  Deep neural networks have emerged as effective tools for computational
imaging including quantitative phase microscopy of transparent samples. To
reconstruct phase from intensity, current approaches rely on supervised
learning with training examples; consequently, their performance is sensitive
to a match of training and imaging settings. Here we propose a new approach to
phase microscopy by using an untrained deep neural network for measurement
formation, encapsulating the image prior and imaging physics. Our approach does
not require any training data and simultaneously reconstructs the sought phase
and pupil-plane aberrations by fitting the weights of the network to the
captured images. To demonstrate experimentally, we reconstruct quantitative
phase from through-focus images blindly (i.e. no explicit knowledge of the
aberrations).
