A scalar field diffracted by a rigid rectangular plate can be computed
with the formula that Otsuki derived by applying the properties of We
ber-Schafheitlin's discontinuous integral (also referred to as the Kob
ayashi potential). This method may be regarded as giving an eigenfunct
ion expansion of the wave functions of the present configuration, alth
ough these functions are expressed by double infinite integrals. Expan
sion coefficients are determined from the matrix equations, and the ma
trix elements are given by double infinite integrals. An algorithm eff
ective for computing these integrals is developed here by using the as
ymptotic expansions for the integrands. As a result, the original inte
gral reduces to a finite double integral plus two finite single integr
als. The numerical results for some diffraction patterns are presented
. With relatively large plates, the results agree well with those obta
ined from the Kirchhoff diffraction integral. (C) 1997 American Instit
ute of Physics.