UTD-diffraction coefficients for higher order wedge diffracted fields

An asymptotic expansion of a multiple integral for knife-edge diffraction is derived. The expansion expresses the field in terms of single-edge diffraction. By considering this expression, a similar expansion for higher order UTD diffracted fields is proposed. By means of a set of transition functions, the result removes some of the shortcomings of the original set out of the UTD when the incident field is not a ray-optical field.