P[x_,y_]:=N1(PDF[MultinormalDistribution[{M1,M2},{{d^2,c* d^2},{c* d^2,d^2}}],{x,y}]+PDF[MultinormalDistribution[{M2,M1},{{d^2,c* d^2},{c *d^2,d^2}}],{x,y}])+N2(PDF[MultinormalDistribution[{M1,M1},{{d^2,c *d^2},{c *d^2,d^2}}],{x,y}]+PDF[MultinormalDistribution[{M2,M2},{{d^2,c *d^2},{c *d^2,d^2}}],{x,y}]);

G[t1_,t2_]:=NIntegrate[Sqrt[P[x,y]]Exp[I t1 x + I t2 y],{x,(M1+M2)/2-L,(M1+M2)/2+L},{y,(M1+M2)/2-L,(M1+M2)/2+L}];