Analytic method for computing video holograms in real time

Abstract

An analytical method for computing a video hologram for a holographic reproduction device having at least one light modulation means is disclosed, wherein a scene split into object points is encoded as a whole hologram and can be seen as a reconstruction from a visibility region, located within a periodicity interval of the reconstruction. The visibility region, together with each object point of the scene to be reconstructed, defines a sub-hologram and the whole hologram is generated from a superposition of sub-holograms, wherein the complex hologram values of a sub-hologram are determined from the wave front of the respective object point to be reconstructed in a modulator region of the light modulation means, by calculating and evaluating the transmission or modulation functions of an imaging element formed in the modulator region. The object point to be reconstructed is located in the focal point of the imaging element.

Claims

1. A method for computing a video hologram of a scene to be reconstructed, the scene to be reconstructed comprising a multitude of object points, for use in a holographic display device with at least one light modulator means, the method comprising the steps of: defining a visibility region within a periodicity interval of the video hologram of the scene to be reconstructed; for each object point, defining a modulator region by the defined visibility region together with each object point of the scene to be reconstructed, where a sub-hologram of an object point of the scene to be reconstructed is computed for each modulator region, and where an entire video hologram is created by superposition of said sub-holograms; determining complex hologram values of a sub-hologram in a modulator region from a wave front of an object point to be reconstructed by computing modulation functions of an imaging element which is modeled in a respective modulator region of said holographic display device, and which includes a focal point in which the object point to be reconstructed lies, where the sub-hologram of said object point is computed using the modulation functions; and tracking a position of the visibility region to a position of an eye of an observer.

2. The method according to claim 1, wherein the modeled imaging element comprises at least one modeled lens.

3. The method according to claim 1, wherein the modeled imaging element comprises at least one modeled prism.

4. The method according to claim 1, comprising for each object point of the scene, performing the following steps: A: Determining the size and position of the sub-hologram as a modulator region, which is given the half-width a and the half-height b, and which is given local coordinates; B: Determining the sub-hologram of a modeled lens in the modulator region, comprising the steps of: B1: Determining the focal length f of the lens preferably as the normal distance of the object point to be reconstructed from the modulator region; and B2: Determining the complex values of the corresponding sub-hologram of the lens using the equation
z.sub.L=exp{+/i*[(/f)*(x.sup.2+y.sup.2)]}, where is the reference wavelength, f is the focal length and (x, y) is the corresponding coordinate pair, and where the + sign indicates a convex lens, where the sign indicates a concave lens; C: Determining the sub-holograms of modeled prisms in the modulator region, comprising the steps of: C1: Determining the linear factor C.sub.x of the prism with horizontal effective direction, which is described by the following equation in the interval x [a, a]
C.sub.x=M*(2/), where M is the inclination of the prism; C2: Determining the linear factor C.sub.y of the prism with vertical effective direction, which is described by the following equation in the interval y [b, b]
C.sub.y=N*(2/), where N is the inclination of the prism; and C3: Determining the complex values of the corresponding sub-hologram of the combined prisms by superposing the two prism terms
z.sub.P=exp{i*[C.sub.x*(xa)+C.sub.y*(yb)]}; D: Superposition of the sub-hologram of the modeled lens and of the sub-hologram of the modeled prisms, where the complex values of the lens and of the prisms are multiplied with
z.sub.SH=z.sub.L*z.sub.p or, symbolically, SH=SH.sub.L*SH.sub.p E: Application of the random phase, where each superposed sub-hologram is assigned with a random phase .sub.z, and where a complex multiplication is performed with
z.sub.SH:=z.sub.SH*exp(i.sub.z) or, symbolically, SH:=SH*exp(i.sub.z); and F: Intensity modulation, where the values of the modulated sub-hologram are given a real intensity factor C with z.sub.SH:=C*z.sub.SH or SH:=C*SH.

5. The method according to claim 4, wherein, considering the position of the sub-holograms, their superposition to form the entire video hologram is computed as the complex sum of the sub-holograms with H.sub.SLM=SH.sub.i.

6. The method according to claim 4, wherein each modulated sub-hologram of an object point is given a random phase, and the random phases of all sub-holograms are evenly distributed.

7. The method according to claim 4, wherein the position of the modulator region is determined in that the centre of the modulator region lies on the straight line through the object point to be reconstructed and the centre of the visibility region.

8. The method according to claim 4, wherein the size of the modulator region is determined by tracing back the visibility region through the object point to the light modulator means.

