Kirchhoff diffraction formulations that use the wave front and the aperture plane for the surfaces of integration were compared. The full Kirchhoff obliquity factor terms distinguishing these two formulations are presented for spherical waves and for Gaussian laser beams. When they are used, identical results are obtained for the two formulations in both the spherical-wave and the Gaussian lase...

We present an experimental study of the angular distribution of light scattered from several rough metallic surfaces, which cover a range of roughness conditions. A BRDF model based on the Kirchhoff approximation was used to demonstrate the relation between surface-height statistics and the angular distribution of the scattered light. To do this, the angular distributions calculated with the BR...

Everyday experience shows that twisted elastic filaments spontaneously form loops. We model the dynamics of this looping process as a sequence of bifurcations of the solutions to the Kirchhoff equation describing the evolution of thin elastic filament. The control parameter is taken to be the initial twist density in a straight rod. The first bifurcation occurs when the twisted straight rod def...

The recent application of tomographic methods to three-dimensional imaging through tissue by use of light often requires modeling of geometrically complex diffuse-nondiffuse boundaries at the tissue-air interface. We have recently investigated analytical methods to model complex boundaries by means of the Kirchhoff approximation. We generalize this approach using an analytical approximation, th...

3-D prestack depth migration is emerging as an industrial imaging tool. Many competing algorithms have been proposed by various authors. Nevertheless, the real bottleneck in 3D prestack processes is the sheer amount of input and output data. This paper reviews the principal migration methods on the basis of their capacity for data manipulation, without evaluating the algorithms themselves. It c...

Real-time location of earthquakes can be achieved by using direct imaging of the recorded wave field based on a Kirchhoff reconstruction method similar to that used in the migration of seismic reflection data. The standard method of event location requires the wave arrival at each sensor to be picked and associated with an event. By using direct imaging, the event is identified once in the imag...

Constructing the seismic image in vertical time, as opposed to depth, eliminates the inherent ambiguity of resolving the vertical P -wave velocity from surface seismic data in transversely isotropic media with a vertical axis of symmetry (VTI media). By ray tracing in the space-time (x-τ)-domain, a traveltime map is built by interpolating the traveltime information along the rays onto a regular...

Two important tools in seismic processing––Kirchhoff migration and demigration operators––are the basis for many imaging problems solution. Due to high numerical and computational requirements, the use of those tools for three dimensions are very computation-costly. This fact has motivated us to investigate Kirchhoff migration operations for simpler types of media in order to provide faster res...

A method for evaluation of scattering from rough surfaces which is similar to the Kirchhoff approximation is considered. However, it is based on a local parabolic approximation of the surface irregularities rather than a tangent plane approximation and two iterations of the surface field integral equation. The method, first proposed by Belobrov and Fuks [Izv. VUZ Radiofiz. 29, 1083-1089 (1986);...