A compact rendering system for establishing a three‐dimensional (3‐D) pointer is possible by combining microwave holography with microstrip antenna arrays to enter 3‐D coordinates of a point in space into computer memory. To obtain the reduction in system size, new solutions are proposed in both the holographic reconstruction algorithms and the receiving planar array antenna. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 397–402, 2001.