9. The method according to claim 8, wherein the complex hologram values are converted into Burckhardt components or two-phase components of the code.

10. The method according to claim 1, wherein the complex hologram values are converted into pixel values of the light modulator means.

11. The method according to claim 1, comprising for each object point of the scene, performing the following steps: A: Determining the size and position of the sub-hologram as a modulator region, which is given the half-width a and the half-height b, and which is given local coordinates; B: Determining the sub-hologram of a modeled lens in the modulator region, comprising the steps of: B1: Determining the focal length f.sub.MR of the lens preferably as the normal distance of the object point to be reconstructed from the modulator region; and B2: Determining the complex values of the corresponding sub-hologram of the lens using the equation $z_L={}^{\left\{\frac{}{f_{\mathrm{MR}}}\left(x^2+y^2\right)\right\}}$ where is the reference wavelength, (x, y) is the corresponding coordinate pair, where the + sign indicates a convex lens, where the sign indicates a concave lens, where f.sub.MR is the focal length of the imaging element being modelled in the modulator region, where f.sub.MR is determined by the equation $f_{\mathrm{MR}}=\frac{1}{\frac{1}{f_{\mathrm{OP}}}-\frac{1}{f_{\mathrm{OSL}}}}$ where f.sub.OSL is the focal length of an optical system lens, and where f.sub.OP is the distance between the light modulator and the object point to be reconstructed; C: Application of the random phase, where each superposed sub-hologram is assigned with a random phase .sub.z, and where a complex multiplication is performed with
z.sub.SH:=z.sub.SH*exp(i.sub.z) or, symbolically, SH:=SH*exp(i.sub.z); and D: Intensity modulation, where the values of the modulated sub-hologram are given a real intensity factor C with z.sub.SH:=C*z.sub.SH or SH:=C*SH.

12. The method according to claim 1, wherein the determination of the complex values of the corresponding sub-hologram of the modelled lens in the modulator region is provided by determining the complex values in one quadrant and where the determined complex values in said quadrant are applied to the other quadrants by using a rule of sign due to the symmetry.

13. The method according to claim 1, wherein if an object point to be reconstructed in space changes its position depending on the observer position, a respective modulator region will remain in a fixed position.

14. The method according to claim 1, wherein if the position of an object point to be reconstructed in space does not change depending on the observer position, the respective modulator region changes in dependence on the observer position.

15. The method according to claim 1, wherein an object point to be reconstructed can be located at any position within the reconstruction space (frustum) while its position is not approximated by way of discretization.

16. A holographic display device for computing a video hologram of a scene, the scene comprising a multitude of object points, with at least one light modulator means, and with a screen means, said device configured to perform the steps of: defining a visibility region within a periodicity interval of the video hologram of the scene to be reconstructed; for each object point, defining a modulator region by the defined visibility region together with each object point of the scene to be reconstructed, where a sub-hologram of an object point of the scene to be reconstructed is computed for each modulator region, and where an entire video hologram is created by superposition of said sub-holograms; determining complex hologram values of a sub-hologram in a modulator region from a wave front of an object point to be reconstructed by computing modulation functions of an imaging element which is modeled in the respective modulator region of said holographic display device, and in whose focal point the object point to be reconstructed lies, where the sub-hologram of said object point is computed using the modulation functions, tracking a position of the visibility region to a position of an eye of an observer, and wherein the screen means is the light modulator means itself on which the video hologram of the scene is encoded.

17. The holographic display device according to claim 16, wherein the determination of the complex values of the corresponding sub-hologram of the modelled lens in the modulator region is provided by determining the complex values in one quadrant and where the determined complex values in said quadrant are applied to the other quadrants by using a rule of sign due to the symmetry.

18. The holographic display device according to claim 16, wherein at least one of the following items or parts thereof is calculated and added onto an entire hologram: a prism, a lens, a random phase value distribution and a predetermined phase value distribution.

19. The holographic display device according to claim 18, wherein the at least one of these items has a size in the x-direction or in the y-direction being in the range of 2 pixels up to a maximum number of pixels in the x-direction or in the y-direction, respectively; or wherein a location of a centrum of the at least one of these items might be anywhere on the entire area of the spatial light modulator; or wherein the at least one of these items has a size in the x-direction or in the y-direction being in the range of 2 pixels up to the maximum number of pixels in the x-direction or in the y-direction, respectively; and a location of a centrum of the at least one of these items might be anywhere on the entire area of the spatial light modulator.

