Device and method for calculating holographic data

Abstract

An apparatus and a method for optimized calculation of 2D sub-holograms for object points of a three-dimensional scene and a pipeline for real-time calculation of holograms are provided. The invention shortens the calculation time of a hologram for representing a three-dimensional scene and/or to reduce the calculation complexity of such a hologram. This is achieved by a 2D sub-hologram of an object point, which has image elements of the spatial light modulator, comprises a half 1D sub-hologram, where the radius of each image element is determined and each image element of the 2D sub-hologram is fixedly assigned to at least one image element of the half 1D sub-hologram with identical or similar radius by way of an electronic circuit, by a method for encoding a hologram, and by a pipeline on the basis of FPGA and/or ASIC.

What is claimed is: 
     
         1 . A method for calculating a 2D sub-hologram for representing an object point of a three-dimensional scene using a holographic display comprising a spatial light modulator with a matrix of image elements, wherein each 2D sub-hologram contains image elements of the spatial light modulator and wherein the method utilizes a rotational symmetry of the 2D sub-hologram in order to encode the 2D sub-hologram into the spatial light modulator, in which
 assigning each image element of the 2D sub-hologram to at least one image element of a half 1D sub-hologram having an identical or similar radius value, wherein the half 1D sub-hologram extends along a section through the 2D sub-hologram from the origin of the 2D sub-hologram up to a maximum radius of the 2D sub-hologram,   calculating values for phase and amplitude for each image element of a half 1D sub-hologram and transferring to all respectively assigned image elements of the 2D sub-hologram,   realizing the assignment of the image elements of the 2D sub-hologram to the image elements of the half 1D sub-hologram in a fixedly encoded manner by way of an electronic circuit.   
     
     
         2 . The method as claimed in  claim 1 , wherein each image element of the 2D sub-hologram is fixedly assigned to at least one image element of the half 1D sub-hologram by way of an electronic circuit such that the radius of the image element of the 2D sub-hologram corresponds to the radius of an image element of the half 1D sub-hologram that is multiplied by a direction-dependent elongation factor. 
     
     
         3 . The method as claimed in  claim 1 , wherein a complex-valued 1D sub-hologram with the polar coordinates of amplitude and phase is transformed after its calculation into a Cartesian coordinate system. 
     
     
         4 . The method as claimed in  claim 1 , wherein intermediate values are generated by linking at least two image elements of the half 1D sub-hologram and image elements of the 2D sub-hologram are assigned to said intermediate values. 
     
     
         5 . The method as claimed in  claim 4 , wherein the intermediate values are generated by virtual multiplication of the number of image elements of the half 1D sub-hologram or by interpolation of the values of at least two image elements of the half sub-hologram. 
     
     
         6 . The method as claimed in  claim 1 , wherein the half 1D sub-hologram extends along the x-axis of the 2D sub-hologram or along the y-axis of the 2D sub-hologram. 
     
     
         7 . A method for calculating a 2D sub-hologram for representing an object point of a three-dimensional scene, in which the rotational symmetry of the 2D sub-hologram is combined with a mirror symmetry, wherein only one quadrant or only one half of a quadrant of the 2D sub-hologram is calculated using the method as claimed in  claim 1  and the remaining three quadrants or the remaining half of the quadrant and the remaining three quadrants are calculated by way of mirroring. 
     
     
         8 . A method for calculating a hologram for representing a three-dimensional scene, in which 2D sub-holograms are generated for all object points of this scene to be represented using a method as claimed in  claim 1 :
 each of the image elements of each 2D sub-hologram according to the location of the object point to be represented with the 2D sub-hologram and the position of an observer of this scene undergoes an offset in the x- and/or in the y-direction, and   adding up the 2D sub-holograms which are positioned thusly with respect to one another.   
     
     
         9 . A method for encoding a hologram of a three-dimensional scene in a spatial light modulator of a holographic display using addition of sub-holograms of individual object points, comprising:
 calculating a sub-hologram segment of a first half of a sub-hologram with a defined segment width for a hologram row,   determining offset positions for the sub-hologram segment of the first half and for a sub-hologram segment of a second half of the sub-hologram, wherein the offset positions define the position within a hologram row at which the sub-hologram segments are added up,   generating the sub-hologram segment of the second half of the sub-hologram by duplication and mirroring of the sub-hologram segment of the first half,   including the sub-hologram segment of the first half and its offset position in a computation path for the first half and the sub-hologram segment of the second half and its offset position are included in a computation path for the second half of the sub-hologram, in which in each case the addition of the sub-hologram segments takes place in hologram row memories which are independent from one another,   aligning the sub-hologram segments according to the ascertained offset positions at the hologram row memory before the addition, and   combining the independent hologram row memories of the first and the second sub-hologram halves.   
     
