Method for producing holograms

Abstract

The invention relates to a method for generating holograms for encoding in a spatial light modulation device for a holographic display for representing a two- and/or three-dimensional scene. The two- and/or three-dimensional scene is decomposed into object points and encoded in a hologram, which is subdivided into subholograms, in the spatial light modulation device. The object points of the scene are encoded into encoding regions on the spatial light modulation device. A size and/or shape of the encoding region is selected in relation to a size and/or shape of a subhologram, assigned to the encoding region, in such a way that crosstalk of higher diffraction orders in a virtual visibility region is reduced.

Claims

1. A method for generating holograms for encoding in a spatial light modulation device for a holographic display for representing a two- and/or three-dimensional scene, comprising: decomposing the scene into object points and encoding in a hologram, which is subdivided into subholograms, in the spatial light modulation device, encoding object points into encoding regions on the spatial light modulation device, and selecting a size and/or shape of an encoding region different than a size and/or shape of a subhologram, assigned to said encoding region in such a way that crosstalk of higher diffraction orders in a virtual visibility region is reduced.

2. The method as claimed in claim 1, wherein the value of the amplitude in the encoding region for the object point is reduced continuously toward the edge region of the encoding region.

3. The method as claimed in claim 1, wherein in the case of a field of view SF≥30 degrees, a virtual visibility region, which is formed parallel to the spatial light modulation device, is calculated for a central region of the spatial light modulation device, where a virtual visibility region, which is formed at an angle to the spatial light modulation device, corresponding to an angle at which an observer looks at the spatial light modulation device, being calculated for edge regions of the spatial light modulation device.

4. The method as claimed in claim 1, wherein a subhologram is generated by means of a geometrical projection of a virtual visibility region in an observer plane through an object point onto the spatial light modulation device.

5. The method as claimed in claim 4, wherein, after the geometrical projection of the virtual visibility region onto the spatial light modulation device, setting the amplitude in the subhologram generated to a constant value for all pixels of the subhologram, respectively reducing the value of the amplitude continuously by a predefined value for pixels present in the edge region of the subhologram, and increasing the subhologram in its extent by pixels in order to generate the encoding region for the object point, the value of the amplitude of these pixels being further reduced continuously up to a threshold value.

6. The method as claimed in claim 5, wherein a value of 1% of the maximum amplitude in the encoding region is selected for the threshold value.

7. The method as claimed in claim 5, wherein a bell-shaped amplitude profile is generated in the encoding region.

8. The method as claimed in claim 4, wherein, after the geometrical projection of the virtual visibility region onto the spatial light modulation device, reducing the subhologram in its extent by pixels in order to generate the encoding region for the object point, setting the amplitude in the encoding region generated to a constant value for all pixels of the encoding region, and respectively reducing the value of the amplitude continuously by a predefined value up to a threshold value for pixels present in the edge region of the encoding region.

9. The method as claimed in claim 8, wherein a value of 1% of the maximum amplitude in the encoding region is selected for the threshold value.

10. The method as claimed in claim 8, wherein a bell-shaped amplitude profile is generated in the encoding region.

11. The method as claimed in claim 1, wherein an apodization function is encoded into the encoding region for the object point in the spatial light modulation device, or calculated values of the encoding region for the object point are multiplied by an apodization function, the apodization function having a maximum amplitude value in the central region of the encoding region and decreasing to a value of 0 toward the edge region of the encoding region.

12. The method as claimed in claim 1, wherein an encoding region is respectively calculated once by means of a Fourier transform for an object point at a particular depth with respect to the spatial light modulation device, the amplitude profile of the calculated subhologram being stored in a look-up table.

13. The method as claimed in claim 1, wherein an encoding region is calculated once by means of a wave propagation method other than a Fourier transform, for an object point at different depths and in different lateral positions with respect to the spatial light modulation device, the amplitude profile of the calculated encoding region being stored in a look-up table.

14. The method as claimed in claim 1, wherein the amplitude profile is respectively stored in a look-up table only for object points having a reference intensity A, while for an object point which has an intensity B and is located at an equal depth with respect to the spatial light modulation device as an object point having an intensity A, the amplitude profile for the individual pixels of the associated encoding region is taken from the look-up table and the amplitudes for each pixel are multiplied by a factor (B/A).sup.2.

15. The method as claimed in claim 1, wherein, in the case of a small distance of the object point with respect to the spatial light modulation device and/or in the case of a large angle of the object point with respect to the virtual visibility region, the encoding region is determined from a subhologram which is calculated with a Fourier transform method and/or by means of Huygens' wavelets.

16. The method as claimed in claim 15, wherein the distance of the object point with respect to the spatial light modulation device is less than 5% of the observer distance with respect to the spatial light modulation device for a display with a size of a virtual visibility region of more than 10 mm, or is less than 10% of the observer distance with respect to the spatial light modulation device for a display with a size of a virtual visibility region of between 5 mm and 10 mm.

