Harnessing coherent-wave control for sensing applications

Imaging techniques such as functional near-infrared spectroscopy and diffuse optical tomography (DOT) achieve deep, noninvasive sensing in turbid media; however, they are constrained by the photon budget, as most of the injected light is lost to scattering before reaching the detector. Wavefront shaping (WFS) can enhance signal strength via interference at specific locations within scattering media, enhancing light-matter interactions and potentially extending the penetration depth of these techniques. Interpretation of the resulting measurements relies on knowing the optical sensitivity---the relationship between changes in the detected signals and perturbations at a specific location inside the medium; however, conventional diffusion-based sensitivity models rely on assumptions that become invalid under coherent illumination. In this work, we develop a microscopic theory for optical sensitivity that captures the inherent interference effects that diffusion theory necessarily neglects. We show analytically that, under disorder averaging with random illumination, the microscopic and diffusive descriptions coincide. Beyond this limit, our framework identifies WFS strategies that enhance sensitivity. We demonstrate that the input state obtained through phase conjugation at a given point inside the system leads to the largest enhancement of optical sensitivity but requires an input wavefront that depends on the target position. In sharp contrast, the maximum remission eigenchannel, corresponding to the largest eigenvalue of the monochromatic remission matrix, leads to a global enhancement of the sensitivity map with a fixed input wavefront. This global enhancement equals the remission enhancement and preserves the spatial distribution of the sensitivity, making it compatible with existing DOT reconstruction algorithms. Our results, validated through extensive numerical simulations, establish the theoretical foundation for integrating wavefront control with diffuse optical imaging, enabling deeper tissue penetration through improved signal strength in biomedical applications.