Optimal Null-Constrained Source-Basis Sensing in a Time-Reversed Young Interferometer
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915933247766528 |
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| author | Wen, Jianming |
| author_facet | Wen, Jianming |
| contents | We develop a general theory of null-constrained parameter estimation in a time-reversed Young (TRY) interferometer, where measurement is performed through programmable source-basis encoding with a fixed detector. We address the fundamental question of how to design source patterns that enforce a true metrological null -- vanishing nominal response at the operating point -- while preserving finite first-order sensitivity to the parameter. Under a general shot-noise-limited channel model, we show that the optimal null-constrained receiver is obtained by projecting the derivative response onto the subspace orthogonal to the nominal background in the inverse-noise metric. This yields a constructive solution in which the optimal source-basis code is given by the inverse-noise-weighted derivative response with its background-parallel component removed. We further derive an exact and universal information-retention law: the locally accessible Fisher information is reduced by a factor $1-χ^2$, where $χ$ quantifies the inverse-noise overlap between the nominal and derivative response vectors. This result establishes a precise geometric interpretation of the cost of null enforcement. Numerical examples demonstrate the null-coded TRY receivers can retain nearly the full local information and can be accurately implemented using binary and positive-only source patterns. These findings identify source-basis null engineering as a distinct and practically viable modality for derivative-mode sensing, with implications for superresolution metrology and programmable optical measurement architectures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_10320 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Null-Constrained Source-Basis Sensing in a Time-Reversed Young Interferometer Wen, Jianming Optics Data Analysis, Statistics and Probability Instrumentation and Detectors Quantum Physics We develop a general theory of null-constrained parameter estimation in a time-reversed Young (TRY) interferometer, where measurement is performed through programmable source-basis encoding with a fixed detector. We address the fundamental question of how to design source patterns that enforce a true metrological null -- vanishing nominal response at the operating point -- while preserving finite first-order sensitivity to the parameter. Under a general shot-noise-limited channel model, we show that the optimal null-constrained receiver is obtained by projecting the derivative response onto the subspace orthogonal to the nominal background in the inverse-noise metric. This yields a constructive solution in which the optimal source-basis code is given by the inverse-noise-weighted derivative response with its background-parallel component removed. We further derive an exact and universal information-retention law: the locally accessible Fisher information is reduced by a factor $1-χ^2$, where $χ$ quantifies the inverse-noise overlap between the nominal and derivative response vectors. This result establishes a precise geometric interpretation of the cost of null enforcement. Numerical examples demonstrate the null-coded TRY receivers can retain nearly the full local information and can be accurately implemented using binary and positive-only source patterns. These findings identify source-basis null engineering as a distinct and practically viable modality for derivative-mode sensing, with implications for superresolution metrology and programmable optical measurement architectures. |
| title | Optimal Null-Constrained Source-Basis Sensing in a Time-Reversed Young Interferometer |
| topic | Optics Data Analysis, Statistics and Probability Instrumentation and Detectors Quantum Physics |
| url | https://arxiv.org/abs/2604.10320 |