  Here we apply a recently developed maximum likelihood method for determining
best-fit parameterised lens models to observations of the rich lensing cluster
Abell 1689. The observations that we use were taken with the ESO/MPG Wide Field
Imager. The wide field-of-view enables us to use the weakly lensed images of
faint background objects on an unsurpassed range of scales,
0.12Mpc/h<R<1.8Mpc/h from the cluster centre, to determine best-fit models for
the 1-parameter singular isothermal sphere (SIS), 2-parameter general power-law
and NFW models, and 3-parameter singular isothermal ellipsoid (SIE). The
best-fit SIS has an Einstein radius of 0.37arcmin (0.043Mpc/h) i.e. a velocity
dispersion of 1028(+35,-42)km/s in an Omega=1.0, Lambda=0.0 cosmology. For the
best-fit NFW profile, the virial radius r_200=1.14Mpc/h and the concentration
parameter c=4.7, giving a virial mass M_200=5.7x10**14 M_solar/h. At q=0.88,
the slope of the best-fit power-law model is slightly flatter than isothermal
(q=1.0), indicating that the galaxies most important in the fitting procedure
lie inside the scale radius r_s. By fitting an SIE, the deviation of the
projected mass distribution from circular symmetry is evident, with a best-fit
axial ratio f=0.74.
