Irradiation is the total energy falling on the surface Let us say we have a surface of area $dA$ with an incoming radition $I_{\lambda}(\textbf{r},\lambda,\hat{s_i})$ where $\hat s_i$ is the direction of the radiation, $\lambda$ is wavelength and $\textbf r$ is location. If $\theta_i$ is the angle between the radiation and the surface normal, then Irradiation $H^{'}_{\lambda}(\textbf{r},\lambda,\hat{s_i})=I_{\lambda}(\textbf{r},\lambda,\hat{s_i})cos\theta_i$