variation $Q\propto \gamma$. For optically opaque solids, as is the case for metals of thickness $l$ with optical absorption length $1<{\alpha }_T\mu$, that are thermally thick, i.e., with a thermal diffusion length $\mu <l$,

$$dp\propto {\alpha }_T\mu .$$

(5)

2.1.3. Acoustic Propagation and Detection

In the thermoelastic regime and under thermal confinement, the time derivative of the temperature field acts as the driving source term of the acoustic field inside solids; this is explicitly illustrated for an aluminum slab (l3 mm thick) [34] and extended to layered media in [35]. Those works also detail how thermal diffusivity couples to the viscous and elastic properties of the medium; the full derivations lie beyond our present scope. Consistent with this framework, under the confinement assumptions the PA field satisfies the driven wave equation

$${\displaystyle \frac{{\partial }^{2}p}{{\partial t}^2}}-c^2{\displaystyle \frac{{\partial }^{2}p}{{\partial x}^2}}=\Gamma {\displaystyle \frac{{\partial }^{2}H}{{\partial t}^2}},$$

(6)

with c as the effective sound speed. Here we adopt a 1-D, normal-incidence description consistent with our geometry, avoiding shear modes and simplifying time-of-flight interpretation. The measured signal S $\propto$ $dp$ at the sensor face with a pressure spectrum P satisfies

$$S\left(\omega \right)=H\left(\omega \right)P\left(\omega \right),$$

(7)

where H($\omega$) is the pressure-to-output transfer function of the sensor-plus-electronics, which can be obtained by calibration or via a layered transfer-matrix model of the sensor stack and couplant [35].

2.2. Material Characterization

The object of interest is a series of five metallic cylinders (aluminum, brass, bronze, copper, and stainless steel), all with an inner diameter, d_in $=4\pm 0.01$ mm, and an outer diameter, d_out $=24.91\pm 0.12$ mm, as shown in Figure 1. The density, sound velocity, and acoustic impedance $Z$ are shown in

Table 1. Density, optical absorption coefficient [36] and sound velocity of the five metal cylinders, ordered by acoustic impedance [37]; metal alloys (*) are restricted to higher numerical uncertainty.

Material	Density $\mathit{\rho }\left[\mathbf{g}/\mathbf{c}{\mathbf{m}}^3\right]$	Optical Absorption Coefficient (532 nm) ${\mathit{\alpha }}_{\mathit{o}}\left[10^6/\mathbf{c}\mathbf{m}\right]$	Sound Velocity (Longitudinal) ${\mathit{v}}_{\mathit{s}}\left[\mathbf{m}\mathbf{m}/\mathsf{\mu }\mathbf{s}\right]$	Acoustic Impedance $\mathit{Z}=\mathit{\rho }{\mathit{v}}_{\mathit{s}}\left[10^6\mathbf{k}\mathbf{g}/{(\mathbf{m}}^2\mathbf{s})\right]$
Water	1.0	$6.27\times {10}^{-10}$	1.48	1.48
Aluminum	2.7	1.205	6.119	16.52
Brass	8.0	0.554 *	4.358	34.86
Bronze	8.3	0.665 *	4.369	36.26
Copper	8.6	0.614	4.662	40.09
Stainless steel	7.6	0.789 *	5.650	42.94

. In PA as well as ultrasound imaging, we are concerned about the difference in $Z$ between two adjacent materials: a small difference implies greater energy transmission, whereas a mismatch induces energy reflection, which typically results in more image artifacts and noise.

The metal sound velocity was obtained experimentally from the arrival time of the PA signal from each of the cylinders, placed in direct contact on the cylinder’s flat, round face with the sensor, and without the beam path passing through the cylinder gap. The arrival time is obtained directly from the signal recorded by the oscilloscope, using the expression of the sound velocity v_s = h/t_a, with respect to the cylinder's height $h$.

