Quantum Limits of Passive Optical Surface Metrology and Defect Detection

TL;DR

This paper establishes quantum limits for passive optical surface metrology, demonstrating that spatial mode sorting can significantly improve defect detection and feature estimation beyond classical methods.

Contribution

It introduces a quantum statistical framework for surface metrology, deriving ultimate bounds and optimal measurements for defect detection and geometrical feature estimation.

Findings

Spatial mode sorting enables near-quantum-limited estimation of surface crack features.

Enhanced defect detectability compared to direct imaging.

Framework applicable to sub-diffraction surface feature characterization.

Abstract

We develop a quantum statistical framework for passive optical surface metrology. Modelling a surface as an incoherent ensemble of point emitters imaged through a diffraction-limited system, we employ techniques from quantum parameter estimation and hypothesis testing to derive ultimate bounds for jointly estimating geometrical features and for deciding the presence or absence of surface defects, and we identify optimal measurements from the geometry of the point-spread-function manifold. As a representative application, we analyse a minimal surface crack model based on three point sources and show that spatial mode sorting can simultaneously enable near-quantum-limited estimation of crack width and depth and markedly enhanced detectability of the crack, compared with direct imaging. Our results pave the way towards enhanced optical inspection and characterisation of sub-diffraction surface features by probing a limited number of spatial modes without any illumination control.