Recent large scale surveys such as Sloan Digital Sky Survey have produced homogeneous samples of multiple-image gravitationally lensed quasars with well-defined selection effects. Statistical analysis on these can yield independent constraints on cosmological parameters. Here we use the image separation statistics of lensed quasars from Sloan Digital Sky Survey Quasar Lens Search (SQLS) to derive constraints on cosmological parameters. Our analysis does not require knowledge of the magnification bias, which can only be estimated from the detailed knowledge on the quasar luminosity function at all redshifts, and includes the consideration for the bias against small image separation quasars due to selection against faint lens galaxy in the follow-up observations for confirmation. We first use the mean image separation of the lensed quasars as a function of redshift to find that cosmological models with extreme curvature are inconsistent with observed lensed quasars. We then apply the maximum likelihood test to the statistical sample of 16 lensed quasars that have both measured redshift and magnitude of lens galaxy. The likelihood incorporates the probability that the observed image separation is realized given the luminosity of the lens galaxy in the same manner as Im et al. (1997). We find that the 95% confidence range for the cosmological constant (i.e., the vacuum energy density) is 0.72 ≤  ≤ 1.0 for a flat universe. We also find that the equation of state parameter can be consistent with −1 as long as the matter density m . 0.4 (95% confidence range). We conclude that the image separation statistics incorporating the brightness of lens galaxies can provide robust constraints on the cosmological parameters.

A focal reducer is developed for CQUEAN (Camera for QUasars in EArly uNiverse), which is a CCD imaging system on the 2.1 m Otto Struve telescope at the McDonald observatory. It allows CQUEAN to secure a wider field of view by reducing the effective focal length by a factor of three. The optical point spread function without seeing effects is designed to be within one pixel (0.28300) over the field of view of 4.82' × 4.82' in optimum wavelength ranges of 0.8 − 1.1 μm. In this paper, we describe and discuss the characteristics of optical design, the lens and barrel fabrications and the alignment processes. The observation results show that the image quality of the focal reducer confirms the expectations from the design.

To perform imaging observations of optically red objects such as high redshift quasars and brown dwarfs, the Center for the Exploration of the Origin of the Universe (CEOU) recently developed an optical CCD camera, Camera for QUasars in EArly uNiverse (CQUEAN), which is sensitive at 0.7-1.1 μm. To enable observations with long exposures, we develop an auto-guiding system for CQUEAN. This system consists of an off-axis mirror, a baffle, a CCD camera, a motor and a differential decelerator. To increase the number of available guiding stars, we design a rotating mechanism for the off-axis guiding camera. The guiding field can be scanned along the 10 arcmin ring offset from the optical axis of the telescope. Combined with the auto-guiding software of the McDonald Observatory, we confirm that a stable image can be obtained with an exposure time as long as 1200 seconds.