Physics-based Learned Design: Optimized Coded-Illumination for Quantitative Phase Imaging
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Coded-illumination based reconstruction of Quantitative Phase (QP) is generally a non-linear iterative process. Thus, using traditional techniques for experimental design (e.g. condition number optimization or spectral analysis) may not be ideal as they characterize linear measurement formation models for linear reconstructions. Deep neural networks, DNNs, are end-to-end frameworks which can efficiently represent non-linear processes and can be optimized over by training. However, they do not necessarily include knowledge of the system physics and, as a result, require an enormous number of training examples and parameters to properly learn the phase retrieval process. Here, we present a new data-driven approach to optimize the coded-illumination patterns of a light-emitting diode (LED) array microscope to maximize a given QP reconstruction algorithm's performance. We establish a generalized formulation that incorporates the available information about the physics of a measurement model as well as the non-linearities of a reconstruction algorithm into the design problem. Our proposed design method enables an efficient parameterization of the design problem, which allows us to use only a small number of training examples to properly learn a design that generalizes well in the experimental setting without retraining. We image both a well-characterized phase target and mouse fibroblast cells using coded-illumination patterns optimized for a sparsity-based phase reconstruction algorithm. We obtain QP images similar to those of Fourier Ptychographic techniques with 69 measurements using only 2 learned design measurements.
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