Prefl=((Abs[0.11636849])^2)
Prad =0.9857
Pabs=1-Prefl-Prad

F[θ_]:=((Cos[(π/2)Cos[θ]])/(Sin[θ]))

D0=((4 π)/(NIntegrate[((F[θ])^2)Sin[θ],{θ,0,π},{ϕ,0,2 π}]))

directivity[θ_]:=D0 ((F[θ])^2)

d=Join[Map[{#[[1]]°,#[[2]]}&,Import["/Users/dschuri/Projects/ECE6962/5/directivity.txt","Table"][[3;;182,{1,3}]]],Map[{-#[[1]]°,#[[2]]}&,Import["/Users/dschuri/Projects/ECE6962/5/directivity.txt","Table"][[183;;362,{1,3}]]]];

Show[ListPolarPlot[d],PolarPlot[directivity[θ],{θ,-π,π},PlotStyle->Red],PlotLabel->"Directivity"]

AF[θ_,ϕ_]:=1+Exp[I π Sin[θ]Cos[ϕ]]+Exp[I 2 π Sin[θ]Cos[ϕ]]

D1=Chop[((4 π)/(NIntegrate[((F[θ])^2)((Abs[AF[θ,ϕ]])^2)Sin[θ],{θ,0,π},{ϕ,0,2 π}]))]

directivity[θ_,ϕ_]:=D1 ((F[θ])^2)((Abs[AF[θ,ϕ]])^2)

d=Map[{#[[2]]°,#[[3]]}&,Import["/Users/dschuri/Projects/ECE6962/5/directivity_ideal_array.txt","Table"][[3;;-1]]];

Show[ListPolarPlot[d],PolarPlot[directivity[π/2,ϕ],{ϕ,-π,π},PlotStyle->Red],PlotLabel->"Directivity"]

Prefl=((Abs[0.20748])^2)
Ptrans2=((Abs[0.19477])^2)
Ptrans3=((Abs[0.19477])^2)
Prad =0.8793
Pabs=1-Prefl-Ptrans2 -Ptrans3 -Prad

Prefl=((Abs[0.18148])^2)
Ptrans1=((Abs[0.19477])^2)
Ptrans3=((Abs[0.09301])^2)
Prad =0.9191
Pabs=1-Prefl-Ptrans1 -Ptrans3 -Prad

d=Map[{#[[2]]°,#[[3]]}&,Import["/Users/dschuri/Projects/ECE6962/5/directivity_array.txt","Table"][[3;;-1]]];

Show[ListPolarPlot[d],PolarPlot[directivity[π/2,ϕ],{ϕ,-π,π},PlotStyle->Red],PlotLabel->"Directivity"]

Apply[Plus,Map[(10.^(#/10))&,{-30.24,-.67,-23.388,-24.02}]]

Apply[Plus,Map[(10.^(#/10))&,{-31.24,-12.92,-.45,-25.14}]]