Huygens principle

The math derivation of Huygens principle in 2D, applied to a plane wavefront propagation, gives the following field complex amplitude at a distance "d" of the initial wavefront (the unit for distances is the wavelength):

Numerical integration gives the expected value (pure delay operator):

But Mathematica(r) fails to derive a close form solution to the above integrale.
Does anybody knows a way to derive it?

Regards,

Jean-Paul