Maximino Avendaño-Alejo

Designing light-emitting diode arrays for uniform near-field irradiance

We analyze the first-order design of light sources consisting of multiple light-emitting diodes (LEDs) to uniformly illuminate a near target plane by considering each single LED as an imperfect Lambertian emitter. Simple approximate equations and formulas are derived for the optimum LED-to-LED spacing, i.e., the optimum packaging density, of several array configurations to achieve uniform near-field irradiance.

Quantitative evaluation of an off-axis parabolic mirror by using a tilted null screen

We report the testing of a fast off-axis surface based on the null screen principles. Here we design a tilted null screen with drop shaped spots drawn on it in such a way that 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. Here the whole surface is tested at once. The test surface has a radius of curvature of r = 20.4 mm (F/0.206). The surface departures from the best surface fit are shown; in addition, we show that the errors in the surface shape are below 0.4 mum when the errors in the determination of the coordinates of the centroids of the reflected images are less than 1 pixel, and the errors in the coordinates of the spots of the null screen are less than 0.5 mm.

Light-emitting diode spherical packages: an equation for the light transmission efficiency

Virtually all light-emitting diodes (LEDs) are encapsulated with a transparent epoxy or silicone gel. Here we analyze the optical efficiency of spherical encapsulants. We develop a quasi-radiometric equation for the light transmission efficiency, which incorporates some ideas of Monte Carlo ray tracing into the context of radiometry. The approach includes the extended source nature of the LED chip and the chip radiance distribution. The equation is an explicit function of the size and the refractive index of the package, and also of several chip parameters such as shape, size, radiance, and location inside the package. To illustrate the use of this equation, we analyze several packaging configurations of practical interest, for example, a hemispherical dome with multiple chips, a flat encapsulation as a special case of the spherical package, and approximate calculations of an encapsulant with a photonic crystal LED or a photonic quasi-crystal LED. These calculations are compared with Monte Carlo ray tracing, giving almost identical values.

Optical path difference in a plane-parallel uniaxial plate

The flux of energy given by the Poynting vector Se and the kt-wave vector normal to the geometrical wavefront for the extraordinary ray propagating through uniaxial crystals can be evaluated by using the theory developed by Avendaño-Alejo et al. [J. Opt. Soc. Am. A 19, 1668 (2002)] and Avendaño-Alejo and Stavroudis [J. Opt. Soc. Am. A 19, 1674 (2002)]. We give here the equations necessary to evaluate the general dispersion angle Se x kt. Additionally we define two new dispersion angles, Se x A and kt x A, where A is the crystal axis vector. With these new dispersion angles we evaluate the optical path length traversed by the extraordinary ray in a plane-parallel uniaxial plate when the crystal axis lies in the plane of incidence.

Caustics in a meridional plane produced by plano-convex conic lenses

We study the formation of caustic surfaces formed in both convex-plano and plano-convex conic lenses by considering a plane wave incident on the lens along the optical axis. By using the caustic formulas and a paraxial approximation, we derive analytic expressions to evaluate the spherical aberration to the third order, and a formula to reduce this aberration is provided. Furthermore, we apply the formulas to evaluate the circle of least confusion for a positive lens as a function of all parameters involved in the process of refraction through the conic lenses.

Testing a fast off-axis parabolic mirror by using tilted null screens

We propose the design of tilted null screens for testing off-axis segments of conic surfaces. The tilt allows us to control the size of the screen and the sensitivity of the test. For positive tilt angles the sensitivity is increased while the size of the screen is reduced in the sagittal caustic region and vice versa in the tangential caustic region. Further analysis and preliminary experimental results are presented for a fast off-axis concave parabolic mirror with an elliptical aperture. An offset distance of XC = 25.4 mm yields radius of curvature at the vertex R = 20.4 mm; major axis of the mirror DM = 49.4 mm; and minor axis Dm = 29.5 mm.

Chromium and ruthenium-doped zinc oxide thin films for propane sensing applications.

Chromium and ruthenium-doped zinc oxide (ZnO:Cr) and (ZnO:Ru) thin solid films were deposited on soda-lime glass substrates by the sol-gel dip-coating method. A 0.6 M solution of zinc acetate dihydrate dissolved in 2-methoxyethanol and monoethanolamine was used as basic solution. Chromium (III) acetylacetonate and Ruthenium (III) trichloride were used as doping sources. The Ru incorporation and its distribution profile into the films were proved by the SIMS technique. The morphology and structure of the films were studied by SEM microscopy and X-ray diffraction measurements, respectively. The SEM images show porous surfaces covered by small grains with different grain size, depending on the doping element, and the immersions number into the doping solutions. The sensing properties of ZnO:Cr and ZnO:Ru films in a propane (C3H8) atmosphere, as a function of the immersions number in the doping solution, have been studied in the present work. The highest sensitivity values were obtained for films doped from five immersions, 5.8 and 900, for ZnO:Cr and ZnO:Ru films, respectively. In order to evidence the catalytic effect of the chromium (Cr) and ruthenium (Ru), the sensing characteristics of undoped ZnO films are reported as well.

Modeling LED street lighting

LED luminaires may deliver precise illumination patterns to control light pollution, comfort, visibility, and light utilization efficiency. Here, we provide simple equations to determine how the light distributes in the streets. In particular, we model the illuminance spatial distribution as a function of Cartesian coordinates on a floor, road, or street. The equations show explicit dependence on the luminary position (pole height and arm length), luminary angle (fixture tilt), and the angular intensity profile (radiation pattern) of the LED luminary. To achieve this, we propose two mathematical representations to model the sophisticated intensity profiles of LED luminaries. Furthermore, we model the light utilization efficiency, illumination uniformity, and veiling luminance of glare due to one or several LED streetlamps.

Caustics caused by refraction in the interface between an isotropic medium and a uniaxial crystal

In general, a caustic by refraction at an arbitrary surface is commonly known as a diacaustic. We study the formation of the diacaustic in a plane interface between an isotropic medium and a uniaxial crystal, for both ordinary and extraordinary rays, when the crystal axis is perpendicular to the plane of incidence and when it lies in the plane of incidence. For the latter case two special positions of the crystal axis with respect to the normal to the refracting surface for the extraordinary rays are treated.

Null Ronchi-Hartmann test for a lens

A method to design Ronchi-Hartmann screens for improved alignment in the testing of fast plano-convex spherical lenses is presented. We design null screens that produce aligned straight fringes for observed patterns. The designs of these null screens are based on knowledge of the caustic by refraction. A qualitative test for a lens is presented.