17. The method as claimed in claim 1, wherein, in the case of a large distance of the object point with respect to the spatial light modulation device and/or in the case of a small angle of the object point with respect to the virtual visibility region, the encoding region is determined from a subhologram which is calculated with a projection method, in which projecting the virtual visibility region through the object point onto the spatial light modulation device and generating a subhologram, allowing the subhologram to be extendible or reducible by pixels in order to generate the encoding region for the object point on the spatial light modulation device, encoding a phase function into the encoding region, and encoding an amplitude function into the encoding region in such a way that the object point is reconstructed with a predetermined intensity.

18. The method as claimed in claim 17, wherein the distance of the object point with respect to the spatial light modulation device is greater than or equal to 5% of the observer distance with respect to the spatial light modulation device for a display with a size of a virtual visibility region of more than 10 mm, or is greater than or equal to 10% of the observer distance with respect to the spatial light modulation device for a display with a size of a virtual visibility region of between 5 mm and 10 mm.

19. The method as claimed in claim 1, wherein a limiting subhologram size is determined, and where, for all object points whose subhologram sizes are greater than or equal to this limiting subhologram size, encoding regions are calculated from subholograms with the projection method, and for all object points whose subhologram sizes are less than this limiting subhologram size, encoding regions are calculated from subholograms with the Fourier transform method or with based on a look-up table.

20. The method as claimed in claim 19, wherein a value of 5 pixels is selected for the limiting subhologram size.

21. The method as claimed in claim 1, wherein those object points for which encoding regions and subholograms are calculated according to a projection method and those object points for which encoding regions and subholograms are calculated according to a wave propagation method are determined by a detected distance or a lateral position of an observer or a viewing angle of the observer at the spatial light modulation device.

22. The method as claimed in claim 1, wherein the extent of the virtual visibility region is selected to be less than or equal to the extent of a diffraction order, particularly where, in the case of a color reconstruction of the scene, the virtual visibility region is adapted in its extent to an extent of a diffraction order for the shortest wavelength used.

23. The method as claimed in claim 1, wherein, for calculation of the amplitude profile for the encoding region, transformation of the light propagation from the object point in an object plane into a complete diffraction order in the observer plane is carried out, amplitudes then being set to a value of 0 in an edge section of the diffraction order in the observer plane in order to generate a virtual visibility region which is reduced in its size in the observer plane.

24. The method as claimed in claim 23, wherein the calculated values for the amplitudes in the diffraction order in the observer plane are multiplied by an apodization function, the extent of which is less than one diffraction order.

25. The method as claimed in claim 24, wherein a rectangle function, a Gaussian function or a cosine function is used as the apodization function.

26. A light modulation apparatus into which a hologram is encoded according to the method as claimed in claim 1.

27. A display representing a two- and/or three-dimensional scene, comprising at least one spatial light modulation device into which a hologram is encoded according to the method as claimed in claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) In the figures:

(2) FIG. 1: shows a schematic representation of a holographic display apparatus, or a display, according to the prior art in a perspective representation,

(3) FIG. 2: shows a graphical representation of the size of a subhologram as a function of the distance of an object point with respect to the plane of a spatial light modulation device,

(4) FIG. 3: shows a graphical representation of an amplitude in the subhologram according to a calculation with the projection method and with the Fourier transform method,

(5) FIG. 4: shows a graphical representation of the amplitude profile in a subhologram according to FIG. 3, an object point being located approximately 17.5 cm in front of the plane of the spatial light modulation device, in the viewing direction at the spatial light modulation device,

(6) FIGS. 5a/b: show graphical representations of the amplitude profile for a spatial light modulation device according to the solid curve according to FIG. 2 for an object point which is located approximately 10 cm in front of the spatial light modulation device, in the viewing direction at the spatial light modulation device,

(7) FIG. 6: shows a graphical representation of the amplitude profile in the subhologram according to a calculation with the projection method with an abrupt transition of the amplitude, and an amplitude profile according to the invention with a constant transition,

(8) FIG. 7: shows schematic representations of intensity distributions, or addressed pixels, on the spatial light modulation device, the individual representations 1) to 6) showing various possibilities of an increase or reduction of the area of a subhologram,

(9) FIG. 8: shows a graphical representation of a rounded encoding region according to the invention,

(10) FIG. 9: shows a schematic representation of the subdivision of a scene to be reconstructed in depth regions for the calculation of encoding regions on a spatial light modulation device,

(11) FIG. 10: shows a schematic representation of the calculation of encoding regions on a curved surface of a spatial light modulation device,

(12) FIGS. 11a,11b: each show a schematic representation of a display with a very large field of view, and

(13) FIG. 12: shows a graphical representation of an apodized amplitude profile in an encoding region.

DETAILED DESCRIPTION OF THE INVENTION

(14) It should briefly be mentioned that elements/parts/components which are the same also have the same references in the figures.

