Intensity-Based Axial Localization at the Quantum Limit

TL;DR

This paper establishes the fundamental limits of axial localization precision using intensity measurements, demonstrating that optimal placement of a camera allows reaching these limits without complex detection schemes.

Contribution

It derives the quantum-limited bounds for axial localization and shows they can be achieved with simple intensity scans at optimal detection planes.

Findings

Achieved axial resolution three orders of magnitude below classical depth of focus.

Identified two optimal detection planes for maximum localization precision.

Validated theoretical bounds with experimental demonstration.

Abstract

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.