20. A holographic display device for computing a video hologram of a scene, the scene comprising a multitude of object points, with at least one light modulator means, and with a screen means, said device configured to perform the steps of: defining a visibility region within a periodicity interval of the video hologram of the scene to be reconstructed; for each object point, defining a modulator region by the defined visibility region together with each object point of the scene to be reconstructed, where a sub-hologram of an object point of the scene to be reconstructed is computed for each modulator region, and where an entire video hologram is created by superposition of said sub-holograms; determining complex hologram values of a sub-hologram in a modulator region from a wave front of an object point to be reconstructed by computing modulation functions of an imaging element which is modeled in the respective modulator region of said holographic display device, and in whose focal point the object point to be reconstructed lies, where the sub-hologram of said object point is computed using the modulation functions, tracking a position of the visibility region to a position of an eye of an observer, and wherein the screen means is an optical element onto which is imaged the video hologram of the scene which is encoded on the light modulator means, or a wave front of the scene which is encoded on the light modulator means.

21. The holographic display device according to claim 20, wherein the optical element is a lens or a mirror.

22. The holographic display device according to claim 20, wherein the determination of the complex values of the corresponding sub-hologram of the modelled lens in the modulator region is provided by determining the complex values in one quadrant and where the determined complex values in said quadrant are applied to the other quadrants by using a rule of sign due to the symmetry.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention will now be explained in more detail with the help of embodiments and in conjunction with the accompanying drawings, wherein

(2) FIG. 1 illustrates the principle on which a holographic display device is based, and a modulator region representing an object point,

(3) FIG. 2a is a side view of the display device with an imaging element comprising a lens and prism,

(4) FIG. 2b shows a modulator region and a vertically effective prism,

(5) FIG. 2c shows a modulator region and a horizontally effective prism,

(6) FIG. 3 shows a flowchart of the method according to this invention, and

(7) FIG. 4 shows an option of the method for the reconstruction of an object point behind the hologram plane.

DETAILED DESCRIPTION

(8) FIG. 1 illustrates the general principle on which a holographic display device (HAE) is based for one observer. The principle applies accordingly to multiple observers. The position of an observer is characterised by the position of his eye or his pupils (VP). The device comprises a light modulator means (SLM), which is identical to the screen means (B) in this embodiment in order to keep things simple; and it superposes the wave fronts which are modulated with information of object points of a scene (3D-S) in at least one visibility region (VR). The visibility region is tracked to the eyes. The reconstruction of a single object point (OP) of a scene (3D S) only requires one sub-hologram (SH) as a subset of the entire hologram (H.sub.SLM) encoded on light modulator means (SLM). The modulator region (MR) is the region of the sub-hologram on the light modulator (SLM). As can be seen in this Figure, the modulator region (MR) only comprises a small subsection of the light modulator means (SLM). According to a most simple embodiment, the centre of the modulator region (MR) lies on the straight line through the object point (OP) to be reconstructed and through the centre of the visibility region (VR). In a most simple embodiment, the size of the modulator region (MR) is determined based on the theorem of intersecting lines, where the visibility region (VR) is traced back through the object point (OP) to be reconstructed to the light modulator means (SLM). Further, the indices of those pixels on the light modulator means (SLM) which are required to reconstruct this object point are thus determined. As can be seen in the Figure, the modulator region (MR) will be given a coordinate system, where the point of origin is located in its centre, the x axis describes the abscissa and the y axis describes the ordinate. The modulator region (MR) has the half-width a and the half-height b.

(9) FIG. 2a is a side view of the holographic display device (HAE) that illustrates the general principle of the method. The modulator region (MR) is derived in analogy to what was said under FIG. 1. This region is located in the hologram plane (HE), where the light modulator (SLM) is disposed. The imaging element (OS), which is here composed of a focusing lens (L) and a prism (P), lies in the modulator region (MR). The Figure only shows the vertically effective prism wedge, and the imaging element (OS) is shown in front of the light modulator means (SLM) to make things clearer.

(10) FIG. 2b shows a horizontally effective prism wedge (PH) in front of the modulator region (MR) together with the coordinates and dimensions used. The prism wedge here runs through the ordinate.

(11) FIG. 2c analogously shows a vertically effective prism wedge (PV), which runs through the abscissa. The two prism wedges are superposed as described below.

