Kochanek (1992) and Mortlock & Webster (2000) applied standard
techniques to determine the rate of lensed quasars expected in a
generic GRS, and a more detailed calculation verified these
results for the 2dF survey
(Mortlock & Webster 2001).
The number of lenses depends principally
on two factors:
the depth of the survey and the quality of the spectra.
The latter, potentially a somewhat ambiguous notion,
can be characterised in terms
of
,
which is defined as follows
(Kochanek 1992):
for a lens in which the galaxy has magnitude
and
the quasar images have total magnitude
,
the presence of the quasar emission lines is detectable if
,
but the quasar
is undetectable if it is fainter than this.
The value of
clearly increases with the
integration time of the observations, but is also critically
dependent on the properties of galaxy and quasar spectra.
Kochanek (1992) estimated
for
the SDSS spectra, and Mortlock & Webster (2000) used
for the lower quality 2dF spectra.
These figures then led to the estimate that the 2dF GRS should yield
about 10 lensed quasars (Mortlock & Webster 2000), although it
could be as low as
(if
)
or as high as
(if
).
Fortunately the value of
appropriate to a given
search technique can be evaluated by analysing
simulated composite lens spectra.