Searching of spread documents on a real desk is an arduous task. The chaos on the desk makes users' searching of the desired documents difficult. In this paper, we propose "Limpid Desk" which supports a document search on a desk by transparentizing the upper layer of a document stack in projection-based mixed reality environments. In the system, the special pattern light which is calculated to compensate the appearances of the upper layer documents as if they are transparent is projected to the stack, and as a result, users can visually access to the lower layer document. We propose a touch sensing method using a thermal image for the input interface of the system. The method realizes that users' touch areas on real documents can be detected with no worn or hold devices. Hence, users can intuitively select the stack, which they would like to transparentize, by their simple touch gestures. We present three intuitive interaction techniques which allow users to figure out what the lower layer document is without physically removing its upper documents. Since the searching space, the manipulating space, and the display space are completely unified onto a real desk, users can directly access to the lower documents without PC monitor and interface. We claim that this kind of spatial consistency of the manipulation is the key for realizing the intuitive interaction.