Sinc interpolation and Ideal reconstruction example

Question

I am trying to apply sinc interpolation on this data set. The patches in the left image is a snapshot of AutoCAD 3d faces. Lux values are calculated for centre of each patch that are in 0.3m x 0.3m dimension.

The middle is a bitmap image of the above data set. Applying below sinc interpolation method results in the right side image. I was expecting to get smooth gradient in the colours but am not sure if the sinc function is applied correctly.

Here is the sinc interpolation method

public ImageFilm ConvolveWithSinc(ImageFilm fs, float Ts)
{
    float Ws = 1 / Ts;
    int N = fs.Width;
    int M = fs.Height;
    ImageFilm fy = new ImageFilm(N, M);
    Vector zero = Vector.ZERO;
    for (int x = 0; x < N; x++)
    {
        for (int y = 0; y < M; y++)
        {
            LightVector sum = LightVector.ZERO;
            double sincSum = 0;
            for (int n = 0; n < fs.Width; n++)//= (int)Ts
            {
                for (int m = 0; m < fs.Height; m++)//= (int)Ts
                {
                    double sinc = (Helper.Sinc(Ws * (x - n)) *
                        Helper.Sinc(Ws * (y - m)));

                    sincSum += sinc;

                    LightVector v = fs.GetPixel(n, m);
                    if (v == zero) continue;

                    sum += v * sinc;
                }
            }
            LightVector c = sum / sincSum;
            if (c.X > 255 || c.Y > 255 || c.Z > 255)
                c = c.Clamp(0, 255);
            fy.SetPixel(x, y, c);
        }
    }
    return fy;
}

I understand that the sampling frequency on the above middle image might be below the Nyquist frequency but I wanted to know if this is the case or I am doing something wrong.

I have tried the above method on a simpler function sin(16*x*x) and the interpolated image looks similar to the original:

UPDATE:

Thanks for the comments. I have modified the code to divide the pixel value by the sum of the two sinc functions. Is this the correct way of normilizing it? The image looks better but it is very blurry.