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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 (Σ[over ˜](2)) 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.

Interferometric Spectroscopy of Scattered Light Can Quantify the Statistics of Subdiffractional Refractive-Index Fluctuations