From Random Fringes to Deterministic Response: Statistical Foundations of Time-Reversed Young Interferometry

TL;DR

This paper reveals that time-reversed Young interferometry exhibits a deterministic fringe response conditioned on source position, contrasting with traditional statistical interpretations, and supports advanced sensing techniques.

Contribution

It introduces a new statistical framework for time-reversed Young interferometry, highlighting its deterministic response and practical advantages over classical interpretations.

Findings

Fringe response is a conditional, deterministic function of source position.

Noise affects only estimation precision, not the fringe itself.

Supports calibration, lock-in readout, null-fringe sensing, and superresolution.

Abstract

Young interference is usually read as the gradual statistical accumulation of random detection events. Here we show that a time-reversed Young (TRY) geometry has a different statistical character: the fringe is not a marginal distribution of detector positions, but a conditional response indexed by a programmed source coordinate. With a fixed detector and a scanned source basis, the observable is an operational hybrid correlator between detector signal and source label. The resulting interference is deterministic at the response-function level, while noise enters only through estimation precision. We formulate this distinction using Fisher information, estimator variance, and noise scaling, clarifying why TRY naturally supports calibration, lock-in readout, null-fringe sensing, and source-plane superresolution.