Gouy Phase Correction for Quasioptical, Dielectric Spectroscopy of Spherical Shells in a Gaussian Beam for Terahertz Corneal Sensing

This study aims to explore the effect of the Gouy phase shift correction on determining refractive index and physical thickness of concentric spherical shells measured by quasioptical terahertz (THz) spectroscopy. The shells consisted of a loss-free quartz layer sitting on a water core which serves as an aqueous half space similar to the cornea's aqueous humour. The reflection of the water-backed quartz shells were measured with a focused Gaussian beam in the 220-330 GHz range. The optics generated a beam with a frequency-independent confocal distance resulting in equal radius of curvature and thus optimal wavefront matching to the sample curvature across the band. Thickness and refractive index were estimated from the measurements using Fresnel's equations and a fixed phase velocity. Parameter extraction was performed a second time where the frequency and axial location dependent phase velocity was corrected by incorporating the expected Gouy phase shift. The correction improved both the thickness and refractive index accuracy. The utility of Gouy phase correction was explored on hydrated corneal phantoms and increased the accuracy of thickness, and anterior and posterior water content estimates.