Nonconvex optimization for optimum retrieval of the transmission matrix of a multimode fiber

Transmission matrix (TM) allows light control through complex media such as multimode fibers (MMFs), gaining great attention in areas like biophotonics over the past decade. The measurement of a complex-valued TM is highly desired as it supports full modulation of the light field, yet demanding as the holographic setup is usually entailed. Efforts have been taken to retrieve a TM directly from intensity measurements with several representative phase retrieval algorithms, which still see limitations like slow or suboptimum recovery, especially under noisy environment. Here, a modified non-convex optimization approach is proposed. Through numerical evaluations, it shows that the nonconvex method offers an optimum efficiency of focusing with less running time or sampling rate. The comparative test under different signal-to-noise levels further indicates its improved robustness for TM retrieval. Experimentally, the optimum retrieval of the TM of a MMF is collectively validated by multiple groups of single-spot and multi-spot focusing demonstrations. Focus scanning on the working plane of the MMF is also conducted where our method achieves 93.6% efficiency of the gold standard holography method when the sampling rate is 8. Based on the recovered TM, image transmission through the MMF with high fidelity can be realized via another phase retrieval. Thanks to parallel operation and GPU acceleration, the nonconvex approach can retrieve an 8685$\times$1024 TM (sampling rate=8) with 42.3 s on a regular computer. In brief, the proposed method provides optimum efficiency and fast implementation for TM retrieval, which will facilitate wide applications in deep-tissue optical imaging, manipulation and treatment

Wavefront shaping: A versatile tool to conquer multiple scattering in multidisciplinary fields

Optical techniques offer a wide variety of applications as light-matter interactions provide extremely sensitive mechanisms to probe or treat target media. Most of these implementations rely on the usage of ballistic or quasi-ballistic photons to achieve high spatial resolution. However, the inherent scattering nature of light in biological tissues or tissue-like scattering media constitutes a critical obstacle that has restricted the penetration depth of non-scattered photons and hence limited the implementation of most optical techniques for wider applications. In addition, the components of an optical system are usually designed and manufactured for a fixed function or performance. Recent advances in wavefront shaping have demonstrated that scattering- or component-induced phase distortions can be compensated by optimizing the wavefront of the input light pattern through iteration or by conjugating the transmission matrix of the scattering medium. This offers unprecedented opportunities in many applications to achieve controllable optical delivery or detection at depths or dynamically configurable functionalities by using scattering media to substitute conventional optical components. In this article, the recent progress of wavefront shaping in multidisciplinary fields is reviewed, from optical focusing and imaging with scattering media, functionalized devices, modulation of mode coupling, and nonlinearity in multimode fiber to multimode fiber-based applications. Apart from insights into the underlying principles and recent advances in wavefront shaping implementations, practical limitations and roadmap for future development are discussed in depth. Looking back and looking forward, it is believed that wavefront shaping holds a bright future that will open new avenues for noninvasive or minimally invasive optical interactions and arbitrary control inside deep tissues. The high degree of freedom with multiple scattering will also provide unprecedented opportunities to develop novel optical devices based on a single scattering medium (generic or customized) that can outperform traditional optical components

Implementation of digital optical phase conjugation with embedded calibration and phase rectification

Abstract Focused and controllable optical delivery beyond the optical diffusion limit in biological tissue has been desired for long yet considered challenging. Digital optical phase conjugation (DOPC) has been proven promising to tackle this challenge. Its broad applications, however, have been hindered by the system’s complexity and rigorous requirements, such as the optical beam quality, the pixel match between the wavefront sensor and wavefront modulator, as well as the flatness of the modulator’s active region. In this paper, we present a plain yet reliable DOPC setup with an embedded four-phase, non-iterative approach that can rapidly compensate for the wavefront modulator’s surface curvature, together with a non-phase-shifting in-line holography method for optical phase conjugation in the absence of an electro-optic modulator (EOM). In experiment, with the proposed setup the peak-to-background ratio (PBR) of optical focusing through a standard ground glass in experiment can be improved from 460 up to 23,000, while the full width at half maximum (FWHM) of the focal spot can be reduced from 50 down to 10 μm. The focusing efficiency, as measured by the value of PBR, reaches nearly 56.5% of the theoretical value. Such a plain yet efficient implementation, if further engineered, may potentially boost DOPC suitable for broader applications