Hologram calculation method

Abstract

To provide a hologram engine for calculating a hologram of a target picture to be displayed on a display device of an optical system.SOLUTION: The target picture comprises a plurality of image points. Each image point is defined by a light-ray path therefrom to an entrance pupil of a viewer. Each light-ray path makes an angle with a display device 804. The hologram engine determines a first sub-hologram of a first subset of the image points of the target picture by, for each image point of the first subset: a) propagating a wave along a propagation path 830 that makes an angle with the display device less than the angle made by the respective light-ray path; and b) determining a contribution of the wave at the display device for each image point of the first subset.SELECTED DRAWING: Figure 8B

Description

[Technical field]

[0001] The present invention relates to a hologram engine and a corresponding method for computing a hologram. More specifically, the present invention relates to a hologram engine for computing a hologram using a modified point cloud method. Even more specifically, the present invention relates to a hologram engine for computing a hologram by reducing the angle of the propagation path along which a wave propagates. Some embodiments relate to a holographic projector, an image generating unit, or a head-up display. [Background technology]

[0002] Light scattered from an object contains both amplitude and phase information. This amplitude and phase information can be captured, for example, on a photosensitive plate by well-known interference techniques to form a holographic recording, or "hologram," containing interference fringes. The hologram can be reconstructed by illuminating it with appropriate light to form a two- or three-dimensional holographic reconstruction, or reconstructed image, that represents the original object.

[0003] Computer-generated holography numerically simulates interference processes. Computer-generated holograms can be calculated with techniques based on mathematical transformations such as the Fresnel transform or the Fourier transform. These types of holograms are sometimes called Fresnel / Fourier transform holograms, or simply Fresnel / Fourier holograms. Fourier holograms can be viewed as a Fourier domain / planar representation of an object, or a frequency domain / planar representation of an object. Computer-generated holograms may be calculated, for example, with coherent ray tracing or point cloud techniques.

[0004] The computer-generated hologram may be encoded onto a spatial light modulator arranged to modulate the amplitude and / or phase of incident light. Light modulation can be achieved using, for example, electrically addressable liquid crystals, optically addressable liquid crystals, or micromirrors.

[0005] Spatial light modulators are typically composed of multiple individually addressable pixels, also called cells or elements. The light modulation type may be binary, multilevel, or continuous. Alternatively, the device may be continuous (i.e., not composed of pixels), in which case the light modulation is continuous across the device. Spatial light modulators may be reflective, in which case the modulated light is reflected at the output. Spatial light modulators may also be transmissive, in which case the modulated light is transmitted at the output.

[0006] The systems described herein can be used to provide holographic projectors, which have applications in head-up displays (HUDs).

[0007] summary Aspects of the present disclosure are defined in the accompanying independent claims.

[0008] Generally speaking, a hologram engine is provided that computes a hologram of a target image in a counter-intuitive yet computationally efficient manner.

[0009] A hologram engine according to the present disclosure is arranged to calculate a hologram of a target image comprising a plurality of image points. The term "hologram engine" therefore refers to a system (e.g., a computational system, a hologram calculator, a data processor, or an image processor) arranged to determine a hologram of an image. The system may comprise a memory arranged to store a hologram and a means for obtaining a hologram based on the image. The system may comprise a computational chip or a processor arranged to calculate a hologram from the image, for example using an algorithm and / or logic circuit. The input to the hologram engine is the image and the output is a hologram of the image. The "hologram engine" may be realized as a field programmable gate array or an application specific integrated circuit. The hologram engine, and more specifically its algorithm or logic circuit, is configured to do this by virtually / computationally propagating a wave (also referred to herein as a "wavelet") associated with each image point along a propagation path and then determining the contribution of the propagated wave at the display device. Based on the determined / simulated contribution of each image point at the display device, a hologram can be calculated. For example, an array of complex amplitude values ​​of the wave at the intersection of the wave with the display device can be determined. This allows for the computation of a hologram that, when properly illuminated, spatially modulates the light incident thereon to form a holographic wavefront from which an image point or respective image points can be reconstructed. In the computation of a phase-only hologram, an array of phase values ​​for the pixels of a display device can be determined. The hologram engine according to the present disclosure can be described as a point cloud approach to hologram computation. Point cloud hologram computation methods are known. However, the hologram engine according to the present disclosure is configured to compute a hologram in a very unconventional and counter-intuitive way. In particular, the inventors have developed a hologram computation method in which the respective propagation paths of the respective image points of at least a subset of the image points of the target image are modified (e.g., reduced).

[0010] Conventionally, the computation of a point cloud hologram may involve virtually propagating waves from each image point to the center of the observer's entrance pupil (within the display window of the optical system constituting the display device). In other words, conventionally, the waves may propagate along a ray path defined between the image point and the center of the entrance pupil. The computation of the hologram is based on the properties (contributions) of the waves propagating along this ray path at the display device. The propagated waves intersect the display device at an angle depending on the center of the entrance pupil and the location of the respective image point. When the computed hologram is properly illuminated, a holographic wavefront is formed, which reconstructs the simulated / propagated waves to propagate such that each image point is holographically reconstructed and appears at its intended location (as defined by the original target image). In other words, conventionally, if the propagated waves intersect the display device at a certain angle, as long as that angle is within the field of view of the display device, the holographically reconstructed point will appear at a position that depends on that angle within the field of view of the system including the display device. The field of view is typically determined by (at least) a) the wavelength of light used to illuminate the display device, and b) the pitch of the pixels of the display device (i.e., the distance between the centers of adjacent pixels). The smaller the pitch, the wider the field of view. A display device can potentially holographically reconstruct image points only within the angular range of its field of view.

[0011] After extensive simulations and experiments, the inventors have discovered that significant advantages, particularly computational efficiency, can be obtained by modifying the hologram computation method to cause each wave to propagate along a propagation path that is modified or selected to have a smaller angle with the display device. In other words, the angle between the propagation path and the display device may be smaller than the angle between the light ray path and the display device. For example, each propagation path may be selected to pass through the display device approximately normal (i.e., approximately perpendicular or approximately parallel to the normal of the display device). This modification causes the waves to propagate as if the associated image point was translated or shifted or moved from its originally defined position in the target image. For example, the propagation path may be modified as if the image point was translated or shifted or moved closer to the center of the target image (or closer to the field of view of the system). In some examples, the propagation path may be modified as if the image point was translated or shifted or moved to be approximately at the center of the target image (or approximately at the field of view of the system). This may be the case when the respective propagation axes are modified to be approximately perpendicular to the display device. Another way to explain this effect is that the starting point of the (modified) propagation path is no longer the respective image point in the target image (as in the past). Without further processing steps, a hologram calculated using the described modified propagation path may result in a holographic reconstruction of the target image in which the image points are located approximately in the center of the field of view and appear to overlap each other. This may not be an accurate reconstruction of the target image, which may contain image points distributed over a range of angles in the field of view (not simply clustered in the center). In other words, in the modified calculation method according to the present disclosure, a significant amount of position information (which was traditionally encoded in the hologram calculation at the wave propagation stage) is lost. At first glance, this approach is very counterintuitive.

[0012] However, the inventors have recognized that it is particularly advantageous for the waves of the hologram calculation method to be propagated along a propagation path that has a small angle with the display device (e.g., is substantially perpendicular to the display device). The inventors have discovered that when the propagation path is modified in this way, the hologram calculation becomes significantly more efficient. For example, the inventors have recognized that the spatial frequency of a hologram of an image point toward the edge of the field of view of a system including a display device is higher than the spatial frequency of a hologram of an image point toward the center of the field of view. In general, the spatial frequency of a hologram of an image point decreases as the image point approaches the center of the field of view (the angle formed by the path from the display device to the image point becomes relatively small and approaches zero). Spatial frequency may refer to the frequency of the complex amplitude at the display device. In a phase-only hologram, a hologram of a point with a relatively high spatial frequency may have a phase that changes rapidly. For example, the phase of adjacent pixels of a display device displaying the hologram may change by close to π. A hologram of a point with a relatively low spatial frequency may have a phase that changes relatively slowly. For example, the phase of adjacent pixels of a display device displaying a hologram may vary by a relatively small fraction of π. The inventors have recognized that by calculating a hologram using the modified propagation paths of the image points as described above, the spatial frequency of the holograms of those image points can be significantly reduced. Importantly, the inventors have recognized that this allows the initial hologram calculation to be performed at a lower resolution. For example, the complex amplitude / phase of the display device may be sampled for a portion of the pixels of the display device. The inventors have recognized that when the spatial frequency is relatively low, the values ​​of the pixels between the sampled pixels may be filled in using interpolation. The inventors have recognized that when the spatial frequency is relatively high, undersampling and interpolation is not possible. This is because the phase / complex amplitude values ​​at the display device may change very quickly, making the interpolation (very) inaccurate and resulting in (serious) aliasing problems.The above modified propagation path allows for an undersampling and interpolation approach.

[0013] The inventors found that the interpolation is computationally less expensive than earlier hologram calculations, and that undersampling significantly improves the computational speed and efficiency of the hologram calculation. For example, the inventors achieved a 5x improvement in computational efficiency compared to traditional point cloud techniques. Memory requirements were also significantly reduced.

[0014] As the skilled reader will appreciate, it is generally desirable to reduce the computational cost (or increase the computational efficiency) of hologram computation. This is particularly important to realize real-time hologram computation with high quality image resolution. In the context of holographic projectors, such as vehicle head-up displays, it is particularly advantageous to realize this real-time hologram computation with as little computational power as possible. The hologram computation method according to the present disclosure contributes to the realization of this real-time holography.

[0015] As discussed above, the modified propagation path has the effect of computing the hologram as if the image point had been translated. Thus, further processing (i.e., further processing after the propagation and contribution determination steps) may be required after the initial hologram computation to return the image point to its correct position. The inventors have recognized that this further processing can be quickly and easily accomplished by using an appropriate phase ramp / gradient function configured to correct for the change in the position of the image point caused by the modified propagation path. The use of a phase ramp or gradient function to translate an image point (by applying an angular "kick" to the light incident on a display device that displays the function) is well known to those skilled in the art. In some embodiments, two phase ramps may be used. For example, a first phase ramp function may be used to correct for the modification of the propagation path in a first dimension (e.g., the x dimension) and a second phase ramp function may be used to correct for the modification of the propagation path in a second dimension (e.g., the y direction). Furthermore, the inventors have recognized that a subset of image points may be treated as a group in the hologram computation. The propagation paths of the image points in the subset may be changed by the same angle (e.g., in both x and y). Sub-holograms for image points in the subset can be calculated using each of the modified propagation paths. One or more phase ramp functions can then be applied to the sub-holograms. Thus, the one or more phase ramp functions can have the effect of correcting the modified propagation paths of all image points in the subset at once (rather than applying a different phase ramp function for each image point individually). The hologram calculation method can iterate through multiple subsets of sub-holograms and repeat the process with the appropriate phase ramp function, so that the reconstructions are effectively assembled using the phase ramp functions. In other words, different phase ramp functions can be applied to different subsets of image points, but within a subset of image points the same phase ramp function can be applied.

