TABLE OF CONTENTS A disk that contains the MatLab computer program used for the computations presented in this text is enclosed with the text. The antenna pattern and the backscattering function used by program on the disk are the ones described in the text. However, other antenna patterns and backscattering functions can be used by modifying the program as described in section 10.3.
The program generates graphs of the quasi-static approximation using the equations given in section 4.2, my exact theory using the equations given in section 9.1, their percent difference, and the ratio BWNL/BWNH. Observe that the ratio BWNL/BWNH is the same as the unnormalized ratio BWL/BWH because the same normalizing factor is used in the numerator and the denominator.
MatLab was used for obtaining the graphs. However, MatLab is a vector processor so that it is computationally efficient for matrix calculations but rather inefficient in performing do-loops. Because the computations required extensive use of do-loops, we have the MatLab data fed to a program written in C ++ where all the computations are performed. The results are then fed back to MatLab for the construction of the graphs.
Each of the integrals I n are integrals over two dimensions. Because an algorithm designed specifically for two dimensions could not be found, I developed one. For the development of the algorithm, first observe that the integral
is simply the volume under the surface with height z = f( x, y
