$HistoryLength = 0;
SetSystemOptions[
  "SparseArrayOptions" -> {"TreatRepeatedEntries" -> 1}];
f[{a_, b_, c_}] :=
  If[a <= 0,
   "NA", {Round[200 b/a], Round[200 c/a], 1000/(a^2 + b^2 + c^2)}];

initialCell =
  Table[{0.1, Sin[[Theta]]/5.0,
    Cos[[Theta]]/5.0}, {[Theta], [Pi]/16, 2 [Pi], [Pi]/16}];

translatedCell[m1_, m2_,
   m3_] := {m1 + (-1)^m1 #[[1]], m2 + (-1)^m2 #[[2]],
     m3 + (-1)^m3 #[[3]]} & /@ initialCell;
A = Flatten[
   Table[translatedCell[m1, m2, m3], {m1, 0, 18}, {m2, -18,
     18}, {m3, -18, 18}], 3];
<< Developer`

B = Cases[f /@ A, Except["NA"]];

F = Cases[B, _?(Abs[#[[1]]] <= 800 && Abs[#[[2]]] <= 800 &)];

G = SparseArray[{-801 + #[[1]], -801 + #[[2]]} -> 1.5/32 #[[3]] & /@
    F];
{n1, n2} = Dimensions[G];

fLor = Compile[{{x, _Integer}, {y, _Integer}}, (0.12/(
    0.12 + x^2 + y^2))^1.15, RuntimeAttributes -> {Listable},
   CompilationTarget -> "C"];
lor = RotateRight[
   fLor[#[[All, All, 1]], #[[All, All, 2]]] &@
    Outer[List, Range[-Floor[n1/2], Ceiling[n1/2] - 1],
     Range[-Floor[n2/2], Ceiling[n2/2] - 1]], {Floor[n1/2],
    Floor[n2/2]}];

Image[Sqrt[1.0 n1 n2]
   Abs[InverseFourier[
     Fourier[G] Fourier[lor]]][TensorProduct]ToPackedArray[{1.0, 0.3,
      0.1}], Magnification -> 1]

initialCell =
  Table[{0.1, Sin[[Theta]]/5.0,
    Cos[[Theta]]/5.0}, {[Theta], [Pi]/16, 2 [Pi], [Pi]/16}];
translatedCell[m1_, m2_,
   m3_] := {m1 + (-1)^m1 #[[1]], m2 + (-1)^m2 #[[2]],
     m3 + (-1)^m3 #[[3]]} & /@ initialCell;
B = Cases[
   f /@ (Flatten[
       Table[translatedCell[m1, m2, m3], {m1, -20, 20}, {m2, -20,
         20}, {m3, -20, 20}],
       3].{{0.5`, -0.7071067811865475`, 0.5`}, {0.5`,
        0.7071067811865475`, 0.5`}, {-0.7071067811865475`, 0.`,
        0.7071067811865475`}}), Except["NA"]];