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

• URL: http://arxiv.org/abs/2603.27407v1
• Date: Sat, 28 Mar 2026 21:05:36 GMT
• Title: Differential source-basis encoding for superresolved parameter estimation in a time-reversed Young interferometer
• Abstract summary: We develop a differential source-encoding protocol for local parameter estimation in a time-reversed Young interferometer.<n>In the local regime, the differential signal separates naturally into an envelope-gradient term, which is also present in noninterferometric differential sensing.<n>This decomposition identifies the physical origin of the interferometric advantage and clarifies why it is regime dependent rather than universal.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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 Cramér--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.

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