Noninvasive optical imaging through complex scattering media presents a major challenge across multiple fields. State-of-the-art techniques, such as reflection matrix decomposition and neural networks, rely on multiple measurements with varying illumination within the sample decorrelation time, making their application challenging in rapidly varying dynamic media. Here, we show that due to commutativity property of the convolution operation, dynamic scattering in isoplanatic imaging is mathematically analogous to varying illumination in static media. This insight allows leveraging matrix-based approaches developed for static scattering to rapidly varying dynamic media. Specifically, we show that the covariance matrix of a set of scattered light camera frames captured through a dynamic scattering sample has the same mathematical form as the reflection matrix of a static medium, with the target object playing the scattering medium’s role. We demonstrate this concept by high-resolution diffraction-limited imaging through dynamic scattering across multiple modalities, from incoherent fluorescence microscopy to coherence-gated holographic reflection imaging.

The detection and localization of a source hidden outside the Line-of-Sight (LOS) traditionally rely on the acquisition of indirect signals, such as those reflected from visible relay surfaces such as floors or walls. These reflected signals are then utilized to reconstruct the obscured scene. In this study, we present an approach that utilize signals diffracted from an edge of an obstacle to achieve three-dimensional (3D) localization of an acoustic point source situated outside the LOS. We address two scenarios - a doorway and a convex corner - and propose a localization method for each of them. For the first scenario, we utilize the two edges of the door as virtual detector arrays. For the second scenario, we exploit the spectral signature of a knife-edge diffraction, inspired by the human perception of sound location by the head-related transfer function (HRTF). In both methods, knife-edge diffraction is utilized to extend the capabilities of non-line-of-sight (NLOS) acoustic sensing, enabling localization in environments where conventional relay-surface based approaches may be limited.

Optical imaging through scattering media is important in a variety of fields ranging from microscopy to autonomous vehicles. Although advanced wavefront shaping techniques have offered several breakthroughs in the past decade, current techniques still require a known guide star and a high-resolution spatial light modulator or a very large number of measurements and are limited in their correction field of view. Here we introduce a guide-star-free, non-invasive approach that can correct more than 190,000 scattered modes using only 25 incoherently compounded, holographically measured, scattered light fields, obtained under unknown random illuminations. This is achieved by computationally emulating an image-guided wavefront shaping experiment, where several virtual spatial light modulators are simultaneously optimized to maximize the reconstructed image quality. Our method shifts the burden from the physical hardware to a digital, naturally parallelizable computational optimization, leveraging state-of-the-art automatic differentiation tools. We demonstrate the flexibility and generality of this framework by applying it to imaging through various complex samples and imaging modalities, including epi-illumination, anisoplanatic multi-conjugate correction of highly scattering layers, lensless endoscopy in multicore fibres and acousto-optic tomography. The presented approach offers high versatility, effectiveness and generality for fast, non-invasive imaging in diverse applications.