TY - JOUR AU - Negi, Ankita AU - Lohse, Leon Merten AU - Velten, Sven AU - Sergeev, Ilya AU - Leupold, Olaf AU - Sadashivaiah, Sakshath AU - Bessas, Dimitrios AU - Chumakov, Aleksandr AU - Brandt, Christina AU - Bocklage, Lars AU - Meier, Guido AU - Roehlsberger, Ralf TI - Energy Time Ptychography for one-dimensional Phase Retrieval JO - Optica VL - 12 IS - 9 SN - 2334-2536 CY - Washington, DC PB - Optica M1 - PUBDB-2025-01379 SP - 1529 - 1538 PY - 2025 N1 - This article has been published. AB - Phase retrieval is at the heart of adaptive optics and modern high-resolution imaging. Without phase information, optical systems are limited to intensity-only measurements, hindering full reconstruction of object structures and wavefront dynamics essential for advanced applications. Here, we address a one-dimensional phase problem linking energy and time, which arises in X-ray scattering from ultrasharp nuclear resonances. We leverage the Mössbauer effect, where nuclei scatter radiation without energy loss to the lattice and are sensitive to their magneto-chemical environments. Rather than using traditional spectroscopy with radioactive gamma-ray sources, we measure nuclear forward scattering of synchrotron X-ray pulses in the time domain, providing superior sensitivity and faster data acquisition. Extracting spectral information from a single measurement is challenging due to the missing phase information, typically requiring extensive modeling. Instead, we use multiple energetically overlapping measurements to retrieve both the transmission spectrum and the phase of the scattering response, similar to ptychographic phase retrieval in imaging. Our robust approach can overcome the bandwidth limitations of gamma-ray sources, opening new research directions, to the best of our knowledge, with modern X-ray sources and Mössbauer isotopes. LB - PUB:(DE-HGF)16 DO - DOI:10.1364/OPTICA.568949 UR - https://bib-pubdb1.desy.de/record/626387 ER -