消失的杂波：通过主动隐身实现快速准确的形状成像
Vanishing Clutter: Fast and Accurate Shape Imaging via Active Cloaking
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中文总结 AI 辅助
该研究针对NSOM中探针干扰导致的成像不适定问题，将主动隐身技术用于消除探针干扰，推导了闭式极小化子，实现了快速准确的亚波长形状重构，性能远优于传统迭代方法。
中文摘要 AI 辅助
在近场扫描光学显微镜（NSOM）中对目标样本进行成像时，测量伪影和探针-样本多次散射导致的数据污染是根本限制因素。对于亚波长分辨率必不可少的探针会固有地扰动局域场，降低信噪比，并使定量形状重构的逆问题高度不适定。我们首先建立了对应正问题模型的适定性，为后续成像提供了严谨基础。随后，我们将主动隐身——传统上是成像的对抗技术——重新用作消除探针诱导干扰的可行机制。我们并非直接从受污染的数据中重构样本，而是通过构建最优控制问题来主动隐身探针，并证明了其极小化子的存在性与稳定性。利用层状等离子体结构中的局域异常共振理论，我们推导出了精确的闭式极小化子，从而避免了最优控制问题计算上难以承受的迭代求解。这种由隐身驱动的干扰消除产生了几乎无探针的测量环境，实现了快速、无伪影的形状重构。大量数值实验表明，与未采用基于隐身预处理、直接应用于受探针污染数据的传统迭代方法相比，该方法可实现准确的形状重构，并显著加速——通常达数个数量级——验证了所提方法在高保真亚波长成像中的鲁棒性和变革性潜力。
英文摘要
Imaging a target sample in near-field scanning optical microscopy (NSOM) is fundamentally limited by measurement artifacts and data contamination from multiple probe-sample scattering. The probe, essential for subwavelength resolution, inherently perturbs the local field, degrading the signal-to-noise ratio and rendering the inverse problem for quantitative shape reconstruction highly ill-posed. We first establish the well-posedness of the corresponding forward model, providing a rigorous foundation for subsequent imaging. We then repurpose active cloaking--conventionally the antagonist of imaging--as an enabling mechanism to eliminate probe-induced interference. Rather than directly reconstructing the sample from corrupted data, we actively cloak the probe by formulating an optimal control problem and prove the existence and stability of its minimizers. Leveraging the theory of localized anomalous resonance in layered plasmonic structures, we derive an exact closed-form minimizer, thereby circumventing the computationally prohibitive iterative solution of the optimal control problem. The resulting cloaking-driven interference removal yields a virtually probe-free measurement environment, enabling fast, artifact-free shape reconstruction. Extensive numerical experiments demonstrate accurate shape reconstruction and dramatic acceleration--often by orders of magnitude--over conventional iterative methods applied directly to probe--contaminated data without cloaking--based preprocessing, validating the robustness and transformative potential of the proposed approach for high-fidelity subwavelength imaging.
