Physical Fidelity of Wave-Based Inverse Problems under Broken Time-Reversal Symmetry
Abstract
Modern coherent imaging commonly treats defocus interference as an undesirable artifact to be suppressed. Here, we show that this interference is instead a deterministic projection shadow associated with broken time-reversal symmetry (TRS) under finite-aperture observation. The resulting non-unitary observation operator imposes irretrievable information loss, making this shadow an unavoidable coherent residual. We demonstrate that suppressing this residual beyond the measurement support can yield physically inconsistent reconstructions by assigning unconstrained components within the null space, thereby disrupting the propagation of the reconstructed complex field. We term this failure mode physical overfitting and introduce the complex-field TRS residual metric, R_TRS(z). By using the measured axial evolution of the projection shadow as a z-resolved physical reference, the metric extends fidelity assessment from two-dimensional (2D) detector-plane agreement to propagation-resolved three-dimensional (3D) complex-field consistency. These results establish a physical constraint on phase-space retrieval and wave-based inverse reconstruction.
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BibTeX
@misc{ou2026physical,
title = {{Physical Fidelity of Wave-Based Inverse Problems under Broken Time-Reversal Symmetry}},
author = {Haiyan Ou and Jiajia Duan and Edmund Y. Lam and Bingzhong Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28266},
eprint = {2609.28266},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28266},
}
RIS
TY - UNPB
TI - Physical Fidelity of Wave-Based Inverse Problems under Broken Time-Reversal Symmetry
AU - Haiyan Ou
AU - Jiajia Duan
AU - Edmund Y. Lam
AU - Bingzhong Wang
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28266
UR - https://arxiv.org/abs/2609.28266
AB - Modern coherent imaging commonly treats defocus interference as an undesirable artifact to be suppressed. Here, we show that this interference is instead a deterministic projection shadow associated with broken time-reversal symmetry (TRS) under finite-aperture observation. The resulting non-unitary observation operator imposes irretrievable information loss, making this shadow an unavoidable coherent residual. We demonstrate that suppressing this residual beyond the measurement support can yield physically inconsistent reconstructions by assigning unconstrained components within the null space, thereby disrupting the propagation of the reconstructed complex field. We term this failure mode physical overfitting and introduce the complex-field TRS residual metric, R_TRS(z). By using the measured axial evolution of the projection shadow as a z-resolved physical reference, the metric extends fidelity assessment from two-dimensional (2D) detector-plane agreement to propagation-resolved three-dimensional (3D) complex-field consistency. These results establish a physical constraint on phase-space retrieval and wave-based inverse reconstruction.
ER -