Light influenced by the turbulent ocean can be fully characterized with the help of the power spectrum of the water’s refractive index fluctuations, resulting from the combined effect of two scalars, temperature and salinity concentration advected by the velocity field. The Nikishovs’ model [ Fluid Mech. Res. 27, 8298 (2000)] frequently used in the analysis of light evolution through the turbulent ocean channels is the linear combination of the temperature spectrum, the salinity spectrum and their co-spectrum, each being described by an approximate expression developed by Hill [ J. Fluid Mech. 88, 541562 (1978)] in the first of his four suggested models. The fourth of the Hill’s models provides much more precise power spectrum than the first one expressed via a non-linear differential equation that does not have a closed-form solution. We develop an accurate analytic approximation to the fourth Hill’s model valid for Prandtl/Schmidt numbers in the interval [3, 3000] and use it for the development of a more precise oceanic power spectrum. To illustrate the advantage of our model, we include numerical examples relating to the spherical wave scintillation index evolving in the underwater turbulent channels with different average temperatures, and, hence, different Prandtl numbers for temperature and different Schmidt numbers for salinity. Since our model is valid for a large range of Prandtl number (or/and Schmidt number), it can be readily adjusted to oceanic waters with seasonal or extreme average temperature and/or salinity or any other turbulent fluid with one or several advected quantities.

Oceanic turbulence is described by the oceanic refractive-index spectrum (ORIS), which considers several important hydrodynamic parameters. Based on ORIS, many optical oceanic quantities can be calculated using numerical integration. However, it is difficult to calculate the analytical solutions. In this paper, an approximate oceanic temperature spectrum is obtained by multiplying the non-Kolmogorov spectrum with a correction factor. By analogy with the obtained temperature spectrum, an approximate salinity spectrum and an approximate coupling spectrum are obtained. A linear summation of these three approximate spectra forms the approximate form of ORIS. The approximate form of ORIS we obtained helps calculate the analytical solutions of the relevant oceanic optical quantities.

Estimating the degree of polarization (DOP) of target signal light ( p targ ) is a critical step in the underwater polarization differential imaging process. It is challenging to accurately estimate the p targ of objects containing multiple attributes in the imaging range. Inspired by the optical polarization characteristics of objects with different DOP, we find a prior of connected domains (CDs) of objects in polarization orthogonal images. Based on this prior, the CDs of low-DOP (LDOP) and high-DOP (HDOP) objects are extracted from the darkest image ( I min ) and brightest image ( I max ) without additional image acquisition. The p targ of LDOP and HDOP objects in the scene can be estimated through the extracted CDs, which realizes the transition from global optimum estimation in the traditional method to local optimum estimation. According to the estimated p targ , the enhanced results of the entire image marked by p targ can be obtained after fusing the enhanced results of the objects in each CD. Experimental results of simple and complex combination scenes of objects show that our method can recognize CDs of LDOP and HDOP objects. We obtained the enhanced results of the entire image, verified the feasibility and robustness of our method, and found that the CDs of LDOP and HDOP objects could be effectively extracted in up to 34.3 NTU of turbid water. The local optimum improves the application ability of underwater polarization imaging in unpredictable scenarios, while the enhanced result of target labeling has potential application value in underwater target recognition and classification.

Under the impact of an infinitely extended edge phase dislocation, optical vortices (screw phase dislocations) with tight spacing induce scintillation enhancement. As the simplest case, the scintillation index of an interfering beam consisting of two Gaussian vortex beams with $\pm 1$ topological charges through weak oceanic turbulence is researched via derivation and phase screen simulation to present this phenomenon. Different combinations of two types of phase discontinuities can be obtained by changing the overlapping degree and the phase difference of two coherent Gaussian vortex beams. The scintillation indexes for them verify that the formation condition of the phenomenon is the coexistence of two types of phase discontinuities. And the enhanced scintillation index can be several orders of magnitude larger than that of a plane wave under weak perturbation (Rytov variance). This phenomenon could be useful for both optical vortex detection and perturbation measurement.

We study multiple scattering of light in a random medium containing both optical turbulence and randomly distributed particles. Based on the form of dielectric correlation function attained, the Dyson equation and Bethe-Salpeter equation for scalar waves are derived. The Bethe-Salpeter equation is then expanded according to the number of scattering times and then simplified to a practical expression for calculations after manipulations. The numerical scheme allows to calculate the field-field correlation function of scalar wave multiple scattering by particles larger than wavelength, and that of propagation in a medium containing both optical turbulence and particles. Theoretical analysis and numerical calculations may have applications in light detection and ranging (LIDAR) and underwater optical systems.