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Abstract
The quality of inverse problem solutions obtained through deep learning is limited by the nature of the priors learned from examples presented during the training phase. Particularly in the case of quantitative phase retrieval, spatial frequencies that are underrepresented in the training database, most often at the high band, tend to be suppressed in the reconstruction. Ad hoc solutions have been proposed, such as pre-amplifying the high spatial frequencies in the examples; however, while that strategy improves the resolution, it also leads to high-frequency artefacts, as well as low-frequency distortions in the reconstructions. Here, we present a new approach that learns separately how to handle the two frequency bands, low and high, and learns how to synthesize these two bands into full-band reconstructions. We show that this “learning to synthesize” (LS) method yields phase reconstructions of high spatial resolution and without artefacts and that it is resilient to high-noise conditions, e.g., in the case of very low photon flux. In addition to the problem of quantitative phase retrieval, the LS method is applicable, in principle, to any inverse problem where the forward operator treats different frequency bands unevenly, i.e., is ill-posed.
Highlights
Phase retrieval: significance and approach overview The retrieval of the phase of electromagnetic fields is one of the most important and most challenging problems in classical optics
In ref. 28, we addressed the influence of the spatial power spectral density (PSD) S (vx, vy) of the example database on the quality of training
The learning to synthesize” (LS)-deep neural network (DNN) reconstruction scheme for quantitative phase retrieval has been shown to be resilient to highly noisy raw intensity inputs while preserving high-spatialfrequency details better than those of ref
Summary
Phase retrieval: significance and approach overview The retrieval of the phase of electromagnetic fields is one of the most important and most challenging problems in classical optics. Since only the intensity of a light beam is observable at THz frequencies and above, the phase may be inferred only indirectly from intensity measurements. Computational approaches to this operation may be classified as interferometric/holographic[7,8], where a reference beam is provided, and noninterferometric, or reference-less, such as direct/iterative[9,10] and ptychographic[11,12], which are both nonlinear, and transport-based[13,14], where the problem is linearized through a hydrodynamic approximation. Direct methods attempt to retrieve the phase from a single raw intensity image, whereas the transport and ptychographic methods implement axial and lateral scanning, respectively. Direct measurement with a defocus is the approach we take here
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