Phase diversity principle. An entrance-aberrated pupil P(ρ,θ) is propagated through an optical system. For a circular pupil, the Fourier propagation between the pupil and the image plane is related to the polar Fourier transform equation PFT[P(ρ,θ)]. If there is a focus aberration, this propagation must be developed as a function of the focus f coefficient: the new optical propagation function becomes PFT^f[P(ρ,θ)]. This mathematical development allows us to express the three image planes by a complete set of modal functions .