[0016] While removing the position / angle information of points in the hologram calculation and then using a phase ramp function to correct for this (returning the points to their original positions) may seem an unconventional and complicated approach, the inventors have shown that changing the propagation path to reduce the angle it makes with respect to the display device improves the computational efficiency of the hologram calculation with no apparent increase in complexity.

[0017] According to a first aspect, a hologram engine is provided. The hologram engine is for computing a hologram of a target image for display on a display device of an optical system. The target image includes a plurality of image points. Each image point is defined or definable by a first path. The first path or ray path of each image point extends from the image point to an entrance pupil of an observer (e.g., the center of the entrance pupil of the observer). Each first path or ray path can be described as ray traceable between the respective image point and the entrance pupil. Each first path or ray path can be described as connecting or linking the respective image point and the entrance pupil. Each first path or ray path (of each image point) is at an angle with respect to the display device of the optical system. In other words, the first path or ray path can correspond to the propagation path (or second path) of the conventional point cloud hologram computation method described above. However, the hologram engine does not propagate waves along the ray paths. Instead, the hologram engine is arranged to determine, for each image point of the first subset, a first sub-hologram of the first subset of image points of the target image by a) propagating a wave along a second or propagation path that makes a relatively small angle with respect to the display device with respect to the angle of the respective first or ray path, and b) determining, for each image point of the first subset, the contribution of the wave at the display device (characterizing the image point). A second or propagation path that makes a small angle with the display device means that the angle that the second or propagation path makes with respect to the display device is relatively small with respect to the angle that the first or ray path makes with respect to the display device. As mentioned above, propagating the wave along a propagation path that makes a small angle with respect to the display device (for each image point of the first subset) (rather than a ray path to the entrance pupil) significantly improves computational efficiency, since the spatial frequency of the calculated hologram may be relatively low.This allows, for example, the hologram to be first undersampled (e.g., calculated at a lower resolution than the native resolution of the display device), and then using interpolation, a full-resolution hologram can be achieved.

[0018] The hologram engine may be configured to determine or form a hologram of the target image. The determined or formed hologram may include a first sub-hologram. As described in more detail below, the hologram engine may be configured to combine the first sub-hologram with a further sub-hologram as part of determining or forming the hologram. The hologram engine may be configured to output, display or store the hologram of the target image.

[0019] The hologram engine may be configured to display the hologram on a display device, such as a spatial light modulator. In some embodiments, the hologram engine can include a display device. In some embodiments, the display device can be external to the hologram engine. The hologram is configured such that when the hologram is displayed on the display device and appropriately illuminated, a first subset of image points of the target target image is holographically reconstructed. The hologram engine may be configured to store the (determined or formed) hologram in a memory. In some embodiments, the hologram engine comprises the memory. In some embodiments, the memory may be external to the hologram engine.

[0020] Throughout this disclosure, the first path may be referred to as the ray path and vice versa. These terms are used interchangeably. Throughout this disclosure, the second path may be referred to as the propagation path and vice versa. These terms are used interchangeably. As used herein, a description of a first path or a light ray path or a propagation path "at an angle" with a display device refers to an angle defined between a normal to the display device and the light ray path or the propagation path. In some embodiments, the display device may extend in a first dimension and a second dimension. The first dimension may be perpendicular to the second dimension. For example, the display device may be substantially quadrangular (e.g., rectangular or square). A first edge of the display device may extend in the first dimension. A second edge of the display device may extend in the second dimension. In some embodiments, the angle formed between the light ray path or the propagation path and the display device may have a component in at least one of the first dimension or the second dimension. In some embodiments, the angle formed between the light ray path and the propagation path may have a component in both the first dimension and the second dimension.

[0021] In some embodiments, the hologram engine is arranged to add one or more grating functions (also referred to herein as phase ramp functions) to the sub-hologram. As the skilled reader will appreciate, a "grating function" or "phase ramp function" is a function that provides a linear transformation of light at the exit pupil of an optical system, including a display device that displays the function. That is, a grating function or phase ramp function includes an array of light modulation values ​​that, when added to a hologram, linearly displaces the replay field with a defined magnitude and direction. The displacement may be measured in pixels, millimeters, or degrees. A phase ramp is also referred to as a phase wedge. The phase values ​​of a phase ramp may be wrapped (e.g., modulo 2π). A wrapped phase ramp may be considered a phase grating. However, the disclosure is not limited to phase-only modulation, and the terms "grating function," "software grating," and "blazed grating" may be used as examples of beam steering functions, such as wrapped modulation ramps. A phase ramp may be characterized by its phase gradient.

[0022] The one or more grating features may be arranged to compensate for the reduced angle of the propagation path of the image points of the first subset. The one or more grating features may be arranged to reverse the reduced angle of the propagation path of the image points of the first subset. This may be such that when the sub-hologram combined with the one or more grating features is properly illuminated, the image points of the first subset are reconstructed to positions in the field of view of the optical system that correspond to their respective positions in the target image. For example, if the angle of the propagation axis is reduced by 3 degrees in the first dimension during the calculation of the sub-hologram, a grating feature may be selected that increases the angle by 3 degrees in the first dimension to compensate. In other words, the one or more grating features may be selected to return the image points of the first subset to their intended positions (as defined by the target image). In some embodiments, the first grating feature may be arranged to compensate for the reduced angle in the first dimension. The second grating feature may be arranged to compensate for the reduced angle in the second dimension. The one or more grating features may be added to the first sub-hologram.

[0023] In some embodiments, the angles made by each of the propagation paths (i.e. the propagation paths associated with the image points of the first subset) with the display device are reduced by substantially the same amount. In other words, the angles of each of the propagation paths may be reduced by the same amount with respect to each angle made by the first path or ray path with its image point and the display device. Since different first paths or ray paths may be associated with each image point of the first subset and each first path or ray path within the first subset may make (slightly) different angles with respect to the display device, the angles of each of the propagation axes within the subset may also be (slightly) different. By reducing the angles made by each of the propagation axes of the first subset by the same amount, a grating function (or grating functions) can be applied to the sub-hologram in one step to have the effect of moving / translating all image points of the first subset to their intended positions.

[0024] In some embodiments, the propagation paths of at least some (optionally all) of the image points of the first subset do not pass through the center of the entrance pupil. As described above, the ray paths depend on the positions of the entrance pupil and the image points. However, the propagation paths along which the waves associated with the image points of the first subset propagate are at a smaller angle. In effect, this moves the virtual start point of the propagation path. It also has the effect that the virtual end point of the propagation path moves so that it does not pass through the center of the entrance pupil. Similarly, the respective propagation paths associated with the image points of the first subset may be positioned such that the respective waves do not pass through the respective image points.

[0025] In some embodiments, each propagation path for the image points of the first subset passes through a first portion of the target image. In other words, the first portion of the target image may be defined as a portion that includes the image points of the first subset. The distance between the first portion and the center of the target image is less than the distance between the image points of the first subset and said center, and may optionally be less than the distance between any image point of the first subset and the center. In other words, the effect of decreasing the angle between the respective propagation axes and the display device is to move the image points closer to the center of the image. Thus, in some embodiments, each propagation path is positioned as if the respective image points were moved in the target image closer to the center of the target image.

[0026] In some embodiments, the reduced angle of at least one propagation path is substantially equal to zero. As mentioned above, the starting angle of each ray path may be (slightly) different. Therefore, typically, not all reduced propagation paths form an angle of exactly zero. Only one of the propagation paths of the first subset (associated with the first point) may be exactly equal to zero. For example, the propagation path associated with the image point at the center of the image points of the first subset may be reduced to exactly zero. Since the other image points of the points of the first subset are relatively close to the first image point, the propagation path associated with each first image point may be described as being substantially equal to zero.

[0027] In some embodiments, the hologram engine is arranged to initially undersample the first sub-hologram. Undersampling the first sub-hologram means that the pixel values ​​of the hologram are determined at a resolution lower than the native resolution of the display device. This may mean that the values ​​of the first sub-hologram are initially determined for a subset of the pixels of the display device. Between each determined pixel value there may be one or more undetermined pixel values. This undersampling may be performed in a step of determining the contribution of the waves in the display device. Undersampling the hologram has the advantage, as mentioned above, that it is computationally efficient. This may be because determining each pixel value of the hologram at this stage is computationally expensive. By undersampling the number of pixel values ​​that need to be determined may be significantly reduced and thus computationally demanding. The hologram engine may be arranged to interpolate the undersampled first sub-hologram at least in a first dimension of the display device in order to determine values ​​for at least some of the undetermined values ​​of the first sub-hologram. In other words, by interpolation the gaps between the determined values ​​of the first sub-hologram may be filled. The inventors recognize that using interpolation to calculate these "missing" values ​​can be much more computationally efficient than determining the wave contributions of every pixel value (i.e., full resolution). However, the inventors also recognize that this interpolation approach is only viable because the spatial frequency of the waves for every image point at the display device is low (due to the small angles of their propagation paths). Thus, the values ​​on the display device change relatively slowly. Therefore, it is acceptable to initially undersample the pixel values. If the values ​​change relatively quickly, the undersampling and interpolation approach can result in significant aliasing problems.

[0028] In some embodiments, the hologram engine is arranged to divide the target image into a plurality of subsets of image points. Each subset of image points may include a plurality of adjacent image points. Each subset of image points may be defined by a discrete angular range. The angular range may be defined as a discrete angular range from the display device. The subset of image points may be defined by adjacent discrete angular ranges. Each angular range may be substantially equal to the other angular ranges. In other words, the hologram engine may be arranged to divide the target image into a plurality of subsets of image points by dividing the target image into a plurality of equally sized angular ranges. The hologram engine may be arranged to identify image points that fall within each discrete angular range. The plurality of subsets of image points may not overlap. Thus, each image point may be part of a single subset. In some embodiments, the hologram engine is arranged to divide the target image into at least n subsets of image points. n is 2 or more, optionally 5 or more, optionally 10 or more, optionally 50 or more. The n subsets of image points may include the first subset.