(15) With the aid of FIGS. 2 to 5, a more detailed description will be given of the generation and calculation of encoding regions on the basis of subholograms on a spatial light modulation device (SLM) of a holographic display, in which the associated object points each have small distances with respect to the SLM.

(16) With respect to the size of a subhologram on the SLM by means of an analytical calculation or by means of the known or conventional projection method, for different types and sizes of an SLM, reference is made in general to FIG. 2 in which the size of the subhologram on the SLM is plotted in pixels against the distance of an object point of a scene to be reconstructed from the SLM. The solid curve shows subhologram sizes as a function of the object point distance with respect to the SLM for an SLM with a resolution of about five megapixels, a pixel pitch of 156 μm and with a distance of an observer with respect to the SLM, or display, of about 2 m. The dashed curve also represented shows subhologram sizes as a function of the object point distance with respect to the SLM for an SLM with an approximate pixel pitch of 30 μm and an approximate distance of an observer with respect to the SLM, or display, of 70 cm. The curves represented in FIG. 2 were calculated for light with a blue wavelength of λ=475 nm. For the subholograms of the solid curve, there is a virtual visibility region with a size of about 6 mm. For the subholograms of the dashed curve, there is a virtual visibility region with a size of about 11 mm.

(17) As can be seen from the graphical representation according to FIG. 2, for the SLM of the solid curve, the size of the subholograms decreases to 4 pixels for object points which are about 18 cm in front of the SLM, or display, and further to 2 pixels for object points which are about 10 cm in front of the SLM, or display. For these subholograms which are very small in their size or extent on the SLM, however, a sufficiently good reconstruction is no longer achieved since the diffraction effects at the edges of the subholograms are more strongly pronounced for these subholograms than for subholograms which are large in their size or extent. Furthermore, it may be possible that crosstalk of higher diffraction orders takes place not only over the edge of the virtual visibility region, but also the entire width or extent of the virtual visibility region. The 18 cm distance in this case corresponds to 9% of the observer distance, and the 10 cm distance corresponds to 5% of the observer distance.

(18) In particular for the SLM of the dashed curve, however, there is already a size of the subhologram of 5 pixels for a distance of the object point with respect to the SLM, or display, of about 1 cm—in this case only about 1.4% of the observer distance. Thus, the relevant depth region is then very small.

(19) It is furthermore to be mentioned that object points, or a scene to be reconstructed, may be generated or represented in front of the display, behind the display, or even in the plane of the display, as seen in the viewing direction of an observer at the display. The plane of the display is usually the plane of the SLM. Object points which lie in the plane of the SLM would expediently, and for simpler calculation, always be one pixel in size, even if the limit value of the size of the subholograms in the analytical calculation, or in the calculation with the projection method, tends toward a value of 0 (zero) there. The size or extent of the subhologram of one pixel rather corresponds to the fact that object points in the plane of the SLM are represented such as on a two-dimensional (2D) SLM.

(20) With respect to differences in the calculation of a subhologram by means of the analytical calculation (calculation by means of the projection method) and the Fourier transform calculation, FIG. 3 shows an amplitude profile in a subhologram.

(21) The solid curve shows the amplitude determined in the subhologram according to the geometrical calculation by means of the projection method, while the dash-dotted curve represents the amplitude determined according to the more exact calculation by means of the Fourier transform method for an SLM according to the solid curve according to FIG. 2, i.e. for a display which has an SLM with a pixel pitch of 156 μm and an observer distance of 2 m, the object point assigned to this subhologram being located about 50 cm in front of the display, or SLM. The amplitude of the subhologram determined with the analytical calculation of the solid curve according to FIG. 3 was in this case adapted to the average level of the amplitude of the subhologram determined or calculated with the Fourier transform method in order to allow simpler comparison. The geometrical calculation of the subhologram by means of projection in this case generates a subhologram having a size of 13 pixels.

(22) The amplitude calculated with the Fourier transform method, which is represented by the dash-dotted curve, in this case shows a smoother profile with overshoots in the central region of the curve and a constant decrease outward or toward the edge region of the curve.

(23) Such differences in the amplitude profile decrease with a larger virtual visibility region. For the SLM with a pixel pitch of 156 μm and for an observer distance of 2 m, for example, for blue light with a wavelength λ=470 nm the virtual visibility region is approximately 6 mm large.

(24) FIG. 4 represents the amplitude profile according to FIG. 3, but for an object point which is located only about 17.5 cm in front of the display and for an SLM according to the dashed curve according to FIG. 2, and therefore for a display which has an SLM with a 30 μm pixel pitch and an observer distance of 70 cm. This means that for the SLM according to the dashed curve according to FIG. 2 and an object point which is located about 17.5 cm in front of the display or the SLM, according to FIG. 4 the solid curve would show an amplitude profile according to the geometrical calculation with the projection method and the dashed curve would show an amplitude profile according to the calculation with the Fourier transform method. In both cases, object point distance 50 cm and observer distance 2 m as shown in FIG. 3, or object point distance 17.5 cm and observer distance 70 cm as shown in FIG. 4, the relative distance of the object point with respect to the SLM is 25% of the observer distance. In the latter case, 30 μm pixel pitch and observer distance of 70 cm, however, the virtual visibility region for blue light with a wavelength of λ=470 nm is about 11 mm large, i.e. about 1.8 times as large as in the example selected in FIG. 3.

