Grating[x_, 
          y_] = (∑_(i = 1)^10)(∑_(j = 1)^4) DiracDelta[x - i]*
              DiracDelta[y - j];
Transform[kx_, 
          ky_] = (∫_0^10)(∫_0^4) Grating[x, 
                y]*(E^(-I (kx*x + 
                        ky*y))) \[DifferentialD]y \[DifferentialD]x;
Plot3D[(((Re[Transform[kx, ky]]))^2), {kx, -10, 10}, {ky, -10, 
        10}, PlotPoints -> 80]

Grating[x_, 
          y_] = (∑_(i = 1)^20)(∑_(j = 1)^20) DiracDelta[
                  x - (2*(Sqrt[3]))*i]*
                DiracDelta[
                  y - 2*j] + (∑_(i = 1)^20)(∑_(j = 1)^20) 
                  DiracDelta[x - (2*(Sqrt[3]))*i - 0.5]*
                DiracDelta[y - 2*j - 1];
Transform[kx_, 
          ky_] = (∫_0^41)(∫_0^41) Grating[x, 
                y]*(E^(-I (kx*x + 
                        ky*y))) \[DifferentialD]y \[DifferentialD]x;
Plot3D[(((Re[Transform[kx, ky]]))^2), {kx, -10, 10}, {ky, -10, 
        10}, PlotPoints -> 100]

Grating[x_, 
          y_] = (∑_(i = 1)^20)(∑_(j = 1)^20) DiracDelta[
                  x - (2/(Sqrt[3]))*i]*
                DiracDelta[
                  y - 2*j] + (∑_(i = 1)^20)(∑_(j = 1)^20) 
                  DiracDelta[x - (2/(Sqrt[3]))*(i - 0.5)]*
                DiracDelta[y - 2*j - 1];
Transform[kx_, 
          ky_] = (∫_0^41)(∫_0^41) Grating[x, 
                y]*(E^(-I (kx*x + 
                        ky*y))) \[DifferentialD]y \[DifferentialD]x;

Plot3D[(((Re[Transform[kx, ky]]))^2), {kx, -5, 5}, {ky, -5, 
        5}, PlotPoints -> 100]

Plot3D[(((Re[Transform[kx, ky]]))^2), {kx, -5, 5}, {ky, -5, 
        5}, PlotPoints -> 100]