Spectroscopic microscopy can quantify the statistics of subdiffractional refractive-index fluctuations in media with random rough surfaces

We previously established that spectroscopic microscopy can quantify subdiffraction-scale refractive index (RI) fluctuations in a label-free dielectric medium with a smooth surface. However, to study more realistic samples, such as biological cells, the effect of rough surface should be considered. In this Letter, we first report an analytical theory to synthesize microscopic images of a rough surface, validate this theory by finite-difference time-domain (FDTD) solutions of Maxwell's equations, and characterize the spectral properties of light reflected from a rough surface. Then, we report a technique to quantify the RI fluctuations beneath a rough surface and demonstrate its efficacy on FDTD-synthesized spectroscopic microscopy images, as well as experimental data obtained from biological cells.