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

In this communication we have analyzed the errors introduced by table lookup when an electromagnetic diffraction integral is performed numerically. We have shown that in order to set the
3\sigma
error of both the real and imaginary components equal to
\varepsilon
, the required table should have at least
K
entries uniformly distributed within a
2\pi
range, where
K \geq 3.85/\varepsilon\sqrt{N}
and
N
is the number of terms used for numerical integration. The maximum deviation of the amplitude (
\bar{R}
) of this integral in this case is also less than
\varepsilon
and the maximum phase deviation is
\tan^{-1} (\varepsilon/\bar{R})
. A numerical example is presented which confirms this prediction.