Hala Kamal

Properties of moire´ magnifiers

Javier Alda Ciudad Universitaria Universidad Complutense de Madrid Facultad de Fisicas Departamento de Optica 28040 Madrid, Spain Abstract. Moire magnification can be observed visually if an array of identical objects is viewed through an array of identical microlenses with a different period. Theoretical analysis and experimental results of the moire image obtained by a moire magnifier are presented. Conditions for erect and inverted moire magnifications are derived and interpreted. Virtual erect images are observed only when the period of the lens array is larger than that of the object array, while inverted images are obtainable in both cases. For equal periods, a uniform field of view results. The relation between the relative size of the periods and the distance between the object and the lens arrays are derived. Expressions for image magnification, orientation and size are deduced. The condition to obtain a demagnified moire pattern is deduced. Rotation of the lens array with respect to the object array results in rotation of the erect and inverted moire patterns in similar and opposite directions, respectively.

Optimization of the input surface of a thick-lens spatial-integrator array for maximum flux transfer efficiency

Summary The radius of curvature of the input surface of a thick lens spatial integrator array is a free parameter that can be customized for a maximum flux transfer efficiency. With this procedure each element is different but the spatial integration feature remains for the whole array. The calculation is based on a real ray-tracing evaluation that also takes into account the transmissivity of the diopters. The flux transfer on the synthetic image is doubled when the input surfaces are propoerly optimized.

Optimum focal length range for thin-lens optical arrays providing spatial integration

Hala KamalDaniel Va´zquezJavier AldaUniversity Complutense of MadridSchool of OpticsOptics DepartmentAv. Arcos de Jalo´n s/n28037 Madrid, SpainE-mail: dvazquez@fis.ucm.esAbstract. A spatial integrator is an optical array characterized by a raytransfer matrix having a zero determinant. The design of a spatial inte-grator is explained using the relations among the geometric parametersof the array and the optical characteristics of its components. We focusour attention on spatial integrators constructed by using units composedof two thin lenses. The spatial integration does not depend on the focallength of the first lens. Although that focal length can be arbitrarily se-lected, we have found a range of its values that increases the amount ofenergy falling on the synthetic image and improves its uniformity. Thisanalysis has been done for spatial integrator arrays having a sphericaldome configuration and having a planar configuration. The study hasbeen done both in the paraxial range and by using real ray-tracing tools.This optimization procedure is of interest in the design of spatial integra-tor arrays for illumination and natural lighting applications.

Design alternatives for a thin lens spatial integrator array

In this paper we analyze different alternatives in the design of optimized optical arrays having spatial integration feature in a plane arrangement. More specifically, we focus our attention in the evaluation of the number of useful individual units, and its contribution to the synthetic image characteristics. The analysis has been made by using matrix optics relations. Two examples of planar thin lens spatial integrator arrays are designed and compared.

Analytical Treatment of Higher-Order Graphs: A Path Ordinal Method for Solving Graphs

Analytical treatment of the composition of higher-order graphs representing linear relations between variables is developed. A path formalism to deal with problems in graph theory is introduced. It is shown how paths in the composed graph representing individual contributions to variables relation can be enumerated and represented by ordinals. The method allows for one to extract partial information and gives an alternative to classical graph approach.