Single-shot and label-free refractive index dispersion of single nerve fiber by triple-wavelength diffraction phase microscopy

Nerve fibers play a critical role in the propagation of electrical impulses in the nervous system, and several studies have demonstrated their electrical and chemical properties. However, because of the lack of practical biophotonics techniques, most of the optical properties of these fibers are unknown. Herein, we propose and demonstrate a novel method of precisely measuring the dispersion of an individual nerve fiber in striatal neurons, using a single-shot label-free triple-wavelength diffraction phase interferometer and employing Cauchy coefficients of the refractive index. Compared with the current techniques of refractive index measurement, the proposed technique employs a common-path arrangement to achieve high temporal stability sensing of dispersion by a monochromatic detector. The dispersion spectra are obtained by reconstructing the triple-color wavefront of the specimen, extracting the thickness from the projected width of the fiber in the image, and then employing a Cauchy relation that is valid for the normal dispersions of transparent materials in the visible range. The feasibility of this technique was confirmed by analyzing the refractive indices of polystyrene microspheres. The technique was then applied to measure refractive index map and dispersion behavior of nerve fibers in medium spiny neurons with high temporal and spatial resolution.