Comparison of vector and scalar diffraction patterns for rectangle

b=1; a=1; k=4π; beta=π/4.0;  (* take the 1/3 root to amplify visibility of small features *)
ScalarDist[th_,p_]:=(((((((1+Cos[th]))^2)/(π^2))   (((Sin[Sin[th]Cos[p] k a/2])^2)/(((Sin[th])^2)((Cos[p])^2)))(((Sin[Sin[th]Sin[p] k b/2])^2)/(((Sin[th])^2)((Sin[p])^2)))))^(1/3))

b=1; a=1; k=4π; beta=π/4.0;  (* take the 1/3 root to amplify visibility of small features *)
VectorDist[th_,p_]:=(((((2(((((Cos[th])^2)+((Sin[th])^2)((Sin[p+beta])^2)))^2))/(π^2))   (((Sin[Sin[th]Cos[p] k a/2])^2)/(((Sin[th])^2)((Cos[p])^2)))(((Sin[Sin[th]Sin[p] k b/2])^2)/(((Sin[th])^2)((Sin[p])^2)))))^(1/3))

Plot3D[ScalarDist[th,p],{th,0,π/2},{p,0,2π}]

Plot3D[VectorDist[th,p],{th,0,π/2},{p,0,2π}]

Plot[{VectorDist[th,0.001],ScalarDist[th,0.001]/1.3},{th,0,π/2},PlotLabel->"Nearly identical shapes of scalar and vector diffraction \n (raised to the 1/3 power to amplify visibility of small features)"]