Wave Elevation for an Array of Columns Under Wave-Current Interactions

A wave and current diffraction model is developed based on the potential flow theory and a high-order boundary element method with the successful treatment of singular and nearly singular integrals. The wave-current diffraction from four mounted cylindrical columns are computed, and the free surface wave elevations among the columns are investigated. The influences of the current speed, wave direction, and column spacing on the wave elevation are examined. Ultimately, the presence of a current has a significant influence on the magnitude, spatial location and occurrence frequency of the maximum wave elevation.

A Geometrical Analysis of Diffraction Based on Fractal Inhomogeneous Space

Although the diffraction of light is a simple experiment in optics, no complete interpretation that satisfactorily describes diffraction in any instance has been developed. Classical physics is unable to describe diffraction phenomena by considering photons solely as particles. In addition, modern mathematical solutions based on the wave-particle duality, including Rayleigh–Sommerfeld diffraction theory, are merely approximations, and fail to provide a model that can be applied to the diffraction caused by both transparent and opaque barriers. This study proposes a diffraction model that can account for both single photons and larger particles, such as electrons, in an inhomogeneous space near the surface of the objects, including the edges of the apertures. Furthermore, a three-dimensional model for calculating the light intensity at any arbitrary observation point is presented. This model provides accurate diffraction simulations and is independent of the near and the far-field zones as well as the aperture material.

PHYSICAL AND MATHEMATICAL MODELING OF THE WAVE QUENCHING CHAMBER WITH THE UPPER PART IN THE FORM OF A PERMEABLE WATERFRONT

This paper presents the results of mathematical and physical modeling of the interaction of waves with the wave chamber on cylindrical supports and the upper part in the form of a permeable waterfront. On the basis of the diffraction model the mathematical modeling of refraction and transformation of waves near the structure is carried out. In the presence of a structure, the transformation of waves is co-accompanied by the phenomena of wave destruction at the edges of the structure and the partial reflection of residual waves from the walls of the protective front. Reflection phenomena cause changes in wave heights along the front of the structure. The results of experimental data are given, which showed that the structure with such a construction is resistant to waves, large soil erosion was not observed.

Diffraction model of a laser speckle interferometer for measuring micro-displacements of objects with scattering surface

On the basis of diffraction transformations of an optical wave field a mathematical model for the formation of speckle modulated interference patterns and signals at the output of a speckle interferometer is developed, which allows us to identify their properties and quantitative parameters. Speckle interferometers based on a Michelson arrangement are considered, where objects with scattering surfaces are used instead of mirrors in the reference and object arms. Results of numerical simulation of speckle modulated interference patterns on the basis of diffraction transformations of wave fields in an interferometer are discussed. Simulated images obtained at the output of the interferometer when focusing laser beams on the scattering surfaces of the controlled and reference objects are considered. Experimental results of using a speckle interferometer with a digital matrix photodetector for measuring the temperature micro-displacements of an object with a scattering surface and a quantitative comparison of experimental data with the results obtained by a numerical experiment using a diffraction model of a speckle interferometer are presented.

VIPR: Vectorial Implementation of Phase Retrieval for fast and accurate microscopic pixel-wise pupil estimation

In microscopy, proper modeling of the image formation has a substantial effect on the precision and accuracy in localization experiments and facilitates the correction of aberrations in adaptive optics experiments. The observed images are subject to polarization effects, refractive index variations and system specific constraints. Previously reported techniques have addressed these challenges by using complicated calibration samples, computationally heavy numerical algorithms, and various mathematical simplifications. In this work, we present a phase retrieval approach based on an analytical derivation of the vectorial diffraction model. Our method produces an accurate estimate of the system phase information (without any prior knowledge) in under a minute.