*J Opt Soc Am A Opt Image Sci Vis ; 37(8): 1381-1389, 2020 Aug 01.*

##### RESUMEN

Placido disk methods for corneal topography use a target with concentric rings in order to obtain measurements of the corneal surface, codifying the topography from the deformations of the rings' image. Knowing exactly how the corneal surface departs from a rotational symmetric shape is difficult by using Placido rings. This is due to the fact that any ray deviations in the angular direction (sagittal transverse aberrations) are not easily detected and measured. This is the so-called skew ray error. For that reason, this technique has been considered as limited, especially when one tries to measure corneal aberrations with large rotational symmetry errors. However, we considered that the Placido disk topography has the potential to obtain a full description of the corneal surface as long as the skew ray error is fixed. Here, we present a solution based in the assumption that a corneal topography calculated with the presence of the skew ray error has hidden information that can be extracted by applying some basis of the classical Hartmann test. To achieve that solution, we improve some aspects of the Hartmann test to be later applied in the processing of Placido disk images. Our solution gives us the ability to solve the skew ray error in a simple and direct method, with an effectiveness that is probed by the computing of some simulated representative surfaces without rotational symmetry and the performance of our algorithm.

*J Ophthalmol ; 2019: 7018937, 2019.*

##### RESUMEN

Prospective, randomized, comparative, and controlled study to estimate the association between angle κ distance and higher-order aberrations (HOAs) with postoperative visual acuity after presbyopia-correcting IOL implantation. Forty-three eyes from 43 patients were included and randomly assigned in two groups for either AT LISA tri 839MP or Acrysof IQ PanOptix IOL implantation. The OPD-Scan III analyzer was utilized to assess the angle κ distance and higher-order aberration (HOAs). Twenty-three eyes were in the Acrysof IQ PanOptix group and 20 patients in the AT LISA tri 839MP group. The uncorrected distance visual acuity (UDVA) for the PanOptix group was 0.092 ± 0.10, whereas for AT LISA tri was 0.050 ± 0.06 (P=0.229). The uncorrected intermediate visual acuity (UIVA) for the PanOptix group was 0.173 ± 0.18, whereas for AT LISA tri, it was 0.182 ± 0.11 (P=0.669). Uncorrected near visual acuity (UNVA) was 0.068 ± 0.04 and 0.085 ± 0.07, respectively (P=0.221). Also, correlation coefficient between HOAs and the Strehl ratio for each group were -0.768 (P < 0.0001) and -0.863 (P=0.0001). Patients implanted with both trifocal IOLs showed excellent postoperative visual performance at all distances at the six-month follow-up visit. No association was found between angle κ distance and postoperative visual acuity regardless of the angle κ magnitude or the two trifocal IOLs inner optical diameter. Also, internal aberrations demonstrated a significant inverse correlation with the Strehl ratio for both trifocal IOLs.

*Appl Opt ; 56(7): 1898-1907, 2017 Mar 01.*

##### RESUMEN

Instead of measuring the wavefront deformations, Hartmann and Shack-Hartmann tests, we measure the wavefront slopes, which are equivalent to the ray transverse aberrations. Numerous different integration methods have been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified in two different categories, i.e., modal and zonal. In this paper, we describe a proposed new zonal procedure. This method finds a different analytical expression for each square cell formed by four sampling points in the pupil of the system. In this manner, a full single analytical expression for the wavefront is not obtained. The advantage is that small localized errors that cannot be adjusted by a single polynomial function can be represented with this method. A second advantage is that the analytical function for each cell is obtained in an exact manner, without the errors in a trapezoidal integration.

