Maria Victoria Perez

Diffraction Patterns and Zone Plates Produced by Thin Linear Axicons

We determine the Fraunhofer and Fresnel diffraction patterns produced by a thin linear axicon when it is illuminated by a plane wavefront. An interferometric method of recording zone plates using l...

Timing jitter smoothing by Talbot effect. I. Variance

A study of the stochastic description of the Talbot effect in the temporal domain under random timing jitter is presented. The relevant statistical quantity is the variance. The variance of a train of pulses, each one affected by random timing jitter, shows peaks in the edges of the pulses. When this train is Talbot-imaged, the variance becomes flattened along the unit interval corresponding to each pulse as a result of the dispersion of the individual pulses of the train. Fractional Talbot devices are also analyzed. In particular, it is shown that this smoothing effect also occurs in Talbot devices leading to N× repetition rates of the original train.

Imaging and transforming transmission through inhomogeneous media with revolution symmetry

Abstract We study the paraxial imaging and transforming transmission through an inhomogeneous medium with spatial revolution symmetry obtaining the image and transform conditions. The medium is characterized by a transmittance function at the output plane similar to the conventional lens transmittance function.

Transmittance function and modal propagation in a conical gradient-index rod.

In this paper we determine the image planes and the transmittance function for a conical gradient-index (GRIN) rod, and we consider the problem of modal propagation.

Description of gradient-index crystalline lens by a first-order optical system

This paper uses the correspondence between the canonical integral transform and the ray-transfer matrix of a first-order optical system to analyse paraxial properties of the crystalline lens of the human eye regarded as a gradient-index (GRIN) medium limited by curved surfaces. Matrix factorization is provided to evaluate cardinal elements and refractive powers of the crystalline lens.

Timing jitter smoothing by Talbot effect. II. Intensity spectrum

The power spectral density of the intensity of jittery trains after an integer temporal Talbot dispersive line is computed in the small-signal approximation. The influence in the spectrum of the optical linewidth and chirp of the Gaussian pulses of the train and also of different pulse-to-pulse timing jitter correlations is addressed. Before entering the Talbot dispersive line, timing jitter produces noise sidebands around the harmonics of the train. The temporal Talbot effect adds a multiplicative factor to the noise spectral density that depends on the characteristics of both the pulses and the dispersive line but not on the pulse-to-pulse correlation or the value of the timing jitters standard deviation. The structure of this multiplicative term is peaked, resulting in narrowband noise patterns in specific locations of the spectrum and, in particular, around the harmonics of the train. Thus the temporal Talbot effect provides a dispersive mechanism for noise filtering. The bandwidth of the dispersion-induced noise peaks is ∼1 order of magnitude below the repetition-rate frequency.

Modal propagation in gradient-index (grin) material

Abstract In this paper, the problem of modal propagation in a GRIN material has been considered. A detailed solution of this problem, by a perturbative method, shows that within the limits of the paraxial approximation one would conclude, erroneously, that perfect image transmission is possible. By a more exact treatment we determine the maximum distance for which can be transmitted an image without estimable loss of information due to modal dispersion.

Fractional Talbot effect in a Selfoc gradient-index lens

The fractional Talbot effect is demonstrated inside a standard 0.25-pitch Selfoc gradient-index lens under uniform illumination. Comparisons with theoretical expressions of positions and magnification of fractional Talbot images are given.

Talbot effect in a tapered gradient-index medium for nonuniform and uniform illumination

A generalization of the Talbot effect to the case of a tapered gradient-index medium for nonuniform and uniform illumination is considered. Self-image positions are changed by a function depending on the taper profile, the illumination, and the periodic object. An analogy with the conventional lens-imaging formula for both types of illumination is presented.

Gradient parameter and axial and field rays in the gradient-index crystalline lens model

Gradient-index models of the human lens have received wide attention in optometry and vision sciences for considering how changes in the refractive index profile with age and accommodation may affect refractive power. This paper uses the continuous asymmetric bi-elliptical model to determine gradient parameter and axial and field rays of the human lens in order to study the paraxial propagation of light through the crystalline lens of the eye.