BUSCADOR RECOLECTA

The second-order characterization of a three-dimensional (3D) state of polarization is provided either by the corresponding 3D coherency matrix or (equivalently) by the associated 3D Stokes parameters. The analysis of the polarization properties that are invariant under orthogonal transformations of the laboratory reference frame allows to define a set of six intrinsic Stokes parameters which provides a simplified interpretation of 3D states of polarization in terms of meaningful physical properties. The rotationally invariant properties of 2D states of polarization are straightforwardly retrieved in a consistent way, so that the 2D intrinsic Stokes parameters are constituted by the intensity, the degree of linear polarization and the degree of circular polarization.

PURPOSE. Stochastic eye models are a method to generate random biometry data with the variability found in the general population for use in optical calculations. This work improves the accuracy of a previous model by including the higher-order shape parameters of the cornea. METHODS. The right eye biometry of 312 subjects (40.8 ± 11.0 years of age) were measured with an autorefractometer, a Scheimpflug camera, an optical biometer, and a ray tracing aberrometer. The corneal shape parameters, exported as Zernike coefficients, were converted to eigenvectors for dimensional reduction. The remaining 18 parameters were modeled as a sum of two multivariate Gaussians, from which an unlimited number of synthetic data sets (SyntEyes) were generated. After conversion back to Zernike coefficients, the data were introduced into ray tracing software. RESULTS. The mean values of nearly all SyntEyes parameters were statistically equal to thos0e of the original data (two one-sided t-test, P > 0.05/109, Bonferroni correction). The variability of the SyntEyes parameters was similar to the original data for most important shape parameters and intraocular distances (F-test, P 0.05/109). The same was seen for the correlations between higher-order shape parameters. After applying simulated cataract or refractive surgery to the SyntEyes model, a very close resemblance to previously published clinical outcome data was seen. CONCLUSIONS. The SyntEyes model produces synthetic biometry that closely resembles clinically measured data, including the normal biological variations in the general population.

Refraction techniques make it possible to determine the most appropriate sphero-cylindrical lens prescription to achieve the best possible visual quality. Among these techniques, subjective refraction (i.e., patient’s response-guided refraction) is the most commonly used approach. In this context, this paper’s main goal is to present a simulation software that implements in a virtual manner various subjective-refraction techniques—including Jackson’s Cross-Cylinder test (JCC)—relying all on the observation of computer-generated retinal images. This software has also been used to evaluate visual quality when the JCC test is performed in multifocal-contact-lens wearers. The results reveal this software’s usefulness to simulate the retinal image quality that a particular visual compensation provides. Moreover, it can help to gain a deeper insight and to improve existing refraction techniques and it can be used for simulated training.

A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different polynomials. Here we present results for surfaces with circular apertures when the first basis function (mode) is a conicoid. The system for aspheres with rotational symmetry is obtained applying an appropriate change of variables to Legendre polynomials, whereas the system for general freeform case is obtained applying a similar procedure to spherical harmonics. Numerical comparisons with standard systems, such as Forbes and Zernike polynomials, are performed and discussed.

Background: The spectral polarization state and dimensionality of random light are important concepts in modern optical physics and photonics. Methods: By use of space-frequency domain coherence theory, we establish a rigorous classification for the electricfield vector to oscillate in one, two, or three spatial dimensions. Results: We also introduce a new measure, the polarimetric dimension, to quantify the dimensional character of light. The formalism is utilized to show that polarized three-dimensional light does not exist, while an evanescent wave generated in total internal reflection generally is a genuine three-dimensional light field. Conclusions: The framework we construct advances the polarization theory of random light and it could be beneficial for near-field optics and polarization-sensitive applications involving complex-structured light fields.

