Positions across the umbra edge used to build the altitude profiles shown in Fig. 19. The positions are defined by parameter c (Eq. (10)) and ranging from c =  −0.6 to 0.9. The definition for the umbra edge is taken for c = 0.6 (vertical solid line), at ≈1 arcmin in the penumbra side with respect to the inflection point, here fixed at abscissa =0. The umbra edge is only about one magnitude fainter than the penumbra at 4 arcmin from the inflection point.