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.
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.
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.
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 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 propagation of wavefronts refracted through separated doublet lenses (SDL), considering a plane wavefront propagating parallel to the optical axis. We provide formulas for the zero-distance phase front refracted through SDL by using Huygens’s principle. Additionally, we obtain formulae to represent the shape of refracted wavefronts propagated at arbitrary distances along the optical axis, as a function of all parameters involved in the process of refraction. Finally, some examples for commercial SDL showing the evolution of the wavefronts arbitrary distances are presented, assuming different wavelengths for the refractive indices of the lenses, displaying dispersion effects produced through SDL.
We have designed a Linear Fresnel Reflector (LFR), with potential applications for solar concentration, by using an exact ray tracing. We have mathematically parameterized the slopes of LFR to provide predefined areas of light concentration. LFR planar mirrors were calculated in such a way that an incident plane wavefront can be focused at minimum absorber area. Finally, prototypes of LFR were manufactured by using a 3D printer, considering a set of small sized mirrors to join up with the aim of producing a linear focus.
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 propagation of wavefronts produced through cemented doublet lenses, considering a plane wavefront propagating parallel to the optical axis. We provide formulas for the zero-distance phase front by using Huygens's principle, also we provide formulae to represent the shape of refracted wavefronts propagated arbitrary distances along the optical axis, which are function of all parameters involved in the process of refraction. We present examples of doublet lenses showing the evolution of the wavefronts arbitrary distances, assuming different wavelengths for the refractive indices of the lenses, for this purpose we compare the dispersion effects produced through this particular kind of lenses.
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