2.3. Experimental Setup

A custom PA tomography setup was designed to implement a dual illumination and detection strategy for the non-destructive evaluation of hollow metallic cylinders. The core configuration, illustrated in Figure 2, essentially utilized two pulsed Nd:YAG lasers for the core challenge to provide sufficient laser fluence F (energy per area). Laser splitters and mirrors could be a viable alternative, but could reduce the pressure spectrum, according to Equation (2). Two acoustic detectors performed in a forward configuration due to optimal signal strength and sensitivity. Also, this method seeks to reach a compromise between linear and circular sensor arrays, placing two sensors in the same plane to obtain simultaneous PA signals in search of symmetry discrepancies in our samples [38,39]. The sequential, multi-angle acquisition was fundamental to synthesizing the enhanced PA tomographic reconstruction. Furthermore, immersing the sensors and samples in water ensures optical coupling for optimal propagation of acoustic waves.

The PA experimental setup consisted of: (1) two Quantel Brilliant b pulsed Nd:YAG lasers operating at the second harmonic (532 nm), with a pulse width of 5 ns and a repetition rate of 10 Hz; (2) a Tektronix DPO5204B digital oscilloscope with 2 GHz bandwidth and a 10 GS/s sampling rate; (3) two Olympus A326S-SU of lead zirconate titanate (PZT) immersion transducers with a central frequency of 5 MHz, a bandwidth of 2.57 MHz, and an element diameter of 9.52 mm; (4) a laptop for data acquisition and processing; (5) a set of metallic cylinders with a central hole, used in computed tomography; and (6) a Thorlabs PDA10A amplified silicon detector.

The sample was mounted on a rotating stage, and both were submerged in water inside an acrylic tank. Sequential illumination on a fixed sample position was performed on two diametrically opposite sides of the cylinder, while acoustic detection was carried out in a forward configuration on the same plane, as illustrated in Figure 2. Sequential measurements with an approximate 10 s acquisition time were obtained for each sample, corresponding to the cardinal positions where the laser beam impinged. In order to determine a recommended number of measurements, we consulted the PATLAB simulation of this case in the following subsection.

2.4. PATLAB Simulation

The PA simulation setup offers the important benefit of validating adequate signal processing and noise reduction with respect to the forward problem, as well as the choice of the reconstruction algorithm that solves the inverse problem of tomography.

PATLAB [40] is a specialized software toolbox in MATLAB R2025a for PA tomography simulation and reconstruction, offering a comprehensive interface for 2D and 3D reconstruction, including the k-Wave toolbox for the acoustic wave transport model. It allows the user to evaluate the effectiveness of the proposed acquisition techniques in this study. PATLAB consists of four modules: (1) loading/simulating inputs, (2) pre-processing, (3) image reconstruction, and (4) display and save.

The PA simulation images were reconstructed using the Delay-and-Sum (DAS) method [27], one of the most widely adopted beamforming algorithms in ultrasound imaging. Due to its simplicity and ease of implementation, DAS has also been commonly applied in PA tomography [24]. The algorithm calculates the sum of the time points associated with each grid point, assuming that the detectors have omnidirectional sensitivity and that signal acquisition is performed over circular geometry for 2D images [40]. Although the method is fast and straightforward, it provides only an approximate reconstruction of the underlying structures [41]. Consequently, its performance is often limited in terms of resolution and artifact suppression when compared to more advanced model-based or iterative reconstruction techniques [42].

To simulate PA signals and reconstruct 2D images of a metal cylinder with a central cavity, PATLAB was used with the integration of k-Wave to model acoustic wave propagation, supporting both signal simulation (forward problem) and image reconstruction (inverse problem). As a potential drawback of the PATLAB simulation, we identify the exclusive simultaneous illumination possibilities, although wave interferences are likely different, when sequential illumination is implemented. Since the object cannot rotate in the PATLAB framework, the dual detector pair will turn around the metal cylinder, as presented by blue dots in Figure 3 (left).

