\[Lambda] = 0.5; k0 = (2 \[Pi])/\[Lambda];
fU = 1/(2 \[Pi]) Integrate[E^(I kx x), {x, -1, 1}];
fres = E^(I k0 z)/(I \[Lambda] z)  Sqrt[z/2] Integrate[E^(-I k0/(2 z) (x2 - x1)^2), {x1, -1, 1}];
fraun = Sqrt[z/2] E^(I k0 z)/(I \[Lambda] z) E^(-I k0/(2 z) x2^2) Integrate[E^(I k0/z (x2 x1)), {x1, -1, 1}];
p1 = Table[
   somm = Table[{x, If[z == 0, HeavisidePi[x/2], Abs[NIntegrate[fU E^(I Sqrt[k0^2 - kx^2] z) E^(I kx x), {kx, -2 k0, 2 k0}]]^2]}, {x, -10 \[Lambda], 10 \[Lambda], \[Lambda]/10}];
   Legended[Show[
     Plot[If[z == 0, HeavisidePi[x2/2], Abs[fres]^2], {x2, -10 \[Lambda], 10 \[Lambda]}, PlotRange -> All, PlotStyle -> {Thick, Orange}],
     Plot[If[z == 0,  10 Sinc[100 x2]^2, Abs[fraun]^2], {x2, -10 \[Lambda], 10 \[Lambda]}, PlotRange -> All, PlotStyle -> {Thick, Cyan}],
     ListPlot[somm, PlotRange -> All, Joined -> True, PlotStyle -> {Thick, Purple}], PlotRange -> {0, 2}, Axes -> False, 
     Epilog -> {Text[Style[StringForm["z=``\[Lambda]", z/\[Lambda]], Medium, Bold], {3, 1.5}]}
     ], LineLegend[{Purple, Orange, Cyan}, {"Rayleigh-Sommerfeld", "Fresnel (paraxial)\napproximation", "Fraunhofer (far field)\napproximation"}] ]
   , {z, 0 \[Lambda], 20 \[Lambda], \[Lambda]/10}];
ListAnimate[p1]