(25) As can be seen in FIG. 4 in comparison with FIG. 3, the overshoots of the amplitude profile of the dashed curve become much less at least in the central region of the subhologram. Comparison between FIGS. 3 and 4 shows that for the larger virtual visibility region with a size of 11 mm and the same relative distance with respect to the SLM of 25% of the observer distance the differences between subholograms which have been calculated with the projection method and subholograms which have been calculated with the Fourier transform method are much less than for a virtual visibility region with a size of only 6 mm.

(26) For an SLM according to the solid curve according to FIG. 2—for the case with a virtual visibility region with a size of 6 mm—FIG. 5a shows an amplitude profile for a subhologram which is generated and calculated by an object point which is located about 10 cm—or 5% of the observer distance—in front of the display or SLM—i.e. closer than the object points considered previously. According to the geometrical calculation of a subhologram with the projection method, the subhologram is then only 2 pixels wide in its size or extent. Only 2 pixels have amplitude values not equal to 0 (zero), and these two amplitudes are equally large. The subhologram determined with the Fourier transform method, however, shows a symmetrical profile over a respectively odd number of pixels of the subhologram determined. Only a central pixel has a high amplitude the left and right neighbors of this pixel having a much lower amplitude. The relative differences of the two calculations of the subhologram would thus be particularly large in this case, as can be seen clearly from the shift of the two curves relative to one another. In the calculation with the projection method, the middle of the subhologram lay between two pixels. In the calculation with the Fourier transform method, the middle of the subhologram also corresponds to the middle of a pixel.

(27) From FIGS. 2 to 5a, it can thus be inferred that the analytical calculation of the subhologram by means of the projection method is advantageously modified for subholograms which are very small in their size or extent, for example in this case for a virtual visibility region with a size of 6 mm and a relative distance of the object points with respect to the display or SLM of 10% of the observer distance, in such a way that the amplitude profile of the subhologram is approximated to the amplitudes of the subhologram determined with the Fourier transform method, by allowing different amplitudes of the individual pixels of the subhologram, or the individual pixels having different amplitudes.

(28) For example, for this distance of an object point from the display or SLM according to FIG. 5a and similar distances, now instead of 2 pixels with the same amplitude, the subhologram is widened to 3 (5 or more) pixels in its extent, and an encoding region on the SLM is therefore provided which has the subhologram determined by means of the projection method and further pixels adjacent thereto. The amplitudes for this encoding region are in this case, for example, taken from the calculation values which were obtained by means of the Fourier transform method.

(29) FIG. 5b shows a subhologram having 5 pixels, the amplitude values of these 5 pixels corresponding to the calculation with the Fourier transform method. As comparison with FIG. 5a shows the Fourier transform method still has small nonzero amplitude values for further pixels. The subhologram with 5 pixels in FIG. 5b, however, represents an already very good approximation to the result of the Fourier transform method.

(30) In this case, depending on additional computational effort, it may be advantageous for the amplitudes for such small distances of object points with respect to the display or SLM to be stored in a value table, also referred to as a look-up table. Since the amplitudes in the present example are symmetrical with respect to the middle of the subhologram, it would be sufficient to store 3 amplitude values in a look-up table.

(31) An encoding region need not, however, be determined exactly with the aid of the values from the Fourier transform method.

(32) FIG. 6 shows a graphical representation of the amplitude profile in the subhologram according to a calculation with the projection method with an abrupt transition of the amplitude and, in comparison therewith, an amplitude profile in an encoding region with a constant transition of the amplitudes from a value of 0 to a value of 1. The amplitude profile in the encoding region was determined from the subhologram by the amplitude being slightly reduced for respectively 4 edge pixels of the subhologram, for example to values of 0.95, 0.85, 0.7 and 0.5 and the amplitude being slightly increased for respectively 3 pixels outside the extent of the subhologram, for example to a value of 0.3, 0.15 and 0.05. An encoding region, which has the subhologram determined by means of the projection method and further pixels adjacent thereto, was thus provided on the SLM. The effort of computation with the Fourier transform method is, however, not necessary in this case.

(33) The method according to the invention of calculating and generating a hologram on an SLM will be described in more detail below.

(34) The region of the encoding of object points on an SLM may, according to the invention, be extended to a region outside the subhologram. In this case, the method with which the subhologram is generated and calculated is largely unimportant.

