Laser beams emitted from space-borne lidars, can only penetrate clouds to a limit of a few optical depths. As a result, only optical depths of thinner clouds (< about 3 for GLAS) are retrieved from the reflected lidar signal. We present a comprehensive study of possible retrievals of optical depth of thick clouds using solar background light and treating the GLAS telescope as a simple solar radiometer. To do so we first calibrate the reflected solar radiation received by the photon-counting detectors of GLAS' 532 nm channel. The solar background radiation is regarded as a noise to be subtracted in the retrieval process of the lidar products. However, once calibrated, it becomes a signal that can be used in studying the properties of optically thick clouds. Three calibration methods are presented: (1) calibration with coincident airborne and GLAS observations; (2) calibration with coincident GOES and GLAS observations of deep convective clouds; (3) calibration from the first principles using optical depth of thin water clouds over ocean retrieved by GLAS active remote sensing. Results from the three methods agree well with each other. Cloud optical depth is retrieved from the calibrated solar background signal using a one-channel retrieval. Comparison with cloud optical depth retrieved from GOES during GLAS overpasses shows that the average difference between the two retrievals is about 25%. Based on this study, optical depths for thick clouds will be provided as a supplementary product to the existing operational GLAS cloud products in future GLAS data releases. Thus cloud optical depth can be retrieved from GLAS for all clouds: from thin transparent to thick opaque.