[0029] The hologram engine may be arranged to perform, for each of the n (or multiple) subsets of image points, a corresponding calculation as described in relation to the first subset above. For example, the hologram engine may be arranged to determine an nth sub-hologram by determining, for each image point of the nth (or each) subset, a contribution of a wave or wavelet at the display device. Each wave (for each image point of each subset) may be propagated along a propagation path. The respective propagation path may be different from the respective ray path of the respective image point. The respective propagation path may be at a reduced angle with respect to the normal of the display device. The advantages described in relation to the increased computational efficiency in calculating the first sub-hologram also apply to the calculation of each of the n sub-holograms (with reduced propagation paths and reduced angles).

[0030] In some embodiments, the angle between the display device and the propagation path associated with each image point in the nth subset is reduced by substantially the same amount. This corresponds to what has been described in relation to the first subset above. In some embodiments, the reduced angle of at least one propagation path associated with an image point in each of the nth subset is substantially equal to zero. Again, the starting angles of the respective ray paths may be (slightly) different. Thus, typically, not all of the reduced angles formed by the propagation paths in the subsets are exactly zero angles. Only one of the propagation paths of the nth subset (path associated with the first point) may be exactly zero. For example, the propagation path associated with the image point at the center of each of the subsets of n image points may be reduced to be exactly equal to zero. However, since the other image points of the nth subset of points are relatively close to the first image point, the propagation path associated with each first image point may be described as being substantially equal to zero.

[0031] In some embodiments, the hologram engine is arranged to add one or more grating (or phase ramp) features to each of the n sub-holograms, the one or more grating features being arranged to compensate for a reduced angle of the propagation path for the nth subset, in some embodiments the amount of reduction in the angle of the propagation path is different for different subsets.

[0032] The hologram engine may be configured to output a hologram of the target image by combining each of the n sub-holograms (for each of the n subsets of image points). The step of outputting the hologram may further comprise combining a respective grating function (applied to each of the n sub-holograms) with the combined n sub-hologram. The step of combining each of the n sub-holograms and / or each of the grating functions may comprise superimposing said sub-holograms and / or grating functions, for example by summing respective phase values ​​at each pixel of the hologram.

[0033] As described above, the hologram engine may be arranged to divide the target image into at least n subsets, calculate sub-holograms for each of the image points of the n subsets using modified propagation paths (reducing the angle with the display device), and apply one or more gradient functions to compensate for the modified propagation paths. The inventors have recognized that the target image can be divided into an optimized number of subsets of image points. In other words, the target image can be divided into an optimized number of angular ranges. For example, grouping image points into subsets is efficient because an equal reduction in the angle of the propagation axis can be applied to all image points and compensated for by adding the same diffraction grating function or functions. If the subsets are too small (i.e., there are a relatively large number of subsets with a relatively small number of image points), the reduced angle and the diffraction grating function or functions will need to be recalculated frequently. However, if the subsets are too large (i.e., there are a relatively small number of subsets, each with a relatively large number of image points), the memory requirements required to store the contributions of all image points will increase significantly. Furthermore, the larger the subset, the larger the deviation of angles made from zero by some propagation paths (if the angles become smaller). This reduces the ability to undersample those points, which may reduce the computational efficiency gains. The exact number of subsets that is deemed optimal will vary depending on the particular system (e.g., the size of the field of view, the resolution of the target image, the size and type of memory used in the system, and the available processing power). However, the inventors have found that the number of subsets of image points (n) can typically be much greater than 2, much greater than 5, much greater than 10, and even much greater than 50. In one example, the inventors divided a target image into at least 10 arrays and at least 10 subsets and achieved significant computational efficiency gains.

[0034] Some of the above features regarding the extension of the hologram computation method to a plurality of subsets of image points may be summarized as follows: The hologram engine may be arranged to group the image points of the target image into a plurality of subsets of at least n. Each subset may include a group of adjacent image points that are in a discrete angular range. In other words, the hologram engine may be arranged to divide the target image / field of view into a plurality of angular ranges. The hologram engine may be arranged to identify which image points fall in a particular angular range to identify the at least n subsets. The hologram engine may be arranged to compute a sub-hologram for each of the n subsets. For example, the hologram engine may be arranged to iteratively process the n subsets in turn and compute the respective sub-holograms. The sub-hologram of the nth subset of image points may be referred to as the nth sub-hologram. In the sub-hologram computation of each of the n subsets of image points, the hologram engine may be arranged to propagate a wave along a propagation path that makes a relatively small angle with respect to the angle made by the respective ray paths of that image point with respect to the display device. The angles of the propagation paths of each image point in the nth subset may be reduced by the same amount (with respect to each ray path of each image point). Preferably, at least one propagation path associated with an image point in each subset may be at an angle equal to zero with respect to the display device. Preferably, the propagation path associated with each image point in each subset may be at an angle substantially equal to zero with respect to the display device. The hologram engine is further configured to determine, for each image point in the nth subset, a contribution of a wave propagated along the (reduced angle) propagation path. Due to the reduced angles of the propagation paths, the hologram calculation is very computationally efficient. For example, the sub-holograms of each subset may be initially undersampled (e.g., determined at a resolution lower than the native resolution of the display device).The hologram engine may be arranged to interpolate each undersampled sub-hologram to a higher resolution (e.g., to a resolution corresponding to the resolution of the display device or to fill empty hologram pixels). In some embodiments, the hologram engine is arranged to compensate for the reduced angle used during the calculation of the sub-hologram by applying one or more compensating gradient functions to each sub-hologram. For example, two gradient functions may be applied to each sub-hologram. A first gradient function is for compensating in a first dimension (e.g., in the x direction) and a second gradient function is for compensating in a second direction (e.g., in the y direction). The gradient functions may act to move the reconstructions of the image points of each subset in a manner opposite to the effective movement caused by the reduced angle of the propagation axis. The inventors have found that it is more convenient to process subsets of image points in groups, rather than performing a process of determining sub-holograms and adding one or more diffraction grating functions to each image point point by point. This is because one or more diffraction grating functions can be added to the sub-holograms of multiple image points (i.e., all image points in the subset) in one step. The added grating feature or features can therefore effectively compensate for the reduced angles of propagation of all image points in the subset in that one step. The hologram engine may be arranged to apply different gradient functions to different sub-holograms. This may be because the different sub-holograms are sub-holograms of image points with different positions (associated with different angular ranges) in the target image. The angles of the propagation paths used in the different sub-hologram calculations may therefore be reduced by different amounts and therefore different gradient functions may be required to compensate for the reduction. The applied gradient functions are said to effectively stitch together the target image (by pushing / moving the respective subsets of image points back to their correct positions in the field of view when the hologram is reconstructed).Although it may seem (at first glance) counter-intuitive and complex to remove angular information when computing the sub-holograms and then reintroduce this angular information using a gradient function, the inventors have discovered that the computational efficiencies achieved by reducing the angles are significant and outweigh the apparent increase in complexity.

[0035] In a second aspect of the disclosure, a hologram engine is provided for computing a hologram for display on a display device of an optical system. The hologram is a hologram of a target image comprising a plurality of image points. The hologram engine is arranged to determine a first sub-hologram of a first plurality of image points of the target image by determining, for each image point, the contribution of a wave (or wavelet) at the display device. The hologram engine is arranged such that the wave follows a second propagation path from each image point to the display device. The second propagation path of each image point defines a second angle with the normal of the display device, which angle is different (preferably smaller) than the first angle that the first propagation path from each image point to the display device makes with the normal of the first display device. In other words, the angle of the second propagation is changed / smaller with respect to the first propagation path. As explained with respect to the first aspect, this means that the sub-hologram is changing relatively slowly (as the wave propagates with a low spatial frequency). This allows undersampling during the initial computation of the sub-hologram, which greatly improves the computational efficiency of determining the values ​​of the sub-hologram. In effect, modifying the propagation path effectively means that a second propagation path propagates from another point to the initial position of the image point defined in the target image, which corresponds to each image point having a modified position with respect to its initial position in the target image.

[0036] In some embodiments, the second angle is less than the first angle. In some embodiments, the second angle is substantially equal to zero (such that the second propagation paths are substantially perpendicular to the plane of the display device). In some embodiments, the first propagation paths of each image point are arranged to pass through an aperture of the display system within a display window of the optical system. In some embodiments, the second propagation paths of at least some of the image points are arranged not to pass through an aperture of the display system within a display window of the optical system.

[0037] In a third aspect of the present disclosure, a hologram engine is provided for computing a hologram of a target image comprising a plurality of image points. The hologram is suitable for display on a display device of the optical system. The hologram engine is arranged to determine a first sub-hologram of a first plurality of image points of the target image. The hologram engine does this by propagating, for each image point, a wave (or wavelet) along a propagation axis from each image point to the display device. A principal angle associated with each image point is defined between the respective propagation axis and a normal to the display device. Determining the first sub-hologram includes modifying a principal angle of the propagation axis of each image point before propagating the wave. In other words, the hologram engine may be arranged such that, prior to propagation, the principal angle is different from the principal angle used during propagation. The initial principal angle is defined by a propagation axis defined from each image point in a display window of the optical system to the display system. Modifying the principal angle prior to propagation has the effect that each image point is moved from an initial position (defined in the target image) before the wave propagates.

[0038] In some embodiments, modifying the principal angle includes reducing the principal angle of the propagation axis. In some embodiments, reducing the principal angle includes reducing the principal angle to substantially zero. This may result in the propagation axis of each image point being substantially perpendicular to the display device. In some embodiments, the hologram engine is further arranged to determine another diffraction grating function to compensate for the change in the principal angle. A change in the principal angle of the propagation axis of each image point may result in a change in the position of said image point. The one or more diffraction gratings may be configured to return the image point to its original position (when the sub-holograms and the diffraction gratings are appropriately illuminated to form a holographic reconstruction of the target image). The hologram engine may be arranged to combine (e.g., superimpose or simultaneously display) the first sub-hologram with one or more first diffraction gratings.

[0039] In a fourth aspect according to the present disclosure, a hologram engine is provided for computing a hologram of a target image comprising a plurality of image points. The hologram is an optical system including a display device arranged to display the hologram and spatially modulate incident light in accordance with the hologram to form a holographic wavefront at least partially received by an entrance pupil of an observer within an observation window (or eyebox) of the optical system. The hologram engine is arranged to identify a plurality of first image points in a first portion of the target image. For each first image point, the hologram engine is arranged to identify, using ray tracing, a ray propagating from the display device to the entrance pupil through the respective first image point. The hologram engine is further arranged to determine a propagation angle of the ray with respect to a normal (at the display device) of the display device. The hologram engine is further arranged to reduce the propagation angle. The hologram engine is further arranged to determine sub-holograms of the plurality of first image points (e.g., determine an array of complex amplitude or phase values) using the reduced propagation angle of each ray.

