China
Africa
Explore chapters and articles related to this topic
Propagation II:Mathematical Models (Part One)
Published in Paul C. Etter, Underwater Acoustic Modeling and Simulation, 2017
Focal surfaces, or caustics, are formed when the refractive properties of the ocean environment focus a number of adjacent rays into close proximity. There are two types of caustics: smooth and cusped. A cusp is actually the intersection of two smooth caustics. Examples of smooth and cusped caustics are presented in Figure 4.4. In optics, a caustic is the envelope of light rays reflected or refracted by a curved surface or object, or the projection of that envelope of rays onto another surface. Caustic can also refer to the curve to which light rays are tangent, defining a boundary of an envelope of rays as a curve of concentrated light. These shapes often have cusp singularities. In the case of sunlight, such concentration of light can burn, thus the name caustic. Stewart and James (1992) proposed using acoustic ray tracing to demonstrate examples of wave propagation (versus the usual examples of light propagation) to illustrate the general wave phenomenon of refraction in a classroom environment.
Use of Ultrasonics in the Nondestructive Testing and Evaluation of Metals
Published in Dale Ensminger, Leonard J. Bond, Ultrasonics, 2011
Dale Ensminger, Leonard J. Bond
Mosfeghi [103] describes a method of using caustics in testing cylindrical objects for radial and surface defects. A caustic is a focal region along which neighboring rays in a beam touch. The method has been used for imaging radial cracks and surface defects in round rods and pipes. The experimental procedure includes locating the test object in an immersion tank, interrogating the part with pulses from a 1.3-cm unfocused wideband 5-MHz transducer, and rotating the sample with the probe fixed in position. In some cases, part of the beam was masked to produce a smaller rectangular beam.
Effects of a circular hole on the propagation behavior of double running cracks under impact loading
Published in Mechanics of Advanced Materials and Structures, 2022
Zhongwen Yue, Yulong Li, Xu Wang, Shuaiming Wang, Haoran Dong, Wei Li, Jun Zhou, Anjia Peng
Under the concentrated loading at the crack tip, the thickness and refractive index of the specimen in the crack tip area will change, resulting in the deflection of the parallel light beam passing through the area. At this time, on the reference plane with the distance of the specimen, a dark spot can be obtained, which is called caustic spots. Around the caustic spots, there is a bright line with concentrated light intensity, which is called caustics. Figure 1 is the schematic diagram of caustics imaging principle, and Figure 2 is the mode I caustic curve at crack tip. In Figure 1, d is the thickness of the specimen, is the stress act on the specimen; is the distance between the specimen and the reference plane. In Figure 2, is the maximum diameter of caustics.
Explicit complex-valued solutions of the 2D eikonal equation
Published in Applicable Analysis, 2022
As already observed in the previous sections, real-valued solutions of (1) describe the propagation of light along rays. Thus, the region swept by rays – the light region – corresponds to the set in which the eikonal is real-valued or, up to some suitable normalization, to the set of critical points of v. The envelope of rays create a so-called caustic that bounds the light region. Outside that region, i.e. beyond the caustic, we have that and up to normalizing an additive imaginary constant, we can assume that v<0, so that the exponentials in (3) or (4) rapidly decay to zero as the wave number k becomes large. This is the so-called shadow region.