t=1+Cos[ξ]

f=Simplify[Exp[I k/2/z(x-ξ)^2]Exp[-I k/2/z(x-ξξ)^2]Exp[-(ξ-ξξ)^2/2/σ^2](1+Cos[2π ξ])(1+Cos[2π ξξ])]

tem=Integrate[f,{ξ,-Infinity,Infinity},Assumptions->{Im[z]==0,σ>0,k>0,z>0}]

res=Integrate[tem,{ξξ,-Infinity,Infinity},Assumptions->{Im[z]==0,σ>0,k>0,z>0}]

res2=res/.{k->1,σ->1000};

(* predmet *)

Plot[(1+Cos[2π ξ])^2,{ξ,-3,3}]

(* kontrola *)

Plot[Abs[res2/.z->0.001],{x,-3,3}]

(* obecna vzdalenost *)

Plot[Abs[res2/.z->0.07],{x,-3,3}]

(* Talbotuv obraz *)

ztal=k n L^2/π

z1=ztal/.{k->1,L->1,n->1}//N

Plot[Abs[res2/.z->z1],{x,-3,3}]

(* inverzni Talbotuv obraz *)

zinvtal=ztal/2

z2=zinvtal/.{k->1,L->1,n->1}//N

Plot[Abs[res2/.z->z2],{x,-3,3}]

(* obrazy pro snizenou koherenci *)

res3=res/.{k->1,σ->0.75};

Plot[Abs[res3/.z->z1],{x,-3,3},PlotRange->{0,All}]

Plot[Abs[res3/.z->z2],{x,-3,3},PlotRange->{0,All}]