1 Erratum to: J Eng Math (2012) 76:157–180 DOI 10.1007/s10665-011-9516-y

In Eqs. (40) to (43), \(\cos [4 \theta _0/3]\) should be replaced by \(\cos [4( \theta _0-\pi /2)/3]\); and in Eq. (44), \(\cos [4 \theta _0/3] \) should be replaced by \(\cos [4( \theta _0-\pi )/3]\).

These corrections do not affect any subsequent formulae appearing in the paper. In carrying out these corrections in the software, for the range of parameters that were used, no significantly discernable changes occurred to the graphs given in Figs. 20–25 already presented. I would also like to make clear that the expressions in my paper are not uniformly valid across the angular rays \(\theta =0,\pi /2,\pi , 3\pi /2, 2\pi \). This is because the derivatives of the diffraction coefficients become infinite along these grazing incidence directions. In the plots presented in the paper interpolation was carried out around these angular directions. I would like to thank Professor Paul Smith of The Mathematics Department, Macquarie University, Sydney, Australia for alerting me to these shortcomings after he ran an accurate numerical check by an integral equation method.