Explanation of one iteration of the Fast and Furious algorithm. At iteration i an image p_i is split into its even p_i, e and odd p_i, o components. The odd component can directly solve for the odd focal-plane electric field y_i (Eq. (5)). Similarly, the even component is used to solve for the absolute value of the even focal-plane electric field |v_i| (Eq. (6)). To solve for the sign of v_i, the previous image p_i − 1, that has a diversity phase Φ_d, is introduced to break the degeneracy (Eq. (9)). The estimates of y_i and v_i together give an estimate of the pupil-plane phase Φ_i (Eq. (10)).