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'.