Conventional holograph relies on dense interference patterns to form continuous 3D images.For large size objects,the local periods of interference patterns are at sub-micrometer scale,which are several orders smaller than the pixels of a 2D liquid crystal screen.To make things worth huge holographic data brings great burden for real time data acquisition,storage,transportation and display.We report here two principles suitable for coherent digital 3D display using low resolution liquid crystal spatial light modulators (SLM),namely complete digital optical phase conjugation and random source constructive interference.Both of them are capable of recreating large size discrete 3D images in the air with large viewing angle,which could be watched in a natural way without eyeglass or eye tracking.Numerical simulation,analytical derivation and experimental measurement,all of them shown that they can attain refraction limited resolution,promising for very sharp 3D images no less than 2D images.To do this,they need only additional depth information compared with 2D display.We provide also a brief discussion on the design of the related liquid crystal SLMs for full complex amplitude modulation as required by the principles.