有限域归一化位置测量中轴可分性的破坏与结构化反演：象限光电探测器案例研究
Breakdown of Axis Separability and Structured Inversion in Finite-Domain Normalized Position Measurements: A Quadrant Photodetector Case Study
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中文总结 AI 辅助
本研究通过象限光电探测器案例，揭示有限域归一化测量中轴可分性破坏的机制，提出轴锚定交叉残差反演（ACRI）方法，以结构化校正离轴偏差，提升多维位置测量的精度。
中文摘要 AI 辅助
有限域归一化空间测量结合了入射场、几何支撑、局部响应和通道加权。这些操作可能破坏原本可分离的响应，因此仅凭精确的单轴校准并不能确立多维测量的可分离性。我们将归一化读数表示为参数依赖的有效测度下的通道权重期望。对于固定的接收和通道算子，局部灵敏度是通道权重与源得分之间的协方差。这种表示区分了轴可分性、参数混合和局部可恢复性，并适用于适当的探测器层级，包括连续电极位置敏感探测器、Shack-Hartmann和金字塔波前传感器、后焦平面分裂检测以及有限像素阵列。象限光电探测器（QPD）提供了一个解析可处理的案例。从完整的二维功率积分出发，我们识别出其最低阶交叉项的空间矩起源。轴校准和系统对称性随后约束了逆映射，从而得到轴锚定交叉残差反演（ACRI）。该QPD实现的数值测试支持灵敏度关系，并表明受约束的交叉校正显著减少了单轴反演所保留的离轴偏差。结果展示了通用测量表示如何指导反演构建，其性能受工作域、校准状态和保持的对称性约束。
英文摘要
Finite-domain normalized spatial measurements combine an incident field, geometric support, local response, and channel weighting. These operations can break an otherwise separable response, so accurate single-axis calibration alone does not establish separability of a multidimensional measurement. We represent normalized readouts as channel-weight expectations under a parameter-dependent effective measure. For fixed reception and channel operators, local sensitivity is the covariance between the channel weight and the source score. This representation distinguishes axis separability, parameter mixing, and local recoverability, and applies at the appropriate detector level to continuous-electrode position-sensitive detectors, Shack--Hartmann and pyramid wavefront sensors, back-focal-plane split detection, and finite pixel arrays. A quadrant photodetector (QPD) provides an analytically tractable case. Starting from the complete two-dimensional power integrals, we identify the spatial-moment origin of its lowest-order cross term. Axis calibration and system symmetry then constrain the inverse map, giving Axis-Anchored Cross-Residual Inversion (ACRI). Numerical tests of this QPD realization support the sensitivity relations and show that the constrained cross correction substantially reduces the off-axis bias retained by single-axis inversion. The results illustrate how the general measurement representation guides inverse construction, with performance bounded by the working domain, calibration state, and preserved symmetries.
发表机构
- Institute of Quantum Electronics, School of Electronics, Peking University（北京大学电子学院量子电子学研究所）
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