After extraction from the ATF Damping Ring, the linear beam optics is matched before injection into a section dedicated to beam diagnostics. Experimentally, vertical emittances in this section have since several years been observed to be larger than expected, byfactors of two to three, with a seemingly strong dependence on intensity. This has motivated studies of the possible sources of emittance growth. One of these is thought to be the non-linearity experienced by the beam during the extraction, as it is transported off-axis through several magnets which are shared with the Damping Ring. Such non-linearity can generate a sensitivity of the emittance to the orbit parameters in the extraction, which would be very undesirable in the newly built ATF2 final focus system, where the same extraction line is used. In this report, a detailed calculation of the modeling of these shared magnets is presented, in order to quantify the magnitudes of both the linear and non-linear fields to be used in the evaluation of the optics and in tracking simulations of the performance of the extraction line.