Josep Arasa

Single dispersive gradient-index profile for the aging human lens

We provide a single gradient-index (GRIN) profile for the crystalline lens in an updated age-dependent emmetropic-eye model. The parameters defining the GRIN profile include their variation with age and the dispersion of the refractive index in order to account for the increase in the positive-wave spherical aberration, for the constant chromatic difference in the refraction of the human eye, as well as for the decrease in the retinal-image quality with aging. In accounting for these ocular properties, the results show that first, the value of the dispersion parameters are invariant with age. Second, those parameters defining the distribution of the lens index cause the lens-center-index value to decrease slightly, and its position along the lens axis changes with age. Furthermore, these findings are in agreement with the lens paradox.

Influence of amount and changes in axis of astigmatism on retinal image quality

We measured retinal image quality in astigmatic eyes, using the double-pass technique. We analyzed the influence of the amount of astigmatism and changes in axis of astigmatism on the eyes optical performance. Different amounts of astigmatism were obtained by variation of the cylindrical power of a lens situated in front of the eye, between 0.25-diopter (D) overcorrection and 1-D undercorrection at intervals of 0.25 D. Changes in the axis of astigmatism were obtained by rotation of the lens, which neutralizes the astigmatism in an angle of +/- 10 degrees at 5 degrees intervals. The results show the decrease in retinal image quality and the increase in the degree of image astigmatism obtained when the amount of astigmatism increases or the angle between the lens and the eye axis is other than zero. In general, the largest variations correspond to when the astigmatism changes from 0 to 0.25 D or when the axis changes from 0 degree to +/- 5 degrees. The reduction in optical performance is smaller in living eyes than in an eye model or in an artificial eye. The aberrations present in the living eye reduce the relative loss of retinal image quality introduced by astigmatism.

A micrometric non-contact profiler for optical quality surfaces

A non-contact technique for obtaining accurate profiles of optical quality surfaces with micrometric accuracy has been developed. The technique is based on the Ronchi test principle, that is, on the study of the interaction of a wavefront reflected on the surface to be profiled with a square-wave transmittance ruling. From the resultant fringe pattern and some basic geometrical optics principles it is possible to measure the local normal to the surface being tested at a set of given points. This local normal map may then be integrated, yielding the surface profile. By use of a theoretically expected surface shape, the main parameters of the surface may then be determined by surface fitting of the measured data to that expected surface shape. Results of the profilometric measurements both of a spherical and of a toroidal surface are presented. The measured profiles are validated by comparison of the radii of curvature obtained using a high precision radioscope with the ones obtained by surface fitting of the measured profiles to their expected surface shapes. Additionally, subtracting the best-fit theoretical surface from the measured profile allows the observation of surface deviations from the theoretical shape to within some tenths of a nanometres.

Design of an interferometric system for the measurement of phasing errors in segmented mirrors

One of the new problems that has to be solved for segmented mirrors is related to periodic phasing, because for such mirrors to exhibit diffraction-limited performance the segments have to be positioned with an accuracy of a fraction of a wavelength. We describe the optical design of an instrument that measures the phasing errors (i.e., tip, tilt, and piston) between two segments under daylight conditions. Its design is based on a high-aperture white-light Michelson interferometer. It was developed at the Center for Sensors, Instruments and Systems Development (CD6) of the Technical University of Catalunya, Spain, and its final testing was carried out on the Gran Telescopio Canarias test workbench.

Zernike coefficients for concentric, circular scaled pupils: an equivalent expression

We present an alternative formal calculation of the scaled Zernike coefficient expansion by means of the inner product of the Zernike polynomials and the wavefront error corresponding to the scaled pupil. The relationship exhibited by the radial polynomials and Bessel functions leads to a general expression in terms of the Gauss hypergeometric function. Direct properties and index selection rules are established, and easy derivation of the non-normalized coefficients is also straightforward.

Profilometry of toroidal surfaces with an improved Ronchi test

An implementation of the well-known Ronchi test technique, which allows for the profilometric measurement of nonrotationally symmetrical surfaces, is presented and applied to the measurement of toroidal surfaces. Both the experimental setup and the data-processing procedures are described, and parameters such as the radius of curvature of the sample surface, the orientation of its principal meridians, and the position of its vertex are measured by means of the values of the local normal to the surface obtained at a set of sampling points. Integration of these local normal values allows for the reconstruction of the three-dimensional profile of the toroidal surface considered with micrometric accuracy, and submicrometric surface details may be calculated by use of surface-fitting procedures. The density of sampling points on the surface may be tailored to fit test requirements, within certain limits that depend on selection of experimental setup.

Simple method for improving the sampling in profile measurements by use of the Ronchi test

We present a simple method for increasing the number of data points obtained during performance of profilometric measurements with the Ronchi test. The method is based on multiple ronchigram acquisitions that are superimposed after a few very simple data-processing operations. The measurement method, experimental setup, and data processing are described in detail from the ronchigram to the measured profile, and experimental results for a concave surface of an spherical ophthalmic lens are provided. The radius of curvature values measured for that surface are compared with the ones obtained with a high-precision radioscope, showing very good agreement and demonstrating the capability of the technique to measure topographic profiles of reflective samples.

Derivation of the propagation equations for higher order aberrations of local wavefronts

From the literature the analytical calculation of local power and astigmatism of a wavefront after refraction and propagation is well known; it is, e.g., performed by the Coddington equation for refraction and the classical vertex correction formula for propagation. Recently the authors succeeded in extending the Coddington equation to higher order aberrations (HOA). However, equivalent analytical propagation equations for HOA do not exist. Since HOA play an increasingly important role in many fields of optics, e.g., ophthalmic optics, it is the purpose of this study to extend the propagation equations of power and astigmatism to the case of HOA (e.g., coma and spherical aberration). This is achieved by local power series expansions. In summary, with the results presented here, it is now possible to calculate analytically the aberrations of a propagated wavefront directly from the aberrations of the original wavefront containing both low-order and high-order aberrations.

Progressive addition lenses power map measurement using Ronchi test techniques

Progressive ophthalmic lenses involve high resolution technological manufacturing processes, due to the particular non-symmetrical, aspherical form of their convex surface. However, the testing of the surfaces is not usually performed using whole-field methods because of the high dynamic range and resolution required for the slope changes in the convex surface. Applying some simple enhancements, a robust Ronchi test technique can be used to obtain accurate power distribution maps of commercial progressive lenses. In this technique, a CCD detector is used as a high resolution slope map, which combined with multiple acquisition techniques, allow for high resolution measurements of both lateral displacement (10-4 m) and slope measurements (10-5 rad) with the required dynamic range in slope measurements for progressive power lenses. The power maps of different types of progressive lenses are presented, showing the differences between lens design and manufacturing. The ability of the enhanced Ronchi test technique to quantitatively map power variations with important slope changes is demonstrated.

Compact System for Photometric Characterization of Automotive Headlamps

We present a system allowing the determination of the distribution of light at any given distance (e.g. 25m) from a light source, by measuring the intensity and direction of the illumination distribution at a closer distance (e.g. near 20 cm). The measurement principle is based on the acquisition of images taken by a CCD matrix-sensor through an optical system focused at infinity. A sequence of images is obtained by moving the camera at different positions in front of the source. The process involves the accumulation of shifted images and corrections for optics (geometrical distortion and vignetting) and electronic shutter (exposure time). We describe the developed experimental set-up and the calibration procedures needed to obtain absolute photometric values. We present results obtained for automotive headlamps: computed relative illumination distribution is very similar to that obtained using a reference given by a measurement tool using a lightmeter. Absolute calibration of the system is performed from the set of measured points