Generally, methods of three-dimensional imaging such as confocal microscopy and computed tomography rely on two essentials: multiple measurements (at a range of focus positions or rotations) and a weakly scattering specimen (to avoid distortion of the focal spot in the confocal microscope or to satisfy the projection approximation in tomography). Here we show that an alternative form of multi-measurement imaging, ptychography, can be extended to three dimensions and can successfully recover images in the presence of multiple scattering and when the projection approximation is not applicable. We demonstrate our technique experimentally using visible light, where it has applications in imaging thick samples such as biological tissues; however the results also have important implications for x ray and electron imaging.
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