radiometric quantity: radiant flux

Question

Irradiance is defined as a ratio of differential flux to differential area, that is: $\frac{d\Omega}{dA}$. What I understand from this is that in the limit when $dA -> 0$ we obtain the density of the flux about a certain point $X$. However, is radiant flux defined at every point in an area of space or a surface? I assume it is not since bundle of photons can not, let's say, hit every point of the surface. That would mean that at a certain point when dA tends to zero there should be radiant flux around the point x, thus, effectively making the limit zero. I would be very grateful if anyone could help me find the flaws in my reasoning.

Answer 1

If I understand your question correctly you are assuming that the light is made up of photons, and because the photons are particles they must pass through the surface at a point. Hence the radiant flux cannot be uniform over the surface.

The problem is that light rays are not made up of photons in any simple sense. This is explained in the answers to What is the relation between electromagnetic wave and photon?.

To the extent that photons are present in a light beam they are delocalised and do not have a position in the sense that a classical particle has a position. The photons would be delocalised over your surface, so the radiant flux would be well defined and continuous everywhere on that surface. The problem you describe does not arise.