[0040] In some embodiments, the hologram engine may be arranged to reduce the propagation angle to approach or substantially equal to zero, such that the light beam of each point is substantially perpendicular to the display device. In other words, the angle may be substantially equal to zero at the display device. The propagation angle of each first image point (first portion of the target image) may be reduced by the same amount. The hologram engine may further be arranged to determine one or more grating functions to compensate for the reduced propagation angle used in determining the sub-holograms. In some embodiments, the hologram engine may further be arranged to combine the sub-holograms with one or more grating functions.

[0041] In a fifth aspect according to the present disclosure, a hologram engine is provided for computing a hologram of a target image comprising a plurality of image points. The hologram may be for display on a display device of an optical system. The hologram engine is arranged to identify a plurality of first image points in a first portion of the target image. The hologram engine is further arranged to relocate (or transform) each first image point from the first portion to a second portion of the target image. The hologram engine is further arranged to determine a first sub-hologram of the relocated first image point (i.e., the first sub-hologram of the relocated first image point when in the second portion). The second portion is located closer to the center of the target image than the first portion. Relocating the first image point to the second portion closer to the center of the target image is advantageous as it means that the image point has been moved to a portion that represents a lower spatial frequency than the first portion. This may mean that the first sub-hologram can be advantageously determined with a lower resolution (i.e., undersampling) compared to the first sub-holograms of the image points in the first portion.

[0042] In a sixth aspect, there is provided a hologram engine for computing a hologram of a target image comprising a plurality of image points. The hologram is displayed on a display device. The hologram engine is arranged to identify a first image point comprised in a first portion of the target image. The hologram engine is further arranged to relocate the first image point from the first portion to a second portion of the target image. The hologram engine is further arranged to determine a first sub-hologram of the relocated first image point. The second portion is located closer to a center of the target image than the first portion.

[0043] The definitions of the fifth and sixth aspects define the invention in terms of a movement of the image point, whereas the definition of the first aspect (and many others) defines the invention in terms of a change in the angle of the propagation path associated with the respective image point. It is clear to the skilled reader that changing the angle of the propagation path has a corresponding effect on the movement of the image point. Thus, the skilled reader will understand that both definitions relate to corresponding concepts. In particular, both the movement of the image point and the change / reduction of the angle of the propagation path have the effect that the spatial frequency of the sub-hologram becomes relatively lower.

[0044] In a seventh aspect, there is provided a method of computing a hologram of a target image for display on a display device of an optical system. The target image includes a plurality of image points. Each image point is defined by a ray path therefrom to an entrance pupil of an observer. Each ray path forms an angle with the display device. The method includes determining a first sub-hologram of a first subset of the image points of the target image. The step of determining the first sub-hologram includes, for each image point of the first subset, a) propagating a wave along a propagation path that forms a relatively small angle with respect to the display device with respect to the angle of the respective ray path, and b) determining, for each image point of the first subset, a contribution of the wave at the display device.

[0045] The method may include determining or forming a hologram of the target image. The determined or formed hologram may include a first sub-hologram. The method may include outputting, displaying, or storing the hologram of the target image.

[0046] The method may include displaying the hologram on a display device, such as a spatial light modulator. The method may include illuminating the hologram, for example illuminating the hologram with light from a light source, such as a laser. The hologram is positioned such that when the hologram is displayed on the display device and appropriately illuminated, a first subset of image points of the target image are holographically reconstructed. Thus, the method may include holographically reconstructing the first subset of image points.

[0047] The method may include storing the (determined or formed) hologram in a memory. In some embodiments, the method further includes adding one or more diffraction grating features to the first sub-hologram, the one or more diffraction grating features being positioned to compensate for the reduced angle of the propagation paths of the image points of the first subset.

[0048] In some embodiments, the method includes identifying or defining a propagation path for each of the first image points prior to propagating the respective waves along the propagation path. The step of identifying or defining the propagation path may include obtaining and modifying the respective ray paths. Modifying the respective ray paths may include reducing an angle that the respective ray paths make with respect to the display device. The angle may be reduced to substantially zero. In other words, the method may include moving each of the image points of the first subset. This is because moving the ray paths has the effect of moving a start point of the ray paths, which may be equivalent to the location of the respective image points. Moving each of the image points of the first subset may involve moving each of the image points closer to a center of the target image. This is because reducing the angle with respect to the display device may have the effect of moving the image points closer to a center of the field of view of the display.

[0049] In some embodiments, the angles between the display device and the propagation paths associated with each image point in the first subset are reduced by substantially the same amount.

[0050] In some embodiments, propagating the waves may include propagating the waves along propagation paths for at least some of the image points of the first subset that do not pass through the entrance pupil. In some embodiments, propagating the waves along propagation paths for the image points of the first subset may include propagating the waves along propagation paths arranged such that each wave does not pass through a respective image point. In some embodiments, each propagation path for the image points of the first subset passes through a first portion of the target image, and a distance between the first portion and a center of the target image is less than a distance between at least one image point of the first subset and the center.

[0051] In some embodiments, determining the first sub-hologram may include initially undersampling the first sub-hologram such that values ​​of the first sub-hologram are initially determined for a subset of pixels of the display device including one or more undetermined pixels between each determined sub-hologram pixel. The method may further include interpolating the undersampled first sub-hologram in at least a first dimension of the display device. The interpolation may be such that values ​​of at least some of the undetermined values ​​of the first sub-hologram are determined.

[0052] In some embodiments, the method includes dividing the target image into at least n subsets of image points, where n is 10 or more. The n subsets may include a first subset. The method may include, for each of the n subsets of image points, determining an nth sub-hologram of the nth subset. This may include, for each image point of the nth subset, determining a wave contribution at the display device. Each wave propagates along a propagation path that makes a relatively small angle with respect to an angle made by each ray path with respect to a normal to the display device. In some embodiments, the angle made by the propagation path associated with each image point in the nth subset with the display device is reduced by substantially the same amount.

[0053] The method is arranged to add one or more diffraction grating features to each sub-hologram of the n subsets, the one or more diffraction grating features being arranged to compensate for the reduced angle of the propagation path of the nth subset. In some embodiments the method of the seventh aspect is a computer-implemented method.

[0054] In an eighth aspect of the present disclosure, there is provided an optical system comprising a display device for displaying a hologram and a processor configured to perform the steps of the method of the seventh aspect.

[0055] In a ninth aspect of the present disclosure there is provided a computer program comprising instructions which, when executed by a computer, cause the computer to perform the steps of the method of the seventh aspect.

[0056] In a tenth aspect of the present disclosure, there is provided a computer readable storage medium comprising instructions which, when executed by a computer, cause the computer to perform the steps of the method of the seventh aspect.

[0057] In an eleventh aspect according to the present disclosure, there is provided an optical system comprising a display device for displaying a hologram and a processor, the processor being configured to perform steps of a method for computing a hologram of a target image for display on the display device of the optical system, the target image comprising a plurality of image points, each image point being defined by a first path therefrom to an entrance pupil of an observer, each first path being at an angle with respect to the display device. The method (which the processor is configured to perform) comprises: determining a first sub-hologram for a first subset of image points of the target image, the determining of the first sub-hologram including, for each image point of the first subset: Propagating the waves along second paths that form a relatively small angle with respect to the respective first paths relative to the display device; and determining, for each image point of the first subset, a contribution of the wave at the display device.

[0058] In a ninth aspect according to the present disclosure, there is provided a computer program comprising instructions that, when executed by a computer, cause the computer to perform steps of a method for computing a hologram of a target image for display on a display device of an optical system. The target image includes a plurality of image points, each image point being defined by a first path therefrom to an entrance pupil of an observer, each first path being at an angle with respect to the display device. The method (which may be executed by a computer program on a computer) comprises: determining a first sub-hologram of a first subset of image points of the target image; Determining the first sub-hologram includes, for each image point of the first subset: Propagating the waves along second paths that form a relatively small angle with respect to the angles of the respective first paths with respect to the display device; and determining, for each image point of the first subset, a wave contribution at the display device.

[0059] In a tenth aspect of the present disclosure, there is provided a computer-readable storage medium comprising instructions that, when executed by a computer, cause the computer to perform the steps of a method for computing a hologram of a target image for display on a display device of an optical system, the target image including a plurality of image points, each image point being defined by a first path therefrom to an entrance pupil of an observer, each first path being at an angle with respect to the display device. The method (which the computer causes to be executed by the instructions) comprises: determining a first sub-hologram of a first subset of image points of the target image; Determining the first sub-hologram includes, for each image point of the first subset: Propagating the waves along second paths that form a relatively small angle with respect to the respective first paths with respect to the display device; and determining, for each image point of the first subset, a contribution of the wave at the display device.

[0060] In this disclosure, the term "replica" is used only to reflect that the spatially modulated light is split and the composite light field is directed along multiple different optical paths. The word "replica" is used to refer to each occurrence or instance of the composite light field after a replication event, such as a partial reflection-transmission by a pupil dilator. Each replica travels along a different optical path. Some embodiments of the present disclosure relate to the propagation of light encoded with a hologram rather than an image, i.e., light spatially modulated with a hologram of an image rather than the image itself. Thus, it can be said that multiple replicas of a hologram are formed. Those skilled in the art of holography will understand that the composite light field associated with the propagation of holographically encoded light varies with the propagation distance. The use of the term "replica" here is independent of the propagation distance, and thus, two branches or paths of light associated with a replication event are still referred to as "replicas" of each other, even if the branches have different lengths. As a result, the composite light field evolves differently along their respective paths. That is, two composite light fields are still considered "replicas" according to the present disclosure, even if they are associated with different propagation distances. provided that they originate from the same replication event or series of replication events.

[0061] A "diffractive light field" or "diffractive light field" according to the present disclosure is a light field formed by diffraction. The diffractive light field may be formed by illuminating a corresponding diffraction pattern. According to the present disclosure, an example of a diffraction pattern is a hologram, and an example of a diffractive light field is a light field forming a holographic light field or a holographic reconstruction of an image. The holographic light field forms a (holographic) reconstruction of an image on a reconstruction plane. The holographic light field propagating from a hologram to a reconstruction plane can be said to include light encoded in the hologram or light within the hologram region. The diffractive light field is characterized by a diffraction angle determined by the minimum feature size of the diffractive structure and the wavelength of the light (of the diffractive light field). According to the present disclosure, a "diffractive light field" can also be said to be a light field forming a reconstruction on a plane spatially separated from a corresponding diffractive structure. An optical system is disclosed herein for propagating the diffractive light field from the diffractive structure to an observer. The diffractive light field can form an image.

