Coordinate systems for acoustic-matter analysis. A Cartesian coordinate system (x, y, z) is introduced supposing a hypothetical spherical scatterer centered at its origin O_P. A second Cartesian coordinate system (u, v, w) is attached to the impinging beam, with origin O_B. The position of O_B with respect to O_P is here denoted as (x₀, y₀, z₀). Attached to the xyz system is a cylindrical coordinate system (ρ, ϕ, z) such that the relative position of O_B can also be written as (ρ₀, ϕ₀, z₀).