2.4.1. Dense Sampling

The simulation of acoustic propagation involved defining the four essential components of k-Wave: the computational grid, the acoustic properties of the medium, the sensor configuration, and the acoustic source. A 2D computational domain of 35 × 35 mm² was used, with a grid spacing of 0.1 mm and centered at (0, 0) mm. The sensor array consisted of 180 equally spaced detectors arranged in a circle of 15.8 mm radius, as dense PA sensing is suggested by the authors of PATLAB [40] for accurate 2D image reconstruction of the internal structure of the object. Two opposite sensor positions are operated 90 times, rotating the cylinder every 2 degrees, and simulated by a 2 × 90 equidistantly distributed circular detector array, respectively. The detector response was modeled with a center frequency of 5 MHz and a 52% bandwidth. The medium was assigned an effective speed of sound of water, without additional attenuation. The acoustic source was defined as a binary image of the object under study, a hollow metal cylinder as described in Section 2.2, assuming omnidirectional illumination and perfect thermoelastic conversion. This concept maximizes the dual illumination strategy. In PATLAB we only locate the light absorber, but not the light sources. A sampling frequency of 50 MHz and a time window of 30 µs were used, consistent with experimental parameters. The simulation generated 2 × 90 almost equal time-series pressure signals, which were arranged into a sinogram of size 180 × $N$, where $N=1000$ is the number of time samples, presented as time series and sinogram in Figure 3. The implemented strategy to PA dense sensing provides a robust raw data set to handle the inherent challenges of the imaging system; no additional noise level is implemented. Nonetheless, this concept oversamples the physical space, as geometrical symmetries may be incorporated to optimize the experimental methodology.

2.4.2. Image Reconstruction

The PA signals generated in the simulation were used to reconstruct the 2D cross-sectional image of the metal cylinder. The Delay-And-Sum (DAS) algorithm was applied using the same computational grid and sampling parameters defined during the simulation Section 2.4.1. We assumed a sensor directivity of 30 degrees, along with omnidirectional sensitivity. The resulting image in Figure 4 clearly delineates the inner and outer edges of the cavity as regions of maximum intensity.

The simulation considered ideal conditions, including uniform acoustic propagation in a non-dispersive, non-attenuating medium and full-field omnidirectional illumination. Although these assumptions do not fully represent real experimental data, appropriate signal processing can help mitigate such limitations. The reconstructed images were normalized and contrast-enhanced to facilitate qualitative and quantitative analysis. Both the preprocessed sinograms and final images were exported for further evaluation using image quality metrics to optimize the reconstruction parameters in future iterations.

2.5. Primal and Dual Experimental PA Signal Processing

Since the object of interest is axisymmetric concerning the centerline of rotation, the experimental setup of Section 2.3 was realized by only four distinct detector positions labeled as “north” (N), “east” (E), “south” (S), and “west” (W) and further implement a reproduction and distribution strategy to fill the physical space densely, see Section 3. Their measurement should give an equivalent amount of information as attained by the simulation 2.4.1 by 180 detectors. By the interpretation that the time sequence reflects the projection of the geometric object of interest, we identify the need to align the time-amplitude signal with the dimensional center of the metal cylinder. Since the time to space projection depends on the acoustic transport velocity, a balance between the sound velocity in water and the corresponding metal is demanded. To attain this balance with an average propagation velocity $v$, the intensity reflection coefficient R², the squared pressure reflection coefficient R, as contemplated in [32], is taken into account. The intensity reflection coefficient from metal to water equals the intensity from water to metal. The pressure reflection coefficient from the solid metal, where the PA effect initiates, to water, the coupling medium, is calculated by

$$R={\displaystyle \frac{Z_{water}-Z_{solid}}{Z_{water}+Z_{solid}},}$$

(8)

where Z = ρv describes the characteristic impedance of the penetrating sound wave (see Table 1); hence, for the solid, one calculates Z_solid = ρ_solidv_solid, while Z_water = ρ_waterv_water ≈ 1.481 × 10⁶ (kg/m²s) = 1.481 MRayl.

Table 2. Acoustic intensity reflection coefficient and thermal diffusion length.

Material	Acoustic intensity Reflection Coefficient ${\mathit{R}}^2\left[\mathit{\%}\right]$	Thermal Diffusion Length $\mathit{\mu }$$\mathbf{for}\mathit{\omega }=2\mathit{\pi }\left[\mathbf{m}\mathbf{m}\right]$
Aluminum	69.8	5.2
Brass	84.4	3.3
Bronze	84.9	2.6
Copper	86.3	5.9
Stainless steel	87.1	1.1

contains the evaluation results of the pressure reflection coefficients $R$ of the present materials in this study.

