Jorge Ares

Direct transformation of Zernike eye aberration coefficients between scaled, rotated, and/or displaced pupils

In eye aberrometry it is often necessary to transform the aberration coefficients in order to express them in a scaled, rotated, and/or displaced pupil. This is usually done by applying to the original coefficients vector a set of matrices accounting for each elementary transformation. We describe an equivalent algebraic approach that allows us to perform this conversion in a single step and in a straightforward way. This approach can be applied to any particular definition, normalization, and ordering of the Zernike polynomials, and can handle a wide range of pupil transformations, including, but not restricted to, anisotropic scalings. It may also be used to transform the aberration coefficients between different polynomial basis sets.

Position and displacement sensing with Shack–Hartmann wave-front sensors

The use of a Shack-Hartmann wave-front sensor as a position-sensing device is proposed and demonstrated. The coordinates of a pointlike object are determined from the modal Zernike coefficients of the wave fronts emitted by the object and detected by the sensor. The position of the luminous centroid of a moderately extended incoherent flat object can also be measured with this device. Experimental results with off-the-shelf CCD cameras and conventional relay optics as well as inexpensive diffractive microlens arrays show that axial positioning accuracies of 74 microm rms at 300 mm and angular accuracies of 4.3 microrad rms can easily be achieved.

Presbyopia compensation with a quartic axicon.

Purpose. The purpose of this study was to evaluate the performance of quartic axicons for presbyopia compensation. The working principle relies on profiting the high depth of focus of the axicons to supplement the reduced accommodation amplitude of presbyopes. Methods. We present the design equations of a particular kind of axicon to compensate a general presbyopia condition using simultaneous vision. A rotationally symmetric polynomial of fourth-order, corresponding to the well-known Seidel spherical aberration term, was chosen as its refractive profile. To validate its performance, we computed the retinal images with Stiles-Crawford apodization for a presbyopic eye compensated with this quartic axicon and compared them with those obtained without compensation or with other available solutions based on the simultaneous vision principle. Results. The quartic axicon provides an important improvement of the image quality for intermediate distance vision in comparison with conventional bifocal and trifocal solutions. The image quality, however, is still not optimum for all distances. Conclusions. The results show the usefulness of the proposed approach and point out the need for developing further adapted optimizations.

Influence of thresholding on centroid statistics: full analytical description

The centroid method is a common procedure for subpixel location that is applied to a large number of optical sensors. In practice, it is always accompanied by thresholding algorithms used to eliminate undesirable background that may decrease precision. We present a full analytical description of the interaction between centroiding and thresholding applied over an intensity distribution corrupted by additive Gaussian noise. An in depth analysis of the most outstanding statistical properties of this relation (mean and variance) is also presented by means of simulated and experimental data. This work provides fundamental concepts to the designers of sensors that are based on centroid measurements to allow them to use thresholding correctly before centroid computation.

Influence of thresholding on centroid statistics

Centroid determination is a relevant task for many optical measurement devices which is very often calculated over thresholded data. In presence of additive gaussian noise for the intensity, the influence of thresholding in the statistical properties of the calculated centroids is described. It has been performed theoretical, simulated and experimental analysis of the purposed influence model obtaining good agreement between them.

Minimum-variance centroid thresholding

Image processing thresholding algorithms are very extended segmentation tools for tracking applications. The centroid of the tracked image distribution use to be a good point of reference for locating it. In this work we show a new thresholding technique which is based in the estimation of the optimum threshold value for achieving the minimal variance in the calculated centroid for the processed image. One experience was done for evaluating its performance qualities. The direct extension of these results to Shack- Hartmann wave-front sensors advantages and possibilities of application of this technique.

Repeatability and Reproducibility of Virtual Subjective Refraction.

Purpose To establish the repeatability and reproducibility of a virtual refraction process using simulated retinal images. Methods With simulation software, aberrated images corresponding with each step of the refraction process were calculated following the typical protocol of conventional subjective refraction. Fifty external examiners judged simulated retinal images until the best sphero-cylindrical refraction and the best visual acuity were achieved starting from the aberrometry data of three patients. Data analyses were performed to assess repeatability and reproducibility of the virtual refraction as a function of pupil size and aberrometric profile of different patients. Results SD values achieved in three components of refraction (M, J0, and J45) are lower than 0.25D in repeatability analysis. Regarding reproducibility, we found SD values lower than 0.25D in the most cases. When the results of virtual refraction with different pupil diameters (4 and 6 mm) were compared, the mean of differences (MoD) obtained were not clinically significant (less than 0.25D). Only one of the aberrometry profiles with high uncorrected astigmatism shows poor results for the M component in reproducibility and pupil size dependence analysis. In all cases, vision achieved was better than 0 logMAR. A comparison between the compensation obtained with virtual and conventional subjective refraction was made as an example of this application, showing good quality retinal images in both processes. Conclusions The present study shows that virtual refraction has similar levels of precision as conventional subjective refraction. Moreover, virtual refraction has also shown that when high low order astigmatism is present, the refraction result is less precise and highly dependent on pupil size.

Linear squares modal estimation of wrapped phases: application to phase unwrapping

Phase unwrapping continues to be an important step in those techniques that obtain the phase from Fourier-transforms; Fringe pattern analysis, Speckle Interferometry, and Phase Recovery among others. In this Letter we propose a fast two-dimensional phase unwrapping algorithm which consists of a reconstruction of the wrapped phase by modal least-squares estimation. This algorithm has been developed to work with continuous phases that can be developed as a linear combination of a set of orthogonal polynomials. Theoretical description of the method and simulations are presented.

New algorithm for spatial phase recovery using intensity measurements

We present a new spatial phase diversity algorithm, using intensity measurements obtained in two different planes: the focal plane, and a displaced plane near to the focal point. The algorithm consists of a hybridization of a kind of Gerchberg-Saxton iterative algorithm with the hybrid one has been performed, finding that we can recover more complicated phases with the new proposed algorithm.