  The memory effect in disordered systems is a key physical phenomenon that has
been employed for optical imaging, metrology, and communication through opaque
media. Under the conventional memory effect, when the incident beam is tilted
slightly, the transmitted pattern tilts in the same direction. However, the
"memory" is limited in its angular range and tilt direction. Here, we present a
general approach to customize the memory effect by introducing an angular
memory operator. Its eigenstates possess perfect correlation for tilt angles
and directions that can be arbitrarily chosen separately for the incident and
transmitted waves, and can be readily realized with wavefront shaping. This
work reveals the power of wavefront shaping in creating any desired memory for
applications of classical and quantum waves in complex systems.
