Ptychography is a coherent diffraction imaging (CDI) technique that has grown rapidly in the past years [1,2]. The original concept was developed to address the missing phase challenge in crystallography . By translating a narrow coherent probe beam on a crystalline specimen, it aspires to extract the phase of Bragg peaks from far-field diffraction patterns. The modern form of this technique was brought to fruition by adopting an iterative phase retrieval framework . Experiment procedures remain the same, where a specimen is laterally translated through a spatially confined probe beam and the diffraction patterns are recorded at the far field. Using the phase retrieval framework, the reconstruction process iteratively imposes two different constraints during the object scanning process: first, the diffraction measurements serve as the Fourier magnitude constraints in reciprocal space; second, the confined probe beam limits the physical extent of the object for each measurement and serves as the support constraint in real space. Ptychography requires no imaging optics downstream of a specimen under investigation. It inherently generates both intensity and phase contrast for quantitative investigation of material properties—a capability that many competing imaging modalities lack. The data redundancy of ptychography further allows it to recover other important system information, including the illumination probe beam [5–8], multiple coherent modes of the probe beam or the object , images at different spectral channels [10–12], multiple depth sections of a 3D object , diffraction data beyond the detector size , and orthogonal modes of an unstable illumination beam , among others. In the past decade, lensless ptychography has captured widespread interest from different imaging communities. In the field of biomedical imaging, it has been demonstrated for optofluidic flow-cytometer screening , urine sediment testing , blood analysis [17,18], malaria parasite screening , high-throughput digital pathology , antibiotic susceptibility testing , microbial limit testing , and large-scale yeast cell culture monitoring , among others. In the field of X-ray optics and extreme ultraviolet (EUV) imaging, it has become an indispensable modality in most synchrotrons and national laboratories worldwide [22,23]. Given that the brightness of coherent X-ray sources is expected to increase by orders of magnitude in the coming years, lensless ptychography has a promising future in imaging different non-crystalline structures on an atomic scale.
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