Optimum classical beam-position sensing

This Letter addresses a canonical imaging problem: how to estimate a small transverse displacement of a laser beam as precisely as possible. This problem is central to many applications, including scanning-probe atomic force microscopy, free-space optical communication, and optomechanics. Based on the geometry of the imaging system, the center wavelength of the laser probe, and the return-path propagation length, the authors identify the optimal spatial mode in which to excite a laser probe, when paired with the most sensitive receiver allowed by quantum estimation theory. Several phase-sensitive, mode-resolving receivers that achieve the mentioned quantum precision limit are presented.