Method of computing a hologram

Abstract

A method of computing a hologram by determining the wavefronts at the approximate observer eye position that would be generated by a real version of an object to be reconstructed. In normal computer generated holograms, one determines the wavefronts needed to reconstruct an object; this is not done directly in the present invention. Instead, one determines the wavefronts at an observer window that would be generated by a real object located at the same position of the reconstructed object. One can then back-transforms these wavefronts to the hologram to determine how the hologram needs to be encoded to generate these wavefronts. A suitably encoded hologram can then generate a reconstruction of the three-dimensional scene that can be observed by placing one's eyes at the plane of the observer window and looking through the observer window.

1 . A method for computing a computer-generated video hologram, where object data defining objects in a three dimensional scene is arranged into a number of virtual section layers, each layer defining a two-dimensional object data set, such that a video hologram data set can be calculated from some or all of these two-dimensional object data sets; comprising the following steps:
 (a) in a first transformation, each two-dimensional object data set of the virtual section layers is transformed to a two-dimensional wave field distribution,   (b) the calculated two-dimensional wave field distributions, for all two-dimensional object data sets of section layers, are added to define an aggregated data set   (c) wherein the first transformation comprises one of (a) applying a Fourier transformation and a first phase factor describing a spherical wave, and (b) applying a Fresnel transformation, and   (d) wherein the object data sets may exhibit an appropriate phase distribution or a pseudo-random phase distribution, in order to reduce speckle noise or to enhance at least one of: brightness efficiency, diffraction efficiency and brightness definition in the reference layer of the scene.   
     
     
         2 . The method according to  claim 1 , wherein the wave field distribution is calculated for a virtual observer window in a reference layer at a finite distance from the video hologram layer. 
     
     
         3 . The method according to  claim 1 , wherein in a second transformation, the aggregated data set is transformed from the reference layer to the video hologram layer, to generate the video hologram data set for the computer-generated video hologram. 
     
     
         4 . The method according to  claim 1 , wherein the transformation which describes a propagation of light between an original section layer and a reference layer is modified such that it comprises a Fast Fourier Transformation (FFT) and two multiplications with phase factors describing spherical waves. 
     
     
         5 . The method according to  claim 4 , wherein the first phase factor depends on coordinates in the original section layer and on a distance between the original section layer and the reference layer, the second phase factor depends on coordinates in the reference layer and on a distance between the original section layer and the reference layer, wherein one or both of these phase factors may be set to a constant value. 
     
     
         6 . The method according to  claim 1 , wherein an iteration process is used for reducing reconstruction errors of the video hologram. 
     
     
         7 . The method according to  claim 2 , wherein an iteration process takes place for at least one transformation between the wave field distribution in the observer window and the hologram layer for compensating for errors of the reconstructed aggregate field in the observer window. 
     
     
         8 . The method according to  claim 1 , where the data of the video hologram data set is assigned to equally spaced points in the video hologram and these points are organized as a matrix. 
     
     
         9 . The method according to  claim 1 , where at least one of the section layers, the hologram layer, the reference layer and the virtual observer window are planar, or where at least one of the video hologram layer, the section layers and the virtual observer window are parallel to each other. 
     
     
         10 . The method according to  claim 2 , where at least one eye of an observer is located near the virtual observer window, so that a reconstructed scene can be seen through the virtual observer window, or in which there are two or more virtual observer windows. 
     
     
         11 . The method according to  claim 1 , where the object data are assigned to object data sets, all of which comprise a same number and matrix structure of values as the aggregated data set and the hologram data set, where the number and structure of values for all data sets is derived from a number of pixels used for encoding the video hologram. 
     
     
         12 . The method according to  claim 8 , where the two-dimensional object data sets and the aggregated data set have a same matrix structure as the video hologram data set. 
     
     
         13 . The method according to  claim 2 , where the virtual observer window in the reference layer is set to be smaller than or equal to a size of a periodicity interval in the reference layer and located completely within one periodicity interval, or wherein the reference layer coincides with a Fourier plane of the hologram. 
     
     
         14 . The method according to  claim 2 , where each object data set is based on an area of the corresponding section layer, which depends on its distance to the reference layer. 
     
     
         15 . The method according to  claim 14 , where the area of each section layer is defined by intersections with imaginary faces which connect edges of the virtual observer window and edges of the video hologram. 
     
     
         16 . The method according to  claim 2 , where the sections layers have distance to the virtual reference layer are set such that an entire reconstructed scene or parts of it appear at least one of in front of and behind the hologram layer. 
     
     
         17 . The method according to  claim 1 , where a Fresnel transformation is divided into individual steps so that these steps can be performed with the help of at least one Fast Fourier transformation (FFT) in conjunction with at least one further processing step in the form of a multiplication with a spherical wave factor. 
     
     
         18 . The method according to  claim 1 , where the first transformation is a Fresnel transformation which comprises the following sub-steps:
 multiplication of an amplitude value of each object point of an original section layer with a first phase factor describing spherical waves, an exponent of said factor depending on squared coordinates in the original section layer and a distance (Dm) between the original section layer and a reference layer,   transformation of the thus calculated products for each object point of the original section layer with the help of a first Fast Fourier transformation from the original section layer to the reference layer,   multiplication of the thus calculated transforms with a second phase factor describing spherical waves, an exponent of said factor depending on squared coordinates in the reference layer and the distance to the original section layer.   
     
