Ray-tracing

In UltraSIM/UlSim the ultrasonic sound propagation from a virtual ultrasonic transducer can be simulated in ray tracing mode in any isotropic and homogeneous 3D geometry, including possible mode conversions phenomenons, etc. The CAD geometry for the simulation is a 3D NURBS surface model of the test object. It can be created in ROBCAD or imported from another 3D CAD system. 

A computer program was compiled to work out the ray-tracing of UV detector of high performance capillary electrophoresis at the investigation of 5 and 6 (98MI59). The capacity factor of 5 at different temperature and at different mobile phase compositions was experimentally determined in bonded-phase chromatography with ion suppression (98MI15). 

Figure 10. Ray-tracing through an immersed grating suitable for CMOS with p = 1800/mm, with a 35-deg prism for 630 < A < 682nm.

Verdaasdonk R.M., Borts C., Ray tracing of optically modified fibertips 1. Spherical probes, Appl. Opt. 1991 30 2159-2171. 

Fig. 8.32 Schematic of ray tracing picture of a resonant mode with light transmitted into the inner boundary. Reprinted from Ref. 68 with permission. 2008 Optical Society of America...

The complexity of the geometry usually necessitates numerical analysis by ray tracing in order to design such beam conditioners and to predict their aberrations. The design principles are straightforward ... 

Shape descriptor derived from ray traces of the molecule s electrostatic surface potential. 

The simplifying assumptions that permit us to consider only specular reflections are no longer met when the wall surfaces contain features that are comparable in size to the wavelength of the sound. In this case, the reflected sound will be scattered in various directions, a phenomenon referred to as difjusion. The source image model cannot be easily extended to handle diffusion. Most auralization systems use another geometrical model, called ray tracing [Krokstad et al., 1968], to model diffuse reflections. A discussion of these techniques is beyond the scope of this paper. 

In this final equation, the factor 1.06 in equ. (2.28d) has been approximated to unity because for the electron spectrometer shown in Fig. 1.17 ray-tracing calculations lead to the result that the spectrometer function deviates slightly from the Gaussian shape (see Fig. 5.25) and gives the value k = 1.00 instead of k = 1.06 as required by an exact Gaussian function. 

There is some freedom to choose T and AV (or Az) in different ways which all yield the same L, because L is the only quantity which is uniquely determined by the ray-tracing procedure (for a preselected q value). However, when L is calculated, one also can determine which points within the actual source region contribute to the spectrometer response. Hence, an appropriate value for Az can be selected, e.g., the value which delivers 90% of the intensity accepted by the spectrometer, and this Az value then fixes the corresponding value for T. Because of their transparent interpretation the quantities T and Az are frequently used, but it should be kept in mind that it is only their product (together with q), i.e., the luminosity L, which is the fundamental quantity. 

This value differs from the one quoted in [DFM87] because of a numerical mistake in the ray-tracing program. 

A sp = 204 meV is obtained which corresponds to (A / )sp — 0.68%. (The photon beam diameter was estimated to be approximately 2 mm according to the ray-tracing results shown in Fig. 4.13 this corresponds to (A / )sp = 0.64%.) Keeping fixed values for T and A sp, it is then possible to analyse the Auger lineshapes obtained at other, in particular lower, photon energies correctly. 

An example of a design of the asymmetric module (photo and ray tracing sketch) is shown in Figure 6. 

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