jinc[x_]:=2 BesselJ[1,x]/x

(* Diffraction through a circular aperture, radius a *)
(* This is the "Airy pattern", which is the central "Airy disk" plus the "Airy rings" *)
(* With a, k, and z all set equal to 1 for simplicity *)
(* Plot of (FT of "top hat")^2 *)
Plot[jinc[kr]^2,{kr,0,20}, PlotRange->All]
Plot3D[jinc[Sqrt[x^2+y^2]]^2,{x,-20,20},{y,-20,20},PlotRange->{0,1}, PlotPoints->100]
DensityPlot[jinc[Sqrt[x^2+y^2]]^2,{x,-20,20},{y,-20,20},PlotRange->{0,1}, PlotPoints->100]
(* now zooming in a bit *)
Plot3D[jinc[Sqrt[x^2+y^2]]^2,{x,-20,20},{y,-20,20},PlotRange->{0,0.02}, PlotPoints->100]
DensityPlot[jinc[Sqrt[x^2+y^2]]^2,{x,-20,20},{y,-20,20},PlotRange->{0,0.02}, PlotPoints->100]

(* A square side length a centered at (2a,0) combined with a circle radius a centered at at (-2a,0) *)
(* With a, k, and z all set equal to 1 for simplicity *)
(* Notice how the result incorporates features of a square, a circle, and a double slit. *) 
sum[x_,y_]:= Exp[I 2 x ](1/(2 Pi) ) Sinc[x/2] Sinc[y/2] + Exp[-I 2 x] (1/2) jinc[Sqrt[x^2+y^2]]
Plot3D[Abs[sum[x,y]]^2,{x,-20 ,20 },{y,-20 ,20},PlotRange->{0,0.4345}, PlotPoints->200]
DensityPlot[Abs[sum[x,y]]^2,{x,-20,20},{y,-20,20},PlotRange->{0,0.4345}, PlotPoints->200]
(* now zooming in a bit *)
Plot3D[Abs[sum[x,y]]^2,{x,-20 ,20 },{y,-20 ,20},PlotRange->{0,0.01}, PlotPoints->200]
DensityPlot[Abs[sum[x,y]]^2,{x,-20,20},{y,-20,20},PlotRange->{0,0.01}, PlotPoints->200]