Seeing Through the Haze: Machine Learning Restores Clarity to Light Signals

Author: Denis Avetisyan

New research leverages the power of artificial intelligence to accurately classify and reconstruct structured light beams distorted by atmospheric turbulence.

The study demonstrates how uniquely patterned light-specifically, 1515 superimposed orbital angular momentum (OAM) states-can be used as distinct class labels, and how these patterns predictably transform upon passing through a disordered medium, offering a pathway for robust signal propagation and classification.

Diffusion models and deep learning classification enhance orbital angular momentum mode identification in turbulent environments.

Accurate propagation of structured light through turbulent media remains a significant challenge due to atmospheric distortions. This work, ‘ML-based approach to classification and generation of structured light propagation in turbulent media’, addresses this by leveraging machine learning for both classifying and generating realistic simulations of light’s behavior. Specifically, a diffusion model is developed to augment training data, substantially improving the classification accuracy of orbital angular momentum (OAM) modes impacted by turbulence. Could this approach pave the way for more robust and reliable free-space optical communication systems?

Harnessing Twisted Light: An Introduction to Orbital Angular Momentum

Conventional radio and optical communication rely on modulating properties like amplitude and frequency of electromagnetic waves, but a largely untapped dimension exists: the shape of the wave itself. Orbital Angular Momentum (OAM) modes represent these unique wave shapes – twisted, helical phases – and offer a pathway to dramatically increase data capacity. Unlike traditional methods which encode information on a single plane, OAM allows for multiple, independent data streams to be carried within a single beam, each defined by a different twist. This is because OAM modes are mutually orthogonal, meaning they don’t interfere with one another, essentially creating multiple ‘channels’ within the same frequency band. $L$ represents the amount of twist and can take on an infinite number of values, theoretically enabling limitless bandwidth expansion. Consequently, harnessing OAM promises communication systems capable of supporting significantly higher data rates, crucial for meeting the ever-growing demands of modern technologies and future applications like holographic communication and high-resolution imaging.

The potential of orbital angular momentum (OAM) modes for vastly increased data transmission rates faces a significant obstacle: atmospheric turbulence. As OAM beams propagate through the atmosphere, variations in air density and temperature cause distortions in the wavefront, effectively scrambling the information encoded within the beam’s unique helical shape. This isn’t merely a blurring of the signal; turbulence introduces random phase shifts that can completely alter the OAM mode, leading to signal fading and errors at the receiver. Consequently, what began as a sharply defined twist carrying substantial data can arrive as a diffuse, unrecognizable pattern, severely limiting both the range and reliability of free-space optical communication systems that rely on OAM multiplexing. Overcoming this distortion is therefore crucial to realizing the promised benefits of OAM-based communication technologies.

The potential of orbital angular momentum (OAM) for boosting data transmission hinges on accurately identifying the ‘twist’ of light at the receiving end, but atmospheric turbulence presents a significant obstacle to this process. Conventional techniques for classifying OAM modes rely on analyzing the precise wavefront of the received signal; however, turbulence introduces random distortions that scramble this information, making accurate identification exceedingly difficult. These distortions effectively blur the unique ‘signature’ of each OAM mode, leading to frequent misclassification and severely limiting the range and reliability of OAM-based communication systems. Consequently, while OAM offers a pathway to vastly increased bandwidth, realizing its full potential requires innovative approaches to overcome the challenges posed by turbulence-induced signal degradation and develop robust mode classification algorithms.

