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| Preprint | PUBDB-2025-01356 |
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2025
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Please use a persistent id in citations: doi:10.3204/PUBDB-2025-01356
Report No.: arXiv:2506.00492
Abstract: 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 of ${}^{57}\mathrm{Fe}$. Leveraging the Mössbauer effect, where ${}^{57}\mathrm{Fe}$ nuclei absorb or emit radiation without energy loss to the lattice, sensitivity to their magneto-chemical environments is achieved. 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 overlapping measurements to retrieve both the transmission spectrum and phase of the nuclei, similar to ptychographic phase retrieval in imaging. Our robust approach can overcome bandwidth limitations of gamma-ray sources, opening new research directions with modern X-ray sources and Mössbauer isotopes other than ${}^{57}\mathrm{Fe}$.
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