where f ( n , n ′ ) is the scattering amplitude that depends on the direction n of the incident wave and the direction n ′ of scattering and d Ω Ω is the differential solid angle. When n = n ′ , the above relation yields the optical theorem since the left-hand side is just twice the imaginary part of f ( n , n ) and since σ σ = ∫ ∫ | f ( n , n ″ ) | 2 d Ω Ω ″ . For scattering in a centrally symmetric field, f depends only on the angle θ θ between n and n ′ , in which case, the above relation reduces to