$Analysis of the OAM code 11011101 demonstrates that its spectral mass is concentrated well below the Nyquist frequency, indicating a high-resolution image formation with minimal spectral leakage, as shown by the source intensity, propagated intensity <span class="katex-eq" data-katex-display="false">|u(z,\cdot)|^{2}</span>, and normalized radial profile <span class="katex-eq" data-katex-display="false">\widetilde{P}\_{I}(r)</span>.$

Analysis of the OAM code 11011101 demonstrates that its spectral mass is concentrated well below the Nyquist frequency, indicating a high-resolution image formation with minimal spectral leakage, as shown by the source intensity, propagated intensity

|u(z,\cdot)|^{2}

, and normalized radial profile

\widetilde{P}\_{I}(r)

Modeling Wave Propagation Through Turbulent Media

The paraxial equation, derived from the Helmholtz equation under the assumption of a slowly varying envelope, is a foundational model for simulating the propagation of structured light beams. This approximation simplifies the wave equation by neglecting rapid spatial variations of the field, allowing for efficient numerical solutions. The equation mathematically describes how the complex amplitude $U(z, \mathbf{r})$ of the optical field evolves with propagation distance $z$ and transverse coordinates $\mathbf{r}$ . It is particularly well-suited for beams with a large Rayleigh range, where diffraction dominates over other effects, and forms the basis for numerous algorithms used in optics and photonics to predict beam shape, focalization, and other propagation characteristics. The paraxial approximation is valid when the angle of propagation is small relative to the wavelength of light.

The Split-Step Fourier Method (SSFM) is a numerical technique employed to solve the paraxial wave equation, which describes the propagation of light-like waves. SSFM operates by alternating between spatial and spectral domains; diffraction is calculated in the spectral domain (where it is a simple multiplication), while non-diffractive processes, such as turbulence-induced phase distortions, are calculated in the spatial domain. This iterative process accurately simulates wave propagation through inhomogeneous media like atmospheric turbulence by stepping forward in propagation distance with appropriately sized steps. The efficiency of SSFM stems from utilizing the Fast Fourier Transform (FFT) to rapidly switch between spatial and spectral representations, enabling computationally feasible simulations of wave behavior in complex environments. The accuracy of the method is dependent on the step size and the specific implementation of the turbulence model.

The Itô Schrödinger Model provides a refined approach to simulating wave propagation through turbulence by incorporating stochastic differential equations that account for the random fluctuations of the refractive index. Empirical measurements utilizing this model have yielded a mean scintillation index of 0.84, which serves as a quantitative measure of the intensity fluctuations caused by turbulence; higher values indicate stronger turbulence. Furthermore, analysis indicates a correlation length of 62.91 ± 8.66 pixels for these turbulence-induced fluctuations, defining the spatial scale over which the refractive index variations are correlated. This parameter is crucial for accurately representing the statistical properties of the turbulent medium in simulations and for interpreting experimental observations.

Simulations with default parameters <span class="katex-eq" data-katex-display="false">(z, \sigma_0, l_0) = (5, 1, 1.5)</span> reveal a representative propagated intensity, its empirical mean, and a scintillation map focused on the region <span class="katex-eq" data-katex-display="false">\Omega_{0.1}</span>, derived from 2020 realizations. — Simulations with default parameters $(z, \sigma_0, l_0) = (5, 1, 1.5)$ reveal a representative propagated intensity, its empirical mean, and a scintillation map focused on the region $\Omega_{0.1}$ , derived from 2020 realizations.

Decoding Distorted Signals: A Deep Learning Approach

Convolutional Neural Networks (CNNs) are utilized to classify the Orbital Angular Momentum (OAM) mode of a transmitted signal despite distortions caused by atmospheric turbulence. The received signal, represented as a turbulence-degraded intensity image, serves as the input to the CNN. These networks leverage convolutional layers to automatically extract relevant features from the image data, identifying patterns indicative of the original OAM mode. This approach bypasses the need for manual feature engineering, allowing the network to learn directly from the data and effectively classify the OAM mode even with significant image degradation. The classification is achieved by mapping the extracted features to specific OAM modes through fully connected layers and a softmax output, providing a probability distribution over the possible modes.

Zero padding is a standard convolutional neural network (CNN) technique used to mitigate information loss at the edges of input images. During convolution operations, pixels near the image boundaries have fewer neighboring pixels to interact with, potentially leading to reduced accuracy in feature extraction. Zero padding adds layers of zero-valued pixels around the image perimeter, effectively extending the spatial dimensions and ensuring that all pixels, including those at the edges, have a complete neighborhood for convolution. This prevents a reduction in feature map size and preserves edge information, contributing to improved CNN performance and more robust feature detection, especially when dealing with limited training data or high-resolution imagery.

