A Concept of Two-Point Propagation Field of a Single Photon: A Way to X-ray Picometer Displacement Detection and Nanometer Resolution 3D X-ray Micro-Tomography

TL;DR

The paper introduces the two-point propagation field (TPPF), a phase-sensitive quantity for single-photon X-ray detection, enabling picometer displacement sensitivity and Fourier-based tomography with potential for significant photon budget reduction.

Contribution

It presents the TPPF concept, analytically derived and shown to enable high-precision displacement detection and non-iterative tomography, bridging quantum measurement and high-resolution X-ray imaging.

Findings

Achieves ~200 pm displacement detection precision with 6 keV X-rays.

Demonstrates TPPF's Fourier-Radon transformation capability for tomography.

Proposes strategies to reduce photon budget by over two orders of magnitude.

Abstract

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.