CIF: Small: Collaborative Research: Signal Processing for Nonlinear Diffractive Imaging: Acquisition, Reconstruction, and Applications

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There is a growing need in biomedical research to observe biological structure and processes on the length scales smaller than 100nm. Conventional optical systems cannot effectively provide such information, however, due to the infamous diffraction limit. The formulation of the diffraction limit fundamentally relies on the presumed linearity in the interaction between the illuminating light and the object. The goal of this project is to overcome the diffraction limit by exploiting nonlinearities from a modern signal processing perspective. This project will lay out theoretical, algorithmic, and instrumentation foundation for nonlinear diffractive imaging. The outcome of this project can open up many possibilities of high-resolution imaging in highly scattering media that are ubiquitous in science and medicine, including histology, cytometry, brain mapping, and drug discovery. The proposed activities will also promote education through the training of students in a wide range of topics within signal processing, computational imaging, and optics, and through related curriculum development efforts where the basic themes of the proposed research will be incorporated in courses taught by the investigators.The focus of this research is to develop computational imaging methods that fully harness the information encoded in two types of nonlinearities: object-light interactions and prior assumptions on the objects. Concretely, the work will focus on: (a) efficient schemes for data acquisition, (b) scalable algorithms for 3D reconstruction, and (c) two novel application platforms for validation. Results from this research will lead to a single, holistic signal processing framework that can maximally extract the information encoded in nonlinear measurements.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.