Ptychography is a powerful computational imaging technique that reconstructs both the complex object function and the illumination probe from overlapping diffraction patterns. While it provides high-resolution, aberration-corrected imaging, its reliance on stepwise mechanical scanning limits acquisition speed. In this work, we propose a fly-scan ptychographic approach that enables continuous sample translation along arbitrary trajectories, significantly reducing measurement time. To account for motion-induced decoherence, we incorporate an object mode decomposition model combined with automatic differentiation for accurate trajectory correction. This method enables diffraction-limited reconstructions without the need for high-speed tracking, allowing fast and precise measurements using standard ptychographic setups.

We present a maximum-likelihood estimation (MLE) framework tailored to event-driven detectors to perform computational image reconstruction and phase retrieval. Using Poissonian photon statistics, we built an event-based loss function that maximizes the probability of having the set of events and non-events given the initial parameters. Our loss function can be utilized in both optical and electron ptychography. We demonstrate experimental reconstructions using data acquired with a Timepix3 detector.

Microscopy with table-top high-harmonic generation (HHG) sources enable high-resolution imaging with excellent material contrast, due to the short wavelength and numerous element-specific absorption edges available in this spectral range. However, accurate characterization of dispersive samples in terms of composition and thickness remains challenging due to the limitations of lens-based optics in this spectral range. Here, we performed spectrally resolved lensless imaging using multiple high harmonics. The diffractive shearing interferometry reconstruction serves as a foundational step for element-sensitive metrology, while ptychographic reconstruction enabled the retrieval of high-precision spectral imaging and quantitative thickness mapping. Our non-destructive method offers a powerful tool to extract both the material composition and layer thicknesses of complex nanostructured samples.

Microscopy with extreme ultraviolet (EUV) radiation enables high-resolution imaging with excellent material contrast because of the short wavelength and numerous element-specific absorption edges available in this spectral range. Table-top high-harmonic generation (HHG) sources offer the additional advantage of generating wide spectra in the EUV and soft X-ray range, making them inherently well-suited for characterizing nanostructures. As lens-based EUV imaging is challenging, lensless imaging methods based on coherent diffraction offer practical advantages and can even allow for quantitative phase measurements of object transmission functions. Here, spectrally resolved lensless imaging of a dispersive sample is performed using multiple high harmonics based on different HHG-based measurement concepts. We characterize the structure and composition of a three-element spiral-shaped object in transmission using multiwavelength diffractive shearing interferometry, as well as single-wavelength structured-illumination ptychography. We find that both methods are capable of retrieving spatially resolved element maps and the corresponding layer thicknesses. Comparing methods, ptychography provides superior accuracy in determining layer thickness, even for stacks of multiple materials, using an extended scattering quotient. These measurement and analysis concepts thus provide a nondestructive way to accurately extract information on the material composition and layer thicknesses of complex nanostructured samples.