A top-down philosophy for accurate numerical ray tracing

Abstract

Several examples of the ease of application and accuracy of ray tracing resulting from the top-down approach are given to demonstrate the results obtainable with today’s small computers. One example of a more traditional approach is given to demonstrate how easy it is to lose computational accuracy to mixing instead of isolating the steps in the solution. The current level of commonly available computing power means that it is important for the ordinary researcher to be aware of powerful integration subroutines. Their extraordinary accuracy makes the payoff worth the effort expended in understanding their use.

Caustic diffraction fields in a downward refracting atmosphere

“…18 The ray model presented in this work can be used for various smooth, nonlinear profiles, such as logarithmic or power profiles. Although efficient ray-tracing algorithms exist, 19,20 ray-tracing computations usually require considerable computing times. The approach presented here, however, makes use of the ordering of rays for smooth profiles, and this results in relatively small computing times.…”

Ray-based inversion accounting for scattering for biomedical ultrasound computed tomography

“…( 57) are described in the literature, see eg. [14,27,30,28,35,26,49]. Specifically, this system of coupled equations has been solved using a second-order variant of Runge-Kutta method [36].…”

Application of the ultrasonic pulse-echo technique for quality control of the multi-layered plastic materials

“…Corresponding uncertainty source of the ultrasound velocity calculation from the reference TOF is Dc c =76 m/s. The influence of the lateral shift of the ultrasonic transducer in respect to the pipe surface has been investigated using the ray tracing approach [26][27][28]. The type B uncertainty of the TOF measurement error caused by the lateral shift 72 mm of the focused ultrasonic transducer is Dt l =76 ns.…”

“…Therefore, the amplitude of the resultant reflection after interference is negative. The mentioned assumptions have been done according to the results presented in [12,[25][26][27][28].…”