The plenoptic function is ideal to describe three-dimensional displays. We propose and demonstrate in this work that plenoptic function is a particularly suitable scenario in the directionally illuminated autostereoscopic display. Guided by this function, backlight structures and functional thin films are designed and applied for wave-vector and amplitude control so that homogeneous viewing is achieved in large viewing volume while display functionality with optical focusing and diverting can be fulfilled. The demonstration of high-quality displays by cloaking various optical defects in an otherwise severely distorted radiance distribution introduced by lens array is presented. We conclude that the scenario adopted in this work is immediately applicable to enhance general performance for autostereoscopy.