# Intensity of pixel area light in reflective shadow map?

In reflective shadow map, there is definition about intensity of pixel area light:

$$I_p(\omega) = \Phi_p \max\{0, \langle n_p | \omega \rangle\}$$

where $\langle | \rangle$ is the dot product, $\Phi_p$ is the reflected radiant flux.

So, an integral of intensity over himisphere is

$$\Phi_p = \int_\Omega I_p \mathrm d \omega = \int_\Omega \Phi_p max\{0, \langle n_p | \omega \rangle\} \mathrm d \omega = \Phi_p \pi$$

Which leads to $\Phi_p = \Phi_p \pi$ ?

Anything wrong with my deduction?

Here's a link to the paper.