Measurement of refractive index in non-planar surfaces with a conoscopic mueller microscope

Resumen

Refractive index (RI) provides information about the propagation of light through a specimen and it is related with some optical and electrical properties of materials. In many cases, certain changes in matter can produce a modification of the refractive index, such as, for example, temperature variations, mechanical stress or changes in the chemical composition of the material. Other materials may present different RI values depending on light propagation direction, as is the case of anisotropic materials. Hence, there are multiple applications in different fields such as biology, pharmacology, mineralogy or material characterization, where the RI value can give interesting information. In this thesis, we have developed an optical method to characterize the RIs of dielectric isotropic samples and uniaxial anisotropic crystals. The particularity of our method is to measure, in a reflection configuration, solid or liquid phases and planar or non-planar surfaces, allowing to characterize optical elements already integrated in optical systems. In-situ characterization of the refractive index is nowadays an unsolved problem of interest for industry and research. Particularly, lenses integrated in optical systems are the major motivation of this work, because they may modify their RI value when inserted into devices. Our proposal was to design, implement and use, for the first time, a conoscopic Mueller microscope working in reflection to measure the RIs of several samples with arbitrary surfaces. The working principle of our microscope is based on measuring the angle-resolved Mueller matrix of any dielectric specimen by using a complete Mueller matrix polarimeter and a high numerical aperture objective (HNAO). Under this scenario, a polarized incident light beam is highly focused over the studied sample, being the spot size smaller than the curvature of the sample surface, this allowing us to measure non-planar surfaces. The reflected cone of light passes through the same HNAO, being collimated and then, it is polarimetrically analyzed. Note that the incident and reflected light cones are formed by light rays with different angles of incidence and polarizations. As a consequence, the proposed conoscopic microscope is able to measure the angle-resolved Mueller matrix in reflection at numerous incident angles simultaneously, obtaining data redundancy without any mechanical motion of the set-up. A camera with high-resolution records the different intensity patterns that ultimately are used to calculate the Mueller matrix image. Data redundancy is function of the maximum angle of incidence of the HNAO and the number of pixels of the camera. A mathematical model was developed to theoretically determine the Mueller matrix image. It is based on the Fresnel coefficients that describe the ratio of the reflected and transmitted electric fields to that of the incident beam on an interface between different optical media. These coefficients depend, on the one hand, on the angle of incidence, the polarization and the frequency (or wavelength) of the incident beam and, on the other hand, on the RIs of the media. The model was tested by performing a collection of simulations and we analyzed the validity of the method by measuring the characteristics of different artificial samples. The model parameters, such as the refractive indices can be calculated by fitting them with the experimental data measured with the conoscopic Mueller microscope. An iterative optimization routine was developed in order to find the best-fit parameters that minimize a merit function based on the Mean Squared Error (MSE) between both experimental and simulated Mueller matrix images. The conoscopic Mueller microscope was finally tested by measuring well-known polarimetric samples with different surface forms.