When the input offset h1 is parallel to the output offset h2, the determinant of the system eq36 is equal to zero. In this case, the 3D AMO operator degenerates to a 2D operator. The fact that the determinant of the system of equations is equal to zero means that the two equations are linearly dependent, and that we are left with only one equation. However, because the operator is two-dimensional, the number of components of the unknown also reduces from two to one. Consequently, another stationary-phase approximation to the AMO integral need to be solved. The new equation is quartic and can be solved using Mathematica to get a solution for the kinematics of the operator. The resulting expression for the 2D AMO operator is presented in equation same_azim.eq of the main text.