Since the late 16th century, scientists have continuously innovated and developed new microscope types for various applications. Creating a new architecture from the ground up requires substantial scientific expertise and creativity, often spanning years or even decades. In this study, we propose an alternative approach called "Differentiable Microscopy," which introduces a top-down design paradigm for optical microscopes. Using all-optical phase retrieval as an illustrative example, we demonstrate the effectiveness of data-driven microscopy design through $\partial\mu$. Furthermore, we conduct comprehensive comparisons with competing methods, showcasing the consistent superiority of our learned designs across multiple datasets, including biological samples. To substantiate our ideas, we experimentally validate the functionality of one of the learned designs, providing a proof of concept. The proposed differentiable microscopy framework supplements the creative process of designing new optical systems and would perhaps lead to unconventional but better optical designs.

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