[0062] The term "hologram" is used to refer to a recording that contains amplitude or phase information, or a combination thereof, about an object. The term "holographic reconstruction" is used to refer to an optical reconstruction of an object formed by illuminating a hologram. The system disclosed herein is described as a "holographic projector". This is because the holographic reconstruction is a real image and is spatially separated from the hologram. The term "replay field" is used to refer to the 2D region in which the holographic reconstruction is formed and perfectly focused. When a hologram is displayed on a spatial light modulator containing pixels, the replay field is repeated in the form of multiple diffraction orders, each of which is a replica of the zeroth order replay field. The zeroth order replay field is the brightest replay field and therefore generally corresponds to the preferred or primary replay field. Unless explicitly stated otherwise, the term "replay field" is taken to refer to the zeroth order replay field. The term "replay plane" is used to refer to the plane in space that contains all the replay fields. The terms "image", "replayed image", and "image area" refer to the area of ​​the replay field that is illuminated by the light of the holographic reconstruction. In some embodiments, an "image" is made up of individual spots called "image spots" or, for convenience, "image pixels."

[0063] The terms "encoding", "writing" or "addressing" are used to describe the process of providing a plurality of pixels of an SLM with a plurality of control values ​​which each determine the modulation level of a respective pixel. The pixels of the SLM are said to be configured to "display" a light modulation distribution in response to receiving the plurality of control values. The SLM is therefore said to "display" a hologram, and a hologram can be viewed as an array of light modulation values ​​or levels.

[0064] It has been found that holographic reconstructions of acceptable quality can be formed from "holograms" that contain only phase information related to the Fourier transform of the original object. Such holographic recordings are sometimes referred to as phase-only holograms. Although the embodiments relate to phase-only holograms, the present disclosure is equally applicable to amplitude-only holography.

[0065] The present disclosure is equally applicable to forming a holographic reconstruction using amplitude and phase information associated with the Fourier transform of the original object. In some embodiments, this is achieved by complex modulation using a so-called full complex hologram, which contains both amplitude and phase information associated with the original object. Such a hologram may be referred to as a full complex hologram, since the value (gray level) assigned to each pixel of the hologram has an amplitude and a phase component. The value (gray level) assigned to each pixel can be represented as a complex number having both an amplitude and a phase component. In some embodiments, a full complex computer-generated hologram is calculated.

[0066] The phase of a pixel of a computer-generated hologram or spatial light modulator, referred to as a phase value, phase component, phase information, or simply phase, may be referred to as an abbreviation of "phase delay". That is, the phase value described is actually a number (e.g., ranging from 0 to 2π) that represents the amount of phase delay provided by that pixel. For example, a pixel of a spatial light modulator described as having a phase value of π / 2 retards the phase of the received light by π / 2 radians. In some embodiments, each pixel of a spatial light modulator is operable at one of a number of possible modulation values ​​(e.g., phase delay values). The term "gray level" may be used to refer to a number of available modulation levels. For example, the term "gray level" may be used to refer to a number of phase levels available in a phase-only modulator for convenience, even if the different phase levels do not provide different shades of gray. The term "gray level" may also be used to refer to a number of complex modulation levels available in a complex modulator for convenience.

[0067] A hologram is therefore composed of an array of grey levels, i.e. an array of light modulation values, such as an array of phase delay values ​​or complex modulation values. A hologram is also considered a diffraction pattern, since it is a pattern that is displayed on a spatial light modulator and causes diffraction when illuminated with light of a wavelength comparable to (and usually shorter than) the pixel pitch of the spatial light modulator. Here we refer to combining holograms with other diffraction patterns, such as diffraction patterns acting as lenses or gratings. For example, a diffraction pattern acting as a grating can be combined with a hologram to transform the replay field on the replay plane, or a diffraction pattern acting as a lens can be combined with a hologram to focus the holographic reconstruction on the replay plane in the near field.

[0068] In the detailed description that follows, different embodiments and groups of embodiments may be disclosed separately, but any feature of any embodiment or group of embodiments may be combined with any other feature or combination of features of any embodiment or group of embodiments, that is, all possible combinations and permutations of features disclosed in this disclosure are contemplated. [Brief description of the drawings]

[0069] Specific embodiments will now be described, by way of example only, with reference to the following figures:

[0070] [Figure 1] FIG. 1 is a schematic diagram showing a reflective SLM generating a holographic reconstruction on a screen. [Diagram 2] FIG. 2 shows an image for projection that includes cross-sections of eight image regions / components V1-V8 and the corresponding hologram channels H1-H8. [Diagram 3] FIG. 3 shows a hologram displayed on an LCOS that directs light to multiple distinct areas. [Figure 4]FIG. 4 shows a system including a display device for displaying the holograms calculated as shown in FIGS. [Figure 5A] FIG. 5A shows a perspective view of a first example two-dimensional pupil expander that includes two replicators, each including a pair of stacked surfaces. [Figure 5B] FIG. 5B shows a perspective view of a first example two-dimensional pupil dilator that includes two replicators, each in the form of a solid waveguide. [Figure 6] FIG. 6 shows a schematic diagram illustrating a conventional point cloud hologram method. [Figure 7A] FIG. 7A shows a hologram of the first image point of the point cloud of FIG. 6 alone. [Figure 7B] FIG. 7B shows a hologram of another image point in the point cloud of FIG. 6 that is different from the first image point. [Figure 8A] FIG. 8A illustrates a first image point of a point cloud in a point cloud hologram according to the present disclosure, including ray paths extending from the first image point. [Figure 8B] FIG. 8B shows the propagation path that the wave travels to calculate the contribution of the first image point to the hologram. [Figure 9] FIG. 9 shows an undersampled sub-hologram. [Figure 10] FIG. 10 shows the target image. [Figure 11] FIG. 11 is a diagram in which the target image in FIG. 10 is divided into a plurality of cells. [Figure 12] FIG. 12 shows a representation of the holographic reconstruction of the sub-hologram of the first cell of FIG. 11, calculated according to the method of the present invention, before one or more diffraction grating functions have been applied to compensate for the reduced angle of the propagation path used in the calculation.

[0071] The same reference numbers are used throughout the drawings to refer to the same or similar parts.

[0072] Detailed Description of the Embodiments The present invention is not limited to the embodiments described below, but is intended to cover the full scope of the appended claims, i.e., the present invention may be embodied in different forms and should not be construed as being limited to the embodiments set forth for illustrative purposes.

[0073] Singular terms may include the plural unless otherwise specified.

[0074] A structure described as being formed on top / bottom or above / below another structure is intended to include the cases where the structures contact each other and even the cases where a third structure is disposed therebetween.

[0075] When describing temporal relationships, for example when the temporal order of events is described as "after," "successor," "next," "prior," etc., the disclosure should be construed to include sequential and non-sequential events unless otherwise specified. For example, unless words such as "just," "immediately," "directly," etc. are used, the description should be construed to include non-sequential cases.

[0076] In this specification, terms such as "first" and "second" may be used to describe various elements, but these elements are not limited by these terms. These terms are used only to distinguish one element from another element. For example, a first element can be referred to as a second element, and similarly, a second element can be referred to as a first element, without departing from the scope of the appended claims.

[0077] Features of different embodiments may be combined or combined with each other in part or in whole and may interoperate with each other in various ways. Some embodiments may be performed independently of each other or together with interdependencies.

[0078] In the present disclosure, the term "substantially" when applied to a structural unit of an apparatus may be interpreted as meaning that the technical characteristics of the structural unit are produced within the technical tolerances of the method used to manufacture it.

[0079] Conventional optical configuration for holographic projection FIG. 1 shows an embodiment in which a computer-generated hologram is encoded into a single spatial light modulator. A computer-generated hologram is the Fourier transform of an object for reconstruction. Thus, the hologram can be said to be a Fourier domain, frequency domain, or spectral domain representation of the object. In this embodiment, the spatial light modulator is a reflective liquid crystal on silicon (LCOS) device. The hologram is encoded into the spatial light modulator and a holographic reconstruction is formed at a light receiving surface in the replay field, e.g., a screen or diffuser.

[0080] A light source 110, e.g., a laser or laser diode, is arranged to illuminate the SLM 140 through a collimating lens 111. The collimating lens provides an approximately planar wavefront of light incident on the SLM. In FIG. 1, the direction of the wavefront is not perpendicular (e.g., 2 or 3 degrees away from true orthogonal to the plane of the transparent layer). However, in other embodiments, an approximately planar wavefront is provided at normal incidence and a beam splitter arrangement is used to separate the input and output optical paths. In the embodiment shown in FIG. 1, light from the light source is arranged to be reflected off the mirror back surface of the SLM and interact with the light modulating layer to form an exit wavefront 112. The exit wavefront 112 is applied to an optical system including a Fourier transform lens 120 focused on a screen 125. More specifically, the Fourier transform lens 120 receives the modulated beam of light from the SLM 140 and performs a frequency-space transformation to generate a holographic reconstruction on the screen 125.

[0081] Specifically, in this type of holography, each pixel of the hologram contributes to the overall reconstruction: there is no one-to-one correlation between a specific point on the replay field (or image pixel) and a specific light-modulating element (or hologram pixel). In other words, the modulated light leaving the light-modulating layer is distributed throughout the entire replay field.

[0082] In these embodiments, the position of the holographic reconstruction in space is determined by the refractive power (focusing power) of the Fourier transform lens. In the embodiment shown in FIG. 1, the Fourier transform lens is a physical lens. That is, the Fourier transform lens is an optical Fourier transform lens, and the Fourier transform is performed optically. Any lens can function as a Fourier transform lens, but the performance of the lens limits the accuracy of the performed Fourier transform. Those skilled in the art understand how to use lenses to perform an optical Fourier transform. In some embodiments of the present disclosure, the lens of the observer's eye performs the conversion from hologram to image.

