On the accuracy of a numerical integration procedure for computing diffraction fields using table lookup

The errors introduced by table-lookup procedures during the numerical performance of an electromagnetic diffraction integral are analyzed and it is found that the setting of the 3(sigma) error of both the real and imagery components in such a way as to equal epsilon requires a table containing at least K entries distributed over a 2(pi) range. K is defined as equal to or greater than 3.85/epsilon (square root of N), where N is the number of terms used for numerical integration. The maximum amplitude deviation (R-bar) of the integral is in this case also less than epsilon, and the maximum phase deviation is arctan (epsilon/R-bar).