(35) In simulations, a diffraction pattern of an individual pixel, apodized cosinusoidally in the transmission, of the SLM used was calculated in the plane of an entrance pupil of an observer's eye. In this case, it was apparent that the region of the diffraction pattern of an individual pixel, or the region of the intensity distribution in the far field of the pixel, i.e. specifically in the plane of the entrance pupil of an observer's eye, with an intensity value of I>0.9× Imax in a first lateral extent (y direction) assumes a value of more than 7 mm and in a second lateral extent (x direction) has a value of more than 20 mm, a pixel having an aspect ratio of 1:3. This means that the subhologram could be widened or extended in the y direction for example by ±3.5 mm and in the x direction for example by ±10 mm in its size. Exclusively this region lying outside the conventional subhologram could also be used for encoding an object point. This means that the diffraction patterns of the neighboring pixels in this region, i.e. also the pixels lying in this region but lying outside the conventional subhologram, also reaches the entrance pupil of the observer's eye and leads to an object point, which does not lie in the region of the subhologram determined by the geometrical projection, being represented on the retina of the eye.

(36) On the basis of these simulations it can be inferred that the diffraction pattern of an individual pixel of the SLM in the plane of the entrance pupil of the eye is significantly more extended than the entrance pupil itself. Conversely, this also means that pixels of the SLM outside the area of the geometrical projection of the entrance pupil of the eye or of the virtual visibility region through an object point onto the SLM may be used in order to generate the desired object points in space, and in order to be able to acquire them by the entrance pupil of the eye. The pixels of the SLM which are used in order to encode an object point in space may therefore partially, or even in particular cases fully, lie outside the projection area of the entrance pupil of the eye or of the projection area of the virtual visibility region on the SLM. Furthermore, it is also possible for the area of the subhologram to be variably thinned, that is to say only particular pixels in the subhologram are employed for encoding the object point.

(37) In the case of a variable thinning, optimization may be carried out on the remaining, i.e. the addressed and unmasked pixels of the SLM, in order to achieve best possible suppression of the background.

(38) By the addressing of pixels over the spatial extent of the conventional subhologram, the number of pixels used for the reconstruction can be increased or else reduced. The addressing of the pixels may also be carried out in a statistically thinned manner and, with a sufficiently large starting number of pixels, may for example be reduced to 80%, 60%, 40% or even 20% of the initial pixels, which in a comparable conventional subhologram may be addressed, or assigned to one or more object points. This is dependent on the individual encoding case.

(39) The removal of the conventional structuring of the subhologram may also be deliberately used to make the spatial frequency components of the diffraction patterns of individual neighboring object points differ from one another in such a way that their superposition, manifested in the form of visible crosstalk, is reduced. The starting point may, for example, in this case be a conventional subhologram to which an amplitude apodization function is applied in order to achieve an encoding region for an object point. This amplitude apodization function differs from the amplitude apodization function of the neighboring subholograms or encoding regions, which encode object points neighboring the first object point, which is encoded by the first encoding region. It is, however, also possible to use as a basis a statistical distribution of the addressing of pixels, which carries this out. The encoding regions may also overlap. It is, however, also possible that the encoding regions do not need to overlap, for example when the pixel number on the SLM is high enough and/or sufficiently existing statistical thinning of the pixels makes it possible to use albeit statistically thinned but nonoverlapping pixel groupings, i.e. different pixel groupings for different object points, these pixel groupings not overlapping, or overlapping only slightly. The different amplitude apodization functions, used for different object points, of the subholograms or encoding regions should in this case not be symmetrical. This is not dependent on whether or not the subholograms are statistically thinned.

(40) In other words, and for better understanding, a diffraction pattern of an individual pixel may be considered in a similar way to an Airy distribution. The height and position of the side lobes in the diffraction pattern are dependent on the amplitude apodization function used for the subhologram. Thus, the side lobes can in general be brought closer to the central peak by a higher numerical aperture, and moved away from it by a smaller numerical aperture. By the approach of using a multiaperture lens, or in general statistically thinned or statistically apodized lens functions in the subhologram, it is possible to shift the side lobes into the background of the diffraction pattern or to modify their position and shape in relation to neighboring diffraction patterns in such a way that crosstalk of neighboring object points becomes minimal. As an evaluation criterion, the image formed on the retina is in this case used. This means that the compression of the angular spectrum of plane waves of the light by the entrance pupil of an observer's eye is to be taken into account.

(41) Sets of amplitude apodization functions of subholograms may be saved with correspondingly produced values of the mutual crosstalk in look-up tables and stored. Simple values are obtained by a convolution, in which case it should be noted that the convolution center is determined by the mutual distance of the assigned object points. In other words, this gives an optimization approach for the reconstruction quality of represented object points perceived by the observer.

