Evaluation of Millimetre-wave Coherent Scattering from a Sea surface covered by Foam modelled as Sequences of Thin Phase-Scattering Screens using Split-Step Fourier Method

This research focused on developing a physical based model of foam covered sea surface as air-bubble coated with thin layers of seawater, that is suitable for investigation of millimetre wave coherent scattering. The propagation media was described as a flat sea-surface covered by foam and modelled as sequences of thin and deep phase scattering screens. The propaga- tion media is a dense random media which comprise randomly distributed air-bubbles that follow a log-normal distribution pattern. The log-normal distribution is a skewed distribu- tion with low geometric mean and large variance which can not be negative but cut-off at zero. The log-normal distribution is a good candidate for modelling random variability from the multiplicative version of the central limit theorem, which proves that many independent, positive random variables are approximately log-normal. The locations and bubble radii of the air-bubbles were described by uniform random numbers. To obtain the bubble size distribution (BSD) and bubble radii the uniform random variate was transformed to normal variate by computing the error function, complementary error function and cumulative error function. The probability density function (PDF) of the inverse error function was obtained by Newton’s method. We estimated the BSD and bubble radii by assuming a geometric mean μg = 500μm and geometric standard deviation σg = 2.0. Three dimensional (3D) sphere packing approach was implemented for filling the air-bubbles in a cubic domain as we assumed that the air-bubbles are spherical in shape. There was need to avoid two adjacent spheres overlapping to ensure efficient packing density. The 3D packed spheres were con- verted to 2D slices of annuli with the outer circle being a thin layer of seawater and the inner circle 80−95% air. The model of sea foam accounts for its mechanical and optical properties which comprises of foam layer thickness, bubble size distribution, foam void fraction, bubble radius, refractive index, sea surface temperature etc. Sea surface roughness and wind speed are physical processes which are significant in evaluation of the sea surface emissivity which helps in measuring brightness temperature of the sea. The split-step Fourier method was adopted as a marching technique well suited for evaluation of the refraction and diffraction effects of scattered millimetre wave due to its interaction with five (5) 2D slices of sea foam layer. Results obtained from the split-step Fourier method represent the angular spectrum as a distorted wavefront and field intensity at the sea surface after forward and backward propagation for thin and deep phase screens. The attenuation in dB and specific attenuation (dB/mm) for incident angles θi = 30◦,45◦ and 60◦ with φ = 0◦ for thin and deep phase screens at various WindSat frequencies 6.8 GHz, 10.7 GHz, 18.7 GHz, 23.8 GHz and 37 GHz are presented. Diffuse scattering is a major attenuation factor for thin phase screen at moderate frequencies while absorption is dominant at high frequencies for deep phase screens.