ResNet-18 and SimpleCNN architectures demonstrate effective performance in classifying orbital angular momentum (OAM) modes from turbulence-degraded images. Evaluations indicate a baseline classification accuracy of 80.44% is achievable utilizing these networks, notably requiring only 25 real training samples per OAM class. This limited dataset size highlights the efficiency of these architectures in extracting relevant features despite significant signal distortion. Both networks offer viable implementation pathways for OAM mode classification systems with minimal training data requirements, suggesting potential for resource-constrained applications.

The normalized confusion matrix demonstrates that the ResNet18 checkpoint, trained with generative augmentation using <span class="katex-eq" data-katex-display="false">\mathbf{v}</span>-prediction / <span class="katex-eq" data-katex-display="false">\mathbf{x}</span>-loss and <span class="katex-eq" data-katex-display="false">\lambda=1</span>, accurately classifies the data. — The normalized confusion matrix demonstrates that the ResNet18 checkpoint, trained with generative augmentation using $\mathbf{v}$ -prediction / $\mathbf{x}$ -loss and $\lambda=1$ , accurately classifies the data.

Augmenting Reality: Data Generation via Diffusion Modeling

Denoising Diffusion Probabilistic Models (DDPMs) represent a generative modeling technique capable of synthesizing realistic turbulence-degraded intensity images. These models operate by progressively adding Gaussian noise to training data until it becomes pure noise, then learning to reverse this process to generate new samples. Specifically, DDPMs utilize a Markov chain to model the diffusion process, allowing for tractable likelihood estimation and high-quality image generation. This approach contrasts with traditional methods by directly learning the data distribution, enabling the creation of diverse and complex synthetic datasets for applications such as optical turbulence mitigation and image classification. The iterative refinement process inherent in DDPMs allows for the generation of images with fine details and realistic speckle patterns characteristic of turbulence-degraded optical signals.

By conditioning the diffusion model on the Orbital Angular Momentum (OAM) class, the generative process is guided to produce synthetic images specifically representative of each OAM mode. This targeted generation allows for the creation of a diverse training dataset where each OAM class is adequately represented, overcoming potential imbalances that could bias downstream classification tasks. The conditioning is implemented by providing the OAM class label as input to the diffusion model during both the forward and reverse diffusion processes, effectively steering the generation towards samples belonging to the specified class. This contrasts with unconditional generation, which produces samples from the overall data distribution without class-specific control.

The implementation of a frequency-domain regularizer within the Denoising Diffusion Probabilistic Model (DDPM) architecture is critical for maintaining the statistical properties of speckle patterns present in turbulence-degraded images. This regularization process ensures the generated synthetic data accurately reflects the frequency characteristics of real-world turbulence, thereby enhancing the realism and utility of the augmented training dataset. Specifically, this approach resulted in a classification accuracy of 94.22% when evaluated using a ResNet18 neural network, demonstrating a significant improvement in performance attributable to the enhanced quality and statistical fidelity of the generated data.

Generated samples demonstrate consistent intensity ranges <span class="katex-eq" data-katex-display="false"> [0, 0.15] </span> across different configurations of the controlled diffusion model. — Generated samples demonstrate consistent intensity ranges $[0, 0.15]$ across different configurations of the controlled diffusion model.

Expanding Horizons: Future Directions and Broader Impact

The convergence of orbital angular momentum (OAM) modes with generative modeling offers a pathway toward dramatically improved free-space optical communication. Traditional free-space links are notoriously susceptible to atmospheric turbulence, which distorts signals and limits data rates; however, leveraging OAM – twisting phases of light – allows for multiple independent communication channels within the same frequency band. This technique, when combined with generative adversarial networks (GANs) trained to correct for turbulence-induced distortions, creates a system capable of reconstructing the OAM modes with significantly enhanced fidelity. Consequently, this combined approach not only boosts the capacity of free-space optical links but also enhances their robustness and reliability, paving the way for high-bandwidth, secure communication in challenging environments, and potentially enabling applications ranging from satellite communication to disaster relief networks.

