Time-resolved XPCS analysis across broad time-scales using multi-tau two-time correlations

We present a multi-tau two-time correlation (MT-2TC) analysis for X-ray photon correlation spectroscopy that enables efficient analysis of large-scale, high-frame-rate datasets collected at modern synchrotron beamlines. The method combines the advantages of the multi-tau autocorrelation and two-time correlation approaches, maintaining sensitivity to non-stationary dynamics while reducing computational complexity and memory requirements from quadratic to linear scaling with the number of frames. This formulation not only improves processing efficiency but also extends the accessible correlation time range, allowing analysis over much broader time scales than conventional techniques. The algorithm is implemented in both dense and sparse data representations, allowing direct processing of sparsified photon-counting data from ultra-fast detectors. We demonstrate the performance of the MT-2TC scheme using experiments on a bulk GeO₂ glass and on a v-Ta₂O₅ thin film conducted at the ESRF ID10 beamline with a 1 kHz Eiger 4M detector. The results show perfect agreement with standard correlation analyses while extending the temporal correlation range by nearly two decades and improving signal-to-noise ratios at long lag times. The MT-2TC approach thus provides a scalable and flexible tool for XPCS at fourth-generation synchrotrons, where enhanced coherent flux and detector speed demand correlation strategies capable of spanning microsecond-to-day timescales.