Dynamic scattering and imaging with coherent, ultrafast, extreme-ultraviolet (EUV) light sources can resolve charge, phonon, and spin processes on their intrinsic length and time scales. However, while lensless computational imaging approaches have been highly successful in static EUV imaging, the data and computational requirements for phase reconstruction are obstacles to quickly acquiring a large series of frames to reconstruct fast time-dependent sample dynamics. In this paper, we demonstrate a noniterative, computational technique for reconstructing dynamic 1D images of the average unit cell in a time-varying periodic sample. The technique can be applied even to a preexisting time series of diffraction data without the Nyquist sampling requirement common to computational imaging and works by analyzing the changing intensities of the far field diffracted orders. Starting from a system of equations relating small changes in far field diffraction to phase and amplitude perturbations at the sample plane, it is shown that under certain conditions, changes to the $n$th diffracted order map exclusively onto the $n$th Fourier component of the perturbation via a closed-form relation. We show through rigorous coupled-wave analysis simulations that our method can provide a good approximation even outside the scalar diffraction theory framework in which it is derived. Finally, we experimentally demonstrate this reconstruction method by exciting 1D nickel nanowires on a diamond substrate using an infrared laser pump pulse and measuring their relaxation using a time-delayed EUV probe pulse to visualize nanoscale phonon dynamics.

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• Crystal structure
• Imaging & optical processing
• Interference & diffraction of light
• Lattice dynamics
• Phonons
• High-harmonic generation
• Light scattering
• Ultrafast femtosecond pump probe