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.
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 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 present an iterative procedure to retrieve the wavefront using a Shack–Hartmann sensor. Traditionally, a uniform array of microlens is used as a domain to reconstruct the wavefront under test; however, this properly works if the wavefront differs slightly from a plane. But generally in optical tests, astronomy, and ophthalmology the wavefronts under test can have appreciable deviations with respect to a plane wavefront. The proposed method considers the reconstruction of the wavefront deformations with respect to a known reference wavefront. At each iteration, the wavefront deformation is used to find a reference wavefront closer to the wavefront under test and a domain closer to the actual domain. When the values of the wavefront deformations are small enough, we can take the reference as the wavefront under test. In addition, we simulate the centroid positions of the spot pattern used to retrieve the wavefront under test using the proposed method. We compare our results with those obtained by three other different approaching methods described in the literature (Modal, Trapezoidal Rule, and Southwell). For the simulations used in this work, our method retrieves wavefronts closer to the real wavefront than the other methods. Also, we apply the proposed method to an experimental case to reconstruct the wavefront under test using a Shack–Hartmann sensor.
We have obtained a formula to represent the wavefront produced by a plano-convex aspheric lens with symmetry of revolution considering a plane wavefront propagating parallel to the optical axis and impinging on the refracting surface, it is called a zero-distance phase front, being it the first wavefront to be out of the optical system. Using a concept of differential geometry called parallel curves it is possible to obtain an analytic formula to represent the wavefront propagated at arbitrary distances through the optical axis. In order to evaluate qualitatively a plano-convex aspheric lens, we have modified slightly an interferometer Tywman-Green as follow: In the reference beam we use a plane mirror and the beam of test we have used a spatial light modulator (SLM) to compensate the phase produced by the lens under test. It will be called a null phase interferometer. The main idea is to recombine both wavefronts in order to get a null interferogram, otherwise we will associate the patterns of the interferogram to deformations of the lens under test. The null phase screens are formed with concentric circumferences assuming different gray levels printed on SLM.
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