Suppose you wanted to do a time-resolved experiment with a molecular beam traveling at, say, 300 m/s involving a mobile excitation (pump) laser that scans across the length of the molecular beam and a stationary detector. So the time-resolution of the experiment depends on how precisely the position of the excitation laser can be fine-tuned, e.g. if the laser can be tuned in the millimeter range, then the time resolution would be in the microsecond time scale. (Don't worry about the path length of the beam to the detector. It's reasonable to imagine that one would be interested in obtaining ns accuracy for a system in which nothing happens for several ms). Also suppose that the velocity distribution of the particles in the beam have a sharp velocity distribution, such that ∆v/v≈0.01. My question is, then, to what degree of accuracy can the excitation laser's position be fine-tuned using modern optics? Obviously the intensity, wavelength, and type of laser will have some effect on the answer, but I'm interested in a ballpark figure anyway. The obvious follow-up question is how, experimentally, does one tune the laser to that level of accuracy? Would relativistic effects start to be an issue at some point? And is the velocity distribution (or, for that matter, the measurement of the velocity) actually going to end up being the limiting factor on time resolution in the end?
Thanks in advance for your answers.