Solving ptychography with a convex relaxation

Ptychography is a powerful computational imaging technique that transforms a collection of low-resolution images into a high-resolution sample reconstruction. Unfortunately, algorithms that are currently used to solve this reconstruction problem lack stability, robustness, and theoretical guarantees. Recently, convex optimization algorithms have improved the accuracy and reliability of several related reconstruction efforts. This paper proposes a convex formulation of the ptychography problem. This formulation has no local minima, it can be solved using a wide range of algorithms, it can incorporate appropriate noise models, and it can include multiple a priori constraints. The paper considers a specific algorithm, based on low-rank factorization, whose runtime and memory usage are near-linear in the size of the output image. Experiments demonstrate that this approach offers a 25% lower background variance on average than alternating projections, the current standard algorithm for ptychographic reconstruction.Comment: 8 pages, 8 figure

X-ray ptychography on low-dimensional hard-condensed matter materials

Tailoring structural, chemical, and electronic (dis-)order in heterogeneous media is one of the transformative opportunities to enable new functionalities and sciences in energy and quantum materials. This endeavor requires elemental, chemical, and magnetic sensitivities at the nano/atomic scale in two- and three-dimensional space. Soft X-ray radiation and hard X-ray radiation provided by synchrotron facilities have emerged as standard characterization probes owing to their inherent element-specificity and high intensity. One of the most promising methods in view of sensitivity and spatial resolution is coherent diffraction imaging, namely, X-ray ptychography, which is envisioned to take on the dominance of electron imaging techniques offering with atomic resolution in the age of diffraction limited light sources. In this review, we discuss the current research examples of far-field diffraction-based X-ray ptychography on two-dimensional and three-dimensional semiconductors, ferroelectrics, and ferromagnets and their blooming future as a mainstream tool for materials sciences

Water Window Ptychographic Imaging with Characterized Coherent X-rays

We report on a ptychographical coherent diffractive imaging experiment in the water window with focused soft X-rays at $500~\mathrm{eV}$. An X-ray beam with high degree of coherence was selected for ptychography at the P04 beamline of the PETRA III synchrotron radiation source. We measured the beam coherence with the newly developed non-redundant array method. A pinhole $2.6~\mathrm{\mu m}$ in size selected the coherent part of the beam and was used for ptychographic measurements of a lithographically manufactured test sample and fossil diatom. The achieved resolution was $53~\mathrm{nm}$ for the test sample and only limited by the size of the detector. The diatom was imaged at a resolution better than $90~\mathrm{nm}$.Comment: 22 pages. 7 figure

Time-domain ptychography

Through dedicated measurements in the optical regime we demonstrate that ptychography can be applied to reconstruct complex-valued object functions that vary with time from a sequence of spectral measurements. A probe pulse of approximately 1 ps duration, time delayed in increments of 0.25 ps is shown to recover dynamics on a ten times faster time scale with an experimental limit of approximately 5 fs.Comment: 5 pages, 4 figures, new title and minor text change