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, ω₀, about an equilibrium position, R₀, 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 ≈  ω₀, the smallest observable amplitude of motion is A = 2 π/ Q_max. In the limit where ω_max≥2 ω₀, 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'.