Three-dimensional fluorescent microscopy via simultaneous illumination and detection at multiple planes.

The conventional optical microscope is an inherently two-dimensional (2D) imaging tool. The objective lens, eyepiece and image sensor are all designed to capture light emitted from a 2D 'object plane'. Existing technologies, such as confocal or light sheet fluorescence microscopy have to utilize mechanical scanning, a time-multiplexing process, to capture a 3D image. In this paper, we present a 3D optical microscopy method based upon simultaneously illuminating and detecting multiple focal planes. This is implemented by adding two diffractive optical elements to modify the illumination and detection optics. We demonstrate that the image quality of this technique is comparable to conventional light sheet fluorescent microscopy with the advantage of the simultaneous imaging of multiple axial planes and reduced number of scans required to image the whole sample volume

An efficient high-order Nystr\"om scheme for acoustic scattering by inhomogeneous penetrable media with discontinuous material interface

This text proposes a fast, rapidly convergent Nystr\"{o}m method for the solution of the Lippmann-Schwinger integral equation that mathematically models the scattering of time-harmonic acoustic waves by inhomogeneous obstacles, while allowing the material properties to jump across the interface. The method works with overlapping coordinate charts as a description of the given scatterer. In particular, it employs "partitions of unity" to simplify the implementation of high-order quadratures along with suitable changes of parametric variables to analytically resolve the singularities present in the integral operator to achieve desired accuracies in approximations. To deal with the discontinuous material interface in a high-order manner, a specialized quadrature is used in the boundary region. The approach further utilizes an FFT based strategy that uses equivalent source approximations to accelerate the evaluation of large number of interactions that arise in the approximation of the volumetric integral operator and thus achieves a reduced computational complexity of $O(N \log N)$ for an $N$-point discretization. A detailed discussion on the solution methodology along with a variety of numerical experiments to exemplify its performance in terms of both speed and accuracy are presented in this paper

Sparsity driven ultrasound imaging

An image formation framework for ultrasound imaging from synthetic transducer arrays based on sparsity-driven regularization functionals using single-frequency Fourier domain data is proposed. The framework involves the use of a physics-based forward model of the ultrasound observation process, the formulation of image formation as the solution of an associated optimization problem, and the solution of that problem through efficient numerical algorithms. The sparsity-driven, model-based approach estimates a complex-valued reflectivity field and preserves physical features in the scene while suppressing spurious artifacts. It also provides robust reconstructions in the case of sparse and reduced observation apertures. The effectiveness of the proposed imaging strategy is demonstrated using experimental data

The Demographics and Atmospheres of Giant Planets with the ELTs

Gas giants are the most readily detectable exoplanets but fundamental questions about their system architectures, formation, migration, and atmospheres have been unanswerable with the current generation of ground- and space-based facilities. The dominant techniques to detect and characterize giant planets $-$ radial velocities, transits, direct imaging, microlensing, and astrometry $-$ are each isolated to a limited range of planet masses, separations, ages, and temperatures. These windows into the arrangement and physical properties of giant planets have spawned new questions about the timescale and location of their assembly; the distributions of planet mass and orbital separation at young and old ages; the composition and structure of their atmospheres; and their orbital and rotational angular momentum architectures. The ELTs will address these questions by building bridges between these islands of mass, orbital distance, and age. The angular resolution, collecting area, all-sky coverage, and novel instrumentation suite of these facilities are needed to provide a complete map of the orbits and atmospheric evolution of gas giant planets (0.3$-$10 $M_\mathrm{Jup}$) across space (0.1$-$100 AU) and time (1 Myr to 10 Gyr). This white paper highlights the scientific potential of the GMT and TMT to address these outstanding questions, with a particular focus on the role of direct imaging and spectroscopy of large samples of giant planets that will soon be made available with $Gaia$.Comment: White paper for the Astro2020 decadal surve

A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems

Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor (ST) resulting from the gradient of a multicomponent image. The proposed approach allows us to penalize the non-local variations, jointly for the different components, through various $\ell_{1,p}$ matrix norms with $p \ge 1$. To facilitate the choice of the hyper-parameters, we adopt a constrained convex optimization approach in which we minimize the data fidelity term subject to a constraint involving the ST-NLTV regularization. The resulting convex optimization problem is solved with a novel epigraphical projection method. This formulation can be efficiently implemented thanks to the flexibility offered by recent primal-dual proximal algorithms. Experiments are carried out for multispectral and hyperspectral images. The results demonstrate the interest of introducing a non-local structure tensor regularization and show that the proposed approach leads to significant improvements in terms of convergence speed over current state-of-the-art methods