We have developed and implemented a selfconsistent density functional method using standard norm-conserving pseudopotentials and a flexible, numerical linear combination of atomic orbitals basis set, which includes multiple-zeta and polarization orbitals. Exchange and correlation are treated with the local spin density or generalized gradient approximations. The basis functions and the electron density are projected on a real-space grid, in order to calculate the Hartree and exchange-correlation potentials and matrix elements, with a number of operations that scales linearly with the size of the system. We use a modified energy functional, whose minimization produces orthogonal wavefunctions and the same energy and density as the Kohn-Sham energy functional, without the need for an explicit orthogonalization. Additionally, using localized Wannier-like electron wavefunctions allows the computation time and memory required to minimize the energy to also scale linearly with the size of the system. Forces and stresses are also calculated efficiently and accurately, thus allowing structural relaxation and molecular dynamics simulations.

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The SIESTA method for ab initio order-N materials simulation

Secret History: Return of the Black Death Channel 4, 7-8pm In 1348 the Black Death swept through London, killing people within days of the appearance of their first symptoms. Exactly how many died, and why, has long been a mystery. This Secret History documentary follows experts as they pick through the evidence and reveal why the plague killed on such a scale. And they ask, what might be coming next?

Medscape

A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Phase shifting algorithms for fringe projection profilometry: A review

We investigate the polarization-to-phase conversion of space-variant polarized light waves. Our analysis can be considered as an extension of Pancharatnam's phase to the case of space-variant polarization. In two particular cases - azimuthally and radially variant polarization - we found striking consequences. Using an azimuthally variant polarizer combined with a circular analyzer, it is possible to induce spin-to-orbital angular momentum exchange and to generate optical vortices of arbitrary charge. Radially variant polarizers with linear or quadratic radial dependence of the transmission direction generate nondiffracting beams or focus light, respectively. Our results are potentially relevant for the design of achromatic wavefront forming (and correcting) elements based strictly on space-variant polarization optics.

Achromatic wavefront forming with space-variant polarizers: Application to phase singularities and light focusing

We demonstrate that the magnetic crosstalk-induced errors associated with point-type optical (Faraday) current sensors working in three-phase electric systems may be minimized by properly designing the geometry of the system. We propose a novel architecture in which the optical path inside the magnetooptical material is parallel to the direction of the neighboring conductors, except in a small loop around the sensor head. This renders the crosstalk effect at least one order of magnitude smaller than in conventional Faraday sensor architectures.

Magnetic Crosstalk Minimization in Optical Current Sensors

We discuss the schlieren imaging of quasi-sinusoidal phase objects. We demonstrate that, when the zero-order (Fourier) spatial component of the input image is not blocked by the schlieren-knife at the Fourier plane, the intensity distribution on the reconstructed image is a linear function of the phase amplitude. In contrast, if the zero order is completely blocked (i.e., dark Schlieren processing), the intensity distribution on the output image becomes essentially a quadratic function of the phase, and thus a direct phase retrieval is not possible. We discuss the possibility of contrast enhancement and present validation experiments.

Bright versus dark schlieren imaging: quantitative analysis of quasi-sinusoidal phase objects.

We present a novel optical method for edge enhancement in color images based on the polarization properties of liquid-crystal displays (LCD). In principle, a LCD generates simultaneously two color-complementary, orthogonally polarized replicas of the digital image used as input. The currently viewed image in standard LCD monitors and cell phone’s screens -which we will refer as the “positive image or true-color image”- is the one obtained by placing an analyzer in front of the LCD, in cross configuration to the back polarizer of the display. The orthogonally polarized replica of this image –the “negative image or complementary-color image”- is absorbed by the front polarizer. In order to generate the positive and negative replica with a slight displacement between them, we used a LCD monitor whose analyzer (originally a linear polarizer) was replaced by a calcite crystal acting as beam displacer. When both images are superimposed laterally displaced across the image plane, one obtains an image with enhanced first-order derivatives along a specific direction. The proposed technique works under incoherent illumination and does not require precise alignment, and thus, it could be potentially useful for processing large color images in real-time applications. Validation experiments are presented.

José A. Ferrari

Papers

Achromatic wavefront forming with space-variant polarizers: Application to phase singularities and light focusing

Magnetic Crosstalk Minimization in Optical Current Sensors

Bright versus dark schlieren imaging: quantitative analysis of quasi-sinusoidal phase objects.

Optical processing of color images with incoherent illumination: orientation-selective edge enhancement using a modified liquid-crystal display.

Transport of intensity equation: Validity limits of the usually accepted solution