Source-linked AI summary
Multimode Optical Fiber Transmission with a Deep Learning Network
Babak Rahmani, Damien Loterie, Georgia Konstantinou, Demetri Psaltis, Christophe Moser
TL;DR
MMFs scramble light, making input-output characterization important for imaging and projection. This paper trains deep CNNs to invert MMF propagation from output speckle measurements, achieving approximately 98% correlation and transfer of unseen image classes.
Problem
MMF scrambling produces speckles, so imaging and projection require characterization of the fiber’s input-output relationship; matrix descriptions also become less accurate as nonlinear power effects increase.
Method
A 12-layer deep CNN is trained to predict SLM input phase or amplitude patterns from MMF output speckle amplitude or hologram measurements.
Results
The CNN reached 97.28% correlation for hologram inputs and 98.25% for amplitude inputs, while Latin-alphabet training transmitted unseen handwritten digits with approximately 90% fidelity.
Takeaways & Limitations
With a suitable input-output image basis, the CNN performs nonlinear inversion and can transfer transmission to image classes absent from training.
Takeaways & Limitations
Fourier-basis training failed to generalize effectively to arbitrary unseen input patterns, and the authors identify basis choice as a limitation.
Abstract
from arXiv · showhide
Multimode fibers (MMF) are an example of a highly scattering medium which scramble the coherent light propagating within them and produce seemingly random patterns. Thus, for applications such as imaging and image projection through a MMF, careful measurements of the relationship between inputs and outputs of the fiber are required. We show, as a proof of concept, that a deep learning neural network can learn the input-output relationship in a 0.75 m long MMF. Specifically, we demonstrate that a deep convolutional neural network (CNN) can learn the non-linear relationships between the amplitude of the speckle pattern obtained at the output of the fiber and the phase or amplitude at the input of the fiber. Effectively the network performs a non-linear inversion task. We obtained image fidelity (correlation) of ~98% compared with the image obtained using the measured matrix of the system. We further show that the network can be trained for transfer learning, i.e. it can transmit images through the MMF which belongs to another class which were not used for training/testing.
1. Introduction
MMFs scramble coherent light into speckles, motivating alternatives to transmission-matrix descriptions. The paper proposes deep CNNs to learn MMF propagation and demonstrates high-fidelity reconstruction plus transfer learning, while identifying basis-dependent generalization limits.
- Motivation: MMFs produce seemingly random output speckles even though propagation is deterministic and linear below a power threshold.At higher launched power, nonlinear effects make the transmission-matrix model progressively less accurate.
- Approach: Deep CNNs are proposed to learn light propagation through MMFs as an alternative to experimentally measured transmission matrices.The longer-term motivation is controlling propagation when nonlinear effects make physical modeling difficult.
- Approach: The network receives output speckle amplitude or raw holograms and predicts the input SLM phase patterns, performing reverse propagation.The holograms contain output phase information, whereas amplitude inputs omit it.
- Results: With 80% of the data, test-set 2D correlations reached 97.28% for holograms and 98.25% for amplitude inputs.These results show accurate reconstruction for the Fourier-basis patterns used in training and testing.
- Limitation: The CNN did not generalize effectively to arbitrary unseen input patterns when trained with Fourier-basis data.The authors hypothesize that the Fourier basis is not appropriate for CNN training.
- Results: Training on handwritten Latin letters enabled transmission of unseen handwritten digits at approximately 90% fidelity, demonstrating transfer learning.The digit class was not used for training or testing.
2. Methods
The experiment measures MMF output holograms from SLM inputs and trains a 12-layer CNN to reconstruct input phase patterns from output measurements. Data are reconstructed, cropped, sampled, and split for optimization and validation.
- Experimental setup: The setup uses a 0.75 m step-index MMF with a 50 μm silica core, numerical aperture 0.22, and 1055 modes.Phase patterns displayed on an SLM are demagnified onto the fiber input facet.
- Experimental setup: An off-axis hologram is formed by interfering the MMF output on a camera with a coherent reference beam.The output facet is relayed to the camera before interference.
- CNN architecture: The CNN has 12 layers: encoder and decoder endpoints surround 10 hidden layers built from convolutional and ReLU operations.Max-pooling reduces image width and height by a factor of two at each layer.
