cat[\[Alpha]_, \[Theta]_, q_, p_] := 
  1/(2 Pi)*1/(1 + Cos[\[Theta]]*Exp[-2 \[Alpha]^2])*(
    Exp[-p^2 - (q + Sqrt[2] \[Alpha])^2] + 
     Exp[-p^2 - (q - Sqrt[2] \[Alpha])^2] +
     2 Cos[\[Theta] - 2 Sqrt[2] \[Alpha]*p]*Exp[-q^2 - p^2]);
rq = 6; rp = 3; t = 0.003; FontS = 20;
For[\[Theta] = 0, \[Theta] <= Pi, \[Theta] += Pi,
 For[\[Alpha] = 1/2, \[Alpha] < 3, \[Alpha] += 1/2, 
  plot = Show[Plot3D[cat[\[Alpha], \[Theta], q, p],
     {q, -rq, rq}, {p, -rp, rp}, ImageSize -> 800,
     Mesh -> {Range[-Floor[rq], Floor[rq] ], 
       Range[-Floor[rp], Floor[rp] ], Range[-1, 1, 1/4]/Pi},
     MeshFunctions -> {#1 &, #2 &, #3 &},
     MeshStyle -> {Directive[Black, Thickness[t] ], 
       Directive[Black, Thickness[t] ], 
       Directive[White, Thickness[t] ]},
     PlotRange -> {-1/Pi, 1/Pi}, PlotPoints -> 81, MaxRecursion -> 4, 
     Method -> {Refinement -> {ControlValue -> 0.02} },
     PlotStyle -> Opacity[0.85], Lighting -> "Classic",
     ColorFunction -> ({RGBColor[1, 1, 0.75], Glow[GrayLevel[0.06] ], 
         Specularity[0.5, 60]} &),
     Axes -> False, Boxed -> False,
     ViewPoint -> 
      FromSphericalCoordinates[{Sqrt[229/20], Pi/3, -0.64 Pi}] ],
    Graphics3D[{Thickness -> t, Black, 
      Line[{ {-rq, rp, 0}, {-rq, -rp, 0}, {rq, -rp, 0} }]}],
    Graphics3D[{Thickness -> t, Black, 
      Line[{ {-rq, rp, -1/Pi}, {-rq, rp, 1/Pi} }]}],
    (* q ticks *)
    Sequence @@ 
     Table[Graphics3D[{Thickness -> t, Black, 
        Line[{ {x, -rp, 0}, {x, -0.2 - rp, 0} }]}], {x, -Floor[rq], 
       Floor[rq]}],
    (* p ticks *)
    Sequence @@ 
     Table[Graphics3D[{Thickness -> t, Black, 
        Line[{ {-rq, y, 0}, {-rq - 0.2, y, 0} }]}], {y, -Floor[rp], 
       Floor[rp]}],
    (*W ticks *)
    Sequence @@ 
     Table[Graphics3D[{Thickness -> t, Black, 
        Line[{ {-rq, rp, z/(2 Pi)}, {-rq - 0.2, rp, 
           z/(2 Pi)} }]}], {z, -2, 2}],
    (* axes labels *)
    Graphics3D[Text[Style["q", FontS, Black], {0, -rp*1.11, -0.07}] ],
    Graphics3D[Text[Style["p", FontS, Black], {-rq*1.11, 0, -0.07}] ],
    Graphics3D[
     Text[Style["W", FontS, Black], {-rq*0.93, rp*0.93, 0.8/Pi}] ],
    Sequence @@ 
     Table[Graphics3D[{Text[
         Style[TextString[x], FontS, 
          Black], {x, -rp - 0.07 Max[rq, rp], -0.003}, {0, 
          1}]}], {x, -Floor[rq], Floor[rq]}],
    Sequence @@ 
     Table[Graphics3D[{Text[
         Style[TextString[y], FontS, Black], {-rq - 0.07 Max[rq, rp], 
          y, -0.003}, {0, 1}]}], {y, -Floor[rp], Floor[rp]}],
    Sequence @@ 
     Table[Graphics3D[{Text[
         Style[If[z == 0, "0", ToString[z/(2 Pi), TraditionalForm] ], 
          FontS, Black], {-rq - 0.3, rp, z/2/Pi}, {1, 0}]}], {z, -2, 
       2}],
    BoxRatios -> {Automatic, Automatic, 8}, PlotRange -> All
    ];
  trim = { {0., .26}, {.97, .86} };
  imgname = 
   "Wignerfunction_catstate_" <> If[\[Theta] == 0, "even_", "odd_"] <>
     TextString[\[Alpha]] <> ".png";
  Export[imgname, 
   ImageResize[
    ImageTrim[Image[plot, ImageResolution -> 400], trim, 
     DataRange -> { {0, 1}, {0, 1} }], 2000, Resampling -> "Linear"] ];
  ] ]