[0083] Hologram Calculation In some embodiments, the computer-generated hologram is a Fourier transform hologram, or simply a Fourier hologram, or a Fourier-based hologram, where an image is reconstructed in the far field using the Fourier transform properties of a positive lens. A Fourier hologram is calculated by a Fourier transform that returns the desired light field at the reconstruction plane to the lens plane. A computer-generated Fourier hologram can be calculated using a Fourier transform. The embodiments relate to Fourier holography and GercHberg-Saxton type algorithms by way of example only. The present disclosure is equally applicable to Fresnel holography and Fresnel holograms, which can be calculated in a similar manner. In some embodiments, the hologram is a phase or phase-only hologram. However, the present disclosure is also applicable to holograms calculated by other techniques, such as those based on point cloud methods.

[0084] In some embodiments, the hologram engine is configured to exclude contributions of light blocked by a limiting aperture of the display system from the hologram calculation. UK Patent Application 2101666.2, filed on February 5, 2021 and incorporated herein by reference, discloses a first hologram calculation method using eye tracking and ray tracing to identify sub-areas of a display device for the calculation of a point cloud hologram that eliminates ghost images. The sub-areas of the display device correspond to apertures of the present disclosure and are used to exclude light paths from the hologram calculation. UK Patent Application 2112213.0, filed on August 26, 2021 and incorporated herein by reference, discloses a second method based on a modified GercHberg-Saxton type algorithm, including cropping the light field according to the pupil of the optical system during hologram calculation. The cropping of the light field corresponds to the determination of the limiting aperture of the present disclosure. UK patent application 2118911.3, filed on December 23, 2021, and incorporated herein by reference, discloses a third method of calculating a hologram, which includes determining an area of ​​a so-called extended modulator formed by a hologram replicator. According to this disclosure, the extended modulator area is also an aperture.

[0085] In some embodiments, a real-time engine is provided that is configured to receive image data and use an algorithm to compute a hologram in real-time. In some embodiments, the image data is a video that includes a series of image frames. In other embodiments, the hologram is pre-computed and stored in computer memory and recalled for display on the SLM as required. That is, in some embodiments, a repository of pre-defined holograms is provided.

[0086] Wide viewing angle using small display devices In a broad sense, the present disclosure relates to image projection. The present disclosure relates to an image projector, including a method of image projection and a display device. The present disclosure also relates to a projection system, including an image projector and a display system. In this projection system, the image projector projects or relays light from a display device to the display system. The present disclosure is equally applicable to monocular and binocular display systems. The display system may include an eye or eyes of an observer. The display system includes an optical element having optical power (e.g., a lens in a human eye) and a display surface (e.g., a retina in a human eye). The projector may be referred to as a "light engine." The display device and the image formed (or perceived) using the display device are spatially separated from each other. The image is formed on the display surface or perceived by the observer. In some embodiments, the image is a virtual image, and the display surface may be referred to as a virtual image surface. In other examples, the image is a real image formed by a holographic reconstruction, and the image is projected or relayed to the display surface. In these other examples, spatially modulated light of an intermediate holographic reconstruction formed in free space or on a screen or other light receiving surface between the display device and the observer is propagated to the observer. In both cases, the image is formed by illuminating a diffractive pattern (such as a hologram or kinoform) that is displayed on a display device.

[0087] A display device is made up of pixels. The pixels of a display can display a diffraction pattern or structure that diffracts light. The diffracted light forms an image at a plane spatially distant from the display device. According to well-known optics, the magnitude of the maximum diffraction angle depends on the size of the pixel and other factors such as the wavelength of the light.

[0088] In an embodiment, the display device is a spatial light modulator, such as a liquid crystal on silicon ("LCOS") spatial light modulator (SLM). Light propagates from the LCOS towards a viewing entity / system, such as a camera or an eye, over a range of diffraction angles (e.g., from zero to a maximum diffraction angle). In some embodiments, magnification techniques can be used to expand the range of available diffraction angles beyond the conventional maximum diffraction angle of the LCOS.

[0089] In some embodiments, the (light of) the hologram itself is transmitted to the eye. For example, the spatially modulated light of the hologram (not yet fully converted into a holographic reconstruction, i.e., an image), which may be informally said to be "encoded" by the hologram, is transmitted directly to the observer's eye. The observer may perceive a real or virtual image. In these embodiments, no intermediate holographic reconstruction / image is formed between the display device and the observer. In these embodiments, the lens of the eye is sometimes said to perform the conversion or transformation from hologram to image. The projection system or light engine may be configured such that the observer effectively views the display device directly.

[0090] In the specification, reference is made to a "light field" which is a "complex light field." The term "light field" simply denotes a pattern of light that has finite size in at least two orthogonal spatial directions, e.g., x and y. The term "complex" is used herein only to indicate that the light at each point in the light field is defined by an amplitude and phase value, and thus may be represented by a complex number or pair of values. For the purposes of hologram calculations, a complex light field is a two-dimensional array of complex numbers, where the complex numbers define the intensity and phase of the light at multiple discrete locations in the light field.

[0091] According to well-known principles of optics, the range of angles of light propagated from a display device that can be observed by the eye or other observational object / system depends on the distance between the display device and the observational object. For example, at a viewing distance of one meter, only a small range of angles from the LCOS can pass through the eye's pupil to form an image on the retina at a particular eye position. The range of angles of light rays propagated from the display device that can pass through the eye's pupil to form an image on the retina determines the portion of the image that is "seen" by the observer. In other words, not all portions of the image are visible from any one point on the viewing surface (e.g., any one eye position within a viewing window such as an eye box).

[0092] In some embodiments, the image perceived by the observer is a virtual image displayed upstream of the display device. That is, the observer perceives the image as being farther away than the display device. Conceptually, the observer can be thought of as looking at the virtual image through a very small "display device-sized window", such as 1 cm in diameter, at a relatively large distance, e.g. 1 meter. The user also sees the display device-sized window through a very small eye pupil. The field of view is therefore narrowed, and the particular angular range that can be seen is highly dependent on the eye position at any given time.

[0093] A pupil expander addresses the problem of how to expand the angular range of light rays propagating from a display device and successfully pass through the pupil of the eye to form an image. The display device is typically (relatively) small and the projection distance is (relatively) large. In some embodiments, the projection distance is at least one order of magnitude, e.g., at least two orders of magnitude, larger than the diameter or width of the entrance pupil and / or aperture of the display device (i.e., the size of the pixel array).

[0094] The use of a pupil expander expands the viewing area (i.e., the user's eyebox) laterally, allowing the user to see the image while still allowing some eye movement. As a skilled artisan will appreciate, in an imaging system, the viewing area (user's eyebox) is the area in which the observer's eyes can perceive the image. The present disclosure includes non-infinite virtual image distances, i.e., near-field virtual images.

[0095] Conventionally, a two-dimensional pupil expander consists of one or more one-dimensional light guides, each formed using a pair of opposing reflective surfaces, with output light from the surfaces forming a display window or eyebox. Light received from a display device (e.g., spatially modulated light from an LCOS) is replicated by the or each of the waveguides such that the field of view (or display area) is expanded in at least one dimension. In particular, the waveguides generate additional light rays or "replicas" by amplitude division of the incident wavefront, thus expanding the display window.

[0096] The display device may have an active or display area that is less than 10 cm, e.g., less than 5 cm or less than 2 cm. The propagation distance between the display device and the display system may be more than 1 m, e.g., more than 1.5 m or more than 2 m. The light propagation distance in the waveguide may be up to 2 m, e.g., up to 1.5 m or up to 1 m. The method can receive an image and determine a corresponding hologram of sufficient quality in less than 20 ms, e.g., less than 15 ms or less than 10 ms.

[0097] In some embodiments, described only as examples of diffractive or holographic light fields according to the present disclosure, the hologram is configured to route light into multiple channels, each corresponding to a different portion (i.e., sub-area) of the image. The channels formed by the diffractive structures are referred to herein as "hologram channels" solely to reflect that they are channels of light holographically encoded with image information. The light in each channel is said to be in the hologram domain, rather than the image or spatial domain. In some embodiments, the hologram is a Fourier or Fourier transform hologram, and thus the hologram domain is the Fourier or frequency domain. The hologram may be a Fresnel or Fresnel transform hologram as well. The hologram may be a point cloud hologram. The hologram is described herein as routing light into multiple hologram channels, each corresponding to a respective image sub-area, to reflect that the image that can be reconstructed from the hologram has a finite size and can be arbitrarily divided into multiple image sub-areas. Importantly, the hologram in this example is characterized by how it distributes image content when illuminated. Specifically, a hologram splits the image content by angles; that is, each point on the image is associated with a unique ray angle in the spatially modulated light formed by the hologram when illuminated; or at least a unique pair of angles, since the hologram is two-dimensional. For the avoidance of doubt, the operation of this hologram is unconventional. The spatially modulated light formed by this special type of hologram, when illuminated, may be split into multiple hologram channels, each defined by a range of ray angles (in two dimensions). From the above, it will be understood that the hologram channels (i.e. sub-ranges of ray angles) that may be considered in the spatially modulated light are associated with respective portions or sub-regions of the image.That is, all of the information needed to reconstruct that portion or subregion of the image is contained within a subrange of angles of the spatially modulated light formed from the hologram of the image. When the spatially modulated light is viewed as a whole, there is not necessarily evidence of multiple separate light channels.

[0098] Nevertheless, the hologram is identifiable. For example, if only a continuous portion or sub-region of the spatially modulated light formed by the hologram is reconstructed, only a sub-region of the image should be visible. If a different continuous portion or sub-region of the spatially modulated light is reconstructed, a different sub-region of the image should be visible. A further distinguishing feature of this type of hologram is that the shape of the cross-sectional area of ​​the hologram channel substantially corresponds to (i.e., is substantially the same as) the shape of the entrance pupil, although the size may differ, at least in the correct plane where the hologram was calculated. Each light / hologram channel propagates from the hologram at a different angle or range of angles. These are exemplary ways of characterizing or identifying this type of hologram, although other methods may be used. In summary, the holograms disclosed herein are characterized and identifiable by how the image content is distributed within the light encoded by the hologram. Again, for the avoidance of doubt, references herein to holograms configured to direct light or angularly split an image into multiple holographic channels are made by way of example only, and the present disclosure is equally applicable to any type of holographic light field, as well as any type of diffractive light field or pupil dilation of a diffractive light field.

[0099] The system can be delivered in a compact and streamlined physical form, making it suitable for a variety of real-world applications where space is limited and real estate is at a premium, such as in Head-Up Displays (HUDs) in vehicles and automobiles.

