Broadband properties of potential and kinetic energies in an oceanic waveguide.

The energetic properties of an acoustic field can be quantified through the potential (Ep) and kinetic (Ek) energies. This article derives broadband properties of Ep and Ek in an oceanic waveguide, with restriction to a far-field context under which the acoustic field can be described by a set of propagating trapped modes. Using a set of reasonable assumptions, it is analytically demonstrated that, when integrated over a wide enough frequency-band, Ep = Ek everywhere in the waveguide, except at four specific depths: z = 0 (sea surface), z = D (seafloor), z = zs (source depth), and z=D-zs (mirrored source depth). Several realistic simulations are also presented to show the relevance of the analytical derivation. It is notably illustrated that, when integrated over third-octave bands, Ep≃Ek within 1 dB everywhere in the far-field waveguide, except in the first few meters of the water column (on a dB scale, no significant difference is found between Ep and Ek for z = D, z = zs, and z=D-zs).

Polarization of ocean acoustic normal modes.

In ocean acoustics, shallow water propagation is conveniently described using normal mode propagation. This article proposes a framework to describe the polarization of normal modes, as measured using a particle velocity sensor in the water column. To do so, the article introduces the Stokes parameters, a set of four real-valued quantities widely used to describe polarization properties in wave physics, notably for light. Stokes parameters of acoustic normal modes are theoretically derived, and a signal processing framework to estimate them is introduced. The concept of the polarization spectrogram, which enables the visualization of the Stokes parameters using data from a single vector sensor, is also introduced. The whole framework is illustrated on simulated data as well as on experimental data collected during the 2017 Seabed Characterization Experiment. By introducing the Stokes framework used in many other fields, the article opens the door to a large set of methods developed and used in other contexts but largely ignored in ocean acoustics.

Expansion-maximization-compression algorithm with spherical harmonics for single particle imaging with x-ray lasers.

In three-dimensional (3D) single particle imaging with x-ray free-electron lasers, particle orientation is not recorded during measurement but is instead recovered as a necessary step in the reconstruction of a 3D image from the diffraction data. Here we use harmonic analysis on the sphere to cleanly separate the angular and radial degrees of freedom of this problem, providing new opportunities to efficiently use data and computational resources. We develop the expansion-maximization-compression algorithm into a shell-by-shell approach and implement an angular bandwidth limit that can be gradually raised during the reconstruction. We study the minimum number of patterns and minimum rotation sampling required for a desired angular and radial resolution. These extensions provide new avenues to improve computational efficiency and speed of convergence, which are critically important considering the very large datasets expected from experiment.