Phase Retrieval with Random Phase Illumination

This paper presents a detailed, numerical study on the performance of the standard phasing algorithms with random phase illumination (RPI). Phasing with high resolution RPI and the oversampling ratio $\sigma=4$ determines a unique phasing solution up to a global phase factor. Under this condition, the standard phasing algorithms converge rapidly to the true solution without stagnation. Excellent approximation is achieved after a small number of iterations, not just with high resolution but also low resolution RPI in the presence of additive as well multiplicative noises. It is shown that RPI with $\sigma=2$ is sufficient for phasing complex-valued images under a sector condition and $\sigma=1$ for phasing nonnegative images. The Error Reduction algorithm with RPI is proved to converge to the true solution under proper conditions

Phase retrieval and saddle-point optimization

Iterative algorithms with feedback are amongst the most powerful and versatile optimization methods for phase retrieval. Among these, the hybrid input-output algorithm has demonstrated practical solutions to giga-element nonlinear phase retrieval problems, escaping local minima and producing images at resolutions beyond the capabilities of lens-based optical methods. Here, the input-output iteration is improved by a lower dimensional subspace saddle-point optimization.Comment: 8 pages, 4 figures, revte

Random projections and the optimization of an algorithm for phase retrieval

Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule. For a general class of algorithms, where the basic iteration is specified by the difference map, solutions are associated with fixed points of the map, the attractive character of which determines the effectiveness of the algorithm. The behavior of the difference map near fixed points is controlled by the relative orientation of the tangent spaces of the two constraint subspaces employed by the map. Since the dimensionalities involved are always large in practical applications, it is appropriate to use random matrix theory ideas to analyze the average-case convergence at fixed points. Optimal values of the gamma parameters of the difference map are found which differ somewhat from the values previously obtained on the assumption of orthogonal tangent spaces.Comment: 15 page

Imaging atom-clusters by hard x-ray free electron lasers

The ingenious idea of single molecule imaging by hard x-ray Free Electron Laser (X-FEL) pulses was recently proposed by Neutze et al. [Nature,406,752(2000)]. However, in their numerical modelling of the Coulomb explosion several interactions were neglected and no reconstruction of the atomic structure was given. In this work we carried out improved molecular dynamics calculations including all quantum processes which affect the explosion. Based on this time evolution we generated composite elastic scattering patterns, and by using Fienup's algorithm successfully reconstructed the original atomic structure. The critical evaluation of these results gives guidelines and sets important conditions for future experiments aiming single molecule structure solution.Comment: 8 pages, 4 figures, submitted to Europhysics Letter

Phase retrieval from single biomolecule diffraction pattern

In this paper, we propose the SPR (sparse phase retrieval) method, which is a new phase retrieval method for coherent x-ray diffraction imaging (CXDI). Conventional phase retrieval methods effectively solve the problem for high signal-to-noise ratio measurements, but would not be sufficient for single biomolecular imaging which is expected to be realized with femto-second x-ray free electron laser pulses. The SPR method is based on the Bayesian statistics. It does not need to set the object boundary constraint that is required by the commonly used hybrid input-output (HIO) method, instead a prior distribution is defined with an exponential distribution and used for the estimation. Simulation results demonstrate that the proposed method reconstructs the electron density under a noisy condition even some central pixels are masked.Comment: 13 pages, 13 figures, submitted for a journa

Compressive Phase Retrieval From Squared Output Measurements Via Semidefinite Programming

Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear program, namely, l1-minimization, guarantees recovery of sparse parameter signals even when the system is underdetermined. In this paper, we consider a more challenging problem: when the phase of the output measurements from a linear system is omitted. Using a lifting technique, we show that even though the phase information is missing, the sparse signal can be recovered exactly by solving a simple semidefinite program when the sampling rate is sufficiently high, albeit the exact solutions to both sparse signal recovery and phase retrieval are combinatorial. The results extend the type of applications that compressive sensing can be applied to those where only output magnitudes can be observed. We demonstrate the accuracy of the algorithms through theoretical analysis, extensive simulations and a practical experiment.Comment: Parts of the derivations have submitted to the 16th IFAC Symposium on System Identification, SYSID 2012, and parts to the 51st IEEE Conference on Decision and Control, CDC 201

Yup’ik perspectives on climate change: “The world is following its people”

The Nelson Island Natural and Cultural History Project originated in the desire of community members in the Yup’ik villages of Chefornak, Nightmute, Toksook Bay, Tununak, and Newtok to document and share their history with their younger generation. To do so, they invited non-Native scientists to join them in village gatherings as well as on a three-week circumnavigation of Nelson Island (Alaska), during which elders reflected on changes in weather patterns, animal migrations, sea-ice conditions, and related harvesting activities. To date, a defining feature of our conversations has been the integrated way in which information is shared and elders’ reticence to distinguish between human impacts on the environment and the “natural” effects of climate change.Le projet d’histoire culturelle et naturelle de l’île Nelson trouve ses origines dans la volonté des membres des communautés yup’ik de Chefornak, Nightmute, Toksook Bay, Tununak et de Newtok de documenter et partager leur histoire avec les jeunes générations. Pour ce faire, ils ont invité des scientifiques non autochtones à se joindre à eux lors de rassemblements communautaires et d’une circumnavigation de l’île Nelson (Alaska) d’une durée de trois semaines. C’est dans ce contexte que les aînés ont exprimé leurs points de vue sur les changements des conditions métérologiques, des migrations des animaux, de l’état de la banquise ainsi que des activités de chasse, de pêche et de cueillette. À ce jour, l’une des caractéristiques déterminantes qui se dégage de nos conversations est la volonté de partager les informations de façon intégrée et la réticence des aînés à distinguer les impacts humains sur l’environnement des effets dits «naturels» du changement climatique

