  We present the weak lensing methodology applied to our multi-colour imaging
survey of X-ray luminous galaxy clusters conducted with the wide field CFH12k
camera. This method, which is converting a fully reduced CFH12k image into
cluster mass constraints, is done in two steps that we explain in detail: (1)
determination of the "true" shape of faint (lensed) galaxies which involves:
object detection strategy, point spread function (PSF) determination, galaxy
shapes measurements with errors; (2) conversion of the faint galaxies catalogue
into useful mass constraints which is done by different lensing techniques
using 1D and/or 2D mass estimates. Finally, we compare the cluster mass model
to the light distribution of cluster members as observed on our imaging data.
To illustrate the method, we apply it to the well studied cluster Abell 1689
(z=0.184). In this cluster, we detect the gravitational shear signal to the
edge of the image at 3 sigma significance. The two-dimensional mass
reconstruction has a ~10 sigma significance mass peak centered on the brightest
cluster galaxy. The weak lensing constraints are well fitted by a NFW mass
profile with $M_{200} = 14.1^{+6.3}_{-4.7}\times 10^{14} M_\sun$, and $c =
3.5^{+0.5}_{-0.3}$ (chi^2=0.33), or by a power law (PL) profile with q=0.75 +-
0.07 and theta_E = 14.6"+-0.3" (chi^2=0.64). The mass-to-light ratio is found
to be almost constant with radius with a mean value of M/L_R = 150 h
(M/L)_\sun. We compare these results to other weak lensing analyses of Abell
1689 presented in the literature and find good agreements in terms of the shear
measurement as well as the final mass estimate.
