ESPCI Paris – PSL (École Supérieure de Physique et de Chimie Industrielles de la Ville de Paris) is a generalist engineering school that has been training innovative, adaptable, and creative engineers with a solid theoretical and experimental background since 1882, aware of societal challenges. It is integrated into a research center internationally recognized in physics, chemistry, and biology (500 publications per year). It is known for its ability to transform knowledge from fundamental research into breakthrough innovations (2 patents per month, 3 startups per year). Distinguished by 6 Nobel Prizes, it hosts 400 engineering students, 530 researchers (including 250 PhD students and 100 post-doctoral fellows) in 10 joint research units, and about 100 support staff for research and teaching.

# Objective:
The objective of this internship is to study and exploit the invariant properties of multimode fibers to enable image recovery through a fiber without fully characterizing the system.

# Summary:
We will use deep learning frameworks to develop new approaches for calibration-free imaging through multimode fibers, based on the study of invariant properties in multimode fibers.

# Context and Motivations:
The control of light propagation in multimode optical fibers is a rapidly growing field of research. Unlike single-mode fibers, multimode fibers are optical waveguides that allow many trajectories or modes to propagate. Therefore, they are intensively studied for optical telecommunications and endoscopic applications. Leveraging spatial degrees of freedom could significantly increase the number of channels for communication applications, similar to MIMO (Multiple-Inputs / Multiple-Outputs) systems used in wireless communications.
Researchers are also investigating how to control and study light propagation in multimode fibers for use as minimally invasive endoscopic imaging devices [1, 2], improving resolution compared to classical endoscopes using fiber bundles. Reconstructing a signal or image is challenging due to the dispersion and unpredictability of light propagation, stemming from system defects and fiber geometry (e.g., bending, twisting). Consequently, an image introduced into a multimode fiber produces an apparently random output pattern.
A first approach to reconstruct a signal or image is to learn the transmission matrix [4], which describes the link between the input and output of an optical system, using techniques developed at the Langevin Institute for scattering media [5]. Recently, it was demonstrated that this matrix can be used to find channels insensitive to strong deformations [6]. However, this requires access to both sides of the system for calibration, which is challenging and only valid as long as the system does not change.
In scattering media, which also scramble input light, invariant properties exist that help retrieve information about an input image without knowing the complete transmission matrix. A good example is the angular memory effect, which postulates that for a given illumination, regardless of the unknown nature of the resulting random pattern, a shift in the input illumination translates to a shift in the output speckle pattern with minimal deformation. Exploiting this phenomenon has enabled the recovery of fluorescent images of objects hidden behind thick scattering media [7].
In multimode fibers, a similar phenomenon, known as the rotational memory effect (RME), has been observed [8]. Recently, we provided a theoretical framework to show that this effect can be significantly enhanced [3].
The project's goal is to find and study invariant properties in multimode fibers to improve the imaging capabilities of current systems. The ultimate goal is to eliminate the need for calibration, allowing one-shot imaging through a multimode fiber for real-time imaging in biological samples.

# Preliminary Results:
For low-disorder fibers, which is typical for short systems (a few centimeters to a few tens of centimeters) used in endoscopic applications, a priori information about the statistics of the transmission matrix can be used even when the actual matrix is unknown. By adding known statistical properties or other a priori knowledge about the image, generally available for microscopy, the image can be reconstructed without calibration. An algorithm adapted from sparse blind deconvolution algorithms [9] allows, in simulation, reconstructing images from the output speckle pattern in one shot, leveraging the rotational memory effect, even if the fiber changes over time.

# Project Description:
Leveraging the Langevin Institute's expertise in the theory and experimental control of light propagation in complex media and multimode fibers, the student will use wavefront shaping techniques to study and measure invariant properties in multimode fibers. The analogy between scattering media and multimode fibers will be explored to apply known results and tools to optical fibers. Experimentally, transmission matrices of multimode fiber systems will be characterized to highlight and study invariant properties. Using custom algorithms and optimized deep learning frameworks (pyTorch), the concepts demonstrated in simulations will be improved and new approaches for calibration-free imaging through multimode fibers will be developed.

# Candidate Profile:
The candidate should have an interest in wave physics, theory, and programming. The internship will require extensive use of Python for interfacing, data acquisition, post-processing, and image reconstruction algorithms.