Rodolfo M. Echarri

Internal reflection in uniaxial crystals. I: Geometrical description

Abstract We give a vector formulation to calculate the direction of the internally reflected rays in a uniaxial crystal. The vector formulae obtained can be applied in general to any direction of the optical axis and any direction of incidence. The reflective indices are also defined, and formulae for them are given in terms of the angle of incidence and of the optical properties of the crystal.

Inhibited reflection in uniaxial crystals

When an ordinary or extraordinary ray that propagates through a birefringent crystal is reflected it gives rise to two reflected rays whose directions may be calculated with formulas similar to Snells law for refraction. When the reflection angle is greater than the incidence angle there is a critical angle for which the reflected ray is grazing, and for values of the incidence angle greater than this critical value the reflected ray no longer exists. We call this phenomenon inhibited reflection. We show how the critical angles may be calculated, and an experiment that visualizes the phenomenon shows good agreement with theory.

Internal reflection in uniaxial crystals. II: Coefficients of transmission and reflection for an ordinary incident wave

Abstract The boundary condition at the interface between a crystal and an isotropic medium have been solved in a general form for the situation when an ordinary ray is incident from the crystal and gives rise to two reflected rays besides the refracted ray. With the formulae obtained, the reflection and transmission coefficients have been calculated as functions of the incidence angle, and a pseudo-Brewster angle was observed to exist for each one of the reflected rays.

Fringe localization in interferometers illuminated by a succession of incoherent line sources

Abstract It is well known that interference fringes formed by an interferometer that is illuminated with a point source are non-localized and, when it is done with an extended source, they are localized. Nevertheless, when the interferometer is illuminated with a discrete succession of points or lines, the localization of the fringes presents some characteristics that are different from those obtained with the former, for example the discrete number of localization surfaces. In this work we obtain the conditions to find the position of the surfaces of localization of these planes for an arbitrary interferometer. Then we apply this method to a wedge interferometer and compare the experimental and theoretical results.

Internal reflection in uniaxial crystals. III, Transmission and reflection coefficients for an extraordinary incident wave

Abstract The boundary conditions have been solved and the reflection and transmission coefficients calculated for an interface between a uniaxial crystal and an isotropic medium when the incident wave is extraordinary. The existence of a pseudo-Brewster angle for each reflected wave has been verified, and the polarizations of the reflected refracted waves have been determined.

Correlation between visual acuity and pupil size

The eye suffers from aberrations that are pupil size dependent and reduce visual performance. Pupil size is often disregarded when visual performance is clinically determined. Considering 23 normal eyes, under natural viewing conditions, visual acuity is here related to pupil size when each subject reads monocularly a Snellen chart of constant luminance placed at 2m.

Shifting of localization planes in optical testing: application to a shearing interferometer

An amplitude-division two-beam interferometer illuminated by a quasi-monochromatic, spatially incoherent, and periodic source yields multiple localization planes of interference fringes. If a thick transmission sample with a few localized phase disturbances in various layers is placed in the interferometer, the disturbances in a layer can be detected, making its images through the two arms coincide with a chosen localization plane. Different layers can be analyzed by means of shifting the localization plane by a variation of the source period without any other changes in the device. Here we illustrate this method by applying it to a shearing interferometer, a classical Wollaston prism placed between crossed polarizers. Experimental images of different observation planes are obtained, and they are in good agreement with the theoretical expectations.

How to increase the sensitivity in a polarization interferometer.

Two methods to measure the difference between the phase shifts in a dielectric reflection and a metal one are compared. Both methods consist of using a Smith-type interferometer, and they differ in the analyzer used.

Fringe localization in wavefront division interferometers

Abstract When an amplitude division interferometer is illuminated by an extended incoherent source the fringes are localized. If the incoherent source is a periodic array of sources or if it continuous, there is a fundamental difference at the observation space and this is the appearance of several (more than one) localization surfaces. In the present paper it is stated that localized fringes can also be obtained in wavefront division interferometers provided the source is incoherent and periodic. As an example, the multiple localization planes in Fresnels biprism are shown and experimental results are compared to the theoretical ones.

Optical testing of perturbations on successive layers: digital discrimination and multilocalized fringes

A two-beam amplitude division interferometer with negligible equivalent aberrations, verifying the equivalent sine condition and illuminated by an incoherent extended periodic source yields various non-classical localization planes. The source period can be chosen so that a non-classical localization plane coincides with the plane where the images of one of the layers of a thick transparent sample are located thus detecting the perturbations present on this layer and blurring defects corresponding to other layers. In the present paper the process of focalizing different layers and making them coincide with nonclassical localization planes is digitally synthesized starting from a videofilm taken on one observation plane as a point source moves. Images acquired using a Wollaston prism as an interferometer are shown.