*Appl Opt ; 56(4): 1215-1224, 2017 Feb 01.*

##### RESUMEN

In a previous work, we introduced the concept of transversal aberrations {U,V} calculated at arbitrary Hartmann-plane distances z=r [Appl. Opt.55, 2160 (2016)APOPAI1559-128X10.1364/AO.55.002160]. These transversal aberrations can be used to estimate the wave aberration function W, as well as the classical transversal aberrations {X,Y} calculated at a theoretical plane z=f, where f is the radius of a reference semisphere. However, when the ray identification is difficult to achieve at z=f, the use of {U,V} can be of great help. In the context of a least-squares fitting of the Hartmann data, the use of {U,V} is proposed by analyzing some simple examples for the case of a W with aberration terms up to the third order. These examples also consider the hypothesis fâ«W, as presented in the majority of the optical applications.

*Appl Opt ; 54(28): E113-22, 2015 Oct 01.*

##### RESUMEN

A least-squares procedure to find the tilts, curvature, astigmatism, coma, and triangular astigmatism by means of measurements of the transverse aberrations using a Hartmann or Shack-Hartmann test is described. The sampling points are distributed in a ring centered on the pupil of the optical system. The properties and characteristics of rings with three, four, five, six, or more sampling points are analyzed with more detail and better mathematical analysis than in previous publications.

*Appl Opt ; 54(9): 2296-301, 2015 Mar 20.*

##### RESUMEN

In this paper we will review some of the many different practical arrangements that have been obtained to measure the transversal aberrations of optical systems based on the odd and vulnerable Hartmann test. There are many optical testing configurations that apparently are not related to the original Hartmann test. However, they are really the same thing and can be considered just a variation of the same basic arrangement, as will be described here.

*Appl Opt ; 53(31): 7422-34, 2014 Nov 01.*

##### RESUMEN

Instead of measuring the wavefront deformations, Hartmann and Shack-Hartmann tests measure wavefront slopes, which are equivalent to ray transverse aberrations. Numerous integration methods have been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified in two different categories, i.e., modal and zonal. Frequently, a least squares fit of the transverse aberrations in the x direction and a least squares fit of the transverse aberrations in the y direction is performed to obtain the wavefront. In this work, we briefly describe a modal method to integrate Hartmann and Shack-Hartmann patterns by means of a single least squares fit of the transverse aberrations simultaneously instead of the traditional x-y separate method. The proposed method uses monomial calculation instead of using Zernike polynomials, to simplify numerical calculations. Later, a method is proposed to convert from monomials to Zernike polynomials. An important obtained result is that if polar coordinates are used, angular transverse aberrations are not actually needed to obtain all wavefront coefficients.

*J Opt Soc Am A Opt Image Sci Vis ; 31(4): 846-51, 2014 Apr 01.*

##### RESUMEN

Instead of measuring the wavefront deformations directly, Hartmann and Shack-Hartmann tests measure the wavefront slopes, which are equivalent to the ray transverse aberrations. Numerous different integration methods have been described in the literature to obtain the wavefront deformations from these measurements. Basically, they can be classified in two different categories, i.e., modal and zonal. In this work we describe a modal method to integrate Hartmann and Shack-Hartmann patterns using orthogonal wavefront slope aberration polynomials, instead of the commonly used Zernike polynomials for the wavefront deformations.

*Appl Opt ; 53(6): 1191-9, 2014 Feb 20.*

##### RESUMEN

The measurement of astigmatic lenses, optical surfaces or wavefronts are a highly studied problem and many different instruments have been commercially fabricated to perform this task. Many of them use a Hartmann arrangement to obtain the result. In this paper, we analyze with detail the algorithms that can be used to make the necessary calculations and propose several alternatives with different advantages and disadvantages. Different mathematical algorithms that are involved in the calculation process have been given whereas any description of the instrument itself is not proposed, but only the different mathematical algorithms that are involved in the calculation process.

