We study the propagation of light in order to efficiently redirect the reflected light on photocatalytic samples placed inside a commercial solar simulator, and we have designed a small-scale prototype of Cycloidal Collectors (CCs), resembling a compound parabolic collector. The prototype consists of either cycloidal trough or cycloidal collector having symmetry of rotation, which has been designed considering an exact ray tracing assuming a bundle of rays propagating parallel to the optical axis and impinging on a curate cycloidal surface, obtaining its caustic surface produced by reflection.
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.
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.
In order to evaluate either qualitative or quantitatively the shape of fast plano-convex aspheric lenses, a method to design null screens type Hartmann is proposed. The null screens are formed with non-uniform spots, which allows to have uniform images at detection's plane. The screens are printed on a foil sheet and placed in front of the lens under test, they are illuminated with a collimated monochromatic beam propagating along the optical axis, in such a way that through the process of refraction will form a uniform spot patterns which are recorded at a predefined plane of detection. Finally, processing properly its image recorded we could be able to get a quantitative evaluation of the lens under test. The designs of these null screens are based on the equations of the caustic surface produced by refraction. A preliminary test for a fast plano-convex aspheric lens with F=# = 0:8 is presented in this work. This method could also be applied to alignment of optical systems.
We study the formation of wavefronts produced by smooth arbitrary surfaces with symmetry of revolution considering a plane wavefront propagating parallel to the optical axis and impinging on the refracting surface. The wavefronts are obtained by using the Malus-Dupin theorem and they represent the monochromatic aberrations which can be called image errors, furthermore their shapes could be modified by changing the parameters of the lens in such a way that if a caustic surface is vanished the optical system produces a perfect image, on the other hand for a caustic possessing a large area it could be applied to design non-imaging optical systems. The shape of the wavefront depends only on the indices of refraction and geometrical properties of the refracting surface such as the first derivative and their parameters associated. This analytic formula has potential applications in the microscopy field, illumination or corrector plates.
We study the formation of caustic produced by smooth arbitrary surfaces considering a plane wavefront propagating parallel to the optical axis and impinging on the refracting surface. We have already seen that the shape of the caustic surface 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 the caustic surfaces is vanished the optical system produces a perfect image, on the other hand for a caustic possessing a large area it could be applied to design no-imaging optical systems. The shape of the caustic depends only on the indices of refraction involved in the process of refraction, the refracting surface which is formed by smooth arbitrary plano-convex lens. We provide an analytic equation for the caustic surface after refraction of a plane wave from every rotationally symmetric surface..
In order to evaluate either qualitative or quantitatively the shape of fast plano-convex aspheric lenses, a method to design null screens type sub-structured Ronchi is proposed. The null screens are formed with nonuniform curves which allows us to have both thin and thick monochrome strips between contiguous curves. The screens are printed on a light transmission modulator and placed in front of the lens under test, they are illuminated with a collimated monochromatic beam propagating along the optical axis, in such a way that through the process of refraction will form a uniform straight fringes pattern which are recorded at a predefined plane of detection, finally processing its image recorded we could be able to get a quantitative evaluation of the lens under test. The designs of these null screens are based on the equations of the caustic surface produced by refraction. The null screens can be printed in gray levels on a light transmission modulator depending on the applied voltage on it. A preliminary test for a fast plano-convex aspheric lens with F=# = 0:8 is presented in this work. This method also could be applied to alignment of optical systems.
A method to design Ronchi-Hartmann null screens for improved alignment in the testing of fast concave conic mirrors is presented. The designs of these null screens are based on knowledge of the caustic by reflection.
We report the qualitative testing of a spherical concave surface with deformation coefficients based on the null-screen principles. The design of cylindrical null screen with curved grid is described; its image, which is formed by reflection on the test surface, becomes an exact square grid if the surface is perfect. Any departure from this geometry is indicative of defects on the surface. In contrast to others tests, here the whole surface is tested at once. The surface under test is 140 mm in diameter and a radius of curvature of 97 mm. The surface is testing during the manufacturing process; departures from the design surface will be analyzed and discussed.
In order to obtain a clearer interpretation of the Intensity Transport Equation (ITE), in this work, we propose an algorithm to solve it for some particular wavefronts and its corresponding intensity distributions. By simulating intensity distributions in some planes, the ITE is turns into a Poisson equation with Neumann boundary conditions. The Poisson equation is solved by means of the iterative algorithm SOR (Simultaneous Over-Relaxation).
We provide analytic formulas for fews aspheric terms either plano-convex or convex-plano aspheric lenses. These
formulas are obtained considering an expansion in Taylor's series from exact caustic equation produced by
aspheric lenses. A comparison between our method and numerical methods of design are presented, showing a
well agreement in order to reduce the spherical aberration.
