Light microscopy is an important driving force for new biological discoveries because of its capability of visualizing micro-scale cell structures and interactions. Fundamentally, optical resolution is bounded by the diffraction limit, preventing observation of biological events with an even smaller scale. However, computational imaging approaches are efficient tools to surpass this limit. In recent years, optimization formulation has become more popular because of its flexibility and efficacy toward information retrieval. In this thesis, we leverage the power of optimization algorithms and new experimental schemes to tackle super-resolution microscopy, both improving existing methods and developing new techniques. We first apply rigorous optimization algorithm analysis to a super-resolution phase microscopy technique, Fourier ptychography. A more accurate noise model and the self-calibration algorithm ensure a better reconstruction quality for this technique. Next, we incorporate optimization into the study of a super-resolution fluorescence microscopy technique, structured illumination microscopy. Super-resolution reconstruction is achieved even with a series of random unknown illumination patterns, which is not possible without proper optimization formulation. Next, we leverage the experience of the previous two projects to propose a super-resolution microscopy method for phase and fluorescence contrast with multi-fold resolution improvement in both 2D and 3D using an unknown speckle illumination composed of high-angle plane waves from Scotch tape as a patterning element. The result is a practical method for achieving multimodal super-resolution with >2x resolution gain, surpassing the limit of the traditional linear structured illumination microscopy. All these outcomes are within the realm of computational super-resolution microscopy, where the optimization algorithm is jointly designed with optics for efficient information retrieval to achieve super-resolution microscopy.




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