AI 中文总结
本研究推导三维空间不变成像系统中任意强度不平衡非相干点源的量子极限距离精度，揭示亚瑞利区域距离信息由点扩散函数二阶位移响应张量决定，建立其与高斯分布几何的联系，提供提升分辨率的策略。
AI 中文摘要
量子超分辨研究表明，传统成像中低于瑞利极限时分离灵敏度的消失，并不一定意味着光场信息的根本性损失。然而，三维成像系统中两个非相干点源间物理距离估计的量子极限，及其与点扩散函数空间结构的依赖关系，在很大程度上仍属未知。本研究推导了三维空间不变成像系统中，具有任意强度不平衡的两个非相干点源间全距离估计的量子极限精度。研究表明，亚瑞利区域内的距离信息仍有限，且由点扩散函数的二阶位移响应张量决定；该张量的本征系统确定了两个源之间的最优相对取向，点扩散函数的反射对称性可进一步为识别最优取向提供简化方法。此几何结构具有坐标不变性，提供了通过物理旋转各向异性成像系统，使其最优主响应方向与源位移对齐来提升分辨率的直接策略。对于一般三维高斯点扩散函数，响应张量与逆空间协方差成正比，建立了量子极限距离精度与高斯分布几何之间的直接联系。
英文摘要
Quantum superresolution reveals that the vanishing of separation sensitivity in conventional imaging below the Rayleigh limit does not necessarily indicate a fundamental loss of information in the optical field. However, the quantum limit for estimating the physical distance between two incoherent point sources in three-dimensional imaging systems and its dependence on the spatial structure of the point-spread function remains largely unknown. In this work, we derive the quantum-limited precision for estimating the full distance between two incoherent point sources with arbitrary intensity imbalance in a three-dimensional spatially invariant imaging system. We show that the distance information remains finite in the sub-Rayleigh regime and is governed by the second-order displacement-response tensor of the point-spread function. The eigensystem of this tensor determines the optimal relative orientation between the two sources, and reflection symmetries of the point-spread function can further provide a simplified means of identifying the optimal orientation. This geometric structure is coordinate invariant and provides a direct strategy for improving resolution by physically rotating an anisotropic imaging system to align its optimal principal response direction with the source displacement. For a general three-dimensional Gaussian point-spread function, the response tensor is proportional to the inverse spatial covariance, establishing a direct connection between quantum-limited distance precision and the geometry of Gaussian distribution.
Comments14 pages, 4 figures
