  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.
