Periodogram-Based Detection of Unknown Frequencies in Time-Resolved Scanning Transmission X-ray Microscopy

Pump-probe time-resolved imaging is a powerful technique that enables the investigation of dynamical processes. Signal-to-noise and sampling rate restrictions normally require that cycles of an excitation are repeated many times with the final signal reconstructed using a reference. However, this approach imposes restrictions on the types of dynamical processes that can be measured, namely, that they are phase locked to a known external signal (e.g., a driven oscillation or impulse). This rules out many interesting processes such as auto-oscillations and spontaneously forming populations, e.g., condensates. In this work we present a method for time-resolved imaging, based on the Schuster periodogram, that allows for the reconstruction of dynamical processes where the intrinsic frequency is not known. In our case we use time of arrival detection of X-ray photons to reconstruct magnetic dynamics without using a priori information on the dynamical frequency. This proof-of-principle demonstration will allow for the extension of pump-probe time-resolved imaging to the important class of processes where the dynamics are not locked to a known external signal and in its presented formulation can be readily adopted for X-ray imaging and also adapted for wider use.