We have designed an optical backplane with free-space optical interconnections using tunable beam deflector arrays and a mirror for terabit per second class bookshelf-assembled asynchronous transfer mode (ATM) switches. Optical beam transmitter arrays and optical beam receiver arrays are placed on the edges of a printed circuit board. Optical beams are deflected individually by the tunable deflector arrays, emitted obliquely and downward, and reflected at the mirror placed on the backplane, passing through some printed circuit boards, and reach the targeted receivers on the edges of printed circuit board. As a preliminary experiment, we show that board-to-board free-space arbitrary optical interconnections are possible using a tunable beam deflector array and 1-mm-pitch 2 x2 optical beam array provided with a vertical cavity surface emitting laser diode, we also show that these optical interconnections are made very stable by attaching reinforcing frames to the printed circuit board. Furthermore, we show that more than 1000 channel interconnections per printed circuit board are possible using a 1-mm-pitch optical beam array. As the speed per channel may be more than 1 Gbit/s, the throughput of the interconnection per board reaches almost the terabit/s level. Using this optical interconnection system is used, ATM switches with a huge capacity of 1.0 to 10 Tbit/s will be possible.