(12) FIG. 3 shows a flowchart of the method according to the present invention. Starting point of the method is a three-dimensional scene (3D S) which is composed of a multitude of object points (OP). Colour and depth information is available for the object points (OP). The visibility of an object point is determined, based on its depth information, depending on the observer position, i.e. that of the eye pupils of the observer. In step (A), size and position of the respective modulator region (MR) in the hologram plane (HE) or on the light modulator means is determined for each visible object point. Following the idea of the invention, the object point (OP) to be reconstructed is interpreted as the focal point of an imaging element which is situated in the hologram plane, and the imaging element is considered to be a combination of a convex lens (L) and vertically and horizontally effective prisms (PV, PH), as shown in FIGS. 2b, 2c. The complex hologram values of the sub-hologram (SH) are computed in a modulator region (MR) of the light modulator means from the wave front of the object point (OP) to be reconstructed, in that the transmittance functions or modulation functions of the imaging element (OS), which is modelled in the modulator region (MR) and in whose focal point the object point (OP) to be reconstructed lies, are computed and analysed. In step (B1), the focal length of the lens (L) is thus determined for each visible object point as the normal distance of the object point (OP) from the hologram plane (HE).

(13) In step (B2), the complex values for the corresponding sub-hologram (SH.sub.L) are determined from
z.sub.L=exp{i*[(/f)*(x.sup.2+y.sup.2)]}
where is the reference wavelength, f is the focal length and (x, y) is the corresponding local coordinate pair. The coordinate system is defined as described above.

(14) In step (C), the sub-holograms (SH.sub.P) of the prisms (P) in the hologram plane are determined. The linear factor C.sub.x of the prism (PH) with horizontal effective direction is determined using the equation
C.sub.x=M*(2/),
where M is the inclination of the prism. The linear factor C.sub.y of the vertically effective prism is found with an analogous equation, but with the inclination N. The complex values of the corresponding sub-hologram (SH.sub.P) are determined by superposing the two prism terms
SH.sub.P:=z.sub.P=exp{i*[C.sub.x*(xa)+C.sub.y*(yb)]}.

(15) One prism term can be omitted if the holographic display device exhibits the characteristic to image the light source into the visibility region (VR).

(16) Now that the sub-holograms (SH.sub.L) of the lens (L) and (SH.sub.P) of the prisms (P) are available, they are superposed in step (D) so to form the combined sub-hologram (SH) by complexly multiplying the complex values of the lens and of the prisms:
z.sub.SH=z.sub.L*z.sub.P
or, symbolically, SH=SH.sub.L*SH.sub.P.

(17) In step (E), the sub-hologram (SH) is given a homogeneously distributed random phase.

(18) In step (F), an intensity modulation is performed, where the sub-hologram (SH) is multiplied with an intensity factor:
z.sub.SH=C*z.sub.SH
or, symbolically, SH:=C*SH.

(19) The combined sub-hologram (SH) of an object point (OP) is now completely available.

(20) In a further process step (G), which may be performed separately, the sub-holograms of the object points are added so to form an entire hologram (H.sub.SLM). The individual sub-holograms (SH.sub.i) of the object points are superposable and are complexly added so to form the entire hologram (H.sub.SLM).

(21) Entire hologram=complex sum of all sub-holograms of the object points with
H.sub.SLM=SH.sub.i
or z.sub.SLM=z.sub.SHi (with regard to a global coordinate system).

(22) The entire hologram (H.sub.SLM) represents the hologram of all object points. It thus represents and reconstructs the entire scene (3D S).

(23) In a final step (H), as already described above, the entire hologram can by way of encoding be transformed into pixel values for a holographic display device which also preferably employs of the principle of sub-holograms. These are in particular, as already mentioned above, devices described in documents WO 2004/044659, WO 2006/027228, WO 2006119760, and DE 10 2006 004 300.

(24) FIG. 4 illustrates that by applying the method object points (OP) which are situated behind the hologram plane (HE) can generally be reconstructed analogously. In that case, the imaging element (OS) analogously comprises the mentioned prisms (P), but the lens in the imaging element is a concave lens (L), for which the wave front can be determined in the same way in the modulator region.

LIST OF REFERENCE NUMERALS

(25) 3D-S Scene VR Visibility regions OP Object point, general OPn Object point, with reference index SH Sub-hologram, general SHL Sub-hologram of a lens SHP Sub-hologram of a prism MR Modulator region SHi Sub-hologram, general, indexed HSLM Total hologram HAE Holographic display device with B Screen means SLM Light modulator means HE Hologram plane VP Observer eyes/observer position OS Projection element L Lens P Prism PH Prism with horizontal effective direction PV Prism with vertical effective direction