Can the quadrupole source be decomposed into a number of independent bars, each emitting spherical waves? Is this a valid approximation? How many bars then?

For example consider the following, approximate the third order (l=2) spherical harmonics of the quadrupole source as a superposition of two orthogonal slits in the u and v direction. At a distance, L>>λ, the phase difference between the contributions from the two slits is equal to, Δφ=(2π/λ)((L^2+u^2)^(1/2)-(L^2+v^2 )^(1/2)), which upon using the binomial expansion for, L≪λ, can be written as, u^2-v^2≈λL=constant. The fringes are thus rectangular hyperbolae.