On the limits of observing motion in time-resolved X-ray scattering

Limits on the ability of time-resolved X-ray scattering (TRXS) to observe harmonic motion of amplitude, A and frequency, ω 0 , about an equilibrium position, R 0 , are considered. Experimental results from a TRXS experiment at the LINAC Coherent Light Source are compared to classical and quantum theories that demonstrate a fundamental limitation on the ability to observe the amplitude of motion. These comparisons demonstrate dual limits on the spatial resolution through Q max and the temporal resolution through ω max for observing the amplitude of motion. In the limit where ω max  ≈  ω 0 , the smallest observable amplitude of motion is A  = 2 π / Q max . In the limit where ω max ≥2 ω 0 , A ≤2 π / Q max is observable provided there are sufficient statistics. This article is part of the theme issue ‘Measurement of ultrafast electronic and structural dynamics with X-rays’.