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, omega(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 omega(max) for observing the amplitude of motion. In the limit where omega(max) approximate to omega(0), the smallest observable amplitude of motion is A= 2 pi/Q(max). In the limit where omega(max) >= 2 omega(0), A <= 2 pi/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'.