Coherent diffractive imaging of graphite nanoparticles using a tabletop EUV source

Coherent Tabletop EUV Ptychography of Nanopatterns

Coherent diffraction imaging (CDI) or lensless X-ray microscopy has become of great interest for high spatial resolution imaging of, e.g., nanostructures and biological specimens. There is no optics required in between an object and a detector, because the object can be fully recovered from its far-field diffraction pattern with an iterative phase retrieval algorithm. Hence, in principle, a sub-wavelength spatial resolution could be achieved in a high-numerical aperture configuration. With the advances of ultrafast laser technology, high photon flux tabletop Extreme Ultraviolet (EUV) sources based on the high-order harmonic generation (HHG) have become available to small-scale laboratories. In this study, we report on a newly established high photon flux and highly monochromatic 30 nm HHG beamline. Furthermore, we applied ptychography, a scanning CDI version, to probe a nearly periodic nanopattern with the tabletop EUV source. A wide-field view of about 15 × 15 μm was probed with a 2.5 μm−diameter illumination beam at 30 nm. From a set of hundreds of far-field diffraction patterns recorded for different adjacent positions of the object, both the object and the illumination beams were successfully reconstructed with the extended ptychographical iterative engine. By investigating the phase retrieval transfer function, a diffraction-limited resolution of reconstruction of about 32 nm is obtained.

Phase retrieval of coherent diffractive images with global optimization algorithms

Coherent diffractive imaging (CDI) or lensless microscopy has recently been of great interest as a promising alternative to electron microscopy in achieving atomic spatial resolution. Reconstruction of images in real space from a single experimental diffraction pattern in CDI is based on applying iterative phase-retrieval (IPR) algorithms, such as the hybrid input–output and the error reduction algorithms. For noisy data, these algorithms might suffer from stagnation or trapping in local minima. Generally, the different local minima have many common as well as complementary features and might provide useful information for an improved estimate of the object. Therefore, a linear combination of a number of chosen minima, termed a basis set, gives an educated initial estimate, which might accelerate the search for the global solution. In this study, a genetic algorithm (GA) is combined with an IPR algorithm to tackle the stagnation and trapping in phase-retrieval problems. The combined GA–IPR has been employed to reconstruct an irregularly shaped hole and has proven to be reliable and robust. With the concept of basis set, it is strongly believed that many effective local and global optimization frameworks can be combined in a similar manner to solve the phase problem.