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Extension of Fourier methods to the calculation of effective depths in heterogeneous media of arbitrary contour
Author(s) -
Starkschall George
Publication year - 1986
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.595820
Subject(s) - intersection (aeronautics) , cartesian coordinate system , fourier transform , fourier series , mathematical analysis , fourier analysis , bipolar coordinates , contour line , series (stratigraphy) , mathematics , point (geometry) , geometry , physics , paleontology , meteorology , engineering , biology , aerospace engineering
The description of patient contours and internal structures by means of truncated Fourier series can be extended to continuous contours of arbitrary shape and location by expressing the x and z Cartesian coordinates of the contour as independent Fourier series in a parameter t . An analytic equation for the intersection of the contour and a ray line is then written as an equation in the parameter t . The equation can be solved using numerical methods yielding the Cartesian coordinates of the intersection point directly.