Ray theory

Although, Kato has shown that the ray theory breaks down approximately 10 fjm from a dislocation core and we caimot apply it to compute the contrast of a dislocation in a quantitative way, it is possible to obtain a large amoimt of qualitative information. 

The simple picture of two interfering rays can be a great help in visualizing what is happening in an acoustic microscope as it is defocused (Quate 1980), and for many intuitive purposes this is quite sufficient. For analytical purposes more substantial theory is needed, and this can be derived both from diffraction optics and from a more rigorous development of ray theory. The simple ray model is vindicated both by the more detailed theoretical models presented in this chapter, and also by quantitative measurements based on them, which will be described in Chapter 8. 

In transmission microscopy of specimens with properties not too different from those of water, Rayleigh waves may safely be disregarded. But in reflection microscopy of specimens of higher stiffness, Rayleigh waves generally play a dominant role. This is recognized explicitly in the ray theory treatment. 

The expression for the period of the oscillations in V(z) can also be derived by ray theory. The ray model is particularly powerful in the analysis of V(z) data. 

J. Pirenne. Physica 21, 971-87 (1955). x-ray, theory isotopic expansion in crystals. 

Cerveny, V., 2001, Seismic ray theory Cambridge University Press, Cambridge, New York, 696 pp. 

Since the composition of the sample is variable, and therefore so is its mass absorption coefficient, it is sometimes necessary to carry out interelement corrections. The values of the correction factors can either be calculated from fundamental theory using commercially available software, or by multilinear regression analysis using the calibration samples. The former is preferred since the latter can force a mathematical fit to the data which bears no relation to X-ray theory. 

Dahm T (1996) Relative moment tensor inversion based on ray theory theory and synthetic tests. Geophys. J. Int. 124 245-257... 

Aki K, Richards PG (1980) Quantitative seismology Theory and methods. Vol. I, WH Freeman and Compaity, San Francisco Dahm T (1996) Relative moment tensor inversion based on ray theory Theory and Synthetic Tests. Geophys. J Int., 124 245-257 Dai ST, Labuz JF, Carvalho F (2000) Softening response of rock observed in plane-strain compression. Trends in Rock Mechanics, Geo SP-102, ASCE, pp 152-163... 

Second mechanism. The second mechanism is that freak wave can result when waves interact with currents. When this situation occurs, ray theory can be used to explain the formation of extreme waves. However, it is not yet known how the statistical properties of surface are related to the properties of currents. From the studies of freak waves generated over a random current, it has been foimd that wave focusing with 1 m/s velocity fluctuations occurs in the imiform current. 

Alternative forms for V are given inside the front cover. The ray theory presented here is restricted to multimode waveguides, i.e. waveguides satisfying V> I, for reasons discussed in Chapters 10 and 36. 

Snyder, A. W. (1974) Leaky-ray theory of optical waveguides of circular cross-section. Appl. Phys., 4, 273-98. 

Ankiewicz, A. (1979) Ray theory of graded non-circular optical fibres. Opt. Quant. Elect., 11, 197-203. 

In Chapters 1 and 2 we introduced the notion of ray transit time. The main contribution to pulse spreading is due to the obvious fact that the ray transit time is different for different ray paths. This effect is known as ray dispersion, and is sometimes referred to as intermodal dispersion, since early investigation used electromagnetic analysis in terms of modes [1], rather than ray theory. In addition to ray dispersion, material dispersion also affects pulse spreading. This effect arises because the materials constituting the fiber have a refractive index which varies with the wavelength of light. 

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