The rate of energy flow through the surface fluctuates at the frequency of the radiation, but radiation detectors only respond to the average rate of flow. This is represented by replacing the Poynting vector with the time average of its norm, giving Φ Φ e ≈ ≈ ∫ ∫ Σ Σ ⟨ ⟨ | S | ⟩ ⟩ cos ⁡ ⁡ α α d A , where ⟨-⟩ is the time average, and α is the angle between n and ⟨ ⟨ | S | ⟩ ⟩ .