An integrated model of the human cornea as a linear biaxial birefringent medium.

A novel model of human corneal birefringence is presented. The cornea is treated as a homogeneous biaxial linear birefringent medium in which the values of the binormal axes angle and organization of the main refractive indices vary continuously from the apex to the limbus. In its central part, the angle between binormal axes is 35°, and para centrally, it smoothly increases to 83.7°. The values of the main refractive indices (nx, ny, nz) change, as well as their order, from nx < nz < ny to nz < nx < ny. The transition between these two states was described with a normal distribution (µ = 0.45, σ = 0.1). The presented model corresponds with the experimental results presented in the literature. To our knowledge, it is the first model that presents the anisotropic properties' distributions of the entire cornea. The presented model facilitates a better understanding of the corneal birefringence phenomenon directly related to its lamellar structure.

In vivo measurements of corneal birefringence properties using the one-way reflective Mueller polarimetry.

This work presents the results of in vivo measurements of human corneal birefringence properties using the one-way reflective polariscope, in which the same module is used to generate and analyze the light polarization state. Data analysis was performed with the use of Mueller polarimetry techniques. The distribution of the azimuth angle and the phase retardation was determined on the paracentral and limbal areas. The results indicate growth of the phase retardation magnitude and the radial orientation of the azimuth angle in the cornea's peripheral region, which confirms our assumptions and the results presented by other researchers.

How a dynamic optical system maintains image quality: Self-adjustment of the human eye.

The eyeball is continually subjected to forces that cause alterations to its shape and dimensions, as well as to its optical components. Forces that induce accommodation result in an intentional change in focus; others, such as the effect of intraocular pressure fluctuations, are more subtle. Although the mechanical properties of the eyeball and its components permit mediation of such subtle forces, the concomitant optical changes are not detected by the visual system. Optical self-adjustment is postulated as the mechanism that maintains image quality. The purpose of this study was to investigate how self-adjustment occurs by using an optical model of the eyeball and to test the requisite optical and biometric conditions.

Polarimeter for measuring the properties of birefringent media in reflective mode.

This work presents a description of a polarimetric system for measuring the properties of birefringent media. In our reflection system the applied Stokes polarimeter acts both as a generator of the light's selected polarization states as well as a light analyzer leaving the examined medium. The method is based on six intensity distribution measurements realized in six different configurations of polarizers/analyzers: four linear and two circular ones. Thus, we have achieved parallel polariscope for linear polarizers and the crossed polariscope for circular polarizers. Such a setup can be easily applied for linearly birefringent media properties measurements including dichroic ones. This measurement setup and the measurement method were successfully tested in a homogeneous medium and a medium with variable phase difference.

Analysis of torsional eye movements using the corneal birefringence pattern.

The literature mentions several invasive methods to measure the degree of the compensatory torsional eye movement during a head-tilt. Nevertheless, none of them have yielded universally clinical tests. This study focuses on an optical system (with a circular polarizer) for noninvasive acquisition of corneal birefringence patterns (isochromes). The acquired isochromes are quadrangular in shape and unique for each eye, as well as independent of the head-rotation angle. The results obtained suggest that isochrome orientation analysis could be an effective method to accurately measure the degree of compensatory torsional eye movement.

Evaluation of a linear birefringence measurement method with increased sensitivity.

The evaluation of a measurement method of linear birefringence with increased sensitivity is presented. The examined method is based on a substantial change of the geometrical phase caused by a small change of an examined medium's birefringence. The measuring setup consists of a linear polarizer, Wollaston compensator, and circular analyzer. The measurement is performed by tracking the phase shift of a fringe pattern. Specific orientation of the elements modifies the setup's response-the sensitivity of the setup can be controlled in a limited measuring range. The present paper concentrates on the factors affecting the setup's sensitivity as well as the accuracy of obtained results. The validity of the proposed approach has been demonstrated by measuring a phase retardance introduced by the liquid crystal retarder. A thousandfold increase in sensitivity has been obtained in the presented experiments, which allows the measurement of retardance introduced by the linear birefringent medium with an accuracy of 0.003° within the limited measuring range.

Imaging Stokes polarimeter based on a single liquid crystal variable retarder.

A description of a compact imaging Stokes polarimeter constructed and tested in our laboratory is presented. Our polarimeter is based on a simple construction using only one retarder and one linear polarizer. Three fast intensity distribution measurements realized in three different configurations of linear and elliptical analyzers allow for calculating the basic polarization parameter distribution of the examined light. Using a liquid crystal variable retarder makes this construction compact and mechanically simple.

Geometric phase of an elliptical polariscope.

The exact formula for calculating the geometric phase in an elliptical polariscope with arbitrary oriented elliptically birefringent nondichroic medium has been presented. The visualization of the obtained results using the Poincaré sphere representation allows the prediction of the effect of the setup geometry on the final result.

Singularities of interference of three waves with different polarization states.

We presented the interference setup which can produce interesting two-dimensional patterns in polarization state of the resulting light wave emerging from the setup. The main element of our setup is the Wollaston prism which gives two plane, linearly polarized waves (eigenwaves of both Wollaston's wedges) with linearly changed phase difference between them (along the x-axis). The third wave coming from the second arm of proposed polarization interferometer is linearly or circularly polarized with linearly changed phase difference along the y-axis. The interference of three plane waves with different polarization states (LLL - linear-linear-linear or LLC - linear-linear-circular) and variable change difference produce two-dimensional light polarization and phase distributions with some characteristic points and lines which can be claimed to constitute singularities of different types. The aim of this article is to find all kind of these phase and polarization singularities as well as their classification. We postulated in our theoretical simulations and verified in our experiments different kinds of polarization singularities, depending on which polarization parameter was considered (the azimuth and ellipticity angles or the diagonal and phase angles). We also observed the phase singularities as well as the isolated zero intensity points which resulted from the polarization singularities when the proper analyzer was used at the end of the setup. The classification of all these singularities as well as their relationships were analyzed and described.

