Propagators with user-defined object-plane pixel size for ptychography

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 complex-valued transmission or reflection function of the sample under investigation from optical diffraction measurements. Specifically, in coherent diffractive imaging (CDI) and ptychography, the reconstruction is the result of an iterative process of numerical forward and backward propagation of coherent light waves between the sample plane and a detector plane. However, in the standard propagation models the pixel size of the reconstructed object image is typically fixed and wavelength dependent. This property forms a limitation for CDI and ptychography with broadband illumination, and limits flexibility in general. Here we compare three propagation models for far-field propagation that allow user-defined pixel size at the object plane. We derive their analytical expressions and observe that all three models are in principle equivalent. 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 different propagator versions. Our results show that the choice of intermediate plane can affect the reconstruction quality due to less strict 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.