All-optical photoacoustic tomography via beam deflection

TL;DR

This work introduces an all-optical photoacoustic tomography modality that records acoustic fields through beam deflection, yielding measurements equivalent to the Radon transform of the pressure gradient $\nabla p$. The forward model integrates multiphysics: a wave equation for PA pressure and an optical sensing operator that maps $\nabla p$ to beam deflections, with data expressed as $\beta = M(\alpha,s;\mathbf{n}',d,\tau) p$ and $M = R(\alpha,s)\,\chi(\mathbf{n}',d,\tau)\,\mathbf{n}'\cdot\nabla$. The inverse problem is solved by decomposing into three directional subproblems solved with ISTA using the adjoint operator, aided by a directional preprocessing $R^{-1}\mathcal{B}_m$ that extracts $\partial p/\partial x_m$; final 3D reconstruction of $p$ is achieved via a Galerkin Poisson solve. Numerical experiments on convergence, the Shepp3D phantom, a cubic field, and spinodal metamaterials demonstrate accurate 3D morphologies and high directional correlations, even under noise and limited data. The approach promises enhanced sensitivity and reduced waveform distortion, offering a path toward scalable, all-optical PA tomography with potential integration with low-cost LED excitation for clinical translation.

Abstract

Photoacoustic imaging (PAI) uniquely combines the advantages of optical contrast with deep tissue penetration capability of acoustic waves, enabling imaging at depths of several centimeters. Conventional photoacoustic imaging methods have relied on pulsed lasers to induce the photoacoustic effect, coupled with arrays of pressure transducers to detect the resulting ultrasound signals. In this work, we propose an alternative all-optical approach that leverages optical deflection to record photoacoustic waves by an array of detection beams. The measured signal is shown to be the Radon transform of the pressure gradients. An optimization-based inversion procedure is used to reconstruct the initial time pressure gradient field. Subsequently, a Galerkin method is used to reconstruct the pressure field from the pressure gradient field. The new modality offers the potential for enhanced sensitivity and reduced signal distortion, advancing the capabilities of photoacoustic imaging beyond traditional transducer-based systems.

Figures (8)

• Figure 1: Schematic of the experimental setup for optical beam deflection tomography. (a) The absorber (shown in green) is irradiated by a short laser pulse and emits acoustic waves (shown in blue). As the acoustic waves propagate to the probe beam array plane $\Gamma$ (shown in light blue), the probing beam array (shown in purple) is deflected with the deflection angle along the $z$-axis recorded by an array of position detectors. The experiment can be repeated with the probe beam array rotated by an incremental angles $\alpha$ on the plane $\Gamma$ for each pulsed excitation. For reconstruction of the image, full rotation through 180 degrees must be recorded. Only one probe laser beam and a detector array are shown. (b) A top view of the probe beam array and detectors.
• Figure 2: Algorithmic framework. The first column illustrates the forward simulation process used to generate synthetic experimental data. Starting from the bottom-left block, the six stages are: (F1) the initial pressure field, (F2) the corresponding pressure gradient field, (F3) the temporal evolution of the gradient field, (F4) its restriction to the measurement plane, (F5) the extraction of Radon transform values at sampled points, and (F6) the inverse Radon transform of the extracted data. The second and third columns depict the inverse reconstruction process. Beginning at the top-center, the seven stages include: (I1) the trial initial pressure gradient field, (I2) its simulated temporal evolution, (I3) the extraction of values at sampled points, (I4) the residual between trial and synthetic data, (I5) the adjoint operation to compute the correction term, (I6) the update of the trial gradient field using the correction, (G1) the formulation of the Poisson equation, and (G2) the final integration to reconstruct the initial pressure field.
• Figure 3: Convergence of the estimated pressure gradient fields and the pressure field (a) Reconstructed 3D morphology of the phantom after 1, 5, 10, and 50 iterations, shown alongside the ground truth. (b) The relative mean square error (RMER) as a function of the iteration numbers. (c) The peak signal-to-noise ratio (PNSR) as a function of the iteration numbers. The ground truth is the Shepp3d phantom with the size of $65^3$. The noise level is set to be zero.
• Figure 4: Comparisons of the ground truth and the predictions for the pressure gradient fields and pressure field. From left to right: (a1, a2, a3, a4): $\frac{\partial p}{\partial x_1}$;(b1, b2, b3, b4): $\frac{\partial p}{\partial x_2}$; (c1, c2, c3, c4): $\frac{\partial p}{\partial x_3}$; (d1, d2, d3, d4): $p$. From top to bottom: (a1, b1, c1, d1): ground truth; (a2, b2, c2, d2): predictions based on the image 0.1; (a3, b3, c3, d3): Difference between the ground truth and the predictions; (a4, b4, c4, d4): The amplitude of the signal as a function of the distance along the white dash-dot line for both the ground truth (solid black line) and the prediction (red dotted line). The ground truth is the Shepp3d phantom with the size of $65^3$. The predictions are obtained from the image 0.1 after 50 iterations and the finite element method. The reconstruction was assuming 65 probe beam positions and detectors separated by 1 mm, a laser duration of 10 ns and a recording duration of 100 $\mu$s. The Pearson correlation coefficients between the reconstructed signals and the ground truths in (a4), (b4), (c4), and (d4) are 96.43$\%$, 98.20$\%$, 99.45 $\%$ and 92.22 $\%$, respectively.
• Figure 5: The new modality outperforms conventional method across different noise levels. (a) Structural similarity index measure (SSIM) and (b) peak signal-to-noise ratio (PSNR) over the relative error amplitude $\epsilon$, introduced as sensor measurement error during the Radon Transform step. The baseline conventional pressure-based approach uses a central frequency of 1 MHz, with a lower cutoff frequency of 0.2 MHz and an upper cutoff frequency of 2 MHz.