The Hubble Deep Field ( North ) and the flanking fields are used investigate the occurrence of multiple weak lensing deflections along the line of sight in relatively deep imaging data ( z _ { lens } \sim 0.6 , z _ { source } \sim 1.2 ) .
Ray tracing simulations of galaxy–galaxy lensing in the HDF-North show that proper inclusion of multiple weak deflections is important for a correct prediction of the net shear for most sources , and for a given source redshift the number of multiple weak deflections is largely insensitive to the cosmography .
The effects of multiple weak deflections on the magnitude of the weak lensing signal are , of course , strong functions of the adopted halo parameters .
Independent of the halo parameters , however , the closest lens to a source ( in projection on the sky ) is not the strongest lens in the case of more than 50 % of the sources which acquire a net shear of \gamma \mathrel { \raise 1.29 pt \hbox { $ < $ } \mkern - 14.0 mu \lower 2.58 pt \hbox { $ \sim$ } } % 0.01 .
In addition , multiple weak deflections result in a tangential shear about the lens centers that is greater than the tangential shear that would occur if source galaxies were lensed solely by the closest lens .
Further , multiple weak deflections give rise to correlated image ellipticities and account for a substantial amount of the total cosmic shear signal on small angular scales in \Lambda CDM and open CDM models .