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.

We report on a method that allows microscopic image reconstruction from extreme-ultraviolet diffraction patterns without the need for object support constraints or other prior knowledge about the object structure. This is achieved by introducing additional diversity through rotation of an object in a rotationally asymmetric probe beam, produced by the spatial interference between two phase-coherent high-harmonic beams. With this rotational diffractive shearing interferometry method, we demonstrate robust image reconstruction of microscopic objects at wavelengths around 30 nm, using images recorded at only three to five different object rotations.