Deep learning reads hidden vortex light codes in random speckle patterns

Physicists have trained two artificial intelligence models to identify the topological charge of Laguerre-Gaussian laser beams from nothing more than a small fragment of the random speckle pattern the beams produce after scattering from a rough surface. The work, published in Applied Physics B, pushes the reliable detection of these swirling optical modes up to topological charges of 50, well beyond the range of most previous deep learning approaches, and shows that a Vision Transformer outperforms a convolutional neural network by roughly 3.3 percentage points, reaching a mean classification accuracy of 98.1 percent.

Laguerre-Gaussian beams are light fields with a phase singularity at their center and helical wavefronts that twist around it. The azimuthal phase varies as exp(iℓφ), where ℓ is the topological charge, and each photon in the beam carries an orbital angular momentum of ℓℏ. Because ℓ can in principle take any integer value, these modes form an effectively infinite dimensional basis, which is exactly what makes them attractive for free-space optical communication: different charges can carry separate data channels through the same beam path. The catch is that the receiver must be able to tell which charge arrived, and the authors argue that accurately identifying the topological charge after the beam has passed through disturbances or traveled long distances is essential for such systems to work.

Traditional detection relies on computer-generated holography with spatial light modulators, often combined with interferometric techniques. These methods run into trouble at high orders because diffraction efficiency degrades. Machine learning has been drafted to help, with convolutional networks analyzing either direct intensity images of the beams or their interferograms, and transfer learning architectures such as AlexNet, VGG16, ResNet, InceptionV3, MobileNet and EfficientNet all pressed into service for classifying Laguerre-Gaussian modes. But the new paper identifies two persistent weaknesses in that literature: most deep learning methods need the full intensity profile of the beam, and most reported speckle-based studies stop at low topological charges.

The full-profile requirement becomes a serious problem at high charges. As ℓ grows, the beams look increasingly alike, because the change in the dark core size is very small, so distinguishing neighboring high-order modes from intensity images alone is nearly impossible. Resizing or interpolating captured data to fit a fixed network input can also suppress high spatial frequency components, alter the speckle correlation length, and introduce artificial spatial structures, meaning the features a network learns may be tied to imaging scale or beam size rather than to the orbital angular momentum itself. Earlier speckle-based work, including a CNN and wavelet scattering framework that identified charges up to ℓ ≤ 16 with accuracies above 90 percent, was restricted to lower orders, and prior studies generally did not report metrics averaged over multiple independent training runs, leaving statistical stability unverified.

The new experiment starts with a linearly polarized helium-neon laser at 632.8 nanometers illuminating a Holoeye PLUTO 2.1 spatial light modulator carrying computer-generated holograms for charges from ℓ = 1 to 50. A 4f lens system with a 12-fold magnification ensures uniform illumination of the modulator, and a second 4f system images the first diffraction order, where the required Laguerre-Gaussian beam is generated. The beam then strikes a static ground glass plate with 220 grit placed at the generation plane. The plate’s inhomogeneities impose a spatially varying random phase, and the interference of the many scattered waves produces a speckle pattern, which a CCD camera records 20 centimeters away for every value of ℓ.

From each recorded speckle image of 2464 by 2056 pixels, the team cut 224 by 224 pixel non-overlapping patches, yielding 99 patches per topological charge and a dataset of 4,950 images spanning 50 classes. Each patch represents roughly one percent of the full speckle pattern, and the point of the exercise was to test whether such small local regions contain enough information to identify the charge. The images were normalized to the range 0 to 1 and split in a stratified fashion into 80 percent training, 10 percent validation and 10 percent test sets, so every class is equally represented in each subset. A second dataset covering charges from −20 to +20 was built to test whether the models could recover not just the magnitude but also the sign of the charge.

Two architectures were compared. SFT-VSNet is a selectively fine-tuned VGG16-based convolutional network in which the first ten layers are frozen while later layers adapt, with a custom classifier head of fully connected layers of 512, 256 and 128 neurons, batch normalization and dropout of 0.5, and a 50-way softmax output. It contains 15.15 million parameters, of which 13.41 million are trainable. FT-ViTSNet is a fully fine-tuned Vision Transformer based on ViT-Base-Patch16-224 pretrained on ImageNet-21k, which divides each speckle patch into 196 non-overlapping 16 by 16 tiles, projects them into a 768-dimensional embedding space and processes them through transformer encoder layers with multi-head self-attention. It carries 86.96 million parameters, almost all trainable. Both models were trained with the Adam optimizer at a learning rate of 10⁻⁵, a batch size of 32 and categorical cross-entropy loss, on an Apple M1 Pro system using TensorFlow.

