Carles Pizarro

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.

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.

Flux spatial emission obtained from technical specifications for a general filament light source

A new, to our knowledge, method for evaluating three-dimensional flux distributions for general filament light sources is presented. The main advantages of the developed model are its generality and its simplicity. From plots of the emitted luminous intensity, usually provided by the lamps manufacturer, in three orthogonal planes a detailed account is given of how to establish flux emission from the light source in any direction. The method involves a selective smoothing procedure, a curve-fitting step, and a final interpolation. A full model is developed for a typical commercial filament bulb (Philips, Model P21W Inco K) that is quite common in many industrial applications. A fourth intensity plot, usually provided by the lamps manufacturer, is used to validate the model. To confirm the validity of the model further, we present an industrial application (the photometric simulation of a car taillight) that uses the modeled Philips Model P21W source. A comparison between simulated data obtained by use of the developed P21W model and measured results at our industrial partners laboratories reinforces the proposed source model.

Third-order aberrations of an AGRIN thin lens as a function of the shape and conjugate variables

This work presents the expressions for the third-order aberrations of a thin lens in air made with an axial gradient index material (AGRIN). These are derived from those corresponding to two homogeneous plano-aspheric thin lenses, with the plano surface in contact, as it has been proposed. Further, they have been expressed as a function of the shape factor, B, and conjugate variable, C, to be consistent with those previously published considering other thin-lens cases. Simple examples of their suitability for obtaining a third-order system predesign are shown.

Analysis of the robustness of the lens GRIN profile in a schematic model eye

In this work, an improvement of a previously-published human eye model with aging is presented. The previous eye model showed the overestimated performance of an averaged MTF at low spatial frequencies at all ages. Since that model had rotationally symmetrical corneal surfaces, these have been modeled to resemble an astigmatic element according to the recent experimental published data and have been included to produce a more accurate eye model. The gradient refractive index (GRIN) profile proposed for the crystalline lens has not been modified to test its robustness. Further, a tilt and decentration of the lens, and only a decentration for the iris, have been permitted in order to fit the average performance of the new eye model with aging. The results demonstrate that the GRIN profile for the crystalline lens fits the model well, since the decentration and/or tilt of the lens and the iris are sufficient free parameters to simulate the performance of the retinal image quality of an emmetropic human eye with aging, having an average astigmatic cornea.

Comparison of flux-tracing-based and diffraction-based strategies for optical system evaluation

We report the comparison between two methods to evaluate optical systems. The flux-tracing method is an extension of the classical ray-tracing methods with additional energetic features. The direct integration method involves the calculation of the integral appearing in the diffraction theory of aberrations. We give a brief outline of the two methods and compare the results on a standard optical system. This will help to put in common the two methods to try to formulate new algorithms for the design of optical systems.

LED misalignment determination in LED illumination optics using hole grid pattern distribution

This paper presents a method for determining the degree of misalignment between a LED and its epoxy encapsulation in a simulated environment. The misalignment is determined by analyzing the light emitted by the optoelectronic component and transmitted through a grid of holes. The results obtained are compared with simulated and experimental registers wherein there is no misalignment between the LED and the epoxy but a displacement of the whole optoelectronic component perpendicularly to the observation axis. We prove that the method used allows us to distinguish between the existence of misalignment inside the optoelectronic component and a simple displacement between the optoelectronic component and the observation axis.

Simulation of imperfections in plastic lenses – transferring local refractive index changes into surface shape modifications

Abstract Injection molded plastic lenses have continuously improved their performance regarding optical quality and nowadays are as usual as glass lenses in image forming devices. However, during the manufacturing process unavoidable fluctuations in material density occur, resulting in local changes in the distribution of refractive index, which degrade the imaging properties of the polymer lens. Such material density fluctuations correlate to phase delays, which opens a path for their mapping. However, it is difficult to transfer the measured variations in refractive index into conventional optical simulation tool. Thus, we propose a method to convert the local variations in refractive index into local changes of one surface of the lens, which can then be described as a free-form surface, easy to introduce in conventional simulation tools. The proposed method was tested on a commercial gradient index (GRIN) lens for a set of six different object positions, using the MTF sagittal and tangential cuts to compare the differences between the real lens and a lens with homogenous refractive index, and the last surface converted into a free-form shape containing the internal refractive index changes. The same procedure was used to reproduce the local refractive index changes of an injected plastic lens with local index changes measured using an in-house built polariscopic arrangement, showing the capability of the method to provide successful results.