What structural length scales can be detected by the spectral variance of a microscope image?

A spectroscopic microscope, configured to detect interference spectra of backscattered light in the far zone, quantifies the statistics of refractive-index (RI) distribution via the spectral variance (Σ˜²) of the acquired bright-field image. Its sensitivity to subtle structural changes within weakly scattering, label-free media at subdiffraction scales shows great promise in fields from material science to medical diagnostics. We further investigate the length-scale sensitivity of Σ˜ and reveal that, in theory, it can detect RI fluctuations at any spatial frequency whatsoever. Based on a 5% noise floor, Σ˜ detects scales from ∼22 to 200-700 nm (exact values depend on sample structure and thickness). In an example involving mass-density distribution characteristic of biological cell nuclei, we suggest the level of chromatin organization, which can be quantified via Σ˜.