Abstract: We transform an LCD into a display that supports both 2D multi-touch and unencumbered 3D gestures. Our BiDirectional (BiDi) screen, capable of both image capture and display, is inspired by emerging LCDs that use embedded optical sensors to detect multiple points of contact. Our key contribution is to exploit the spatial light modulation capability of LCDs to allow lensless imaging without interfering with display functionality. We switch between a display mode showing traditional graphics and a capture mode in which the backlight is disabled and the LCD displays a pinhole array or an equivalent tiled-broadband code. A large-format image sensor is placed slightly behind the liquid crystal layer. Together, the image sensor and LCD form a mask-based light field camera, capturing an array of images equivalent to that produced by a camera array spanning the display surface. The recovered multi-view orthographic imagery is used to passively estimate the depth of scene points. Two motivating applications are described: a hybrid touch plus gesture interaction and a light-gun mode for interacting with external light-emitting widgets. We show a working prototype that simulates the image sensor with a camera and diffuser, allowing interaction up to 50 cm in front of a modified 20.1 inch LCD.