Evaluated over three independent training runs with a different stratified data split in each, FT-ViTSNet achieved a mean classification accuracy of 98.1 percent for charges from 1 to 50, beating the CNN by approximately 3.3 percent. The confusion matrices show almost no off-diagonal elements for the transformer, while the CNN shows more crosstalk between adjacent modes for ℓ ≥ 30. The reason lies in the physics of the speckle itself. Measuring the intensity autocorrelation of the patterns, the team found the speckle grain size falls from 82.8 micrometers, or 24 CCD pixels, at ℓ = 1 to 13.8 micrometers, or 4 pixels, at ℓ = 50. Higher-order beams therefore produce finer speckle structures, but the rate of change slows with increasing charge, so neighboring high-order modes generate very similar local patterns. Convolutional networks, which rely on local receptive fields, get confused by this local similarity, whereas the transformer’s global attention can pick up broader structural features such as annular symmetry and radial energy distribution. Although scattering scrambles the optical field, information about the incident mode remains encoded in the statistical correlation properties of the speckle, which the ViT is better positioned to exploit. The trade-off is speed: the transformer’s patch embedding and self-attention operations make its inference time longer, so the CNN offers a favorable accuracy-latency compromise when detection must keep pace with symbol or frame rates.

The signed-charge results flip the ranking. For ℓ from −20 to +20, SFT-VSNet performed slightly better than FT-ViTSNet. Sign detection is genuinely hard because Laguerre-Gaussian intensity profiles are angularly symmetric, so +ℓ and −ℓ modes are intensity-degenerate and indistinguishable from intensity alone; the handedness lives in the helical phase, which is never measured explicitly but becomes indirectly encoded in the statistical properties of the scattered field. The speckles of opposite charges are strongly correlated and differ only subtly in the spatial arrangement of their grains, and in small local patches those differences can nearly vanish, so the models sometimes misclassify the sign while still getting the magnitude right. The CNN’s local feature extraction suits these fine asymmetries at moderate charges, while the transformer excels at the global complexity of high orders. The authors suggest this complementarity points toward hybrid convolutional-transformer architectures, such as dual-branch networks or CvT- and CoAtNet-style backbones, that could fuse local and global representations, though such designs lie beyond the present study.

Compared with prior speckle-based approaches, the framework uses purely experimental speckle images up to ℓ = 50, needs only a one-percent patch without resizing or preprocessing, validates signed charges, and reports metrics averaged over three runs. The authors note their experiments used a fixed optical configuration with a static diffuser and a single propagation distance, and they flag extension to dynamically varying diffusers and atmospheric turbulence as future work. Within those limits, the ability to identify high-order modes from small intensity patches relaxes receiver aperture requirements, simplifies receiver design, and, the authors argue, makes the approach suitable for practical free-space optical links, scattering-rich environments and multimode optical systems, where retraining under moderate parameter changes could be handled by fine-tuning rather than full retraining.

Subject of Research: Deep learning classification of high-order Laguerre-Gaussian beam topological charges from scattered speckle patterns

Article Title: Higher-order spatial mode detection leveraging deep learning on random optical patterns

Article References: Mutupuri, S. S., Ansari, M. H., Anamalamudi, S., Kumar, R., Prabhakar, S., & Salla, G. R. (2026). Higher-order spatial mode detection leveraging deep learning on random optical patterns. Applied Physics B, 132(10), Article 107. https://doi.org/10.1007/s00340-026-08717-x

Image Credits: AI Generated

DOI: 10.1007/s00340-026-08717-x

Keywords: Laguerre-Gaussian beams, topological charge, orbital angular momentum, speckle patterns, deep learning, Vision Transformer, convolutional neural network, free-space optical communication, transfer learning, optical scattering, VGG16, spatial light modulator