The transition of the binary gravitational lens from the equal mass case to
small (planetary) mass ratios q is studied. It is shown how the limit of a
(pure shear) Chang-Refsdal lens is approached, under what conditions the
Chang-Refsdal approximation is valid, and how the 3 different topologies of the
critical curves and caustics for a binary lens are mapped onto the 2 different
topologies for a Chang-Refsdal lens with pure shear. It is shown that for wide
binaries, the lensing in the vicinity of both lens objects can be described by
a Taylor-expansion of the deflection term due to the other object, where the
Chang-Refsdal approximation corresponds to a truncation of this series. For
close binaries, only the vicinity of the secondary, less massive, object can be
described in this way. However, for image distances much larger than the
separation of the lens objects, any binary lens can be approximated by means of
multipole expansion, where the first non-trivial term is the quadrupole term.
It is shown that an ambiguity exists between wide and close binary lenses,
where the shear at one of the objects due to the other object for the wide
binary is equal to the absolute value of the eigenvalues of the quadrupole
moment for the close binary. This analysis provides the basis for a
classification of binary lens microlensing events, especially of planetary
events, and an understanding of present ambiguities.Comment: 20 pages in LaTeX2e format with 9 embedded PostScript figures;
figures modified and embedded; accepted for publication in A&