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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.17863 |
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Table of Contents:
- We introduce the two-point propagation field (TPPF), a real-valued, phase-sensitive quantity defined as the functional derivative of the single-photon detection probability with respect to an infinitesimal opaque perturbation placed between the source and detection slits. The TPPF is analytically derived and shown to exhibit a stable, high-frequency sinusoidal structure with periods of 4~7 nm near the X-ray detection slit. This structure enables shot-noise-limited displacement detection with $\sim200 pm$ precision for 6 keV X-rays, using total photon counts on the order of $1\times10^{7}$ and detector photon counting as low as 287. Beyond displacement detection, the TPPF physically performs a Fourier-Radon transformation of the projection data, providing a pathway to non-iterative frequency-domain tomography. Two conceptual strategies, a central blocker and off-axis multi-slit arrays, are estimated to lower the required incident photon budget by more than one order of magnitude each, yielding combined reductions of two to three orders of magnitude with near-term detector development. The TPPF concept, originally developed in a perturbative study of single-particle propagation, bridges quantum measurement questions with practical high-resolution X-ray physics. This work provides the foundational physics required for future discrete sampling and 3D numerical reconstruction algorithms.