Sorry if it causes confusion but I got the bit about integrals and the delta
functions wrong. Later I use integrals over x and y with an additional
exp(-i(kx*x+ky*y)) to give the delta functions. The full set of integrals
over kx1, ky1 etc can only be carried out much much later when they are used
to integrate the functions ht(kx,ky,t) etc. forward in time.
Regards,
David Webb.