Disclosed are methods and systems for displaying images, and for implementing volumetric user interfaces. One exemplary embodiment provides a system comprising: a light source; an image producing unit, which produces an image upon interaction with light approaching the image producing unit from the light source; an eyepiece; and a mirror, directing light from the image to a surface of the eyepiece, wherein the surface has a shape of a solid of revolution formed by revolving a planar curve at least 180 around an axis of revolution.

Method for computing the code for the reconstruction of three-dimensional scenes which include objects which partly absorb light or sound. The method can be implemented in a computing unit. In order to reconstruct a three-dimensional scene as realistic as possible, the diffraction patterns are computed separately at their point of origin considering the instances of absorption in the scene. The method can be used for the representation of three-dimensional scenes in a holographic display or volumetric display. Further, it can be carried out to achieve a reconstruction of sound fields in an array of sound sources.

Disclosed are methods and systems for displaying images, and for implementing volumetric user interfaces. One exemplary embodiment provides a system comprising: a light source; an image producing unit, which produces an image upon interaction with light approaching the image producing unit from the light source; an eyepiece; and a mirror, directing light from the image to a surface of the eyepiece, wherein the surface has a shape of a solid of revolution formed by revolving a planar curve at least 180 around an axis of revolution.

A volumetric display system including a volumetric display for displaying a scene viewable as a three-dimensional floating-in-the-air scene in a display space, enabling a user to reach a first object into the display space, a location determination unit locating real objects in the display space, providing a location of the first object when the first object is inserted into the display space, and a computer for receiving the location of the first object, detecting when the location of the first object is at a location where an object is displayed in the three-dimensional scene, thereby determining that the first object is viewable as touching the displayed object following a detection of the first object viewable as touching the displayed object, producing a new three-dimensional scene displaying the displayed object as if manipulated by the first object. Related apparatus and methods are also described.

Methods, apparatus, devices, and systems for three-dimensional (3D) displaying objects are provided. In one aspect, a method includes obtaining data including respective primitive data for primitives corresponding to an object, determining an electromagnetic (EM) field contribution to each element of a display for each of the primitives by calculating an EM field propagation from the primitive to the element, generating a sum of the EM field contributions from the primitives for each of the elements, transmitting to each of the elements a respective control signal for modulating at least one property of the element based on the sum of the EM field contributions, and transmitting a timing control signal to an illuminator to activate the illuminator to illuminate light on the display, such that the light is caused by the modulated elements of the display to form a volumetric light field corresponding to the object.