Northwestern University, Evanston, Illinois 60208, USA.
Phys Rev Lett. 2013 Jul 19;111(3):033903. doi: 10.1103/PhysRevLett.111.033903.
Despite major importance in physics, biology, and other sciences, the optical sensing of nanoscale structures in the far zone remains an open problem due to the fundamental diffraction limit of resolution. We establish that the expected value of spectral variance (Σover ˜) of a far-field, diffraction-limited microscope image can quantify the refractive-index fluctuations of a label-free, weakly scattering sample at subdiffraction length scales. We report the general expression of Σ[over ˜] for an arbitrary refractive-index distribution. For an exponential refractive-index spatial correlation, we obtain a closed-form solution of Σ[over ˜] that is in excellent agreement with three-dimensional finite-difference time-domain solutions of Maxwell's equations. Sensing complex inhomogeneous media at the nanoscale can benefit fields from material science to medical diagnostics.
尽管在物理学、生物学和其他科学领域具有重要意义，但由于分辨率的基本衍射限制，远场纳米结构的光学传感仍然是一个未解决的问题。我们证明了远场、衍射受限显微镜图像的光谱方差（Σover ˜)的期望值可以定量测量无标记、弱散射样品在亚衍射长度尺度下的折射率波动。我们报告了任意折射率分布的Σ[over ˜]的一般表达式。对于指数折射率空间相关，我们得到了Σ[over ˜]的封闭形式解，该解与麦克斯韦方程的三维有限差分时域解非常吻合。在纳米尺度上感应复杂的非均匀介质可以使从材料科学到医学诊断等领域受益。
