Quantum-Noise Limited Distance Resolution of Optical Range Imaging Techniques

The most common optical distance imaging methods (triangulation, interferometry and time-of-flight ranging) can all be described in a unified way as linear shift-invariant systems in which the determination of distance corresponds to the measurement of a spatial or temporal phase. Since the ultimate precision of such a phase measurement is limited by quantum noise of the involved photons or photocharges, the eventual distance resolution of the three optical ranging methods depends in the same way on quantum noise. Evidence from literature supports our basic assertion that photon and photocharge numbers have a Poisson distribution under most experimental conditions. This allows us to derive our main result that the quantum-noise limited distance resolution of the three optical ranging methods is proportional to the inverse of the signal's modulation amplitude times the square root of the background level. The equation for the precision of the three optical distance measurement techniques contains the method's experimental parameters in a single factor, from which the optimum distance range of the three techniques can easily be deduced: 1 nm-1 mum for interferometry, 1 mum-10 m for triangulation, > 0.1 m for time-of-flight ranging, if visible or near infrared light is used.