4.    Phase object [solution]

The wavelength of the light in the mica is l/m = 322 nm, so the mica is 5l/4 thick and it introduces a phase shift of p/2 to the light that passes through it.  This means that that portion of the Fourier transform is multiplied by i.  Let us assume that the slit extends from –a/2 to a/2 in the x and y directions.  The mica covers the region x < 0.  Thus the transmission function becomes

Since the x and y coordinates separate, we can calculate F(u) and multiply it by

.

To convert from u to the diffraction angle q, recall that  so that   A graph of this function (along the horizontal axis) is shown here, together with the function for a slit with no mica.