a basic question: jinc function in coherent and incoherent system

I am learning Fourier optics recently and I have a problem of the jinc function.

In optical systems, digital image is blurred with the kernel of jinc function
[itex]h(x,y)=jinc(r)=\frac{J_1(2\pi r / \lambda)}{ 2\pi r / \lambda}[/itex]

in the coherent system, the blurred image
[itex] g(x,y) = |h(x,y) \star f(x,y)|^2 [/itex]
where f(x,y) is the unblurred image and [itex]\star[/itex] indicates the convolution.

I assume we should normalize h, so that we have
[itex] \sum_{x,y} h(x,y) = 1[/itex]
in a discrete form.

And in the incoherent system, the blurred image
[itex] g(x,y) = |h|^2 * |f(x,y)|^2 [/itex]
Do we need to normalize h differently as?
[itex] \sum_{x,y} |h(x,y)|^2 = 1[/itex]

if doing so, it seems that the blurred image is darker in the coherent system. if not, the blurred image in the incoherent system is darker.

which one is correct?

thanks