Active Convolved Illumination with Deep Transfer Learning for Complex Beam Transmission through Atmospheric Turbulence

TL;DR

This work investigates pairing active convolved illumination (ACI) with data-driven neural networks to mitigate complex beam distortions caused by atmospheric turbulence. By developing a physics-informed ACI framework and a transfer-learning CNN (DnCNN) approach, the authors explore how learned representations can complement ACI's correlation-injection mechanism. The study demonstrates feasible integration pathways, showing that ACI preserves structure while DL reduces residual distortions, with the hybrid approach offering the strongest reconstruction performance under moderate-to-severe turbulence. The results highlight the need for geometry-aware, high-capacity DL architectures and physics-informed training to fully harness ACI in dynamic propagation environments, pointing to future differentiable, end-to-end learning pipelines and real-time adaptive illumination strategies.

Abstract

Atmospheric turbulence imposes a fundamental limitation across a broad range of applications, including optical imaging, remote sensing, and free-space optical communication. Recent advances in adaptive optics, wavefront shaping, and machine learning, driven by synergistic progress in fundamental theories, optoelectronic hardware, and computational algorithms, have demonstrated substantial potential in mitigating turbulence-induced distortions. Recently, active convolved illumination (ACI) was proposed as a versatile and physics-driven technique for transmitting structured light beams with minimal distortion through highly challenging turbulent regimes. While distinct in its formulation, ACI shares conceptual similarities with other physics-driven distortion correction approaches and stands to benefit from complementary integration with data-driven deep learning (DL) models. Inspired by recent work coupling deep learning with traditional turbulence mitigation strategies, the present work investigates the feasibility of integrating ACI with neural network-based methods. We outline a conceptual framework for coupling ACI with data-driven models and identify conditions under which learned representations can meaningfully support ACI's correlation-injection mechanism. As a representative example, we employ a convolutional neural network (CNN) together with a transfer-learning approach to examine how a learned model may operate in tandem with ACI. This exploratory study demonstrates feasible implementation pathways and establishes an early foundation for assessing the potential of future ACI-DL hybrid architectures, representing a step toward evaluating broader synergistic interactions between ACI and modern DL models.

Figures (7)

• Figure 1: The dataset used for training the DL model was synthetically generated using randomly generated concentric ring patterns. For each target, the diameter and radial position of each ring were independently sampled within predefined degrees of freedom, resulting in variations in ring width and spacing, even among targets with the same number of rings, as illustrated in row (a). Additionally, the total number of rings per target was randomly selected, further increasing structural diversity, as shown in row (b). This design enables the model to generalize across a wide range of spatial frequencies and geometric configurations.
• Figure 2: The average NCC between reconstructed outputs and their corresponding ground truth targets across the test set is shown. The "Input" refers to the test set without any DL enhancement (for $C_n^2 = 0.7 \times 10^{-14}\,\textrm{m}^{-2/3}$), where NCC is computed for each target and averaged across the set. Multiple loss functions were evaluated for training the DL model, and the performance of each configuration was assessed by comparing the DL outputs to the ground truth using NCC. The resulting average NCC for each loss function is displayed for comparison.
• Figure 3: Three randomly generated targets composed of the same number of concentric rings but with varying feature sizes are presented. Each target was selected to correspond to similar isoplanatic patch ($\theta_s/\theta_t$) conditions while leading to different turbulence severity ($\Delta l_t/\Delta l_s$) during atmospheric propagation. Column (a) shows the ground truth targets. Column (b) presents the targets after propagation through atmospheric turbulence with a refractive index structure constant of $C_n^2 = 0.7 \times 10^{-14}\,\textrm{m}^{-2/3}$. Column (c) shows the outputs from our DL model applied to the results in column (b). In column (d), the targets are reconstructed after propagation through the same atmospheric conditions with ACI applied. The reconstructions in column (d) are then processed by the DL model, yielding the final results in column (e). The NCC between each reconstruction and its ground truth is denoted by $\xi$.
• Figure 4: A representative target is propagated through atmospheric turbulence and reconstructed under various scenarios for three different turbulence levels ($C_n^2 = 0.7 \times 10^{-14}$, $1.7 \times 10^{-14}$, and $2.7 \times 10^{-14}\,\textrm{m}^{-2/3}$). Column (a) shows the ground truth target. Column (b) presents the target after propagation through turbulence. Column (c) displays the output of our DL model applied to the results in column (b). Column (d) shows reconstructions with ACI applied during propagation. These ACI-enhanced reconstructions are further refined using the DL model, with the final outputs shown in column (e). In all columns, turbulence distortion severity increases from rows 1 to 3. The NCC between each reconstruction and the ground truth is denoted by $\xi$.
• Figure 5: Three targets with various numbers of rings are shown, each propagated under a fixed turbulence strength of $C_n^2 = 0.7 \times 10^{-14}\,\textrm{m}^{-2/3}$. Column (a) shows the ground truth targets. Column (b) presents the targets after propagation through atmospheric turbulence and subsequent reconstruction. In column (c), the targets are reconstructed with ACI applied during propagation. Column (d) shows the ACI-based reconstructions averaged over ten independent atmospheric realizations. These averaged results are further refined using the DL model, with the final outputs shown in column (e). The NCC between each reconstruction and its corresponding ground truth is denoted by $\xi$.