     
         19 . The method according to  claim 1 , where the second transformation is also a Fresnel transformation which comprises the following sub-steps:
 multiplication of each complex amplitude value of the reference data set with a third phase factor describing spherical waves, an exponent of said factor depending on squared coordinates in the reference layer and a distance between the reference layer and the hologram layer,   transformation of the thus calculated products of the complex amplitude values with the help of a second fast Fourier transformation from the reference layer to the hologram layer,   multiplication of the thus calculated transforms with a fourth phase factor describing spherical waves, an exponent of said factor depending on squared coordinates in the hologram layer and a distance between the hologram layer and the reference layer, so to get hologram values for the hologram data set used for encoding.   
     
     
         20 . The method according to  claim 18 , where one or both of the phase factors describing spherical waves may be set to a constant value. 
     
     
         21 . The method according to  claim 1 , where at least one of the first transformation and the second transformation is a Fourier transformation. 
     
     
         22 . The method according to  claim 1 , which comprises the following sub-steps for correcting point values of the computer-generated video hologram by way of iteration:
 A) the aggregated data set from an original three-dimensional scene is defined as a target function for the first transformation,   B) back-transformation of original complex amplitude values of the target function to the hologram layer to get matrix point values of the hologram data set,   C) derivation of parameters of the hologram data set for a light modulator matrix,   D) transformation of the Derivation of parameters to the reference layer to get a distribution of complex up-dated amplitude values in the virtual observer window,   E) forming a difference of the distribution of complex up-dated amplitude values and original values of the target function,   F) back-transformation of this difference to a distribution of difference point values in the hologram layer,   G) subtraction of the distribution from the video hologram data set and updating the hologram data set,   H) repeating of the steps C) to G)   I) termination of the iteration when an approximation accuracy has been reached.   
     
     
         23 . The method of  claim 1 , in which depth information is the same for all object data sets. 
     
     
         24 . The method of  claim 23 , in which a device that generates the hologram can switch from a three dimensional mode to a two dimensional mode, depending on at least one of inputs and what mode a user selects. 
     
     
         25 . A digital signal processing device for computing computer-generated video holograms with digital slicer means, which assigns object data defining objects in a three dimensional scene to a number of virtual section layers, each section layer defining a separate object data set, such that a video hologram data set for a video hologram can be calculated from some or all of these object data sets, containing:
 (a) first transformation means for computing from each object data set a separate, two-dimensional wave field distribution, and buffer memory means for buffering transformed object data sets,   (b) adding means for adding the transformed object data of all section layers to generate a wave field expression of an aggregated data set,   (c) wherein the first transformation comprises one of (a) applying a Fourier transformation and a first phase factor describing a spherical wave, and (b) applying a Fresnel transformation, and   (d) wherein the object data sets may exhibit an appropriate phase distribution or a pseudo-random phase distribution, in order to reduce speckle noise or to enhance at least one of:   brightness efficiency, diffraction efficiency and brightness definition in the reference layer of the scene.   
     
     
         26 . The device according to  claim 25 , comprising second transformation means for transforming the aggregated data set to a hologram layer situated at a finite distance and parallel to the reference layer, to generate the hologram data set for the aggregated video hologram. 
     
     
         27 . The device according to  claim 25 , which comprises at least one independently working transformation means for performing transformations, said device containing:
 First multiplication means for multiplying an amplitude value of values of an original object data set with a first phase factor describing spherical waves, an exponent of said factor depending on squared coordinates in the respective original layer and a distance to a target layer,   Fast Fourier transformation means for transforming the products of the first multiplication means from their original layer to the target layer, and   Second multiplication means for multiplying that transform with another phase factor describing spherical waves, an exponent of said factor depending on squared coordinates in the target layer and a distance between target layer and original layer, and   one or both of these phase factors may be set to a constant value.   
     
     
         28 . The device according to  claim 27 , where for the execution of the fast Fourier transformations all data sets have a number of discrete matrix point values, said number being an nth power of 2. 
     
     
         29 . The device according to  claim 25 , which includes a multi-channel digital signal processor for independent and simultaneous execution of frequently re-occurring computation routines. 
     
     
         30 . The device according to  claim 25 , which includes a multitude of independently working sub-processors which comprise simultaneously executed transformation routines and a resource manager which dynamically assigns transformations required for computation to available transformation routines depending on a content of the three-dimensional object, in order to be able to simultaneously execute at least a certain number of transformations. 
     
     
         31 . The device according to  claim 25 , which is a multi-channel processor for simultaneous computation of the hologram data sets for both eyes. 
     
     
         32 . The device according to  claim 25 , which includes object data set controlling means for comparing contents of corresponding object data sets in hologram computations with different original object data, in order to execute like transformations only once in one of two signal processor channels and to co-use the transforms in the other channel. 
     
     
         33 . The device according to  claim 25 , where one or all of the phase factors describing spherical waves may be set to a constant value. 
     
     
         34 . The device according to  claim 25  adapted to switch from a three dimensional mode to a two dimensional mode, depending on at least one on inputs and what mode a user selects. 
     
     
         35 . The method according to  claim 19 , where one or both of the phase factors describing spherical waves may be set to a constant value.