Coherent Diffraction Imaging of Single 95nm Nanowires

Photonic or electronic confinement effects in nanostructures become significant when one of their dimension is in the 5-300 nm range. Improving their development requires the ability to study their structure - shape, strain field, interdiffusion maps - using novel techniques. We have used coherent diffraction imaging to record the 3-dimensionnal scattered intensity of single silicon nanowires with a lateral size smaller than 100 nm. We show that this intensity can be used to recover the hexagonal shape of the nanowire with a 28nm resolution. The article also discusses limits of the method in terms of radiation damage.Comment: 5 pages, 5 figure

Calculation of an optimized telescope apodizer for Terrestrial Planet Finder coronagraphic telescope

One of two approaches to implementing NASA's Terrestrial Planet Finder is to build a space telescope that utilizes the techniques of coronagraphy and apodization to suppress diffraction and image exo-planets. We present a method for calculation of a telescope's apodizer which suppresses the side lobes of the image of a star so as to optimally detect an Earth-like planet. Given the shape of a telescope's aperture and given a search region for a detector, we solve an integral equation to determine an amplitude modulation (an apodizer) which suppresses the star's energy in the focal plane search region. The method is quite general and yields as special cases the product apodizer reported by Nisenson and Papaliolios (2001) and the Prolate spheroidal apodizer of Kasdin et al (2002), and Aime et al (2002). We show computer simulations of the apodizers and the corresponding point spread functions for various aperture-detector configurations.Comment: 16 Pages, 9 figures, Accepted for publication in June issue of PAS

Simulation of superresolution holography for optical tweezers

Optical tweezers manipulate microscopic particles using foci of light beams. Their performance is therefore limited by diffraction. Using computer simulations of a model system, we investigate the application of superresolution holography for two-dimensional (2D) light shaping in optical tweezers, which can beat the diffraction limit. We use the direct-search and Gerchberg algorithms to shape the center of a light beam into one or two bright spots; we do not constrain the remainder of the beam. We demonstrate that superresolution algorithms can significantly improve the normalized stiffness of an optical trap and the minimum separation at which neighboring traps can be resolved. We also test if such algorithms can be used interactively, as is desirable in optical tweezers

Inversion of the Diffraction Pattern from an Inhomogeneously Strained Crystal using an Iterative Algorithm

The displacement field in highly non uniformly strained crystals is obtained by addition of constraints to an iterative phase retrieval algorithm. These constraints include direct space density uniformity and also constraints to the sign and derivatives of the different components of the displacement field. This algorithm is applied to an experimental reciprocal space map measured using high resolution X-ray diffraction from an array of silicon lines and the obtained component of the displacement field is in very good agreement with the one calculated using a finite element model.Comment: 5 pages, 4 figure

Solution to the twin image problem in holography

While the invention of holography by Dennis Gabor truly constitutes an ingenious concept, it has ever since been troubled by the so called twin image problem limiting the information that can be obtained from a holographic record. Due to symmetry reasons there are always two images appearing in the reconstruction process. Thus, the reconstructed object is obscured by its unwanted out of focus twin image. Especially for emission electron as well as for x- and gamma-ray holography, where the source-object distances are small, the reconstructed images of atoms are very close to their twin images from which they can hardly be distinguished. In some particular instances only, experimental efforts could remove the twin images. More recently, numerical methods to diminish the effect of the twin image have been proposed but are limited to purely absorbing objects failing to account for phase shifts caused by the object. Here we show a universal method to reconstruct a hologram completely free of twin images disturbance while no assumptions about the object need to be imposed. Both, amplitude and true phase distributions are retrieved without distortion

Accurate phase retrieval of complex point spread functions with deep residual neural networks

Phase retrieval, i.e. the reconstruction of phase information from intensity information, is a central problem in many optical systems. Here, we demonstrate that a deep residual neural net is able to quickly and accurately perform this task for arbitrary point spread functions (PSFs) formed by Zernike-type phase modulations. Five slices of the 3D PSF at different focal positions within a two micron range around the focus are sufficient to retrieve the first six orders of Zernike coefficients.Comment: 8 pages, 4 figure

Thermodynamic Properties of Generalized Exclusion Statistics

We analytically calculate some thermodynamic quantities of an ideal $g$-on gas obeying generalized exclusion statistics. We show that the specific heat of a $g$-on gas ($g \neq 0$) vanishes linearly in any dimension as $T \to 0$ when the particle number is conserved and exhibits an interesting dual symmetry that relates the particle-statistics at $g$ to the hole-statistics at $1/g$ at low temperatures. We derive the complete solution for the cluster coefficients $b_l(g)$ as a function of Haldane's statistical interaction $g$ in $D$ dimensions. We also find that the cluster coefficients $b_l(g)$ and the virial coefficients $a_l(g)$ are exactly mirror symmetric ($l$=odd) or antisymmetric ($l$=even) about $g=1/2$. In two dimensions, we completely determine the closed forms about the cluster and the virial coefficients of the generalized exclusion statistics, which exactly agree with the virial coefficients of an anyon gas of linear energies. We show that the $g$-on gas with zero chemical potential shows thermodynamic properties similar to the photon statistics. We discuss some physical implications of our results.Comment: 24 pages, Revtex, Corrected typo

Modeling of Interstellar Scintillation Arcs from Pulsar B1133+16

The parabolic arc phenomenon visible in the Fourier analysis of the scintillation spectra of pulsars provides a new method of investigating the small scale structure in the ionized interstellar medium (ISM). We report archival observations of the pulsar B1133+16 showing both forward and reverse parabolic arcs sampled over 14 months. These features can be understood as the mutual interference between an assembly of discrete features in the scattered brightness distribution. By model-fitting to the observed arcs at one epoch we obtain a ``snap-shot'' estimate of the scattered brightness, which we show to be highly anisotropic (axial ratio >10:1), to be centered significantly off axis and to have a small number of discrete maxima, which are coarser the speckle expected from a Kolmogorov spectrum of interstellar plasma density. The results suggest the effects of highly localized discrete scattering regions which subtend 0.1-1 mas, but can scatter (or refract) the radiation by angles that are five or more times larger.Comment: 14 pages, 4 figures, submitted to Astrophysical Journa

A unified evaluation of iterative projection algorithms for phase retrieval

Iterative projection algorithms are successfully being used as a substitute of lenses to recombine, numerically rather than optically, light scattered by illuminated objects. Images obtained computationally allow aberration-free diffraction-limited imaging and the possibility of using radiation for which no lenses exist. The challenge of this imaging technique is transfered from the lenses to the algorithms. We evaluate these new computational ``instruments'' developed for the phase retrieval problem, and discuss acceleration strategies.Comment: 12 pages, 9 figures, revte

Evolutionary determination of experimental parameters for ptychographical imaging

The Ptychographical Iterative Engine (PIE) algorithm is a recently developed novel method of Coherent Diffractive Imaging (CDI) that uses multiple overlapping diffraction patterns to reconstruct an image. This method has successfully produced high quality reconstructions at both optical and X-ray wavelengths but the need for accurate knowledge of the probe positions is currently a limiting factor in the production of high resolution reconstructions at electron wavelengths. This paper examines the shape of the search landscape for producing optimal image reconstructions in the specific case of electron microscopy and then shows how evolutionary search methods can be used to reliably determine experimental parameters in the electron microscopy case (such as the spherical aberration in the probe and the probe positions)