An array of light-emitting diodes (LEDs) assembled upon a spherical surface can produce a wider angle distribution of light than a typical array (i.e., an array assembled by mounting LEDs into a flat surface). Arranging each single LED into an optimal placement, the uniformity of the illumination of a target can be improved. We derive approximate formulas and equations for the optimum LED-to-LED angular spacing of several spherical arrangements for uniform far-field irradiance. These design conditions are compact and simple tools that incorporate an explicit dependence on the half-intensity viewing angle (half width half maximum angle) of LEDs.

We study the dynamics of multistable coexisting rotating waves that propagate along a unidirectional ring consisting of coupled double-well Duffing oscillators with different numbers of oscillators. By employing time series analysis, phase portraits, bifurcation diagrams, and basins of attraction, we provide evidence of multistability on the route from coexisting stable equilibria to hyperchaos via a sequence of bifurcations, including the Hopf bifurcation, torus bifurcations, and crisis bifurcations, as the coupling strength is increased. The specific bifurcation route depends on whether the ring comprises an even or odd number of oscillators. In the case of an even number of oscillators, we observe the existence of up to 32 coexisting stable fixed points at relatively weak coupling strengths, while a ring with an odd number of oscillators exhibits 20 coexisting stable equilibria. As the coupling strength increases, a hidden amplitude death attractor is born in an inverse supercritical pitchfork bifurcation in the ring with an even number of oscillators, coexisting with various homoclinic and heteroclinic orbits. Additionally, for stronger coupling, amplitude death coexists with chaos. Notably, the rotating wave speed of all coexisting limit cycles remains approximately constant and undergoes an exponential decrease as the coupling strength is increased. At the same time, the wave frequency varies among different coexisting orbits, exhibiting an almost linear growth with the coupling strength. It is worth mentioning that orbits originating from stronger coupling strengths possess higher frequencies.

We describe a new algorithm for phase determination from a single interferogram with closed fringes based on an unwrapping procedure. Here we use bandpass filtering in the Fourier domain, obtaining two wrapped phases with sign changes corresponding to the orientation of the applied filters. An unwrapping scheme that corrects the sign ambiguities by comparing the local derivatives is then proposed. This can be done, assuming that the phase derivatives do not change abruptly among adjacent areas as occurs with smooth continuous phase maps. The proposed algorithm works fast and is robust against noise, as demonstrated in experimental and simulated data.

Digital Processing Techniques for Fringe Analysis | InTechOpen, Published on: 2017-02-15. Authors: Jesús Muñoz Maciel, Francisco Javier Casillas Rodríguez, Miguel Mora González, et

The flagship monthly journal of SPIE, Optical Engineering (OE) publishes peer-reviewed papers reporting on research and development in all areas of optics, photonics, and imaging science and engineering.