Energy Time Ptychography for one-dimensional phase retrieval

TL;DR

This paper introduces a novel energy-time ptychography method for one-dimensional phase retrieval in X-ray scattering, enabling phase and spectral information extraction from single measurements using overlapping data.

Contribution

It presents a new ptychographic approach for phase retrieval in nuclear resonant scattering, overcoming traditional bandwidth limitations and enhancing sensitivity with synchrotron X-ray sources.

Findings

Successfully retrieves phase and transmission spectrum from single measurements.

Overcomes gamma-ray source bandwidth limitations.

Enhances sensitivity and data acquisition speed in nuclear resonant scattering.

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. We leverage the M\"ossbauer 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 with modern X-ray sources and M\"ossbauer isotopes.