Differential source-basis encoding for superresolved parameter estimation in a time-reversed Young interferometer

TL;DR

This paper introduces a differential source-encoding protocol for enhanced local parameter estimation in a time-reversed Young interferometer, leveraging programmable source patterns to improve measurement sensitivity.

Contribution

It presents a novel differential encoding method that exploits the source plane as a measurement basis, providing a physical understanding of interferometric advantages and demonstrating improved estimation performance.

Findings

Strong and robust gain over raster sampling in numerical examples.

Interferometric advantage depends on the parameter regime, not universal.

Time-reversed Young geometry is a practical platform for differential interferometric metrology.

Abstract

We develop a differential source-encoding protocol for local parameter estimation in a time-reversed Young interferometer, where the source plane is used not merely as a scan coordinate but as a programmable measurement basis. Two sequential positive-only source patterns implement an antisymmetric differential probe about a chosen operating point, converting the deterministicc source-coordinate response into a derivative-gradient sensing channel. In the local regime, the differential signal separates naturally into an envelope-gradient term, which is also present in noninterferometric differential sensing, and an interference-gradient term, which is specific to the time-reversed Young fringe law. This decomposition identifies the physical origin of the interferometric advantage and clarifies why it is regime dependent rather than universal. Using a shot-noise-limited Poisson model, we derive the corresponding Fisher information and Cram\'er--Rao bounds and compare the protocol with raster sampling in the same geometry and with a matched noninterferometric differential baseline. Representative numerical examples show a strong and robust gain over raster sampling, while the additional improvement from the time-reversed Young interference is parameter dependent but can be substantial in favorable regimes. The results establish the time-reversed Young geometry as a practically simple platform for programmable differential interferometric metrology.