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    Differential source-pattern encoding for enhanced local displacement estimation in a time-reversed Young interferometer

    Jianming Wen*

    • Department of Electrical and Computer Engineering, Binghamton University, Binghamton, New York 13902, USA

    • *Contact author: jwen7@binghamton.edu

    Phys. Rev. Applied 26, 044066 – Published 22 October, 2026

    DOI: https://doi.org/10.1103/bc7b-blgt

    Abstract

    We develop a differential source-pattern protocol for local displacement estimation in a time-reversed Young interferometer, where the source plane is used not merely as a scan coordinate but as a programmable measurement pattern. A signed antisymmetric pattern is implemented by two sequential positive-only source branches, as required by intensity-only source hardware, and the two branch counts are retained as the complete measurement record. Near a quadrature operating point, the local differential signal separates into an envelope-gradient term and a time-reversed-Young interference-gradient term. We connect the localized response kernel to a concrete scanned-excitation measurement of a displaced fluorescent, quantum-dot, or transmissive microfeature and give a representative experimental parameter set. We distinguish the exact finite-spacing response from its derivative approximation, enforce an equal launched-photon budget in all comparisons, and derive the Fisher information both for the full Poisson count pair and for the scalar difference, which follows a Skellam distribution. The numerical results show a clear advantage over a fixed raster sample in the representative regime, while the additional interferometric contribution can enhance, leave unchanged, or suppress the information relative to a matched noninterferometric differential measurement. An optimized direct measurement remains the stronger ideal benchmark when all nuisance quantities are known. The results therefore establish practical design rules for robust local displacement metrology rather than a universal claim of two-feature superresolution.

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