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 comment on the recent Letter by Cai et al. [Opt. Lett. 28, 1808 (2003)] in which an approach to phase-shifting interferometry with arbitrary phase steps was proposed. Cai et al. based their method of phase shifting on the idea that the intensities of the reference and object beams can be measured previously, which actually makes the whole posterior phase-shifting procedure absolutely unnecessary. Their method is also based on the statement that the phase of the Fresnel diffraction pattern of a test object if generally a spatially random distribution, which in most situations is wrong.

Comment on "Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps".

Improved method for Faraday current sensor data processing

One-shot 3D scanning by combining sparse landmarks with dense gradient information

Visualization of phase objects using incoherent illumination

We comment on a recent Letter [Opt. Lett.35, 4121 (2010)OPLEDP0146-959210.1364/OL.35.004121], in which the authors discuss an optimal pulse-width modulation (OPWM) method for sinusoidal fringe generation. We consider that the comparison of the squared binary method (SBM) and the sinusoidal pulse-width modulation (SPWM) method has considerable deficiencies.

José A. Ferrari

Papers

Comment on "Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps".

Improved method for Faraday current sensor data processing

One-shot 3D scanning by combining sparse landmarks with dense gradient information

Visualization of phase objects using incoherent illumination

Optimal pulse-width modulation for sinusoidal fringe generation with projector defocusing: comment