The effective propagation velocity $c$ represents the average speed at which the PA wave travels from the illuminated region of the metal cylinder toward the detector, in forward mode, through alternating layers: metal, water, metal, and water. Since part of the wave is transmitted and part is reflected at each interface, the propagation speed must account for both effects. Inspired by the approach used in layered acoustic media [43,44,45], the effective velocity can be estimated by weighting the sound speeds in the metal $v_{solid}$ and in water $v_{water}$ according to the acoustic reflection coefficient $R$:

$$\begin{gathered} c=R^2{v}_{solid}+\left(1-R^2\right)\left\{R^2{v}_{water}+\left(1-R^2\right)\left[R^2{v}_{solid}+\left(1-R^2\right)v_{water}\right]\right\} \\ =\left\{R^2\left[{1+\left(1-R^2\right)}^2\right]\right\}{v}_{solid}+\left[R^2+{\left(1-R^2\right)}^2\right]v_{water} \end{gathered}$$

(9)

Physically, $c$ describes how fast the acoustic energy effectively propagates toward the detector after interacting with several metal–water interfaces. A higher reflection coefficient $R$ indicates that most of the wave energy remains in the solid, increasing $c$, while a lower $R$ means stronger transmission into water and a reduced effective speed. Incorporating this effective value into the alignment of PA signals allows a more accurate temporal calibration and enhances the fidelity of image reconstruction in heterogeneous or multilayer media. According to this average propagation of the acoustic PA wave in Figure 5, we center the PA time sequence over the metal cylinder.

The effective propagation velocity is not merely a physical parameter in PA; it is a critical determinant of image fidelity and quantitative accuracy. Its scientific importance stems from the fact that PA image reconstruction is an inverse problem that relies on knowing the speed of sound to map received signals back to their origin. An incorrect velocity model introduces artifacts, mislocations, and blurring, directly limiting the technology's resolution and functional imaging capabilities.

The experimental setup with two opposing forward PA detection systems will offer temporal sequences each, but the direction of the underlying PA transport is not linked to the spatial coordinates. We propose to interpret one forward PA signal g in the backward direction and register its mirrored time sequence g′ in the temporal system of the other PA signal. Both signals are represented in vectors of the same length, and we look for their element-wise Hadamard product $g\odot g\text{'}$. This way, we realize all possible combinations of detector positions on the circular detector array, evaluated in the experimental setup (labeled by N, E, S, W): (N, E), (N, S), (N, W), (E, S), (E, W), (S, W). Figure 6 shows all dual PA signals.

The derived six dual time sequences of every metal define dual sinogram information that offers 2D tomographic reconstructions. In this regard, we proceed as in the PATLAB simulation of Section 3.3 and obtain dual DAS reconstruction in Figure 7 for the five cylinder sections. Once the 1D PA signals are processed according to the dual illumination methodology, the tomographic section image of the cylinder can be reconstructed according to filtered back projection methods.

3. Results

According to the image reconstruction strategy in Section 2.4.2, we develop 2D PA tomography with the experimental primal and dual signals (Section 2.5) for a total of 180 detectors, equally distributed around a circular array of radius 15.8 mm. We reproduce the four primal signals measured at positions N, E, S, W, 45 times and distribute them equally around the detector array. Equivalently, we replicate the six dual signals (N, E), (N, S), (N, W), (E, S), (E, W), (S, W), 30 times, and again assign them evenly to the 180 detectors in the circle. We compare the results as illustrated in Figure 7, presenting the DAS PA tomographic section image of the bronze cylinder. The primal image contains many artifacts that are likely to result from internal acoustic reflections. The dual image represents a much smoother domain over the metal area but requires further signal enhancement to visualize the internal structure (hollow cylinder).

To prevent loss of information, no filters or pre-processing strategies are implemented in PATLAB or externally. At first sight, the dual reconstruction in Figure 7 resembles more the simulation section image in Figure 4 (right). In order to evaluate the results more objectively with respect to the image reconstruction resolution of the PATLAB simulation, we implement the following to quantify the error between the experimental approach and the simulated study.

3.1. Dissimilarity

Three distance measures are used to evaluate the signal processing approach for PA image reconstruction. The less the difference, the better the match between the experimental performance and the computational simulation. The dissimilarity quantification of the PA results is listed in Figure 8. Excluding the material with the highest acoustic impedance, stainless steel, the dual processing results in a profitable outcome for PA tomographic image reconstruction.

