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

Phase-Induced Amplitude Apodization of Telescope Pupils for Extrasolar Terrestrial Planet Imaging

In this paper, an alternative to the classical pupil apodization techniques (use of an amplitude pupil mask) is proposed. It is shown that an apodized pupil suitable for imaging of Extrasolar planets can be obtained by reflection of an unapodized flat wavefront on 2 mirrors. By carefully choosing the shape of these 2 mirrors, it is possible to obtain a contrast better than 10^{9} at a distance smaller than 2 \lambda/d from the optical axis. Because this technique preserves both the angular resolution and light gathering capabilities of the unapodized pupil, it allows efficient detection of terrestrial extrasolar planets with a 1.5m telescope in the visible.Comment: 9 pages, 9 figures, Accepted for publication in A&A. Postscript file with full-resolution figures can be found at http://www.naoj.org/staff/guyon/publications/PIAA.p

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

Bayesian algorithms for recovering structure from single-particle diffraction snapshots of unknown orientation: a comparison

The advent of X-ray Free Electron Lasers promises the possibility to determine the structure of individual particles such as microcrystallites, viruses and biomolecules from single-shot diffraction snapshots obtained before the particle is destroyed by the intense femtosecond pulse. This program requires the ability to determine the orientation of the particle giving rise to each snapshot at signal levels as low as ~10-2 photons/pixel. Two apparently different approaches have recently demonstrated this capability. Here we show they represent different implementations of the same fundamental approach, and identify the primary factors limiting their performance.Comment: 10 pages, 2 figure

Image processing as state reconstruction in optics

The image reconstruction of partially coherent light is interpreted as the quantum state reconstruction. The efficient method based on maximum-likelihood estimation is proposed to acquire information from registered intensity measurements affected by noise. The connection with totally incoherent image restoration is pointed out. The feasibility of the method is demonstrated numerically. Spatial and correlation details significantly smaller than the diffraction limit are revealed in the reconstructed pattern.Comment: 10 pages, 5 figure

Pulse shaping by phase-modulated fiber gratings in transmission

We propose a novel approach to pulse shaping using a phase-modulated fiber Bragg gratings (FBGs) in transmission. This enables the simplification of the device fabrication while retaining the substantial advantages of FBGs in transmission

The Universe is not a Computer

When we want to predict the future, we compute it from what we know about the present. Specifically, we take a mathematical representation of observed reality, plug it into some dynamical equations, and then map the time-evolved result back to real-world predictions. But while this computational process can tell us what we want to know, we have taken this procedure too literally, implicitly assuming that the universe must compute itself in the same manner. Physical theories that do not follow this computational framework are deemed illogical, right from the start. But this anthropocentric assumption has steered our physical models into an impossible corner, primarily because of quantum phenomena. Meanwhile, we have not been exploring other models in which the universe is not so limited. In fact, some of these alternate models already have a well-established importance, but are thought to be mathematical tricks without physical significance. This essay argues that only by dropping our assumption that the universe is a computer can we fully develop such models, explain quantum phenomena, and understand the workings of our universe. (This essay was awarded third prize in the 2012 FQXi essay contest; a new afterword compares and contrasts this essay with Robert Spekkens' first prize entry.)Comment: 10 pages with new afterword; matches published versio

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

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