*J Opt Soc Am A Opt Image Sci Vis ; 30(12): 2595-604, 2013 Dec 01.*

##### RESUMEN

Adaptive optics (AO) imaging methods allow the histological characteristics of retinal cell mosaics, such as photoreceptors and retinal pigment epithelium (RPE) cells, to be studied in vivo. The high-resolution images obtained with ophthalmic AO imaging devices are rich with information that is difficult and/or tedious to quantify using manual methods. Thus, robust, automated analysis tools that can provide reproducible quantitative information about the cellular mosaics under examination are required. Automated algorithms have been developed to detect the position of individual photoreceptor cells; however, most of these methods are not well suited for characterizing the RPE mosaic. We have developed an algorithm for RPE cell segmentation and show its performance here on simulated and real fluorescence AO images of the RPE mosaic. Algorithm performance was compared to manual cell identification and yielded better than 91% correspondence. This method can be used to segment RPE cells for morphometric analysis of the RPE mosaic and speed the analysis of both healthy and diseased RPE mosaics.

##### Asunto(s)

Células Epiteliales/fisiología , Epitelio Pigmentado de la Retina/patología , Algoritmos , Animales , Automatización , Simulación por Computador , Fluorescencia , Humanos , Procesamiento de Imagen Asistido por Computador , Luz , Macaca , Microscopía Fluorescente/métodos , Distribución Normal , Oftalmoscopía/métodos , Óptica y Fotónica , Epitelio Pigmentado de la Retina/citología*Appl Opt ; 50(7): 1057-64, 2011 Mar 01.*

##### RESUMEN

The main constraint of classical off-axis reflecting systems is the primary astigmatism that has long been a research topic of interest. This astigmatism in off-axis spherical reflective imaging systems can be eliminated by using the proper configuration. These configurations could be derived from the marginal ray fans equation, and they are valid for small angles of incidence. The conditions for the astigmatism compensation in configurations with two and three off-axis mirrors have been derived and analyzed, which have not been reported previously. The expression that defines the conditions for primary astigmatism compensation in a four-mirror system is presented. This shows that the marginal ray fan equation can be used to obtain the condition for astigmatism compensation of a reflective system with any number of mirrors. The developed methodology is verified by ray-tracing analysis of some examples.

*Appl Opt ; 50(1): 66-73, 2011 Jan 01.*

##### RESUMEN

We present, analyze, and evaluate expressions for the wavefront aberrations in an off-axis spherical mirror. These formulas are derived from the optical path difference between an ellipsoid and a sphere, assuming a relatively small pupil and a small angle of incidence, as will be described in detail. Some well-known and also some useful new aberration expressions are obtained. They can be used to design and analyze cavities, spectrographs, and retinal adaptive optics imaging systems.

*Opt Express ; 17(21): 18906-19, 2009 Oct 12.*

##### RESUMEN

Expressions for minimal astigmatism in image and pupil planes in off-axis afocal reflective telescopes formed by pairs of spherical mirrors are presented. These formulae which are derived from the marginal ray fan equation can be used for designing laser cavities, spectrographs and adaptive optics retinal imaging systems. The use, range and validity of these formulae are limited by spherical aberration and coma for small and large angles respectively. This is discussed using examples from adaptive optics retinal imaging systems. The performance of the resulting optical designs are evaluated and compared against the configurations with minimal wavefront RMS, using the defocus-corrected wavefront RMS as a metric.

*Appl Opt ; 45(22): 5629-35, 2006 Aug 01.*

##### RESUMEN

We present the approximate polynomial expression for an ellipsoid with rotational symmetry about its major axis, which is on the y-z plane and at angle theta with respect to the z axis. These expressions have many possible useful applications in optics as shown. The main optical properties of these types of inclined ellipsoidal surface will be reviewed.

*Appl Opt ; 44(20): 4228-38, 2005 Jul 10.*

##### RESUMEN

In the classical Hartmann test the wave front is obtained by integration of the transverse aberrations, joining the sampled points by small straight segments, in the so-called Newton integration. This integration is performed along straight lines joining the holes on the Hartmann screen. We propose a modification of this procedure, considering the cells of four holes of the Hartmann screen to fit a small second-power wave front recovering each square. This procedure has some important advantages, as described here.