Marc Allain

Three-dimensional high-resolution quantitative microscopy of extended crystals

Hard X-ray lens-less microscopy raises hopes for a non-invasive quantitative imaging, capable of achieving the extreme resolving power demands of nanoscience. However, a limit imposed by the partial coherence of third generation synchrotron sources restricts the sample size to the micrometer range. Recently, X-ray ptychography has been demonstrated as a solution for arbitrarily extending the field of view without degrading the resolution. Here we show that ptychography, applied in the Bragg geometry, opens new perspectives for crystalline imaging. The spatial dependence of the three-dimensional Bragg peak intensity is mapped and the entire data subsequently inverted with a Bragg-adapted phase retrieval ptychographical algorithm. We report on the image obtained from an extended crystalline sample, nanostructured from a silicon-on-insulator substrate. The possibility to retrieve, without transverse size restriction, the highly resolved three-dimensional density and displacement field will allow for the unprecedented investigation of a wide variety of crystalline materials, ranging from life science to microelectronics.

On global and local convergence of half-quadratic algorithms

This paper provides original results on the global and local convergence properties of half-quadratic (HQ) algorithms resulting from the Geman and Yang (GY) and Geman and Reynolds (GR) primal-dual constructions. First, we show that the convergence domain of the GY algorithm can be extended with the benefit of an improved convergence rate. Second, we provide a precise comparison of the convergence rates for both algorithms. This analysis shows that the GR form does not benefit from a better convergence rate in general. Moreover, the GY iterates often take advantage of a low cost implementation. In this case, the GY form is usually faster than the GR form from the CPU time viewpoint.

Three-dimensional edge-preserving image enhancement for computed tomography

Computed tomography (CT) images exhibit a variable amount of noise and blur, depending on the physical characteristics of the apparatus and the selected reconstruction method. Standard algorithms tend to favor reconstruction speed over resolution, thereby jeopardizing applications where accuracy is critical. In this paper, we propose to enhance CT images by applying half-quadratic edge-preserving image restoration (or deconvolution) to them. This approach may be used with virtually any CT scanner, provided the overall point-spread function can be roughly estimated. In image restoration, Markov random fields (MRFs) have proven to be very flexible a priori models and to yield impressive results with edge-preserving penalization, but their implementation in clinical routine is limited because they are often viewed as complex and time consuming. For these practical reasons, we focused on numerical efficiency and developed a fast implementation based on a simple three-dimensional MRF model with convex edge-preserving potentials. The resulting restoration method provides good recovery of sharp discontinuities while using convex duality principles yields fairly simple implementation of the optimization. Further reduction of the computational load can be achieved if the point-spread function is assumed to be separable. Synthetic and real data experiments indicate that the method provides significant improvements over standard reconstruction techniques and compares well with convex-potential Markov-based reconstruction, while being more flexible and numerically efficient.

Noise models for low counting rate coherent diffraction imaging

Coherent diffraction imaging (CDI) is a lens-less microscopy method that extracts the complex-valued exit field from intensity measurements alone. It is of particular importance for microscopy imaging with diffraction set-ups where high quality lenses are not available. The inversion scheme allowing the phase retrieval is based on the use of an iterative algorithm. In this work, we address the question of the choice of the iterative process in the case of data corrupted by photon or electron shot noise. Several noise models are presented and further used within two inversion strategies, the ordered subset and the scaled gradient. Based on analytical and numerical analysis together with Monte-Carlo studies, we show that any physical interpretations drawn from a CDI iterative technique require a detailed understanding of the relationship between the noise model and the used inversion method. We observe that iterative algorithms often assume implicitly a noise model. For low counting rates, each noise model behaves differently. Moreover, the used optimization strategy introduces its own artefacts. Based on this analysis, we develop a hybrid strategy which works efficiently in the absence of an informed initial guess. Our work emphasises issues which should be considered carefully when inverting experimental data.

High resolution three dimensional structural microscopy by single angle Bragg ptychography

Coherent X-ray microscopy by phase retrieval of Bragg diffraction intensities enables lattice distortions within a crystal to be imaged at nanometre-scale spatial resolutions in three dimensions. While this capability can be used to resolve structure-property relationships at the nanoscale under working conditions, strict data measurement requirements can limit the application of current approaches. Here, we introduce an efficient method of imaging three-dimensional (3D) nanoscale lattice behaviour and strain fields in crystalline materials with a methodology that we call 3D Bragg projection ptychography (3DBPP). This method enables 3D image reconstruction of a crystal volume from a series of two-dimensional X-ray Bragg coherent intensity diffraction patterns measured at a single incident beam angle. Structural information about the sample is encoded along two reciprocal-space directions normal to the Bragg diffracted exit beam, and along the third dimension in real space by the scanning beam. We present our approach with an analytical derivation, a numerical demonstration, and an experimental reconstruction of lattice distortions in a component of a nanoelectronic prototype device.

Super-resolution photoacoustic fluctuation imaging with multiple speckle illumination

In deep tissue photoacoustic imaging, the spatial resolution is inherently limited by acoustic diffraction. Moreover, as the ultrasound attenuation increases with frequency, resolution is often traded-off for penetration depth. Here we report on super-resolution photoacoustic imaging by use of multiple speckle illumination. Specifically, we show that the analysis of second-order fluctuations of the photoacoustic images combined with image deconvolution enables resolving optically absorbing structures beyond the acoustic diffraction limit. A resolution increase of almost a factor 2 is demonstrated experimentally. Our method introduces a new framework that could potentially lead to deep tissue photoacoustic imaging with sub-acoustic resolution.

Strain in a silicon-on-insulator nanostructure revealed by 3D x-ray Bragg ptychography

Progresses in the design of well-defined electronic band structure and dedicated functionalities rely on the high control of complex architectural device nano-scaled structures. This includes the challenging accurate description of strain fields in crystalline structures, which requires non invasive and three-dimensional (3D) imaging methods. Here, we demonstrate in details how x-ray Bragg ptychography can be used to quantify in 3D a displacement field in a lithographically patterned silicon-on-insulator structure. The image of the crystalline properties, which results from the phase retrieval of a coherent intensity data set, is obtained from a well-controlled optimized process, for which all steps are detailed. These results confirm the promising perspectives of 3D Bragg ptychography for the investigation of complex nano-structured crystals in material science.

Far-field diffraction microscopy at λ/10 resolution

Tomographic diffraction microscopy is a three-dimensional quantitative optical imaging technique in which the sample is numerically reconstructed from tens of holograms recorded under different angles of incidence. We show that combining the measurement of the amplitude, the phase, and the polarization of the field scattered by the sample with an approximate knowledge of the sample permittivity allows reconstruction of spatially complex samples up to 50 nm resolution. This technique should be particularly useful for imaging objects made of known materials.

Analysis of the depth resolution limit of luminescence diffuse optical imaging

We introduce a methodology to determine quantitatively the depth resolution limit in luminescence diffuse optical imaging. The approach is based on a Cramer-Rao statistical analysis, a noise model, and calculations of photon transport in tissues. We illustrate the method in the case of luminescence imaging in a brain-skull model, showing its potential applications in molecular imaging on small animals.

Improving the axial and lateral resolution of three-dimensional fluorescence microscopy using random speckle illuminations

We consider a fluorescence microscope in which several three-dimensional images of a sample are recorded for different speckle illuminations. We show, on synthetic data, that by summing the positive deconvolution of each speckle image, one obtains a sample reconstruction with axial and transverse resolutions that compare favorably to that of an ideal confocal microscope.