[0100] According to the present disclosure, pupil dilation is provided for diffracted light or diffracted light comprising diverging ray bundles. The diffracted light field is defined by a "light cone". Thus, the size of the diffracted light field (defined on a two-dimensional plane) increases with the propagation distance from the corresponding diffractive structure (i.e., the display device). The pupil dilator can be said to replicate a hologram or form at least one replica of a hologram to convey that the light delivered to the observer is spatially modulated according to the hologram.

[0101] In some embodiments, two one-dimensional waveguide pupil expanders are provided, each one-dimensional waveguide pupil expander arranged to effectively expand the size of the system's exit pupil by forming multiple replicas or copies of the spatial light modulator's exit pupil (or the light at the exit pupil). The exit pupil can be understood to be the physical area where the light is output by the system. It can also be said that each waveguide pupil expander is arranged to expand the size of the system's exit pupil. It can also be said that each waveguide pupil expander is arranged to expand / increase the size of the eyebox where the observer's eyes can be positioned to see / receive the light output by the system.

[0102] Channeling the Light Holograms formed according to some embodiments angularly split the image content to provide multiple hologram channels that can have cross-sectional shapes defined by the aperture of the optical system. The hologram is calculated to provide this channeling of the diffracted light field. In some embodiments, this is accomplished during the hologram calculation by taking into account the aperture (virtual or real) of the optical system, as described above.

[0103] 2 and 3 show examples of this type of hologram that can be used in conjunction with the pupil dilation devices disclosed herein, although this example should not be considered limiting with respect to this disclosure.

[0104] FIG. 2 shows an image 252 for projection that includes eight image regions / components V1 to V8. FIG. 2 shows eight image components as an example, but image 252 can be divided into any number of components. FIG. 2 also shows an encoded light pattern 254 (i.e., a hologram) that can reconstruct image 252 when transformed, for example, by the lenses of an appropriate display system. Encoded light pattern 254 is composed of first to eighth sub-holograms or components H1 to H8 that correspond to the first to eighth image components / regions V1 to V8. FIG. 2 further shows how a hologram resolves image content by angle. Thus, a hologram is characterized by the light channeling it performs. This is illustrated in FIG. 3. Specifically, the hologram in this example directs light to multiple separate regions. The separate regions are disks in the example shown, but other shapes are also envisioned. The size and shape of the optimal disk may be related to the size and shape of the aperture of the optical system, such as the entrance pupil of the observation system, after propagation through the waveguide.

[0105] FIG. 4 shows a system 400 that includes a display device for displaying the holograms calculated as shown in FIGS.

[0106] The system 400 includes a display device, which in this arrangement includes an LCOS 402. The LCOS 402 is arranged to display a modulation pattern (or "diffraction pattern") that includes a hologram and to project the holographically encoded light towards an eye 405 that includes a pupil acting as an aperture 404, a lens 409, and a retina (not shown) that acts as a viewing surface. There is a light source (not shown) arranged to illuminate the LCOS 402. The lens 409 of the eye 405 performs the conversion from the hologram to an image. The light source may be of any suitable type. For example, it may be a laser light source.

[0107] The vision system 400 further comprises a waveguide 408 disposed between the LCOS 402 and the eye 405. The presence of the waveguide 408 ensures that all angular content from the LCOS 402 is received by the eye, even at the relatively long projection distances shown in the figure, because the waveguide 508 acts as a pupil expander. This method is well known and will only be briefly described here.

[0108] Briefly, the waveguide 408 shown in FIG. 4 is comprised of a substantially elongated structure. In this example, the waveguide 408 is comprised of an optical slab of refractive material, although other types of waveguides are well known and may be used. The waveguide 408 is positioned, for example, at an oblique angle, to intersect with the light cone (i.e., the diffracted light field) projected from the LCOS 402. In this example, the size, location, and position of the waveguide 408 are configured such that light from each of the eight ray bundles in the light cone enters the waveguide 408 through a first planar surface of the waveguide 408 (closest to the LCOS 402) and is guided at least partially along the length of the waveguide 408 before being emitted through a second planar surface (closest to the eye) substantially opposite the first surface. As will be well understood, the second planar surface is partially reflective and partially transmissive. In other words, as each ray of light travels from a first plane through the waveguide 408 and strikes a second plane, some of the light is transmitted out of the waveguide 408 and some is reflected off the second plane back to the first plane. The first plane is reflective, so all of the light that strikes the first plane from within the waveguide 408 is reflected to the second plane. Thus, some of the light is refracted between the two planes of the waveguide 408 before being transmitted, while other light is reflected and undergoes one or more reflections (or "bounces") between the planes of the waveguide 408 before being transmitted.

[0109] FIG. 4 shows a total of nine "reflection" points B0 to B8 along the length of the waveguide 408. As shown in FIG. 2, light associated with all points (V1-V8) of the image is transmitted from the waveguide at a respective "reflection" from the second plane of the waveguide 408, but only light from one angular portion of the image (e.g., any light from V1 to V8) has a trajectory that allows it to reach the eye 405 from a respective "reflection" point B0 to B8. Furthermore, light from different angular portions of the image V1 to V8 reaches the eye 405 from a respective "reflection" point. Thus, in the example of FIG. 4, each angular channel of encoded light reaches the eye only once from the waveguide 408.

[0110] The waveguide 408 forms multiple replicas of the hologram at respective "reflection" points B1 to B8 along its length, corresponding to the direction of pupil expansion. As shown in FIG. 5, the multiple replicas are linearly extrapolated to corresponding multiple replica or virtual display devices 402'. This process corresponds to "unfolding" the light paths in the waveguide, where the replica light rays are extrapolated to a "virtual surface" without internal reflections in the waveguide. Thus, the light of the expanded exit pupil is considered to originate from a virtual surface (also referred to herein as an "expansion modulator") that includes the display device 402 and the replica display device 402'.

[0111] Although this specification has generally described virtual images, in which the eye must transform the modulated light it receives to form a perceived image, the methods and arrangements described herein can also be applied to real images.

[0112] 2D pupil dilation Although the arrangement shown in Figure 4 includes a single waveguide that provides pupil dilation in one dimension, pupil dilation can be provided in multiple dimensions, such as two dimensions. Additionally, while the example of Figure 4 uses a hologram calculated to create channels of light that correspond to different portions of an image, this disclosure and the systems described below are not limited to such types of holograms.

[0113] FIG. 5A shows a perspective view of a system 500 that includes two replicators 504, 506 arranged to expand a light beam 502 in two dimensions.

[0114] In the system 500 of FIG. 5A, the first replicator 504 is comprised of a first pair of surfaces stacked parallel to each other and arranged to provide replication (or pupil dilation) similar to the waveguide 408 of FIG. 4. The first pair of surfaces have similar (possibly identical) size and shape to each other and are substantially elongated in one direction. A collimated light beam 502 is directed to the input of the first replicator 504. As will be familiar to the skilled reader, due to the process of internal reflection between the two surfaces and partial transmission of light from each of a number of output points of one of the surfaces (the top surface as shown in FIG. 5A), the light of the light beam 502 is replicated in a first direction along the length of the first replicator 504. Thus, a first number of replica light beams 508 are emitted from the first replicator 504 towards the second replicator 506.

[0115] The second replicator 506 comprises a second pair of surfaces stacked parallel to each other and arranged to receive each of the collimated rays of the first plurality of rays 508 and further arranged to provide a replica, i.e., a pupil dilation, by expanding each of those rays in a second direction substantially perpendicular to the first direction. The first pair of surfaces are of similar (possibly identical) size and shape to each other and are substantially rectangular. The second replicator implements a rectangular shape because it has a length along a first direction to receive the first plurality of rays 508 and a length along a second orthogonal direction to provide a replica in the second direction. Due to a process of internal reflection between the two surfaces and partial transmission of light from each of a plurality of output points of one of the surfaces (the top surface as shown in FIG. 5A), the light of each ray in the first plurality of rays 508 is replicated in the second direction. Thus, a second plurality of light beams 510 is emitted from the second replica device 506, the second plurality of light beams 510 including replicas of the input light beam 502 along each of the first and second directions. The second plurality of light beams 510 can thus be considered to include a two-dimensional grid or array of replica light beams.

[0116] 5A in combination provides a two-dimensional replicator (or a "two-dimensional pupil dilator"). Thus, a replica light beam 510 may be emitted along a light path to an extended eyebox of a display system, such as a head-up display.

[0117] In the system of Figure 5A, the first replicator 504 is a waveguide including a pair of elongated linear reflective surfaces stacked parallel to one another, and similarly, the second replicator 504 is a waveguide including a pair of rectangular reflective surfaces stacked parallel to one another. In other systems, the first replicator is a solid elongated linear waveguide and the second replicator is a solid planar rectangular waveguide, each of which includes a solid optically transparent material such as glass. In this case, the pair of parallel reflective surfaces are formed by a pair of opposing major sidewalls, each of which optionally includes a reflective and a reflective-transmissive surface coating, familiar to the skilled reader.

[0118] FIG. 5B shows a perspective view of a system 500 that includes two replicators 520, 540 arranged to replicate a light beam 522 in two dimensions, the first replicator being a solid, elongated waveguide 520 and the second replicator being a solid, planar waveguide 540.

[0119] In the system of FIG. 5B, the first replicator / waveguide 520 is positioned such that its pair of elongated parallel reflective surfaces 524a, 524b are perpendicular to the plane of the second replicator / waveguide 540. Thus, the system includes an optical coupler positioned to couple light from the output port of the first replicator 520 to the input port of the second replicator 540. In the illustrated arrangement, the optical coupler is a flat / folding mirror 530 positioned to fold and rotate the optical path of the light to achieve the required optical coupling from the first replicator to the second replicator. As shown in FIG. 5B, the mirror 530 is positioned to receive light from the output port / reflective / transmissive surface 524a of the first replicator / waveguide 520, which includes a one-dimensional array of replicas extending in the first dimension. Mirror 530 is tilted at an angle that provides waveguiding and replica formation along its length in the second dimension to redirect the received light onto a light path to an input port of a (fully) reflective surface of second replicator 540. Mirror 530 is one example of an optical element capable of redirecting light in the manner illustrated, and it will be appreciated that one or more other elements may be used instead to perform this task.

[0120] In the illustrated arrangement, the (partially) reflective-transmissive surface 524a of the first replicator 520 is adjacent to the input port of the first replicator / waveguide 520 and receives the input beam 522 at an angle for guiding and replicating along its length in the first dimension. Thus, the input port of the first replicator / waveguide 520 is located at the input end of the same surface as the reflective-transmissive surface 524a. The skilled reader will appreciate that the input port of the first replicator / waveguide 520 may be located in other suitable locations.

