I have created a 3D plot and a contour plot for the same (Wigner) function, but as you see the contour plot is not right. It has some "extra" regions in gray color (ovals). What is going wrong?
The 3D plot code is 

    Plot3D[2/((2 + 2/E^8) \[Pi]) (Exp[-2 (4 - 4 x + x^2 + y^2)] + 
    Exp[-2 (4 + 4 x + x^2 + y^2)] + 
    2 Exp[-2 (x^2 + y^2)] Cos[8 y]), {x, -4, 4}, {y, -4, 4}, 
    PlotRange -> Full, Exclusions -> None, PlotPoints -> 180, 
    FaceGrids -> {{0, -1, 0}, {1, 0, 0}, {0, 0, -1}}, 
    FaceGridsStyle -> Directive[Blue, Dotted], Boxed -> False, 
    BoxRatios -> {1, 1, 1}, 
    AxesLabel -> {"x", "y", "\!\(\*SubscriptBox[\(W\), \(c\)]\)(x,y)"}, 
    LabelStyle ->   {Bold, Black, FontSize -> 16}]

The contour plot code is

    ContourPlot[
    2/((2 + 2/E^8) \[Pi]) (Exp[-2 (4 - 4 x + x^2 + y^2)] + 
    Exp[-2 (4 + 4 x + x^2 + y^2)] + 
    2 Exp[-2 (x^2 + y^2)] Cos[8 y]), {x, -3, 3}, {y, -3, 3}, 
    PlotLegends -> Automatic, 
    PlotPoints -> 180]

And here are the figures:
[![enter image description here][1]][1]
[![enter image description here][2]][2]

The real contour plot is taken from a textbook (Quantum Optics by Girish Agarwal, Cambridge U Press, 2013, page 80):

[![enter image description here][3]][3]

To emphasize that it is not a problem for a special case, here I have added another code and figure. You can see the "ugly" ovals are definitely incorrect.

    ContourPlot[
    1/((2 + 2/E^16) \[Pi])
    2 (E^(((2 + 2 I) - x - I y) ((-2 + 2 I) + x - I y)) + 
    E^(((-2 - 2 I) - x - I y) ((2 - 2 I) + x - I y)) + 
    E^((-x - I y) (x - I y)) Cos[4 Im[(2 - 2 I) (x + I y)]]), {x, -4, 
    4}, {y, -4, 4}, PlotLegends -> Automatic, 
    ColorFunction -> "Rainbow", FrameLabel -> {"x", "y"}, Frame ->  True,
    FrameStyle -> Directive[Black, 18], PlotPoints -> 180, 
    PlotRange -> All, PlotRangePadding -> 0]

 [![enter image description here][4]][4]


  [1]: https://i.sstatic.net/mPaWn.jpg
  [2]: https://i.sstatic.net/hiCfC.jpg
  [3]: https://i.sstatic.net/SwiZg.jpg
  [4]: https://i.sstatic.net/PJLPe.jpg