(42) FIG. 7 shows different types of the addressing of pixels on the SLM. These types of addressing may be used in order to reconstruct object points of a two-dimensional and/or three-dimensional scene with a particular number of pixels, the reconstruction being acquirable by the entrance pupil of an eye of an observer observing the scene. In general, a statistical selection or statistical thinning of a subhologram or encoding region may be carried out in a complex-valued fashion, i.e. with respect to the amplitude transparency and the phase transparency of the pixels. The representations in FIG. 6 may in general show an address grid of complex-valued pixels, but also simply an intensity grid or an array of intensity values, which may for example be binary or else take values of between 0 and 1. The use of a binary grid of the addressing or simply of the intensity distribution serves to simplify the representation. Grids of the—weighted—addressing and also grids of the intensity may extend continuously.

(43) In FIG. 7, representation 1) shows an intensity distribution or addressed pixels of a subhologram SH, the subhologram SH having the same size or extent in each representation 1) to 6). The region of the subhologram SH is shown by means of a dashed line or outline.

(44) Representation 2) shows a statistical extension of the addressed pixels or of the subhologram SH to pixels which lie outside the subhologram SH. In other words, the subhologram has been increased in its size or extent by providing pixels lying outside it, which likewise contribute to the encoding of an object point in the SLM, to form an encoding region. The encoding region generated in this way therefore comprises the subhologram SH, all pixels of the subhologram SH, and further pixels of the SLM which lie outside the subhologram SH, here illustrated as white. In this case, in representation 2), only isolated pixels lying in the edge region of the subhologram SH, which in addition to the subhologram SH contribute to the generation of the encoding region, are shown. It is of course also possible that the subhologram SH may be increased in its size or extent in order to generate an encoding region in such a way that all pixels lying around the edge region of the subhologram SH may be used for the encoding of an object point, i.e. statistical thinning of the pixel extension lying outside the subhologram is not provided. For example, the subhologram SH may be extended in the upper, lower, left and right region by 3 or even 5 pixels, in which case the amplitudes of these pixels and pixels at the inner edge region of the subhologram are then assigned corresponding amplitude values so that a constantly decreasing amplitude profile is provided toward the edge region of the encoding region.

(45) In representation 3), statistical masking of the addressing of pixels inside a subhologram SH is shown. As can be seen, individual pixels, here illustrated as black, do not contribute to the encoding of an object point in the SLM.

(46) Statistical addressing of pixels inside and outside a subhologram SH is shown in representation 4) of FIG. 6. This illustration shows that both pixels in the subhologram may be reduced and, at the same time, the subhologram may be extended by pixels outside it. The encoding region for an object point therefore comprises the subhologram thinned by pixels and the pixels, here illustrated as white, lying outside the subhologram.

(47) Representation 5) shows addressing, which is not statistically thinned, of pixels fully outside a subhologram SH. As can be seen, no pixels which encode an object point in the SLM lie inside the subhologram SH. In this embodiment, the pixels which encode the object point in the SLM lie fully outside the area of the subhologram SH.

(48) In contrast to representation 5), representation 6) likewise shows addressing of pixels which lies fully outside a subhologram, but in this case there is statistically thinned addressing of the pixels outside the subhologram SH. In this embodiment as well, as in the embodiment of representation 5), no pixels which encode an object point in the SLM lie inside the subhologram SH. In this embodiment, the pixels which encode the object point in the SLM lie fully outside the area of the subhologram SH, and specifically in this case only particular statistically determined pixels are provided for encoding the object point.

(49) FIG. 8 shows rounded encoding regions KB in conjunction with rectangular or square subholograms SH assigned to the encoding regions KB in representations a) to d).

(50) Representation a) of FIG. 8 shows an example of an encoding region KB which is smaller than the subhologram SH that is obtained from a calculation with the projection method. Schematically shown is an SLM with, in this example, square pixels which are intended to be represented by the gray lines inside the subhologram SH. The subhologram which is calculated by means of the projection method for an object point and is represented by the solid line is, in this example, likewise square and 20×20 pixels in size.

(51) As shown in FIG. 4 with the aid of a section through a subhologram, in the case of larger subholograms there are also differences in the edge region of the subholograms between the calculation with the Fourier transform method and with the projection method—particularly in the graphical representation of FIG. 4, in which the amplitude profile of the Fourier transform method (black curve) has overshoots, but the amplitude profile of the subhologram calculated with the projection method has a constant amplitude.

(52) In two dimensions, in a subhologram configured to be rectangular or square, these differences between the subholograms calculated with the projection method and with the Fourier transform method are particularly large in the corner regions of the subhologram, because here overshoots of the horizontal and vertical amplitude profiles are added together. Simpler calculation of a subhologram with the projection method may generate crosstalk due to higher diffraction orders in the corners. Such perturbing crosstalk may, however, advantageously be reduced when an encoding region is selected which is smaller in its size than the region of the subhologram area calculated by means of the projection method.

(53) In particular, it may be advantageous to select an approximately rounded shape of a subhologram. In the example shown in FIG. 8, the encoding region KB is selected in such a way that a circle is defined with a diameter which corresponds to the edge length of the square subhologram SH, shown here by the dotted line.

