Differentiable Microscopy Designs an All Optical Quantitative Phase Microscope

Ever since the first microscope by Zacharias Janssen in the late 16th century, scientists have been inventing new types of microscopes for various tasks. Inventing a novel architecture demands years, if not decades, worth of scientific experience and creativity. In this work, we introduce Differentiable Microscopy ($\partial\mu$), a deep learning-based design paradigm, to aid scientists design new interpretable microscope architectures. Differentiable microscopy first models a common physics-based optical system however with trainable optical elements at key locations on the optical path. Using pre-acquired data, we then train the model end-to-end for a task of interest. The learnt design proposal can then be simplified by interpreting the learnt optical elements. As a first demonstration, based on the optical 4-$f$ system, we present an all-optical quantitative phase microscope (QPM) design that requires no computational post-reconstruction. A follow-up literature survey suggested that the learnt architecture is similar to the generalized phase concept developed two decades ago. We then incorporate the generalized phase contrast concept to simplify the learning procedure. Furthermore, this physical optical setup is miniaturized using a diffractive deep neural network (D2NN). We outperform the existing benchmark for all-optical phase-to-intensity conversion on multiple datasets, and ours is the first demonstration of its kind on D2NNs. The proposed differentiable microscopy framework supplements the creative process of designing new optical systems and would perhaps lead to unconventional but better optical designs.