In this work we present near field microwave images of microelectronic circuits and their interpretation to
complement the conventional optical analysis. We show a highly simplified design of a resonant probe with
dynamically tunable capacitive coupling and with high sensitivity. Images were obtained by measuring the
microwave reflection coefficient operating a 7 GHz. This design represents a simplified and highly effective
approach to implementing near field microwave microscopy.
A new design of a null Hartman's screen to test quantitatively a fast plano-convex conic lens is presented. The
design of the null screen is based on the caustic produced by refraction through the lens. Additionally, the null
screen can be used to improve the alignment in optical systems. A quantitative evaluation of medium precision
by using a trapezoidal integration method is presented.
We derive simple formulas for the caustic produced by a positive convex-plano and plano-convex conic lens
by considering a plane wave incident on the lens along the optical axis. By using these equations a paraxial
approximation for the caustics are provided in both configurations. Also, by using these equations it is possible
to obtain the third order coefficient of spherical aberration. Changing the parameters of the lens (refraction
index, conic constant, radius of curvature, thickness of the lens, etc.) we can modify the shape of the caustic,
furthermore there are cases where the spherical aberration changes from positive to negative when we vary
exclusively the conic constant. A formula for the Principal Surface as a function of the height also is given. We
believe that the method to obtain the caustic that we report is straightforward, obtaining a relationship between
caustics, wavefronts, and measurements of the spherical aberrations.
In this work we report a method for testing a parabolic trough solar collector (PTSC) based on the null screen
principles. For surfaces with symmetry of revolution a cylindrical null screen is used, now, for testing the PTSC we
use a flat null screen. The design of the null screen with ellipsoidal spots is described; its image, which is formed by
reflection on the test surface, becomes an exact square array of circular spots if the surface is perfect. Any departure
from this geometry is indicative of defects on the surface. The flat null screen design and the surface evaluation
algorithm are presented. Here the surface is tested in sections and the evaluation of the shape of the surface is
performed with stitching method. Results of the evaluation for a square PTSC with 1000 mm by side (F/0.49) are
We extend the principles of the null screen method for testing a fast ellipsoidal concave mirror by designing a null cylindrical screen, located around the near focal point of the ellipsoid (being parallel to the optical axis) and the observing CCD camera is near the far focal point. We present the formulae to design the screen in such a way that the image on the CCD is a perfect square grid; the departures of the surface from a perfect ellipsoidal shape are observed as deformations of the grid in the image. We show qualitative experimental results.
The generalized ray tracing for the extraordinary ray through uniaxial crystals developed by M. Avendanyo-Alejo and O. Stavroudis, is applied to investigate the optical path difference between the ordinary and the extraordinary rays in a plane parallel uniaxial plate. When a ray of light from a monochromatic source S is incident on the surface of a plane parallel uniaxial plate, two rays: an ordinary ray and an extraordinary ray will propagate inside the plate until they are refracted at the second interface of the plate. These two rays are orthogonally polarized so they do not interfere unless a polarizer is placed after the plate to make the parallel components of their respective electric fields interfere. In the present work we analyze the optical path difference traversed by the ordinary ray and the extraordinary ray.
We propose the design of tilted null screens in order to test the off-axis segments of conic surfaces. Furthermore we reduce the size of the screen in order to increase the performance of the test. The sensitivity is increased while the size of the screen is reduced in the saggital caustic region and vice versa in the tangential caustic region. Further analysis and experimental results are presented, for an off-axis concave parabolic mirror which has an elliptical aperture, with a distance offset Xc=25.4mm, the radius of curvature at the vertex R= 20.4mm, major axis of the mirror DM=49.4mm and minor axis Dm=29.5mm.
Ray tracing formulas in a plane-parallel uniaxial plate bounded by an isotropic medium is analyzed when the crystal axis lies in the incident plane, and when its orientation is arbitrary. We present the behavior of the critical angle for the extraordinary ray as a function of the crystal axis position with respect to the normal to the refracting surface.
In early published contributions we obtain ray tracing formulas for uniaxial crystals. In the present contribution we show the ray tracing for an uniaxial cartesian oval, when the crystal axis lies in the incident plane. The uniaxial crystals have two refracted rays (ordinary and extraordinary rays). When the object is placed at infinity, the ordinary rays have a common focus called the distal focus. For the extraordinary ray the uniaxial cartesian oval show spherical aberration produced by the medium itself. In order to reduce the spherical aberration we analyze several cases for the orientation of the crystal axis, this improve the performance on this optical design.