(54) Inside the pixel grid, pixels are then selected as associated with the encoding region in such a way that they approximate this circular shape, shown here by the dashed line.

(55) According to representation b) of FIG. 8, a rectangular subhologram SH may in a similar way be replaced with an approximately elliptical encoding region KB, by calculating an ellipse whose major and minor axes correspond to the long and short edge lengths of the rectangle of the subhologram SH.

(56) The invention is not, however, restricted to this case. In general, the diameter of the circle or the axes of the ellipse for the encoding region may also differ from the edge lengths of the subhologram.

(57) The circle diameter or the axes of the ellipse for the encoding region may accordingly also be smaller according to representation c) of FIG. 8 or slightly larger according to representation d) of FIG. 8 than the subhologram. As shown by representation d) of FIG. 8, an encoding region KB could for example be formed or generated in such a way that it is slightly larger than the subhologram SH in the horizontal direction and in the vertical direction, but smaller in the diagonal direction.

(58) Subdivision of a three-dimensional scene S to be reconstructed into depth regions TB.sub.G for calculation of encoding regions KB from subholograms SH with the projection method and other depth regions TB.sub.K for calculation of encoding regions KB from subholograms SH with the Fourier transform method is shown schematically in FIG. 9.

(59) FIG. 9 in this case schematically shows a display D comprising an SLM and a virtual visibility region VW, which may in this case also be referred to as a virtual observer window, through which an observer, shown here by an observer's eye, can observe the reconstructed scene S. The three-dimensional scene S to be reconstructed can be represented in a frustum F, a so-called observer region, which is spanned from the virtual visibility region VW to the SLM, in which case the frustum F may extend backward beyond the SLM, as indicated. The three-dimensional scene S is decomposed into object points Pn. Here, by way of example, the object points P1 to P4 of the three-dimensional scene S are shown. The object points P1 and P3 lie behind the SLM as seen from an observer plane BE. The object points P2 and P4 therefore lie in front of the SLM. As can be seen from FIG. 9, the object points P1 and P2 have larger distances with respect to the SLM than the object points P3 and P4.

(60) The three-dimensional scene S is in this case divided into a depth region TB.sub.G with a larger distance from the SLM, both in front of and behind the SLM, in which for example the object points P1 and P2 lie, and into a depth region TB.sub.K close to the SLM. This is indicated in FIG. 9 by the two thick vertical lines, which are intended to represent the separation planes. For example, the object points P3 and P4 lie in the depth region TB.sub.K close to the SLM. As indicated in FIG. 9, the expression “close to the SLM” may in general mean a different absolute distance in front of the SLM than behind the SLM. For example, the region may be defined by a minimum size of the subhologram in pixels. The depth region TB.sub.K close to the SLM may, for example, be defined in such a way that this depth region TB.sub.K comprises subholograms SH having a horizontal or vertical extent of less than 5 pixels. The 5 pixel extent of the subholograms is generally achieved at a larger distance behind the SLM than in front of the SLM, as seen from the observer plane BE.

(61) For the object points P1 and P2, which are further away from the SLM than the object points P3 and P4 and lie in the depth region TB.sub.G, in this configuration subholograms SH.sub.1 and SH.sub.2 are calculated according to the projection method. For the object points P3 and P4 which have a short distance with respect to the SLM and lie in the depth region TB.sub.K, subholograms SH are calculated according to the Fourier transform method. The encoding regions on the SLM are respectively determined and generated from these subholograms SH, SH.sub.N for the respective object points P.sub.N.

(62) In an alternative configuration, precalculated values may also be taken from a look-up table for the encoding regions of the object points P3 and P4.

(63) FIG. 10 schematically represents the way in which the encoding regions on a curved or bent surface of an SLM can be calculated. In this case, the object points P1 to P4 are again shown, which are in front of or behind the SLM as seen from the observer plane BE. The curved surface of the SLM may be a display which itself has a bent shape. In the context of this description, it may however also be an image of an SLM, for example in a head-up display, which assumes a bent shape because of aberrations of an imaging system provided therein, for example because of field of curvature, even though the physical SLM itself is configured to be flat.

(64) For calculation with the projection method, the position and size of the subhologram on the curved SLM may be determined in a similar way as a flat SLM by tracing rays from the virtual visibility region VW through the object point P.sub.N to the SLM. This is shown schematically in FIG. 10 for the object points P1 to P4 and the associated subholograms SH.sub.1 to SH.sub.4. From the subholograms SH.sub.1 to SH.sub.4, associated encoding regions are then calculated in which the object points P1 to P4 are encoded on the SLM. If it is the case that the encoding region for an object point has the same size or extent and the same shape as the associated subhologram, then in FIG. 10 as well as in FIGS. 9, 11a and 11b the subhologram shown also represents the encoding region.

(65) The phase profile in the subhologram may be determined from the path differences of the rays from the object point to the centers of the various pixels inside the subhologram. From this, an encoding region may then be determined in which the amplitude profile inside the encoding region is selected to be constant and constantly decreasing toward the edge region of the encoding region.