The innovative techniques developed for mitigating atmospheric turbulence in free-space optical communication possess a surprising versatility, extending far beyond data transmission. This methodology, centered on generative models and convolutional neural networks, addresses a fundamental challenge in any wave-based sensing or imaging system – the distortion caused by unpredictable environmental factors like atmospheric turbulence or scattering from complex media. Consequently, applications ranging from astronomical observations and LiDAR remote sensing to underwater acoustic imaging and medical ultrasound could benefit from this approach. By effectively ‘cleaning’ distorted wavefronts, these techniques promise sharper, more reliable data acquisition, unlocking enhanced resolution and accuracy in diverse fields where clear signal reception is paramount.

Ongoing investigations are geared towards refining the generative models currently employed, with an emphasis on enhancing their capacity to accurately predict and compensate for atmospheric distortions. Simultaneously, researchers are actively exploring more efficient convolutional neural network (CNN) architectures – streamlining computational demands without sacrificing performance. This dual approach – optimizing both the generative component and the CNN processing – promises to yield substantial gains in the robustness and speed of free-space optical communication systems. Ultimately, these improvements aim to facilitate higher data transmission rates and extended operational ranges, paving the way for more reliable and widespread deployment of this technology in diverse applications, from satellite communication to autonomous vehicle networks.

Analysis of the OAM code 11011101 under default parameters (<span class="katex-eq" data-katex-display="false">z=5</span>, <span class="katex-eq" data-katex-display="false">\sigma_0=1</span>, <span class="katex-eq" data-katex-display="false">l_0=1.5</span>) reveals stable autocorrelation functions, demonstrated by the empirical mean and standard deviation of the radial ACF (left) and the distribution of correlation lengths (right). — Analysis of the OAM code 11011101 under default parameters ( $z=5$ , $\sigma_0=1$ , $l_0=1.5$ ) reveals stable autocorrelation functions, demonstrated by the empirical mean and standard deviation of the radial ACF (left) and the distribution of correlation lengths (right).

The pursuit of clarity through complex systems is paramount, as demonstrated by this research into mitigating turbulence’s effect on structured light propagation. The successful integration of diffusion models with real-world data to enhance OAM mode classification echoes a fundamental principle: a seamless interface-in this case, the decoded signal-should be nearly invisible, allowing the underlying information to flow unhindered. As Grigori Perelman once stated, “It is better to be a pig than a human.” While seemingly disparate, this sentiment, in context, highlights a rejection of superficiality; a preference for underlying truth over appearances. Similarly, this work strips away the noise of atmospheric disturbance to reveal the pure form of the OAM modes, achieving a kind of mathematical elegance through robust data processing.

The Road Ahead

The pursuit of clarity through turbulence is, predictably, not yet complete. This work establishes a promising synergy between data-driven synthesis and the inherent challenges of propagating structured light. However, the elegance of a solution isn’t measured solely by improved classification accuracy, but by the minimization of necessary artifice. The current approach, while demonstrably effective, relies on a substantial augmentation of real data with generated samples – a functional necessity, perhaps, but one that hints at an incomplete understanding of the turbulence itself.

Future iterations should consider moving beyond simple performance metrics. A truly refined model would not merely cope with distortion, but anticipate it, generating not just plausible data, but data that reveals the underlying physics of the atmospheric channel. This demands a deeper integration of physical models within the diffusion process, a move toward systems where data augmentation isn’t a corrective measure, but an informed prediction.

Ultimately, the ideal design unites form and function. A system capable of both robust OAM classification and insightful turbulence characterization represents not merely a technical achievement, but a harmonious convergence of information and reality. Every system element should occupy its place, creating cohesion, and diminishing the need for brute-force data generation. That remains the elusive, and worthwhile, objective.

Original article: https://arxiv.org/pdf/2604.14208.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/