Intensity-Based Axial Localization at the Quantum Limit

We derive fundamental precision bounds for single-point axial localization. For the case of a Gaussian beam, this ultimate limit can be achieved with a single intensity scan, provided the camera is placed at one of two optimal transverse detection planes. Hence, for axial localization there is no need of more complicated detection schemes. The theory is verified with an experimental demonstration of axial resolution three orders of magnitude below the classical depth of focus.