Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Fermat's principle

Sortuj według:

Ogranicz wyniki do:

Image reconstruction in ultrasound transmission tomography using the Fermat’s Principle

Kania Konrad, Maj Michał, Rymarczyk Tomasz, Adamkiewicz Przemysław, Gołąbek Michał

Przegląd Elektrotechniczny

2020

R. 96, nr 1

186--189

The article presents image reconstruction in ultrasonic transmission tomography using the Fermat principle. The application consists of an ultrasound tomograph built by the authors and an algorithm implemented to solve the problem of image reconstruction. The solution enables the analysis of processes taking place in the facility without interference. The obtained tomographic imaging can be a picture of the geometry of the examined area. This allows location in the analysed area. The work developed an algorithm based on the Fermat principle as a technique of low computational complexity for real-time image reconstruction using an ultrasound tomograph.

W artykule przedstawiono rekonstrukcja obrazu w ultradźwiękowej tomografii transmisyjnej z wykorzystaniem zasady Fermata. Aplikacja składa się z tomografu ultradźwiękowego zbudowanego przez autorów oraz zaimplementowane algorytmu do rozwiązywania zagadnienia rekonstrukcji obrazu. Rozwiązanie umożliwia analizę procesów zachodzących w obiekcie bez ingerencji. Uzyskane obrazowanie tomograficzne może być obrazem geometrii badanego obszaru. Pozwala to na lokalizację w analizowanym obszarze. W pracy opracowano algorytm oparty na zasadzie Fermata jako technice o niskiej złożoności obliczeniowej do rekonstrukcji obrazu w czasie rzeczywistym za pomocą tomografu ultradźwiękowego.

Spectral ray tracer: a class of accurate two-point ray tracers

Dębski W., Ando M.

Acta Geophysica Polonica

2004

Vol. 52, nr 1

1-14

The recent development of high resolution seismic tomography and the in-creasing necessity for high precision seismic (acoustic) source locations calls for robust and very precise numerical methods of estimating of seismic (acoustic) wave travel times and propagation ray paths. This paper deals with two issues. First of all we present a ray path tracing algorithm based on the parameterization of ray paths by a series of Chebyshev polynomials. This pseudo-spectral method combined with the accurate Gauss-Lobbato integration procedure allows to reach a very high relative accuracy of travel time calculation, of the order of t/t 10(-7). The pseudo-spectral representation of sought ray paths turns the ray tracing problem into a numerical optimization task which, depending on the requirements, can be solved by a properly chosen optimizer. The used numerical representation designates the developed algorithm for tomography/location applications when no sharp interfaces occur. Secondly, we consider the question of the accuracy of the ray path tracing and travel time calculations. Achieving the highest tracing accuracy in terms of both accurate travel time estimation and precise spatial tracing (ray path geometry) requires a very careful analysis of all classes of errors. Some of them are caused by the numerical approximation (discretization) of the (continuous) physical law underlying a chosen computational algorithm. We demonstrate that these errors can degrade the ray tracing accuracy even by two orders of magnitude. To suppress this type of inaccuracy we propose to use a damping mechanism which introduces a kind of "tension" to the numerically generated ray paths. When properly applied, it suppresses the artificial spatial oscillations caused by the approximation errors and improves the ray tracing accuracy. The damping mechanism can also be regarded as the a priori requirement to keep the physical ray path trajectory as simple (smooth) as possible.