(66) As an alternative, Huygens' wave propagation from the object point to the SLM may be carried out with the sampling respectively of one value per pixel on the SLM. The phase profile then essentially corresponds to the preceding procedure. The amplitude profile is likewise calculated from the wave propagation.

(67) As an alternative, Huygens' wave propagation from the object point to the virtual visibility region and further Huygens' wave propagation from the virtual visibility region to the SLM are also possible.

(68) FIGS. 11a and 11b respectively show a display or an SLM having a very large field of view. In these examples, the field of view is approximately 100 degrees and is shown by the dashed outer lines.

(69) In FIG. 11a, an observer's eye is located in the central region or centrally in front of the SLM and looks through the virtual visibility region VW perpendicularly at the SLM, and likewise perpendicularly at an object point P1. For this object point P1, a subhologram SH.sub.1 is calculated, and an encoding region is calculated therefrom, as would also be the case for an SLM having a small field of view, as for example according to FIG. 9. In particular, the virtual visibility region VW lies in a plane, the observer plane BE, parallel to the SLM.

(70) FIG. 11b shows the same SLM or display with the same position of the observer as in FIG. 11a, but now for the case in which the eye pupil of the eye or the head of the observer moves or rotates in order to observe an object point P2 in the outer region or in the edge region of the field of view. Rotation of the eye pupil of the observer's eye may for example be detected with a camera, so that gaze tracking can be carried out.

(71) The calculation of the hologram of the scene to be reconstructed or of an object may, however, alternatively also be carried out independently of the viewing direction and take into account only the lateral position and the distance of the eye with respect to the SLM so that an observer can observe the edge of the SLM or display from this position deliberately only with a rotated head or eye. In such a case, according to FIG. 11b, the encoding region for an object point P2 may be calculated as if there were a virtual visibility region VW.sub.new tilted relative to the SLM in such a way that the virtual visibility region VW.sub.new is perpendicular to the connecting line of its middle through P2 to the SLM. This leads to a different size of the subhologram SH.sub.2, or also of the encoding region generated therefrom on the SLM, than would be the case when calculating a subhologram or encoding region from a virtual visibility region VW.sub.standard which is parallel to the SLM. This modified size and position of the subhologram and of the encoding region generated therefrom achieves an improved visible reconstruction of the object point P2 for the observer's eye.

(72) Furthermore, in a refined configuration of this exemplary embodiment, it is possible for the calculation of encoding regions on the SLM to be carried out with continuous rotation of the virtual visibility region over the field of view or the region of view.

(73) As an alternative, in another configuration of the exemplary embodiment according to FIG. 11b for rotation of the virtual visibility region VW only large angles of the field of view, for example angles of more than 30 degrees, are taken into account. Alternatively, the field of view may be divided into angle sections, a calculation with a virtual visibility region which is fixed inside the angle section, but optionally tilted, respectively being carried out for these angle sections.

(74) FIG. 12 shows in representation a) a subhologram having a rectangular amplitude profile. This means that the amplitude profile has a constant value inside the subhologram and a value of zero outside the subhologram.

(75) In comparison therewith, an encoding region having an amplitude profile apodized in a sine-squared shape is likewise shown in representation a). In addition, this encoding region is selected here to be slightly larger than the size of the subhologram. The invention is not, however, restricted thereto. This means that the encoding region may also be equal to or smaller than the subhologram, as already described in relation to FIGS. 7 and 8. Instead of a sine-squared-shaped amplitude profile, it is however also possible to use other functions, for example a Gaussian function, in order to generate an apodized amplitude profile.

(76) FIG. 12 shows in representation b) an apodized amplitude profile in an encoding region in conjunction with a subhologram. The use of an apodized amplitude profile may also be combined with a change in the shape of the encoding region in comparison with the subhologram, as shown by way of example in FIG. 8. Thus, for example, for a round or circular encoding region, a radial amplitude profile may also advantageously be used, i.e. an amplitude decreasing radially toward the edge with the distance with respect to the middle of the encoding region in all directions.

(77) Representation b) of FIG. 12 schematically shows for illustration a square subhologram SH, which is shown by means of the dashed line, and in comparison therewith a round encoding region KB with an amplitude constantly decreasing radially from its middle.

(78) In a similar way, encoding regions having an amplitude decreasing elliptically toward the edge region may also be used for rectangularly configured subholograms.

(79) Advantages of the Fourier transform method for calculating and generating subholograms and of the projection method for direct subhologram calculation may therefore be combined according to the invention, if such a combination is advantageous for calculation and generation of a hologram on an SLM for a scene or object to be reconstructed.

(80) The invention is not restricted to the exemplary embodiments represented here. In conclusion, it should yet particularly be pointed out that the exemplary embodiments described above merely serve to describe the teaching claimed, but do not restrict it to the exemplary embodiments.