Discontinuity third harmonic generation microscopy for label-free imaging and quantification of intraepidermal nerve fibers.

Label-free imaging methodologies for nerve fibers rely on spatial signal continuity to identify fibers and fail to image free intraepidermal nerve endings (FINEs). Here, we present an imaging methodology-called discontinuity third harmonic generation (THG) microscopy (dTHGM)-that detects three-dimensional discontinuities in THG signals as the contrast. We describe the mechanism and design of dTHGM and apply it to reveal the bead-string characteristics of unmyelinated FINEs. We confirmed the label-free capability of dTHGM through a comparison study with the PGP9.5 immunohistochemical staining slides and a longitudinal spared nerve injury study. An intraepidermal nerve fiber (IENF) index based on a discontinuous-dot-connecting algorithm was developed to facilitate clinical applications of dTHGM. A preliminary clinical study confirmed that the IENF index was highly correlated with skin-biopsy-based IENF density (Pearson's correlation coefficient R = 0.98) and could achieve differential identification of small-fiber neuropathy (p = 0.0102) in patients with diabetic peripheral neuropathy.

Compressive imaging of subwavelength structures: periodic rough surfaces.

A compressed sensing scheme for near-field imaging of corrugations of relative sparse Fourier components is proposed. The scheme employs random sparse measurement of near field to recover the angular spectrum of the scattered field. Surprisingly, it can be shown heuristically and numerically that under the Rayleigh hypothesis the angular spectrum is compressible and amenable to compressed sensing techniques. Iteration schemes are developed for recovering the surface profile from the angular spectrum. The proposed nonlinear least squares in the Fourier basis produces accurate reconstructions even when the Rayleigh hypothesis is known to be false.