They are calculating by determining the bracketing values u m (r) and u m+1 (r) for each a i (r), such that u m (r) < a i (r) < u m+1 (r). Then a i (r) is calculated from a straight line interpolation between u m (r) and u m+1 (r) (see Fig. for an illustration). This interpolation scheme is robust and avoids numerical instabilities that may arise in nonlinear fits.