Suppose we have a single slit along the y−direction of width b where the aperture function...

Suppose we have a single slit along the y−direction of width b where the aperture function is constant across it at a value of  What is the diffracted field if we now apodize the slit with a cosine function amplitude mask? In other words, we cause the aperture function to go from  at the center to 0 at ±b/2 via a cosinusoidal dropoff.