Illustration of the K-estimator. We show three nested cylinders representing three bins of transverse separations. The number of galaxy pairs inside each blue cylindrical shell from a₁ = 0 to ±a₂ is N_0, a2, the number of pairs in each red cylindrical shell between a₃ − a₂ and −a₂ − ( − a₃) is N_a2, a3. The K-estimator for each shell is then the ratio of pair counts between the inner (blue) segment to the total (blue plus red) segment. For illustration purposes we depict linear R_ij bins, although in practice we use a logarithmic binning scheme.