pw = 6*72;
r = 0.3;
array = Table[{x, y}, {x, -2, 2}, {y, -2, 2}];
array = ArrayFlatten[array, 1];
array = {Red, Disk[#, r] & /@ array};
figure = Graphics[array];
figure = Show[figure, ImageSize -> pw];
Export[NotebookDirectory[] <> "Image.pdf", figure]
(*Now add mask*)
{mx, my} = ImageDimensions[figure];(*Mask dimensions*)
mask =
 Image[
    Table[Sqrt[x^2 + y^2], {x, -1, 1, 2/(mx - 1)}, {y, -1, 1, 2/(my - 1)}],
   ColorSpace -> "Grayscale"] // ColorNegate;
figure = SetAlphaChannel[figure, mask];
Export[NotebookDirectory[] <> "ImageAndMask.pdf", figure]