考虑平衡约束的单轴高能X射线衍射层析成像：弹性残余应变解的唯一性与稳定性
Single-axis high-energy X-ray diffraction tomography for elastic residual strain: uniqueness and stability of solutions in the presence of equilibrium constraints
- The University of Newcastle（纽卡斯尔大学）
- University of Manchester（曼彻斯特大学）
- Pontificia Universidad Católica de Chile（智利天主教 Pontificia 大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究证明结合力学平衡约束后，单轴高能X射线衍射层析数据可唯一重建各向同性弹性样品的三维弹性应变，并推导了相关稳定性估计。
AI中文摘要：
已明确，高能X射线衍射产生的单轴横向射线变换层析数据不足以通用重建三维弹性应变。本文证明，结合力学平衡约束后，对于弹性常数已知、泊松比非零的各向同性弹性样品，该问题可唯一求解。基于Desai与Lionheart的重建框架（N.M. Desai, W.R.B. Lionheart，二阶张量场横向射线变换的三轴数据显式重建算法，Inverse Problems 32(11)(2016)115009），我们在傅里叶域构建该受约束单轴层析问题，证明所得系统在有限个测度为零的特征平面外处处可逆。对于有界样品，这足以确立重建的唯一性。我们进一步推导条件稳定性估计，量化各应变分量重建相关的正则性要求。
英文摘要：
It is well-established that single-axis Transverse Ray Transform tomography data from high-energy X-ray diffraction is insufficient for general reconstruction of three-dimensional elastic strain. In this paper we show that, when combined with the constraint of mechanical equilibrium, this problem becomes uniquely solvable for isotropic elastic samples with known elastic constants and non-zero Poisson's ratio. Building on the reconstruction framework of Desai and Lionheart [N.M. Desai, W.R.B. Lionheart, An explicit reconstruction algorithm for the transverse ray transform of a second rank tensor field from three axis data, Inverse Problems 32 (11) (2016) 115009], we formulate this constrained single-axis tomography problem in the Fourier domain and show that the resulting system is invertible everywhere outside a finite collection of measure zero characteristic planes. In the case of bounded samples, this is sufficient to establish uniqueness for reconstructions. We further derive conditional stability estimates that quantify the regularity requirements associated with reconstruction of the various strain components.