Geometric phase: two triangles on the Poincaré sphere.

The method of obtaining the dynamic and geometric part of the phase introduced by a birefringent medium in two kinds of interferometric experiments is presented. The mathematical formulas for the phases obtained using Jones formalism are visualized with the specific triangles on the Poincaré sphere. Generally, these triangles are similar to those used in the Pancharatnam's original construction developed by Courtial to calculate the Pancharatnam geometric phase for the light passing through a single birefringent plate. In these graphical constructions following Courtial's idea, we used the points representing both of the birefringent medium's eigenvectors. This allowed the most intuitive explanation of the mechanism of dividing the whole phase shift introduced by the birefringent plate into two different parts: dynamical and geometrical. The considered constructions were used as a description of two simple experiments with a birefringent medium in a Mach-Zehnder interferometer and a polariscopic setup. The experimental verifications of our theoretical predictions should convince the reader of the correctness of the assumed model.

Adjustment method of an imaging Stokes polarimeter based on liquid crystal variable retarders.

The description of adjustment of an imaging Stokes polarimeter constructed and tested in our laboratory is presented. Our polarimeter's operation is based on six fast intensity distribution measurements realized in six different configurations of linear and circular analyzers. Using liquid crystal variable retarders (LCVRs) makes this construction compact and mechanically simple. However, new problems arise with proper azimuthal alignment as well as with proper LCVR voltage adjustment. Three basic steps of the adjustment procedure adapted to the specific construction of our polarimeter are described in detail. Some remarks concerning the critical parameters of the used CCD camera's parameters are also presented, as well as experimental verifications of the setup's accuracy acquired due to the proper adjustment process.

Dynamic polarization states and birefringence distributions measurements in spatial elliptical polariscope using Fourier analysis method.

A new method to measure the light polarization state and the birefringent media parameters is proposed. We have used the setup described previously, consisting of two pairs of the linear Wollaston and circular compensators which form a set of two spatially modulated elliptical compensators. We have modified this setup introducing some carrier frequencies in all compensators and assuming that the second linear one would introduce the frequency which is a multiplicity of the basis frequency of the first linear compensator. Both of these modifications allow calculating all polarization parameters of polarized light or birefringent medium from only one measured intensity distribution of the light outcoming the described setup. They allow measuring not only the parameters of homogeneous beams/mediums but also x,y-distributions of all desired parameters, like azimuth and ellipticity angles of the light or first medium eigenvector and the phase difference introduced by this medium. The proposed calculation method comprises of Fourier analysis of obtained intensity distribution with some manipulation of coordinate system and filtration of obtained data. This method is claimed to be simple and fast enough to be treated as a real-time method.

Compact spatial polariscope for light polarization state analysis.

A new setup established to measure the light polarization state and the birefringent media parameters is proposed. The described setup consists of two pairs of the linear Wollaston compensators and circular compensators which form a set of two spatially modulated elliptical compensators. These compensators could be used separately as a spatial generator of polarization states and as an analyzer. Using them together allows us to establish a polariscopic setup in which the birefringent media parameters could be measured. When analyzing both the light polarization state and the birefringent media parameters the singular points in the output light intensity appear. The coordinates of these points depend linearly on the azimuth and ellipticity angles of the examined light or on the eigenvectors of the birefringent medium, while the measured light maximum value corresponds to the phase shift for the measurements of the birefringent medium parameters. Neither movable parts nor active elements are needed and no complicated analysis of output light should be made to calculate the desired quantities.

Measurements of the small wave tilt using the optical vortex interferometer with the Wollaston compensator.

A classical Mach-Zehnder two-beam interferometer was modernized using the Wollaston compensator, which allowed obtaining a stable set of specific optical markers--optical vortices. This new interferometer setup that generated optical vortices was used to measure small angle tilt. The theoretical basis of setups behavior has been described. The value of the described setup was confirmed by practical experiments.

Measurements of birefringent media properties using optical vortex birefringence compensator.

We present some applications of the optical vortex birefringence compensator, based on the C polarization type singularities generated using two Wollaston compensators. The theory and experimental results of birefringent media properties measurements are presented. The possibility of the simultaneous measurement of both the azimuth angle and the phase retardance has been analyzed and experimentally verified.

Generation of vortex-type markers in a one-wave setup.

What we believe to be a new arrangement of an optical vortex interferometer (OVI) is presented. In the proposed configuration the optical vortex lattice is generated in a one-wave setup by use of birefringent elements--Wollaston compensators. The obtained vortex lattice is regular and stable, which is necessary for predicted applications. The new OVI configuration allows the measurement of waves and optical media properties.

Optical vortices generation using the Wollaston prism.

A new setup of interferometers is proposed in which the set of specific optical markers--optical vortices--could be generated. The classical Mach-Zender two-beam interferometer has been modernized using the Wollaston prism. In this setup, the optical vortices could be obtained for a wide range of both beam parameters. The numerical analysis and experiments confirm our theoretical predictions.