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.

/pdf/the-siesta-method-for-ab-initio-order-n-materials-simulation-1q65k8c3vq.pdf

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

A robust one-beam interferometer with external phase-delay control is described. The device resembles a Mach-Zehnder interferometer in which the two arms are together in one collimated beam. However, the proposed device is not an amplitude-division interferometer but a wave-front division one. The phase-delay control occurs at the interferometer output with the help of two polarizing beam splitters, a quarter-wave plate, a Faraday rotator, and a polarizer. An additional phase delay is introduced by application of an electrical current to the Faraday rotator or by rotation of the polarizer (the latter is of topological origin), which permits the use of techniques of phase-stepping interferometry.

Robust one-beam interferometer with phase-delay control.

Three-dimensional profiling by sinusoidal fringe projection using PSI-algorithms are distorted by the nonlinear response of digital cameras and commercial video projectors. To solve the problem, we present a fringe generation technique that consists of projecting and acquiring a temporal sequence of strictly binary color patterns, whose (adequately weighted) average leads to sinusoidal fringe patterns with the required number of bits, which allows for a reliable three-dimensional profile using a PSI-algorithm. Validation experiments are presented.

Color encoding of binary fringes for gamma correction in 3-D profiling.

Phase objects can be characterized using well-known methods such as shear interferometry and deflectometry, which provide information on the partial derivatives of the phase. It is often believed that for phase retrieval it is strictly necessary to have knowledge of two partial derivatives in orthogonal directions. In the praxis, this implies that the measurements have to be performed along two dimensions, which often requires a rotation of the object or rotation of the shear direction. This is time consuming and errors can be easily generated from the process of rotation, especially for image registration in the axial direction. In the present Letter, we will demonstrate that only one partial derivative often suffices to recover the phase, and we will discuss under which conditions that is possible. Simulations and validation experiments are presented.

Phase retrieval from one partial derivative.

A novel one-beam interferometer based on beam folding is described. The device resembles a Mach–Zehnder interferometer in which the two arms are located together in one collimated beam. Different halves of the same beam interfere with the help of a mirror—with its reflecting surface along the axis of the optical system—placed near the focal plane of the imaging lens. Phase-delay control is achieved by application of an electrical potential to a Pockels cell, which permits the use of techniques of phase-stepping interferometry.

One-beam interferometer by beam folding.

A phase step interferometry system using polarization shifting is described. The device is essentially a Mach-Zehnder interferometer in which the polarization of light travelling through one arm is orthogonal to the polarization of light travelling through the other arm. At the interferometer output we place a quarter-wave plate with its fast axis at with respect to the polarization directions and a polarizer. By rotating the polarizer, the interfering waves acquire an extra phase (of topological origin) to that expected from the calculations of optical path lengths, and thus, arbitrary phase shifts can be induced. Then, from a set of interferograms recorded while the reference phase is changed, the `dynamical' phase difference (e.g. the phase profile of an object placed in one of the interferometer arms) can be reconstructed by using techniques of phase-shifting interferometry.

https://iopscience.iop.org/article/10.1088/0963-9659/7/1/009/pdf

José A. Ferrari

Papers

Robust one-beam interferometer with phase-delay control.

Color encoding of binary fringes for gamma correction in 3-D profiling.

Phase retrieval from one partial derivative.

One-beam interferometer by beam folding.

Polarization-shifting method for step interferometry