- Preprocessing: Raw holograms are Fourier-transformed, masked around the holographic real order, inverse-transformed, and cropped from 576×576 to 51×51 pixels.This preprocessing reconstructs field amplitudes and substantially speeds training.
- Training: The network maps output field amplitude or hologram intensity to the corresponding SLM phase pattern, optimized with MSE and ADAM.The selected learning rate is 10^-4.
- Data: The transmission matrix uses 1961 plane-wave patterns measured 50 times, while training retains 100 angles per measurement.This produces 5000 input-output image pairs, split into 4000 training and 1000 validation samples.
3. Results
The CNN reproduced input phase patterns with high validation correlation and performed similarly when trained on raw hologram intensity. Its generalization depended on the input-pattern class: Latin-alphabet training enabled transfer to handwritten digits, whereas Fourier-basis training failed on an arbitrary cross image.
- Validation performance: 98.25% correlation was achieved between labels and reconstructed phases on the validation set.The result was reported for the phase-reconstruction experiment.
- Validation performance: 76% fidelity was achieved on the validation dataset using all 1961 input-output images measured 10 times.Training with this expanded dataset took approximately 14 hours.
- Raw hologram input: 98.25% versus 97.28% correlation showed similar inverse-propagation performance for raw hologram intensity and optical field amplitudes.Raw hologram training took approximately 2 hours 30 minutes and required learning additional phase information between propagating modes.
- Generalization limits: Fourier-basis training failed to reconstruct an arbitrary cross image because the CNN did not learn generalized fiber transmission.The cross produced an output speckle outside the category represented by the plane-wave phase patterns.
- Transfer learning: Latin-alphabet training enabled CNN reconstruction of handwritten digits and other image classes through transfer learning.The experiment changed the input-output image basis class and evaluated reconstruction on images from a different class.
4. Conclusion
Using suitable input-output image patterns, a 12-layer CNN transmitted handwritten digits after training on handwritten Latin-alphabet images. The network used output amplitude to infer input amplitude or phase, achieving approximately 90% fidelity through computational MMF transmission.
- 4. Conclusion: A 12-layer CNN trained on handwritten Latin-alphabet patterns transmitted handwritten digits with ~90% fidelity.The digits belonged to a class not used for training.
- 4. Conclusion: The network performed a non-linear inversion by using output amplitude to infer the input SLM amplitude or phase.The transmission matrix was measured experimentally with Fourier-basis inputs, then used for computational field propagation.
- 4. Conclusion: The experiments used optical intensities too low to create non-linear effects, while the authors suggest extension to complex non-linear phenomena in MMFs.The reported study therefore demonstrates the approach in the linear regime.
I B MSE
The CNN uses a multi-block convolutional architecture and is evaluated through reconstruction error and 2D correlation across several input conditions. The figures also show hologram preprocessing, failures on unseen pattern classes, and transfer-learning reconstructions.
- CNN architecture: The CNN schematic comprises input and output blocks surrounding 10 hidden blocks, with convolutional processing and max-pooling operations.The input block maps images through 64 convolutional filters.
- Hologram reconstruction: Raw holograms are Fourier transformed, masked in the Fourier domain, and inverse transformed to reconstruct the object optical field amplitude.The reconstruction figure presents the raw hologram, its logarithmic Fourier amplitude, and the inverse transform of the masked region.
- Performance evaluation: Figure 4 evaluates MSE and 2D correlation between labels and CNN-reconstructed phase patterns when MMF output field amplitudes are used as input.The comparison is shown for both training and validation data.
- Performance evaluation: Figure 5 evaluates MSE and 2D correlation for reconstructed input phase patterns when raw holograms are supplied to the CNN.The plots compare training and validation performance across iterations.
- Generalization: The CNN fails to reconstruct the proper phase pattern for an input image category not used during training.The corresponding comparison is shown between the input phase image and the CNN-computed phase image.
- Transfer learning: Figures 7 and 8 assess reconstruction for handwritten alphabets and transfer learning to digits and a heart image, reporting MSE, 2D correlation, and fidelity.The transfer-learning examples include reconstructed amplitude and phase patterns for digits and an amplitude reconstruction for a heart picture.