The experimental data is used to train complex-weighted models with a range of regularisation approaches.

Predicting the effects of physical perturbations on optical channels is critical for advanced photonic devices, but existing modelling techniques are often computationally intensive or require exhaustive characterisation. We present a novel data-efficient machine learning framework that learns the perturbation-dependent transmission matrix of a multimode fibre. To overcome the challenge of modelling the resulting highly oscillatory functions, we encode the perturbation into a Fourier Feature basis, enabling a compact multi-layer perceptron to learn the mapping with high fidelity. On experimental data from a compressed fibre, our model predicts the output field with a 0.995 complex correlation to the ground truth, improving accuracy by an order of magnitude over standard networks while using 85\% fewer parameters. This approach provides a general tool for modelling complex optical systems from sparse measurements.

We are motivated by the recent development of dedicated optics-based hardware for rapid random projections which leverages the propagation of light in random media.

This work presents a n approach to the inverse design of scattering systems by modifying the transmission matrix u sing reinforcement learning . We utilize Proximal Policy Optimization to navigate the highly non - convex landscape of the object function to achieve three types of transmission matri ces: (1) F ixed - ratio power conversion and z ero - transmission mode in r ank - 1 matri ces, (2) exceptional points with degenerate eigenvalues and unidirectional mode conversion, and (3) uniform channel participation is enforced when transmission eigenvalues are degenerate . Engineering wave propagation is a fast - moving domain. S ingularit ies of the scattering matrix (SM), or sub - SM, such as the transmission matrix (TM) or reflection matrix (RM) encode the scattering behavior of a n open system and can be exploited in sensing, switching, lasing and energy deposition [1,2] . Open system s can be described by effective non - Hermitian Hamiltonians, and their resonance frequencies corresponds to poles of SM. Frequency points at which the response vanishes are described by zeros, which are also usually complex value. Incident radiation is completely absorbed when a zero of the SM is brought to the real axis. Such coherent perfect absorption (CPA) is the time reversal of an outgoing wave at the lasing threshold [4] .

Multimode optical fibres are hair-thin strands of glass that efficiently transport light. They promise next-generation medical endoscopes that provide unprecedented sub-cellular image resolution deep inside the body. However, confining light to such fibres means that images are inherently scrambled in transit. Conventionally, this scrambling has been compensated by pre-calibrating how a specific fibre scrambles light and solving a stationary linear matrix equation that represents a physical model of the fibre. However, as the technology develops towards real-world deployment, the unscrambling process must account for dynamic changes in the matrix representing the fibre's effect on light, due to factors such as movement and temperature shifts, and non-linearities resulting from the inaccessibility of the fibre tip when inside the body. Such complex, dynamic and nonlinear behaviour is well-suited to approximation by neural networks, but most leading image reconstruction networks rely on convolutional layers, which assume strong correlations between adjacent pixels, a strong inductive bias that is inappropriate for fibre matrices which may be expressed in a range of arbitrary coordinate representations with long-range correlations. We introduce a new concept that uses self-attention layers to dynamically transform the coordinate representations of varying fibre matrices to a basis that admits compact, low-dimensional representations suitable for further processing. We demonstrate the effectiveness of this approach on diverse fibre matrix datasets. We show our models significantly improve the sparsity of fibre bases in their transformed bases with a participation ratio, p, as a measure of sparsity, of between 0.01 and 0.11. Further, we show that these transformed representations admit reconstruction of the original matrices with < 10% reconstruction error, demonstrating the invertibility.

In this paper we tackle the problem of recovering the phase of complex linear measurements when only magnitude information is available and we control the input. We are motivated by the recent development of dedicated optics-based hardware for rapid random projections which leverages the propagation of light in random media. A signal of interest $\mathbf{\xi} \in \mathbb{R}^N$ is mixed by a random scattering medium to compute the projection $\mathbf{y} = \mathbf{A} \mathbf{\xi}$, with $\mathbf{A} \in \mathbb{C}^{M \times N}$ being a realization of a standard complex Gaussian iid random matrix. Two difficulties arise in this scheme: only the intensity ${|\mathbf{y}|}^2$ can be recorded by the camera, and the transmission matrix $\mathbf{A}$ is unknown. We show that even without knowing $\mathbf{A}$, we can recover the unknown phase of $\mathbf{y}$ for some equivalent transmission matrix with the same distribution as $\mathbf{A}$. Our method is based on two observations: first, changing the phase of any row of $\mathbf{A}$ does not change its distribution; and second, since we control the input we can interfere $\mathbf{\xi}$ with arbitrary reference signals. We show how to leverage these observations to cast the measurement phase retrieval problem as a Euclidean distance geometry problem. We demonstrate appealing properties of the proposed algorithm on both numerical simulations and in real hardware experiments. Not only does our algorithm accurately recover the missing phase, but it mitigates the effects of quantization and the sensitivity threshold, thus also improving the measured magnitudes.

One of the biggest challenges in the field of biomedical imaging is the comprehension and the exploitation of the photon scattering through disordered media. Many studies have pursued the solution to this puzzle, achieving light-focusing control or reconstructing images in complex media. In the present work, we investigate how statistical inference helps the calculation of the transmission matrix in a complex scrambling environment, enabling its usage like a normal optical element. We convert a linear input-output transmission problem into a statistical formulation based on pseudolikelihood maximization, learning the coupling matrix via random sampling of intensity realizations. Our aim is to uncover insights from the scattering problem, encouraging the development of novel imaging techniques for better medical investigations, borrowing a number of statistical tools from spin-glass theory.

Linear problems appear in a variety of disciplines and their application for the transmission matrix recovery is one of the most stimulating challenges in biomedical imaging. Its knowledge turns any random media into an optical tool that can focus or transmit an image through disorder. Here, converting an input-output problem into a statistical mechanical formulation, we investigate how inference protocols can learn the transmission couplings by pseudolikelihood maximization. Bridging linear regression and thermodynamics let us propose an innovative framework to pursue the solution of the scattering-riddle. A major interest in biomedical imaging is the comprehension ofthe light scattering through disordered media: many recent studies have achieved light-focusing and image reconstructioneven through complex biological tissues [1,2].

We use complex-weighted, deep networks to invert the effects of multimode optical fibre distortion of a coherent input image. We generated experimental data based on collections of optical fibre responses to greyscale input images generated with coherent light, by measuring only image amplitude (not amplitude and phase as is typical) at the output of \SI{1}{\metre} and \SI{10}{\metre} long, \SI{105}{\micro\metre} diameter multimode fibre. This data is made available as the {\it Optical fibre inverse problem} Benchmark collection. The experimental data is used to train complex-weighted models with a range of regularisation approaches. A {\it unitary regularisation} approach for complex-weighted networks is proposed which performs well in robustly inverting the fibre transmission matrix, which fits well with the physical theory. A key benefit of the unitary constraint is that it allows us to learn a forward unitary model and analytically invert it to solve the inverse problem. We demonstrate this approach, and show how it can improve performance by incorporating knowledge of the phase shift induced by the spatial light modulator.