Polarization-sensitive coherent diffractive imaging using HHG

High harmonic generation (HHG) from lasers have attractive properties for probing ultrafast dynamics at the nanoscale. The spectral range of high harmonics at the extreme-UV and soft-X-rays (λ∼ 100 nm–1 nm, ℏω∼ 10 eV–1 keV) enables element specificity, the short wavelengths combined with high spatial coherence allows for imaging with nanometric spatial resolution, the extremely short pulse durations provide access to dynamics faster than a femtosecond (1 fs=10−15 s), and all that, on a compact system. In this chapter, we focus on experimental aspects of imaging with high harmonics. First, we present the experimental system and the image reconstruction procedure. Second, we show experimental results from the various configurations that were used throughout this project. Finally, we discuss mechanisms that played an important role in this imaging effort, and would contribute to the advancement of nanoscale imaging

Yaqulget Qaillun Pilartat (What the Birds Do): Yup'ik Eskimo Understanding of Geese and Those Who Study Them

Traditional knowledge of the effects of storm surges and changing coastal ecology on the breeding habits of geese (specifically black brant) in the coastal wetlands of southwestern Alaska was documented in a project initiated by non-Native biologists and an anthropologist. The project was both implemented and controlled by the local nonprofit regional corporation, which employed village researchers to interview elders and record their understandings of goose biology and habitat as related to storm surges. Although local and scientific understandings of brant behaviour generally agree on what is occurring (i.e., foraging habits, effects of past floods and coastal storm surges, and changes in nesting grounds), they do not always agree on why these changes are taking place. At the request of village researchers, interviews also documented Native residents' perception of geese as nonhuman persons and the non-Native view of geese as manageable wildlife, and they expressed deep resentment toward the nonlocal control that researchers and wildlife managers represent. Many feel that local control of their land and their lives is more in jeopardy than the geese. Moreover, respect for elders is as important as respect for animals in affecting management processes at the community level, creating potential conflict which younger Yup'ik men and women with training in biology find difficult to resolve. Along with articulating resistance to control, elders' testimony presents possible solutions to this contentious issue, solutions founded on personal relations between community members and scientists. Villagers' statements reflect their view that how non-Natives work in the area is as important as what is accomplished. Cooperative management of research projects like this one appears to be as important as any specific research policy or results.Un projet lancé par des biologistes allochtones et un anthropologue a permis de documenter le savoir traditionnel sur les effets des ondes de tempête et des changements dans l'écologie côtière des moeurs reproductrices de l'oie (en particulier de la bernache noire) dans les habitats côtiers marécageux du Sud-Ouest alaskien. Ce projet a été à la fois mis en oeuvre et supervisé par la corporation régionale locale à but non lucratif, qui a fait appel aux chercheurs du village pour interviewer les aînés et transcrire leurs connaissances de la biologie et de l'habitat de l'oie en relation avec les ondes de tempête. Bien que les connaissances locales et scientifiques sur le comportement de la bernache s'accordent en général sur les phénomènes qui se produisent (c.-à-d. moeurs alimentaires, effets des inondations et des ondes de tempêtes qui ont eu lieu sur le littoral dans le passé et changements dans les sites de nidification), ces connaissances ne s'accordent pas toujours sur les raisons de ces changements. À la demande des chercheurs du village, les interviews ont aussi fait état de la perception qu'avaient les résidents autochtones de la recherche et de la réglementation allochtone dans les habitats côtiers marécageux. Les aînés ont clairement exprimé qu'il existe un conflit entre la façon yupik de voir en l'oie une personne non humaine et la vision allochtone de l'oie comme une ressource que l'on peut gérer. Ils ont de plus exprimé une profonde rancoeur envers le contrôle non local que représentent les chercheurs et les gestionnaires de la faune. Un grand nombre pensent que le contrôle local de leur territoire et de leurs vies est plus en danger que l'oie elle-même. De plus, le respect envers les aînés est aussi important que le respect envers les animaux dans ce qui affecte les procédés de gestion au niveau communautaire, ce qui crée un conflit potentiel que les jeunes Yupik des deux sexes ayant suivi une formation en biologie trouvent difficile à résoudre. Parallèlement à cette expression de la résistance au contrôle, le témoignage des aînés présente des solutions possibles à cette question litigieuse, solutions qui se basent sur les relations personnelles entre les membres de la communauté et les scientifiques. Au dire des villageois, la façon dont les allochtones travaillent dans la région est aussi importante que ce qu'ils accomplissent. La gestion coopérative des projets de recherche tels que celui-ci apparaît aussi importante que tout résultat ou politique de recherche spécifique