Strong lensing has developed into an important astrophysical tool for probing both cosmology and galaxies ( their structure , formation , and evolution ) .
Using the gravitational lensing theory and cluster mass distribution model , we try to collect a relatively complete observational data concerning the Hubble constant independent ratio between two angular diameter distances D _ { ds } / D _ { s } from various large systematic gravitational lens surveys and lensing by galaxy clusters combined with X-ray observations , and check the possibility to use it in the future as complementary to other cosmological probes .
On one hand , strongly gravitationally lensed quasar-galaxy systems create such a new opportunity by combining stellar kinematics ( central velocity dispersion measurements ) with lensing geometry ( Einstein radius determination from position of images ) .
We apply such a method to a combined gravitational lens data set including 70 data points from Sloan Lens ACS ( SLACS ) and Lens Structure and Dynamics survey ( LSD ) .
On the other hand , a new sample of 10 lensing galaxy clusters with redshifts ranging from 0.1 to 0.6 carefully selected from strong gravitational lensing systems with both X-ray satellite observations and optical giant luminous arcs , is also used to constrain three dark energy models ( \Lambda CDM , constant w and CPL ) under a flat universe assumption .
For the full sample ( n = 80 ) and the restricted sample ( n = 46 ) including 36 two-image lenses and 10 strong lensing arcs , we obtain relatively good fitting values of basic cosmological parameters , which generally agree with the results already known in the literature .
This results encourages further development of this method and its use on larger samples obtained in the future .