My issue here is the fact that the slits are supposed to infinite in the ##y##-direction. With what's given in the assignment, I'd define the apparatus function ##a(x,y)## as
$$
a(x,y) = \begin{cases} 1 & , \, ( 9d \leq |x| \leq 10d ) \wedge (y \in \mathbb{R}) \\ 0 & , \, \text{else}...