Improving Acquisition Speed of X-Ray Ptychography Through Spatial Undersampling and Regularization

X-ray ptychography is one of the versatile techniques for nanometer resolution imaging. The magnitude of the diffraction patterns is recorded on a detector, and the phase of the diffraction patterns is estimated using phase retrieval techniques. Most phase retrieval algorithms make the solution well-posed by relying on the constraints imposed by the overlapping region between neighboring diffraction pattern samples. As the overlap between neighboring diffraction patterns reduces, the problem becomes ill-posed, and the object cannot be recovered. To avoid the ill-posedness, we investigate the effect of regularizing the phase retrieval algorithm with image priors for various overlap ratios between the neighboring diffraction patterns. We show that the object can be faithfully reconstructed at low overlap ratios by regularizing the phase retrieval algorithm with image priors such as Total-Variation prior and Structure Tensor Prior. We also show the effectiveness of our proposed algorithm on real data acquired from an IC chip with a coherent X-ray beam.