## 2. Basic equationsThe distortion of images of background galaxies depends on the
dimensionless surface mass density of the lens, which is the physical
surface mass density divided by the critical
surface mass density . If we now consider the
background sources to be distributed in redshift, then the critical
surface mass density depends on the redshift Here and are the
angular diameter-distances from the observer to the lens at redshift
and to the source at redshift we obtain for the dimensionless surface mass density
at angular position for
a source at redshift The function relates the `lensing strength'
for a source with redshift In particular, for sources with redshift smaller than that of the
lens, the `lensing strength' vanishes. For the rest of this paper, we
consider a single cluster lens at redshift , and
drop the second argument of Since the shear is related linearly to the
surface mass density, its dependence on source redshift is the same as
for , so the . The
magnification of an image with position
and a source redshift The cluster is non-critical for sources at redshift © European Southern Observatory (ESO) 1997 Online publication: July 3, 1998 |