Fast processing of underwater polarization imaging based on optical correlation.

Underwater polarization differential imaging requires the estimation of different parameters, and the parameters can be accurately obtained by using optical correlation. However, optical correlation as a criterion function to estimate parameters takes a lot of time. To expedite the parameters' estimation process, we propose two operations to process underwater polarization images. One operation is to update the analyzer angle range to reduce the number of processed images. The other is image downsampling, which reduces the amount of calculation for the corresponding images. In experiments, we confirmed the feasibility of our method. We have obtained an average of 42 times the calculation speed increase under the conditions of updating the analyzer angle range 3 times and reducing the image scale by 16 times. The results of our method are consistent with those of traditional methods. This established method is conducive to the practical application of underwater polarization differential imaging.

Oceanic non-Kolmogorov optical turbulence and spherical wave propagation.

Light propagation in turbulent media is conventionally studied with the help of the spatio-temporal power spectra of the refractive index fluctuations. In particular, for natural water turbulence several models for the spatial power spectra have been developed based on the classic, Kolmogorov postulates. However, as currently widely accepted, non-Kolmogorov turbulent regime is also common in the stratified flow fields, as suggested by recent developments in atmospheric optics. Until now all the models developed for the non-Kolmogorov optical turbulence were pertinent to atmospheric research and, hence, involved only one advected scalar, e.g., temperature. We generalize the oceanic spatial power spectrum, based on two advected scalars, temperature and salinity concentration, to the non-Kolmogorov turbulence regime, with the help of the so-called "Upper-Bound Limitation" and by adopting the concept of spectral correlation of two advected scalars. The proposed power spectrum can handle general non-Kolmogorov, anisotropic turbulence but reduces to Kolmogorov, isotropic case if the power law exponents of temperature and salinity are set to 11/3 and anisotropy coefficient is set to unity. To show the application of the new spectrum, we derive the expression for the second-order mutual coherence function of a spherical wave and examine its coherence radius (in both scalar and vector forms) to characterize the turbulent disturbance. Our numerical calculations show that the statistics of the spherical wave vary substantially with temperature and salinity non-Kolmogorov power law exponents and temperature-salinity spectral correlation coefficient. The introduced spectrum is envisioned to become of significance for theoretical analysis and experimental measurements of non-classic natural water double-diffusion turbulent regimes.

Spatial power spectrum of natural water turbulence with any average temperature, salinity concentration, and light wavelength.

The power spectrum of water optical turbulence is shown to vary with its average temperature ⟨T⟩ and average salinity concentration ⟨S⟩, as well as with light wavelength λ. This study explores such variations for ⟨T⟩∈[0∘C,30∘C], ⟨S⟩∈[0ppt,40ppt] covering most of the possible natural water conditions within the Earth's boundary layer and for visible electromagnetic spectrum, λ∈[400nm,700nm]. For illustration of the effects of these parameters on propagating light, we apply the developed power spectrum model for estimation of the scintillation index of a plane wave (the Rytov variance) and the threshold between weak and strong turbulence regimes.

Wide-range Prandtl/Schmidt number power spectrum of optical turbulence and its application to oceanic light propagation.

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.

Practical approximation of the oceanic refractive index spectrum.

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.