We have designed a Linear Fresnel-type Reflector (LFR) to reduce the area of light concentration based on the caustic surfaces produced by reflection. The LFR is designed by a set of planar mirrors, which appropriately have slopes in such a way that input energy can be focused at predefined absorber area. Also, losses due to riser steps were obtained from a geometrical point of view, to reduce and reconfigure the LFR shape in order to facilitate its manufacture. Finally, a LFR prototype will be fabricated on a single aluminum sheet where their grooves will be molded through CNC machine.
We study the formation of caustic produced by refraction through conic surfaces, considering a point source placed along the optical axis at arbitrary distances from the vertex of refracting surface. We demand that the optical surface is represented by a mathematical function, which is smooth, continuous, and derivable. We implement an exact ray trace to obtain a monoparametric equation that describes a family of refracted rays, which are propagated as a function of the angle of emission from the point source for each ray. Subsequently, by using the envelope’s method, we provide an analytical equation for the caustic surface as a function of all the parameters involved in the process of refraction. We analyze the paraxial approximation assuming a very small angle about the axis of the system. Additionally, we provide a formula, which describes the conditions for total internal reflection. Finally, we present the formation of caustic surfaces by considering a liquid polymer in a rotating vessel forming a paraboloid surface, also we present the caustic surface produced by the package of a Light Emitting Diode, to produce an uniform illumination pattern.
A method for designing afocal achromatic doublet is presented. We have implemented an exact ray trace through a separated doublet lens considering a plane wavefront propagating along the optical axis. The analytic equation of both the caustic surface and the back focal length for separated doublet lenses are provided. Demanding that the back focal length tends to infinity, we impose the conditions to design afocal optical systems, obtaining sixth and fourth degree polynomials as a function of the radii of curvature. In order to produce an afocal achromatic optical system, we solve numerically a set of two nonlinear equations assuming two spectral lines. Therefore, we have two unknowns which are the curvature radii for both the front surface and the rear surface. The contribution of this work is to provide simple formulas for designing optical beam expander or reducer devices based on separated doublets.
We study the formation of caustic surfaces produced by simple lenses, considering a point source placed at arbitrary position along the optical axis. It is well known that the shape of the caustic is directly related to the image errors introduced by an optical system, and it can be modified by changing the parameters involved in the process of refraction. Implementing an exact ray tracing, we have obtained an analytic equation that describes a family of rays that are propagated radially from the point source placed at arbitrary distances along the optical axis as a function of an angle of emission of the source. Once obtained the parametric equation that describes the family of all the rays refracted through the singlet lens, we provide an analytical equation for the caustic surface as a function of all the parameters involved in the process of refraction. Additionally, assuming a paraxial approximation, we obain Gauss equation of image forming and some examples are presented.
We study the formation of caustic surfaces produced by cemented doublet lenses, considering a plane wavefront propagating parallel to the optical axis and neglecting the refractive index of the optical cement between two simple lenses which are in contact. We have already seen that the shape of caustic surfaces can represent the monochromatic aberrations that we call image errors; furthermore the shape of the caustic can be modified by changing the parameters of design for two conic lenses in contact, in such a way that if we are able to vanish the caustic, the optical system produces either an image without spherical aberration or longitudinal chromatic aberration reduced, commonly known as spherochromatism. The shape of the caustic surface is a function of the indices of refraction involved in the process of refraction, and all the parameters of two simple lenses. We provide an analytic equation for the caustic surfaces in a meridional plane and an example is presented.
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