The $L1$-distance between the PATLAB simulation $f$ and an experimental measurement $g$ (primal or dual), also known as the Manhattan distance or the mean error performance, is evaluated according to

$$L1(f,g)={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N\left|f\left(i\right)-g\left(i\right)\right|.$$

(10)

The $L2$-distance between $f$ and $g$, or the Euclidean distance or the root mean squared error, is defined by

$$L2(f,g)={\displaystyle \frac{1}{N}}\sqrt{{\sum }_{i=1}^N{\left(f(i\right)-g\left(i\right))}^2.}$$

(11)

The entropy of an image is a quantitative measure of its information content [46]. Based on this information, the entropy distance $Ed$ (also known as joint entropy by Shannon [47]) between the simulation image $F(j,:)=f$ of all PA time sequences and the experimental image $G(j,:)=g$ for the j-th measurement is calculated following

$$Ed(F,G)=entropy\left(G\right)-entropy\left(F\right).$$

(12)

The MATLAB function entropy is a measure that quantifies the information about the image content, taking into account the histogram information. Its output is a single scalar value that gives a clue about the uncertainty or randomness in the PA data. Higher entropy indicates a richer distribution of pixel intensities, meaning more detail and texture, whereas lower entropy suggests redundancy or loss of information. A high entropy distance means the PA measurements and its simulation are very different and complex when considered together.

3.2. Similarity

In order to quantify how similar the experimental PA information with respect to the PATLAB simulation is, we implement three structural measures. Two of them refer to the space or time domain and offer a direct overall comparison between two images. Images that reveal patterns, textures, and orientations are typically evaluated in the Fourier or frequency domain. By looking at the structure globally, we evaluate a third image measure by incorporating the Fourier transform of the PA information. The similarity quantification of the PA results is listed in Figure 9.

The CCF evaluation gives a measure of the cross-correlation of two discrete time sequences, as implemented in MATLAB in terms of the function XCORR. The higher the results, the more similar the experimental and simulation time sequences [48,49]. We focus on its maximal element by

$$CCF(f,g)=max\left(XCORR\right(f,g\left)\right)$$

(13)

Further, the structural similarity is evaluated by MATLAB’s SSIM function, as seen in [50,51]. The same SSIM measure applied to the absolute value of the PA signals in the Fourier domain, |FFT(f)| and |FFT(g)| is also listed in Figure 9 as F-SSIM [52].

3.3. Signal-to-Noise Ratio

The signal-to-noise ratio (SNR) is a measure that compares the level of a desired signal, in this case the simulation data, to the level of background noise, here experimental data, either the primal or the dual case. While the fractional evaluation in Section 3.1 and Section 3.2 measures the power of the noise of the experiment, SNR informs about its variance. Figure 10 displays the quantitative evaluation of the results obtained.

Based on the quantitative analysis in Section 3.1, Section 3.2, and Section 3.3, the results show that dual illumination significantly improves image fidelity, contrast, and noise reduction. The quantitative metrics presented in Figure 8, Figure 9 and Figure 10 provide objective evidence of the dual method's superiority. For all metals except stainless steel, the dual processing yielded lower distances to the simulated ideal signal, indicating a closer match to the expected outcome. The increase in cross-correlation and structural similarity values for the dual images further confirms their enhanced fidelity and closer resemblance to the simulated benchmark. Dual signal processing offers a closer approach to SNR = 1, which confirms less variance in noise in experimentally processed data. In summary, the presented results suggest that the dual processing successfully reduced the randomness and uncertainty in the data, resulting in a cleaner, less noisy image that contains more structured information.

4. Discussion

The implementation of a dual illumination and detection strategy in PA tomography for hollow metallic cylinders has demonstrated significant advantages over traditional unidirectional (primal) approaches. The results confirm that this method effectively mitigates several key limitations inherent in conventional PAT systems, particularly those related to artifacts, resolution, and contrast in industrial NDT applications.

