\Lambda = 0.5; k0 = (2 \Pi])/\Lambda];
fU = 1/(2 \Pi]) IntegrateE^(I kx x), {x, -1, 1}];
fres = E^(I k0 z)/(I \Lambda z) Sqrtz/2 IntegrateE^(-I k0/(2 z) (x2 - x1)^2), {x1, -1, 1}];
fraun = Sqrtz/2 E^(I k0 z)/(I \Lambda z) E^(-I k0/(2 z) x2^2) IntegrateE^(I k0/z (x2 x1)), {x1, -1, 1}];
p1 = Table
somm = Table[{x, Ifz == 0, HeavisidePix/2], AbsNIntegratefU E^(I Sqrtk0^2 - kx^2 z) E^(I kx x), {kx, -2 k0, 2 k0}]]^2]}, {x, -10 \Lambda], 10 \Lambda], \Lambda/10}];
LegendedShow
PlotIfz == 0, HeavisidePix2/2], Absfres^2], {x2, -10 \Lambda], 10 \Lambda]}, PlotRange -> All, PlotStyle -> {Thick, Orange}],
PlotIfz == 0, 10 Sinc100 x2^2, Absfraun^2], {x2, -10 \Lambda], 10 \Lambda]}, PlotRange -> All, PlotStyle -> {Thick, Cyan}],
ListPlotsomm, PlotRange -> All, Joined -> True, PlotStyle -> {Thick, Purple}], PlotRange -> {0, 2}, Axes -> False,
Epilog -> {TextStyleStringForm"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}];
ListAnimatep1