Single-shot imaging with randomized structured illumination at a free electron laser

Stroboscopic nanoscale imaging with free electron laser light is revolutionizing our understanding of fast dynamics in heterogeneous systems. The short wavelength of X-ray and extreme ultraviolet radiation makes it possible to achieve nanoscale resolution, while resonance with atomic transitions gives access to electronic and magnetic degrees of freedom. Here, we report on our implementation of a recently developed imaging method, randomized probe imaging, at a free electron laser. The advantage of randomized probe imaging over existing methods is its compatibility both with extended and strongly scattering samples. Our implementation delivers robust single-shot reconstructions at up to a full-pitch resolution of 400 nm over a field of view with a 40 μm diameter. We also demonstrate single-shot imaging of magnetic domain structures using circular dichroism at resonance, paving the way to future time-resolved studies of magnetic dynamics, shock physics, and the dynamics of collective electronic phases.

💡 Research Summary

This paper presents the first implementation of Randomized Probe Imaging (RPI) at a free‑electron laser (FEL) and demonstrates its capability to produce high‑quality, single‑shot images of both structural and magnetic samples. RPI uses a randomized zone plate (RZP) to generate a speckle‑like structured illumination on the specimen. The illumination field is first characterized by a conventional ptychography scan, providing an accurate probe function that is then fed into the RPI reconstruction algorithm. In the experiment, 20.8 nm, ~60 fs FEL pulses from the FERMI facility were directed through an RZP whose outer zone width was 200 nm, setting a theoretical full‑pitch resolution of 400 nm. A gold Siemens star on a 30 nm Si₃N₄ membrane served as a structural test object, while a Pt/Co/Ta multilayer film was used to assess magnetic contrast via X‑ray magnetic circular dichroism at the Co M₃ edge.

Each single‑shot diffraction pattern contained roughly 1.2 × 10⁷ photons (≈490 photons per 200 nm resolution element). Using the cdtools package with automatic differentiation, three incoherent probe modes, position refinement, background modeling, and a super‑resolution scheme, the authors reconstructed the probe with a 73 nm pixel pitch. The RPI algorithm, which imposes a band‑limiting constraint on the object and incorporates the known probe, was then applied to 650 × 650 pixel objects (160 nm pixel size).

Across 128 consecutive shots, the reconstructions were remarkably consistent. Spectral signal‑to‑noise ratio (SSNR) analysis showed that the vast majority of images surpassed the design resolution of 400 nm; the worst case was 420 nm. Averaging up to 64 shots further improved SSNR, reaching a pixel‑level SSNR of ~3 and reducing the normalized mean‑squared error to just under 5 %. The authors also demonstrated that the periodic spokes of the Siemens star are clearly resolved at the 400 nm pitch, confirming the claimed resolution.

For magnetic imaging, left‑ and right‑hand circularly polarized FEL pulses were used. Ptychography reconstructions displayed a clear contrast reversal, confirming magnetic origin. Single‑shot RPI under left‑hand circular polarization achieved a full‑pitch resolution of 2.22 µm; averaging 12 or more shots pushed the resolution to the pixel‑limited 1.04 µm, with both amplitude and phase maps revealing the domain structure.

A comprehensive literature survey of 102 datasets from 97 FEL phase‑imaging papers (covering CDI, ILH, FTH, and SSP) was performed. The authors extracted the highest reported resolution and space‑bandwidth product (SBP) for each method. RPI occupies a unique region of high SBP combined with moderate resolution: its structural images have an SBP of 2.5 × 10⁴ (equivalent to a 160 × 160 pixel image), while magnetic images reach SBPs of 3.6 × 10³ (≈60 × 60 pixels) for 64‑shot averages and 8.0 × 10² (≈28 × 28 pixels) for single shots. No FEL CDI image, and only one FTH image, surpasses this SBP, and RPI outperforms the current state‑of‑the‑art single‑shot ptychography (SSP) in both resolution and SBP.

In summary, the work demonstrates that RPI is a robust, mask‑less, and experimentally simple technique that works equally well for extended, strongly scattering, and weak‑contrast magnetic samples. Its compatibility with single‑shot operation, modest photon fluence requirements, and straightforward beamline geometry make it especially attractive for time‑resolved studies of ultrafast magnetic dynamics, shock‑wave propagation, and collective electronic phase transitions at FEL facilities.