We study the formation of caustic surfaces produced by convex conic lenses, considering a linear set of point sources displayed on a plane, this linear array is placed at arbitrary position along the optical axis. The caustic surface can be defined as the envelope for either reflected or refracted rays propagating through an optical system. Implementing an exact ray trace, we have obtained an analytic equation that describes a parametric family of refracted rays propagating through a convex conic lens and by computing its envelope, we provide an exact equation for the caustic surface as a function of all the parameters involved in the process of refraction. Considering the geometric center of a conic surface, we have located the parabasal image for each point source produced by refraction, and by extending this concept for a set of point sources placed along a linear array, we obtain the image surface which is the locus where the succession of paraxial images are located. Finally, using a commercial 3D printer, we have fabricated a convex conic lens along with its image curved surface to implement a preliminary test to study the image formation for extended objects, with potential applications in uniform illumination systems.
Traditionally, the Fresnel-type lens design often assumes thin lenses, since lenses of finite thickness cannot be completely described in analytical terms, then a numerical solution has to be found. We implement an exact ray trace considering a plane wavefront incident by reducing as much as possible the area of light concentration, while increasing the concentration ratio of energy. In such a way that we have mathematically determined a function to compute groove angles, to refract a bundle of rays from each planar echelon, which are propagated into a predetermined area of energy collection. In addition, we can evaluate the performance of the Fresnel-type lens design for a solar collector. Thus, an analytical formula to calculate the optical efficiency is obtained, in terms of the geometrical losses widely studied for nonimaging systems, such as blocking losses. Finally, the proposed aspherical Fresnel lens design is fabricated using a commercial 3D printer and subsequently polishing the surface for better performance. In this fashion we could test the performance of the manufactured prototype.
In this work we propose a procedure to divide a regular off-axis conic surface, which defines the parent surface represented by a parametric equation, in order to describe the optical surface for an off-axis Fresnel-type reflector, in such a way that this mathematical representation allows us to implement an exact ray trace considering a plane wavefront incident on the surface. Additionally, we can simulate the performance of a preliminary prototype proposed for designing a solar collector.
We study different approaches to describe the evolution of wavefronts refracted through two simple lenses forming an achromat separated by finite distance (dialyte for short), assuming a plane wavefront incident propagated along the optical axis impinging on the optical system. This allows us to quantitatively evaluate the best optical design containing the minimum amount of spherical aberration produced by the optical system under test. Based on this study, we have implemented an interferometric array for testing a dialyte placing a reference mirror at predefined position along the optical axis, which permits to compensate the optical phase and properly produce a null interferogram to evaluate the performance for this kind of optical systems.
We design two different Hartmann type null screens based on an exact ray trace for testing a fast plano-convex aspherical condenser. The first null screen is designed for testing the external convex surface or periphery area for the condenser by reflection. We have implemented an exact ray trace assuming a point source placed along the optical axis, emitting a bundle of rays, which are reflected by the surface under test, to obtain a non-uniform array of spots, which are printed on paper sheet and wrapped on a plastic cylinder fabricated by using additive manufacture. Subsequently, by reversibility Principle’s after by reflection we obtain a uniform array pattern displayed at the detection plane. Alternatively, to evaluate the whole area for the condenser, the second null screen is designed for testing the central convex area for the condenser by refraction. Thus, we have implemented an exact ray trace assuming an incident plane wavefront, these rays are refracted through the lens under test, to obtain a non-uniform array of drop spots, which are printed on plastic sheet and placed in front of the lens under test. Finally, assuming the reversibility Principle’s after by refraction we obtain a uniform array pattern displayed at the detection plane. For this method, we have called Hartmann type hybrid null screens.
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.
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 bi-conic lenses, considering a plane wavefront propagating parallel to the optical axis. 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 the lens in such a way that if we are able to vanish the caustic, the optical system produces an image without spherical aberration, alternatively caustic surfaces having a large area could be applied to design non-imaging optical systems, such as diffusers of light. 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 the bi-conic lens. We provide an analytic equation for the caustic surface in a meridional plane and some examples are presented.
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