     
         10 . The method as claimed in  claim 9 , wherein the sub-hologram segment is transformed after the calculation from the polar coordinate system into a Cartesian coordinate system. 
     
     
         11 . The method as claimed in  claim 9 , wherein the alignment takes place by way of
 mapping a non-aligned sub-hologram segment onto two neighboring segments which are aligned at the hologram row memory by way of displacement by the difference value of an integer multiple of the number of elements of a segment and the offset position (within a segment) determined for this sub-hologram segment, and zero-padding the still remaining elements of the two neighboring segments,   adding up the two neighboring aligned segments in two independent hologram row memories.   
     
     
         12 . The method as claimed in  claim 11 , wherein the displacement of the sub-hologram segment is effected by way of a pipeline having a number of stages, corresponding to the number of elements of a sub-hologram segment, wherein in each stage the elements are displaced by one element until the ascertained difference value is reached, and are passed on along the remaining stages without displacement, or by way of a fixed logic, in which the displacement is selected according to the difference value by a multiplexer. 
     
     
         13 . The method as claimed in  claim 9 , wherein the respective method steps are repeated according to the number of used hologram rows for a 2D encoding. 
     
     
         14 . The method as claimed in  claim 9 , wherein the sub-hologram segment of the first half is generated such that it is already aligned and is added up in an independent hologram row memory. 
     
     
         15 . The method as claimed in  claim 14 , wherein the sub-hologram segment of the second half of the sub-hologram is generated by duplication and mirroring of the sub-hologram segment of the first half and linked to the sub-hologram segment stored in the previous cycle, the elements of the current sub-hologram segment are displaced by the difference value of an integer multiple of the number of elements of a segment and the offset position determined for said sub-hologram segment, and the sub-hologram segment that is aligned at the memory is separated off and added up in a hologram row memory. 
     
     
         16 . The method as claimed in  claim 9 , the 2D sub-holograms of which are calculated using an apparatus for calculating a 2D sub-hologram for representing an object point of a three-dimensional scene using a holographic display and/or using a method for calculating a 2D sub-hologram for representing an object point of a three-dimensional scene using a holographic display comprising a spatial light modulator with a matrix of image elements, wherein each 2D sub-hologram contains image elements of the spatial light modulator and wherein the method utilizes a rotational symmetry of the 2D sub-hologram in order to encode the 2D sub-hologram into the spatial light modulator, in which
 assigning each image element of the 2D sub-hologram to at least one image element of a half 1D sub-hologram having an identical or similar radius value, wherein the half 1D sub-hologram extends along a section through the 2D sub-hologram from the origin of the 2D sub-hologram up to a maximum radius of the 2D sub-hologram,   calculating values for phase and amplitude for each image element of a half 1D sub-hologram and transferring to all respectively assigned image elements of the 2D sub-hologram,   realizing the assignment of the image elements of the 2D sub-hologram to the image elements of the half 1D sub-hologram in a fixedly encoded manner by way of an electronic circuit.   
     
     
         17 . The method as claimed in  claim 9 , the 2D sub-holograms of which are calculated using an apparatus for calculating 2D sub-hologram for representing an object point of a three-dimensional scene using a holographic display and/or using a method for encoding a hologram of a three-dimensional scene in a spatial light modulator of a holographic display using addition of sub-holograms of individual object points, comprising:
 calculating a sub-hologram segment of a first half of a sub-hologram with a defined segment width for a hologram row,   determining offset positions for the sub-hologram segment of the first half and for a sub-hologram segment of a second half of the sub-hologram, wherein the offset positions define the position within a hologram row at which the sub-hologram segments are added up,   generating the sub-hologram segment of the second half of the sub-hologram by duplication and mirroring of the sub-hologram segment of the first half,   including the sub-hologram segment of the first half and its offset position in a computation path for the first half and the sub-hologram segment of the second half and its offset position are included in a computation path for the second half of the sub-hologram, in which in each case the addition of the sub-hologram segments takes place in hologram row memories which are independent from one another,   aligning the sub-hologram segments according to the ascertained offset positions at the hologram row memory before the addition, and   combining the independent hologram row memories of the first and the second sub-hologram halves.