Eduardo Tepichín

Experimental demonstration of optical Mathieu beams

We report the first experimental observation of zero-order Mathieu beams which are fundamental non-diffracting solutions of the wave equation in elliptic cylindrical coordinates.

Arbitrarily high focal depth with a quasioptimum real and positive transmittance apodizer

Focal depth is assessed by the average value of the square modulus of the slope associated with the complex amplitude along the optical axis. Then, the calculus of variations is used for identifying the optimum apodizer, characterized by a Strehl ratio vs defocus with high focal depth, for a specified light throughput. We show that a certain Lorentzian profile is a quasioptimum solution for the above requirements. This apodizer has real and positive transmittance, and it can be modified to achieve arbitrarily high focal depth. A closed formula relates focal depth to light throughput.

Optical implementation of the fractional Hilbert transform for two-dimensional objects

The classical Hilbert transform can be implemented optically as a spatial-filtering process, whereby half the Fourier spectrum is pi-phase shifted. Recently the Hilbert transform was generalized. The generalized version, called the fractional Hilbert transform, is quite easy to implement optically if the input is one dimensional. Here we show how to implement the fractional Hilbert transform for two-dimensional inputs. Hence the new transform is now suitable for image processing.

Apodization of annular apertures: Strehl ratio

We show that for any rotationally symmetric apodizer on the full aperture, there is a family of apodizers on the annular aperture with the same functional Strehl ratio vs defocus (W(20)) and vs spherical aberration (W(40)). However, in the latter case, the coefficients W(20) and W(40) are reduced by the factors (1 - epsilon(2)) and (1 - epsilon(2))(2) respectively, where is the central obscuration ratio. We indicate that the best focal plane is shifted from W(20) = - W(40) to W(20) = -(1 + epsilon(2)) W(40). These general results allow us to design and to compare novel apodizers on annular apertures which reduce the influence of W(20) and W(40). The Strehl ratios of a novel family of apodizers are discussed to illustrate our general results.

Advanced Surface Ablation for Presbyopia Using the Nidek EC-5000 Laser

PURPOSE To present 1 to 6-month follow-up results of laser in situ keratomileusis (LASIK) using multizone presbyopic advanced surface ablation (PASA) with a peripheral near zone. METHODS LASIK was performed on 28 eyes of 17 patients (10 men and 7 women; mean age 49.8 years with a range of 37 to 62 years). Eyes had primary or enhancement treatments with the Nidek EC-5000 excimer laser. Three techniques were used: 1) total transepithelial ablation, 2) surface ablation for far vision ametropia correction, and 3) concentric peripheral near zone presbyopia correction (technique developed by Dr. A. Telandro with a modified nomogram by Dr. R. Cantú for surface ablation). One surgeon (RC) performed all surgery. RESULTS We present the preoperative and postoperative measurements for far and near uncorrected visual acuity, total high order aberrations, spherical aberration (Z-12), asphericity Q index, eccentricity corneal shape factor, and total coma and trefoil aberrations. Increases occurred in negative spherical aberration, negative asphericity index, and positive eccentricity corneal shape factor. CONCLUSIONS Advanced surface ablation for presbyopia with a concentric peripheral near zone is a promising approach for surgical correction of presbyopia and potentially could be used with any advanced surface ablation procedure. Increases in negative spherical aberration and asphericity/ eccentricity indices seemed to increase the depth of focus of the eye, improving the near vision.

Objective quality of vision in presbyopic and non-presbyopic patients after pseudoaccommodative advanced surface ablation.

PURPOSE To analyze the objective quality of vision at 6 months postoperatively after pseudoaccommodative (presbyopic) advanced surface ablation (PASA). METHODS The study comprised 62 eyes of 35 patients with 6-month follow-up that underwent primary or secondary treatments using PASA. Pre- and postoperative results of distance and near uncorrected visual acuity (UCVA), spherical aberration (coefficient of the Z12 Zernike polynomial), and the asphericity (Q) index were reviewed. The corresponding wavefront maps (total, low, and high order aberrations) and the corresponding point spread function and modulation transfer function (MTF) were also calculated. RESULTS Our results show that PASA improves distance and near mean UCVA, increases negative spherical aberration and negative asphericity index, and improves the corresponding MTF. CONCLUSIONS Pseudoaccommodative advanced surface ablation is a promising approach for the surgical correction of presbyopia with distance refractive error (myopia and hyperopia with or without astigmatism). This PASA technique could theoretically be used in non-presbyopic patients with refractive error or post cataract patients with monofocal intraocular lenses. The increase in negative spherical aberration and asphericity/eccentricity index seems to increase the depth of focus of the eye, improving the near vision and compensating the age-related lens changes. Rather than creating a multifocal cornea, PASA appears to create an improved aspheric (prolate) ablation profile.

Anterior corneal profile with variable asphericity.

We present a corneal profile in which the eccentricity, e(Q=-e(2)), has a nonlinear continuous variation from the center outwards. This nonlinear variation is intended to fit and reproduce our current experimental data in which the anterior corneal surface of the human eye exhibits different values of e at different diameters. According to our clinical data, the variation is similar to an exponential decay. We propose a linear combination of two exponential functions to describe the variation of e. We then calculate the corneal sagittal height by substituting e in the first-order aspherical surface equation to obtain the corneal profile. This corneal profile will be used as a reference to analyze the resultant profiles of the customized corneal ablation in refractive surgery.

Talbot interferometer with simultaneous dark and bright fields

We describe an optical setup for implementing a Talbot interferometer that uses two mutually incoherent sets of self-images to simultaneously produce interference bands due to dark and bright fields. A spatial filter can be used to visualize these fields without interference fringes. Experimental results are included.

Objective performance of a set of uncorrected 20/20 normal eyes: clinical reference

In recent years we have been working in the characterization of the objective average performance of a set of uncorrected human eyes with a 20/20 visual acuity, described as the resultant average wavefront aberration function (WA), point-spread function (PSF), modulation transfer function (MTF), and power refractive maps. This objective performance has been used as our clinical reference to analyze the objective pre- and post-operated performance in laser refractive surgery in different situations. We show some of our current results obtained from the application of our clinical reference.

A new model for the anterior corneal surface using higher-order aspheric surfaces and variable eccentricity

Contact lenses manufacturers and ophthalmologists who perform laser surgery to correct visual problems depend on an accurate model of the anterior corneal surface. Several models have been suggested in the past, going from Gullstrands initial idea to the aspheric profiles and to Bonnets profile based on anatomical data. Clinical evidence shows, however, that the anterior corneal surface is characterized by a variable eccentricity, contrary to the hypothesis on which the current models are based. We present, in this work, a new model for the anterior corneal surface in terms of higher-order aspheric surfaces in which the eccentricity at a given point of the cornea is a continuous function of its distance to the optical axis. We also establish the conditions under which the different conic and Bonnets profiles are recovered from our model. Finally, we present our preliminary results using this model.