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.

The chemical and structural properties of a specimen can often be inferred by determining its complex refractive index. Ellipsometry is the standard method to measure the complex refractive index [1]. In ellipsometry, the complex refractive index is retrieved by acquiring absolute reflectivity changes for different states of the incident light (varying polarization or angle of incidence). While ellipsometry works well for bulk and thin-film specimens without transverse structure, imaging an object with spatially varying refractive index is difficult. Scanning ellipsometry uses a tightly focussed beam which requires accurate knowledge of the beam properties and more complex analysis. Furthermore, the signal is averaged over the spot size, limiting spatial resolution. Other implementations like imaging ellipsometry require an imaging setup with high-NA optics, which lead to measurement errors caused by aberrations and other defects. This becomes especially problematic when decreasing the wavelength in the extreme ultraviolet (EUV) regime, to improve spatial resolution.

Lensless imaging techniques have been developed to visualize objects with high robustness and unprecedented resolution. Lensless imaging is based on the numerical reconstruction of the transmission or reflection function of a sample from optical diffraction measurements. Specifically, coherent diffractive imaging (CDI) and ptychography involve an iterative process of numerical propagation of coherent light waves between the sample and detector plane. However, in the standard propagation models, the pixel size of the reconstructed object image is typically fixed and wavelength-dependent, which limits CDI and broadband ptychography. Here we investigate three propagation models for far-field propagation that allow user-defined pixel size at the object plane. These propagators are the two-step Fresnel, scaled angular spectrum, and chirp-Z transform. We derive their analytical expressions and observe that all three models are mathematically equivalent, although they have a different physical origin. Each propagator can be written in two distinct versions, which conceptually represent propagation via different intermediate planes. We perform propagation simulations and ptychographic reconstructions on experimental data to compare the performance of these two different versions. We also investigate how sampling bandwidth requirements can affect the model accuracy due to physical errors associated with cropping of high spatial frequencies. Our results show that the choice of the intermediate plane can affect the reconstruction quality due to different sampling bandwidth requirements, which enables a wider choice of pixel sizes in the object plane. Our analysis provides guidelines for selecting an optimized object pixel size when performing reconstructions on broadband CDI and ptychography data.

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.

Ptychography is a computational imaging technique that enables the reconstruction of the amplitude and phase of an object and an illumination field using a series of recorded diffraction patterns [1]. Compared to conventional imaging techniques, ptychographic measurements offer more comprehensive information about the reconstructed object without requiring high-quality lenses, while also accommodating correction of experimental imperfections such as distance inaccuracies, angular misalignments, and other experimental errors. However, as ptychography is not a single-shot measurement technique, it is time-consuming, with a significant part of the measurement time attributed to the scanning process. Such mechanical scanning is inherently slow due to the acceleration limitations of the sample stage and the time required for stabilization [2].

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.

We show how to utilize ptychographic measurements in reflection, to obtain maps of height and complex refractive indices, using visible and extreme ultraviolet light sources. This technique enables flexible, high-resolution imaging of multi-element microstructures.