发表机构
Institut für Physik und Astronomie, Universität Potsdam（波茨坦大学物理与天文学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构建光子 lantern 波前传感的 Fisher 与量子 Fisher 信息框架，推导其灵敏度极限并与其他传感器基准对比，揭示其性能与量子极限的关联及相关灵敏度指标的关系。
AI 中文摘要
光子 lantern 是一种原生适用于单模光纤馈电仪器的全光子波前传感器，但其性能几乎总是通过特定的重建算法来表述，掩盖了该器件自身编码的波前信息量。我们从第一性原理出发，推导了光子 lantern 波前传感器的 Fisher 信息和 Cramer-Rao 理论，通过显式多参数量子 Fisher 信息计算将其与量子 Cramer-Rao 界进行基准测试，并将其与两个已建立的框架关联：Chambouleyron 等人（2023）的傅里叶滤波噪声传播模型，以及 Haffert 等人（2023）的经典/量子灵敏度极限。将 lantern 视为从像差系数到 N 个输出强度的确定性映射，我们推导了泊松和读出噪声 Fisher 信息矩阵（FIM）、每模 CRLB、强度单形上的每光子 Fisher-Rao 几何，以及与通量和估计器无关的灵敏度度量 β，其量子上限为 β=2。lantern CRLB 按 N_ph^(-1/2) 缩放，且逐模受限于每光子 1/2 rad 均方根的量子极限。该多参数界可联合饱和：相位生成元是实且对易的，因此平均 Uhlmann 曲率消失，波前传感在同时估计的模式之间不存在量子不相容性，将 Haffert 等人的单模上限扩展至所有低阶模式。我们进一步表明，Chambouleyron 等人的光子噪声灵敏度 s_γ 恰好是我们每光子 FIM 的对角线，而 CRLB 使用其逆的对角线；二者仅在 FIM 为对角时重合，因此 s_γ 对模式混合 lantern 而言是乐观的。该框架与器件无关：它返回与估计器无关的灵敏度，在 β≤2 的共同尺度上可与 pyramid、Zernike 和 PIAA-ZWFS 传感器进行比较。
英文摘要
The photonic lantern is an all-photonic wavefront sensor native to single-mode-fibre-fed instruments, but its performance is almost always quoted through a specific reconstruction algorithm, obscuring how much wavefront information the device itself encodes. We develop, from first principles, the Fisher-information and Cramer-Rao theory of the photonic-lantern wavefront sensor, benchmark it against the quantum Cramer-Rao bound via an explicit multi-parameter quantum-Fisher-information calculation, and relate it to two established frameworks: the Fourier-filtering noise-propagation model of Chambouleyron et al (2023) and the classical/quantum sensitivity limit of Haffert et al (2023). Treating the lantern as a deterministic map from aberration coefficients to N output intensities, we derive the Poisson and read-noise Fisher information matrices (FIM), the per-mode CRLB, the per- photon Fisher-Rao geometry on the intensity simplex, and a flux- and estimator-independent sensitivity metric beta with quantum ceiling beta = 2. The lantern CRLB scales as N_ph^(-1/2) and is bounded, mode by mode, by the quantum limit of 1/2 rad rms per photon. That multi-parameter bound is jointly saturable: the phase generators are real and commuting, so the mean Uhlmann curvature vanishes and wavefront sensing carries no quantum incompatibility between simultaneously estimated modes, extending Haffert et al's single-mode ceiling to all low-order modes at once. We further show that the photon-noise sensitivity s_gamma of Chambouleyron et al is exactly the diagonal of our per- photon FIM, whereas the CRLB uses the diagonal of its inverse; the two coincide only for a diagonal FIM, so s_gamma is optimistic for a mode-mixing lantern. The framework is device-agnostic: it returns estimator-independent sensitivities comparable on a common beta <= 2 scale with pyramid, Zernike and PIAA-ZWFS sensors.
Comments17 pages, 4 figures, 1 table
