Fundamental bounds on the precision of classical phase microscopes

TL;DR

This paper provides a theoretical framework to compare and optimize the phase estimation precision of classical phase microscopes, highlighting the importance of wavefront shaping for achieving optimal accuracy.

Contribution

It introduces a general method to calculate the Cramér-Rao bound for linear optical systems, guiding the design of more precise classical phase microscopes.

Findings

Wavefront shaping enhances phase measurement precision.

The framework applies to various microscopy techniques.

Optimal design requires wavefront optimization.

Abstract

A wide variety of imaging systems have been designed to measure phase variations, with applications from physics to biology and medicine. In this work, we theoretically compare the precision of phase estimations achievable with classical phase microscopy techniques, operated at the shot-noise limit. We show how the Cram\'{e}r-Rao bound is calculated for any linear optical system, including phase-contrast microscopy, phase-shifting holography, spatial light interference microscopy, and local optimization of wavefronts for phase imaging. Through these examples, we demonstrate how this general framework can be applied for the design and optimization of classical phase microscopes. Our results show that wavefront shaping is required to design phase microscopes with optimal phase precision.