Phase and Index of Refraction Imaging by Hyperspectral Reflectance Confocal Microscopy

A hyperspectral reflectance confocal microscope (HSCM) was realized by CNR-ISC (Consiglio Nazionale delle Ricerche-Istituto dei Sistemi Complessi) a few years ago. The instrument and data have been already presented and discussed. The main activity of this HSCM has been within biology, and reflectance data have shown good matching between spectral signatures and the nature or evolution on many types of cells. Such a relationship has been demonstrated mainly with statistical tools like Principal Component Analysis (PCA), or similar concepts, which represent a very common approach for hyperspectral imaging. However, the point is that reflectance data contains much more useful information and, moreover, there is an obvious interest to go from reflectance, bound to the single experiment, to reflectivity, or other physical quantities, related to the sample alone. To accomplish this aim, we can follow well-established analyses and methods used in reflectance spectroscopy. Therefore, we show methods of calculations for index of refraction n, extinction coefficient k and local thicknesses of frequency starting from phase images by fast Kramers-Kronig (KK) algorithms and the Abeles matrix formalism. Details, limitations and problems of the presented calculations as well as alternative procedures are given for an example of HSCM images of red blood cells (RBC).