The acoustic impedance of the materials plays a critical role in both signal processing and image quality. The high impedance mismatch between the metals and water results in a high pressure reflection coefficient (R > 69.8% for all materials), meaning a large portion of the generated acoustic energy is reflected at the interface. While this strong reflection is needed for the detection principle, it also leads to complex internal reverberations that manifest as artifacts in the primal reconstructions. The dual processing approach appears to compensate for these effects, unless the artifacts dominate the space; stainless steel apparently passes this limit and fails the distance measure under the implemented experimental parameters.

The sound velocity within each metal, which we measured experimentally, is another crucial parameter. The sequence of sound velocities (Aluminum > Stainless steel > Copper > Bronze ≈ Brass) directly influences the time-of-flight of acoustic waves and thus the accuracy of the reconstruction algorithm in the primal mode. The proposed average propagation velocity model for the dual processing, which weights the sound velocity in metal and water by the reflection coefficient, apparently balances this influence.

The thermal properties, specifically the thermal diffusion length, also influence the PA signal generation. Materials with a shorter thermal diffusion length (like bronze) confine heat more effectively (see Section 2.1), leading to a more efficient thermoelastic expansion and a stronger initial PA signal. This may explain why the numerical evaluation of bronze is quantitatively much better than that of brass, although both materials have similar acoustic impedance and sound velocity.

By using a single, simple geometry across five different metals, we intentionally isolated the variables of acoustic impedance, thermal diffusivity, and sound velocity. This controlled approach allowed us to demonstrate that the material properties are a primary source of artifact. Likewise, the reconstructed PA images reflect the combined influence of optical (absorption and scattering) and acoustic (sound propagation) properties, where materials with higher absorption coefficients yield images of greater contrast and edge definition, while those with lower absorption appear less intense and less defined—illustrating the intricate interplay between optical and acoustic behaviors that ultimately determines image quality. Experimentally, this relationship is illustrated in Figure 5 for the primary configuration and in Figure 6 for the dual configuration. In the dual case, where the signals appear cleaner, it can be seen that stainless steel produces the noisiest signals, whereas bronze yields the cleanest ones. Although stainless steel exhibits a high optical absorption coefficient—typically leading to high-intensity signal generation—it also has a very high acoustic reflection coefficient, which can introduce noise due to multiple internal reflections. In contrast, bronze possesses an intermediate acoustic reflection coefficient and a relatively high absorption coefficient, resulting in a better signal-to-noise ratio. Ultimately, the image quality depends on the complex interplay between the optical and acoustic properties of the materials, and determining which effect predominates is not straightforward.

A limitation of this study is the assumption of ideal conditions in the simulation (e.g., uniform illumination, no acoustic attenuation). In practice, dual PA illumination and detection are limited in space and by the sensitivity of the detectors. Future work will focus on denser dual measurement strategies, incorporating different volumes, geometries, and materials, and exploring iterative reconstruction algorithms that can further suppress artifacts and improve quantitative accuracy.

5. Conclusions

This study successfully developed and validated a dual illumination and detection photoacoustic tomography strategy specifically designed for the non-destructive evaluation of hollow metallic cylinders. The dual configuration effectively mitigates artifacts, enhances image contrast and spatial resolution, and compensates for acoustic reflections arising from metal–water impedance mismatches. The results reveal that material properties—specifically acoustic impedance, sound velocity, and thermal diffusion length—play a decisive role in determining signal quality and reconstruction fidelity. The proposed effective propagation velocity model successfully balances transmission and reflection effects, improving the quantitative accuracy of dual-mode reconstructions. Among the analyzed metals, bronze exhibited the most favorable performance due to its optimal optical absorption and acoustic reflection combination.

The key conclusions are enhanced image quality by effective dual signal processing for metals with acoustic impedance < 42 × 106 kg/(m²s) = 42 MRayl, as demonstrated by quantitative PA signal evaluation. This technique addresses the industry's critical limitations of existing NDT methods by offering a non-contact, high-contrast, and high-resolution imaging solution for detecting internal structures and potential defects in symmetric metal components.

Overall, the findings confirm that dual illumination and detection constitute a robust and efficient strategy for improving image quality in PAT-based non-destructive testing, with future work focusing on denser measurement geometries and iterative reconstruction algorithms to further enhance performance.