X-ray ptychography using physics-enhanced implicit neural representations

We introduce the Deep Ptychographic Iterative Engine (DeePIE), which leverages physics-enhanced implicit neural representations (INRs) for robust ptychographic reconstruction. DeePIE represents the complex object field via two coordinate-based networks that map each spatial coordinate directly to its corresponding amplitude and phase value, while the probe field is represented as a set of learnable parameters. The two networks and the probe field are jointly optimized directly from the measured diffraction patterns through the X-ray ptychographic forward model, without relying on ground-truth images. Both simulation studies and real X-ray ptychography experiments at 1.77 nm (700 eV) on biological samples consistently demonstrate that DeePIE delivers superior reconstruction stability and image quality compared to conventional methods. Moreover, DeePIE allows for arbitrary-scale upsampling due to the inherently continuous property of INRs. These findings demonstrate that DeePIE has strong potential for applications such as semiconductor inspection as well as life and materials sciences.