A scheme for automatic computation of Fock-type integrals

The evaluation of Fock-type integrals-i.e., integrals that are formally the Fourier transform of a slowly varying factor comprising a quotient of terms containing Airy functions and their derivatives-is developed in a computationally efficient way. The integrals are evaluated by use of a simple extension of a Fourier quadrature method that is related to the discrete Fourier transform. The resulting quadrature is applicable to both surface-field and reflected-field Fock integrals for a lossy impedance surface. The computation is believed to be efficient enough to allow the use of these functions in field computations codes where the Fock integrals must be computed on an as-needed basis.