We present a novel approach to x-ray microscopy based on a multilayer zone plate which is positioned behind a sample similar to an objective lens. However, unlike transmission x-ray microscopy, we do not content ourselves with a sharp intensity image; instead, we incorporate the multilayer zone plate transfer function directly in an iterative phase retrieval scheme to exploit the large diffraction angles of the small layers. The presence of multiple diffraction orders, which is conventionally a nuisance, now comes as an advantage for the reconstruction and photon efficiency. In a first experiment, we achieve sub-10-nm resolution and a quantitative phase contrast.
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