Based on the mathematical model of the propagation of an acoustic signal in a fluctuating medium, the inverse problem is formulated, which includes determination a function that describes the deviation of the bottom level from the average specified horizontal plane. In the single-scattering approximation and the narrow directivity pattern of the receiving antenna, the solution of the direct problem is obtained. As a solution to the inverse problem, a nonlinear differential equation is obtained for a function describing the deviation of the bottom relief. A numerical analysis of the solution of the equation is carried out. The dependence of the reconstruction of the lower surface on the curvature of the function describing the relief is shown.
The problem of determination of refractive indices for layered medium under known outgoing radiation is considered. It is assumed, that the Stokes parameters of radiation at the boundary of medium are known. To solve the problem, we propose a special indicator function. This function has singularity as its argument tends to unknown values of the refractive index. The results of numerical experiments are discussed.
Authors study a problem of determining the bottom topography of a fluctuating ocean using the data of side-scan sonars. Based on a kinetic model of acoustic radiative transfer authors obtain a formula for determining a function describing small deviations of the bottom surface from a middle level. Numerical experiments have been done on modeling data that demonstrate the accuracy of the obtained formula.
The kinetic model, describing sound propagation in a randomly inhomogeneous medium with diffuse reflection by Lambert's cosine law on the bottom surface, is considered. Based on it the inverse problem of bottom scattering reconstruction is formulated. An explicit solution is deduced by using a narrow receiving directivity pattern and a pointwise isotropic source. Numerical experiments for the analysis of the impact of the finite pulse and the finite receiving directivity pattern on the received signal are done.
Finish polishing of optics with magnetic media has evolved extensively over the past decade. Of the approaches conceived during this time, the most recently developed process is called magnetorheological finishing (MRF). In MRF, a magnetic field stiffens a fluid suspension in contact with a workpiece. The workpiece is mounted on the rotating spindle of a computer numerically controlled machine. Driven by an algorithm for machine control that contains information about the MRF process, the machine deterministically polishes out the workpiece by removing microns of subsurface damage, smoothing the surface to a microroughness of 10 angstroms rms, and correcting surface figure errors to less than 0.1 micrometers p-v. Spheres and aspheres can be processed with the same machine set-up using the appropriate machine program. This paper describes MRF and gives examples which illustrate the capabilities of a pre-prototype machine located at the Center for Optics Manufacturing.