Tabletop systems are currently being focused on and many applications using these systems are being developed. In such tabletop systems, how to recognize real objects on the table is an essential and important issue. In existing tabletop systems, 2-D markers have been often used. However, their black-and-white pattern, which means nothing to humans, spoils the appearance of the object. We developed transparent markers on a liquid crystal display (LCD) tabletop system by using the polarization features of the LCD and optical films. In particular, through experiments with various kinds of optical films, we found that two half-wave plates make the markers rotation invariant. By using the transparent markers, tangible transparent Magic Lenses(TM) applications were developed.