Lets say I have three surfaces, one with pattern A, one with pattern B and the third with A and B overlapped. Will the diffraction pattern be a simple addition of the diffraction patterns from A and B?

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\begin{aligned} u_A(u,v) \propto \textrm{FT}[t_A(x,y)] \\ u_B(u,v) \propto \textrm{FT}[t_B(x,y)] \end{aligned}
$$u_{tot}(x,y) = u_A \ast u_B$$.