Precision of the Absorbing Boundary Conditions

My friends does the boundary conditions that we apply in FDTD simulations absorb perfectly all the sacttered waves or untill some value they absorb do you know about this ? Because i ahve tried the ABCs of Gerrit Mur from the book of Kunz tehy don't absorb exactly, but at least the value of the scatterd wave become
around 0.00001 is this okey or i wrote the code wrong ?
And moreover if we can apply the exact code of PML from Berengers paper is that absorbing completely all the wave also untill some level ,

I am waitning for your ideas and answers
Thanks
With my best regards

May you send me the codes that you have written for the ABC so that I can suggest you the way how you improve it.