The concept of degree of polarization for electromagnetic waves, in its general three-dimensional version, is revisited in the light of the implications of the recent findings on the structure of polarimetric purity and of the existence of nonregular states of polarization [J. J. Gil et al., Phys Rev. A 95, 053856 (2017)]. From the analysis of the characteristic decomposition of a polarization matrix R into an incoherent convex combination of (1) a pure state R-p, (2) a middle state R-m given by an equiprobable mixture of two eigenstates of R, and (3) a fully unpolarized state Ru-3D, it is found that, in general, R-m exhibits nonzero circular and linear degrees of polarization. Therefore, the degrees of linear and circular polarization of R cannot always be assigned to the single totally polarized component R-p. It is shown that the parameter P-3D proposed formerly by Samson [J. C. Samson, Geophys. J. R. Astron. Soc. 34, 403 (1973)] takes into account, in a proper and objective form, all the contributions to polarimetric purity, namely, the contributions to the linear and circular degrees of polarization of R as well as to the stability of the plane containing its polarization ellipse. Consequently, P-3D constitutes a natural representative of the degree of polarimetric purity. Some implications for the common convention for the concept of two-dimensional degree of polarization are also analyzed and discussed.

It has recently been demonstrated that a general three-dimensional (3D) polarization state cannot be considered an incoherent superposition of (1) a pure state, (2) a two-dimensional unpolarized state, and (3) a 3D unpolarized state [J. J. Gil, Phys. Rev. A 90, 043858 (2014)10.1103/PhysRevA.90.043858]. This fact is intimately linked to the existence of 3D polarization states with fluctuating directions of propagation, but whose associated polarization matrices R satisfy rank R=2. In this work, such peculiar states are analyzed and characterized, leading to a meaningful general classification and interpretation of 3D polarization states. Within this theoretical framework, the interrelations among the more significant polarization descriptors presented in the literature, as well as their respective physical interpretations, are studied and illustrated with examples, providing a better understanding of the structure of polarimetric purity of any kind of polarization state.

While any 2D mixed state of polarization of light can be represented by a combination of a pure state and a fully random state, any Mueller matrix can be represented by a convex combination of a pure component and three additional components whose randomness is scaled in a proper and objective way. Such characteristic decomposition constitutes the appropriate framework for the characterization of the polarimetric randomness of the system represented by a given Mueller matrix and provides criteria for the optimal filtering of noise in experimental polarimetry.

We propose systems of orthogonal functions qn to represent optical transfer functions (OTF) characterized by including the diffraction-limited OTF as the first basis function q0 = OTFperfect. To this end, we apply a powerful and rigorous theoretical framework based on applying the appropriate change of variables to well-known orthogonal systems. Here we depart from Legendre polynomials for the particular case of rotationally symmetric OTF and from spherical harmonics for the general case. Numerical experiments with different examples show that the number of terms necessary to obtain an accurate linear expansion of the OTF mainly depends on the image quality. In the rotationally symmetric case we obtained a reasonable accuracy with approximately 10 basis functions, but in general, for cases of poor image quality, the number of basis functions may increase and hence affect the efficiency of the method. Other potential applications, such as new image quality metrics are also discussed.

A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different polynomials. Here we present results for surfaces with circular apertures when the first basis function (mode) is a conicoid. The system for aspheres with rotational symmetry is obtained applying an appropriate change of variables to Legendre polynomials, whereas the system for general freeform case is obtained applying a similar procedure to spherical harmonics. Numerical comparisons with standard systems, such as Forbes and Zernike polynomials, are performed and discussed., This research was supported by the Spanish Ministry of Economía y Competitividad and the European Union MTM2014-52859 and FIS2014-58303.

We propose systems of orthogonal functions qn to represent optical transfer functions (OTF) characterized by including the diffraction-limited OTF as the first basis function q0 OTF perfect. To this end, we apply a powerful and rigorous theoretical framework based on applying the appropriate change of variables to well-known orthogonal systems. Here we depart from Legendre polynomials for the particular case of rotationally symmetric OTF and from spherical harmonics for the general case. Numerical experiments with different examples show that the number of terms necessary to obtain an accurate linear expansion of the OTF mainly depends on the image quality. In the rotationally symmetric case we obtained a reasonable accuracy with approximately 10 basis functions, but in general, for cases of poor image quality, the number of basis functions may increase and hence affect the efficiency of the method. Other potential applications, such as new image quality metrics are also discussed., This research was supported by the Spanish Ministry of Economía y Competitividad and the European Union MTM2014-52859 and FIS2014-58303.

We present some comments to the paper 'Orthogonal basis with a conicoid first mode for shape specification of optical surfaces: comment'., This research was supported by the Spanish Ministry of Economía y Competitividad and the European Union MTM2014-52859 and FIS2014-58303.