[0121] Thus, the arrangement of FIG. 5B allows the first replicator 520 and the mirror 530 to be provided as part of a relatively thin first layer in a plane in the first and third dimensions (illustrated as the xz-plane). In particular, the size or "height" of the first planar layer in which the first replicator 520 is disposed is reduced in the second dimension (illustrated as the y-dimension). The mirror 530 is configured to direct light away from the first layer / plane in which the first replicator 520 is disposed (i.e., the "first planar layer") and to a second layer / plane above and substantially parallel to the first layer / plane in which the second replicator 540 is disposed (i.e., the "second planar layer"). Thus, the overall size or "height" of the system including the first and second replicators 520, 540 and the mirror 530 disposed in the stacked first and second planar layers in the first and third dimensions (illustrated as the xz-plane) is compact in the second dimension (illustrated as the y-dimension). The skilled reader will appreciate that many variations of the arrangement of FIG. 5B are possible and contemplated for implementing the present disclosure.

[0122] The image projector can be arranged to project a diverging or diffracted light field. In some embodiments, the light field is encoded with a hologram. In some embodiments, the diffracted light field comprises a diverging bundle of light rays. In some embodiments, the image formed by the diffracted light field is a virtual image.

[0123] In some embodiments, the first pair of parallel / complementary surfaces are elongated, or elongated, surfaces that are relatively long along a first dimension and relatively short along a second dimension, e.g., relatively short along each of the other two dimensions, each dimension being substantially orthogonal to each of the other dimensions. The process of reflection / transmission of light between the first pair of parallel surfaces is configured such that light propagates within the first waveguide pupil dilator, and the general direction of propagation of the light is the direction in which the first waveguide pupil dilator is relatively long (i.e., its "elongated" direction).

[0124] Disclosed herein is a system that uses diffracted light to form an image and provide an eyebox size and field of view suitable for practical applications (e.g., head-up displays in the automotive industry). Diffracted light is light that forms a holographic reconstruction of an image from a diffractive structure (e.g., a hologram, such as a Fourier or Fresnel hologram). The use of diffraction and diffractive structures requires a high density display device with very small pixels (e.g., 1 micrometer), which in practice means a small display device (e.g., 1 cm). The inventors addressed the problem of how to provide 2D pupil dilation using a diffracted light field (e.g., diffracted light with diverging (non-parallel) ray bundles).

[0125] In some embodiments, the display system includes a pixelated display device, such as a spatial light modulator (SLM) or a liquid crystal on silicon (LCoS) SLM, configured to provide or form diffracted or divergent light. In such an embodiment, the aperture of the spatial light modulator (SLM) is the limiting aperture of the system. That is, the aperture of the spatial light modulator, more specifically, the size of the area that bounds the array of light-modulating pixels contained within the SLM, determines the size (e.g., spatial extent) of the light bundle that can exit the system. According to this disclosure, it is stated that the exit pupil of the system is expanded by the use of at least one pupil expander, reflecting that the exit pupil of the system (limited by a small display device with pixel size for light diffraction) is made larger or larger or larger in spatial extent.

[0126] A diffracting or diverging optical field is said to have an "optical field size" defined in a direction substantially perpendicular to the direction of propagation of the optical field. Because light diffracts / diverges, the optical field size increases with propagation distance.

[0127] In some embodiments, the diffracted light field is spatially modulated according to a hologram. In other words, in such aspects, the diffracted light field comprises a "holographic light field". The hologram may be displayed on a pixelated display device. The hologram may be a computer generated hologram (CGH). It may be a Fourier hologram, a Fresnel hologram, a point cloud hologram, or any other suitable type of hologram. The hologram may optionally be calculated to form channels of holographic light, each channel corresponding to a different respective portion of the image that the observer is intended to see (or perceive, in the case of a virtual image). The pixelated display device may be configured to display multiple different holograms in succession or sequence. Each of the aspects and embodiments disclosed herein may be applied to the display of multiple holograms.

[0128] An output port of the first guide-wave pupil expander may be coupled to an input port of a second guide-wave pupil expander arranged to direct a diffracted light field comprising some, preferably a majority, preferably all, of a replica of the light field output by the first guide-wave pupil expander from its input port to a respective output port by internal reflection between a third pair of parallel surfaces of the second guide-wave pupil expander.

[0129] The first waveguide pupil dilator may be arranged to provide pupil dilation or duplication in a first direction and the second waveguide pupil dilator may be arranged to provide pupil dilation or duplication in a second, different direction. The second direction may be substantially orthogonal to the first direction. The second waveguide pupil dilator may be arranged to maintain the pupil dilation provided by the first waveguide pupil dilator in the first direction and to dilate (or duplicate) a portion, preferably a majority, preferably all, of the duplication received from the first waveguide pupil dilator in a second, different direction. The second waveguide pupil dilator may be arranged to receive the optical field directly or indirectly from the first waveguide pupil dilator. One or more other elements may be provided along a propagation path of the optical field between the first and second waveguide pupil dilators.

[0130] The first waveguide pupil dilator may be substantially elongated and the second waveguide pupil dilator may be substantially planar. The elongated shape of the first waveguide pupil dilator may be defined by a length along a first dimension. The planar, i.e. rectangular, shape of the second waveguide pupil dilator may be defined by a length along a first dimension and a width, i.e. width, along a second dimension substantially orthogonal to the first dimension. The dimension, i.e. length, along the first dimension of the first waveguide pupil dilator corresponds to the length, i.e. width, along the first or second dimension of the second waveguide pupil dilator, respectively. A first surface of the pair of parallel faces of the second waveguide pupil dilator, including the input port, may be shaped, dimensioned and / or positioned to correspond to an area defined by the output ports on the first surface of the pair of parallel faces of the first waveguide pupil dilator, such that the second waveguide pupil dilator is positioned to receive the respective replicas output by the first waveguide pupil dilator.

[0131] The first and second waveguide pupil expanders can jointly provide pupil dilation in a first direction and a second direction perpendicular to the first direction, and optionally a plane containing the first and second directions is substantially parallel to the plane of the second waveguide pupil expander. In other words, the first and second dimensions defining the length and width, respectively, of the second waveguide pupil expander are parallel to the first and second directions (or the second and first directions) in which the waveguide pupil expander provides pupil dilation, respectively. The combination of the first waveguide pupil expander and the second waveguide pupil expander may be generally referred to as a "pupil expander."

[0132] The expansion / duplication provided by the first and second waveguide expanders can be said to have the effect of expanding the exit pupil of the display system in each of two directions. The area defined by the expanded exit pupil defines an expanded eyebox region from which an observer can receive light of the input diffracted or divergent light field. The eyebox region can be said to be located on or define the display surface.

[0133] The two directions in which the exit pupil is expanded may be coplanar or parallel to the first and second directions in which the first and second waveguide pupil expanders provide duplication / magnification. Alternatively, in an arrangement that includes another element, such as the optical combiner, e.g., a windshield (or windscreen) of a vehicle, the exit pupil may be considered as an exit pupil from the other element, such as the windshield. In such an arrangement, the exit pupil may not be coplanar and parallel to the first and second directions in which the first and second waveguide pupil expanders provide duplication / magnification. For example, the exit pupil may be substantially perpendicular to the first and second directions in which the first and second waveguide pupil expanders provide duplication / magnification.

[0134] The field plane and / or eyebox region may be non-coplanar or non-parallel to the first and second directions in which the first and second waveguide pupil dilators provide duplication / dilation. For example, the field plane may be substantially perpendicular to the first and second directions in which the first and second waveguide pupil dilators provide duplication / dilation.

[0135] To provide suitable launch conditions for achieving internal reflection within the first and second waveguide pupil expanders, the elongated dimension of the first waveguide pupil expander may be tilted relative to the first and second dimensions of the second waveguide pupil expander.

[0136] Combiner shape correction An advantage of projecting a hologram into the eyebox is that optical compensation can be encoded into the hologram (see, for example, EP 2 936 252, incorporated herein). The present disclosure is compatible with holograms that compensate for the complex curvature of an optical combiner used as part of a projection system. In some embodiments, the optical combiner is a vehicle windshield. Details of this approach are described in EP 2 936 252, and the detailed features of those systems and methods are not repeated here as they are not essential to the novel teachings of the present disclosure, but are merely illustrative of configurations that would benefit from the teachings of the present disclosure.

[0137] Control device The present disclosure is also compatible with optical configurations including a control device (e.g., an optical shutter device) for controlling the delivery of light from the light channeling hologram to the observer. The holographic projector may further comprise a control device arranged to control the delivery of the angular channel to the eyebox location. UK Patent Application 2108456.1, filed June 14, 2021, and incorporated herein by reference, discloses at least one guided wave pupil expander and a control device. The reader will understand from at least this prior disclosure that the optical configuration of the control device is essentially based on the user's eyebox location and is compatible with any hologram computation method that achieves light channeling as described herein. The control device can be said to be an optical shutter or aperture device. The optical shutter device comprises a 1D array of apertures or windows, each of which is independently switchable between a light-transmitting state and a light-non-transmitting state to control the delivery of the hologram light channel and its replica to the eyebox. Each aperture or window may comprise a plurality of liquid crystal cells or pixels.

[0138] Point cloud hologram calculation FIG. 6 shows a schematic diagram representing a conventional point cloud hologram method. FIG. 6 is composed of a point cloud 602 (i.e., a cloud of image points), a display device 604 (or hologram plane), and an entrance pupil 606. The display device 604 is disposed between the entrance pupil 606 and the point cloud 602, and in this example is a pixelated liquid crystal on silicon spatial light modulator. In this example, the position of the entrance pupil 606 is determined by eye tracking of the observer. The method described here is performed virtually (i.e., it is a simulation). Thus, FIG. 6 is merely representative of what is performed by the computation during the computation of a point cloud hologram. Furthermore, each step of the method is performed virtually. For example, when waves are described as propagating, the waves are not physically propagated through a physical system. Instead, virtual waves are virtually propagated through features of a virtual system. The display device 604 in this example represents a plane on which the hologram will be displayed after it has been computed. As will be explained in more detail below, the goal of the point cloud hologram computation is to determine a hologram that can be (physically) displayed on the display device 604. Thereby, when a hologram is suitably (physically) illuminated with coherent light, a (physical) holographic wavefront is formed which is relayed to the observer's actual entrance pupil, giving the appearance of a holographic reconstruction of a three-dimensional point cloud.

[0139] In this example, point cloud 602 is a three-dimensional point cloud, where the points represent an object or scene. In particular, point cloud 602 represents a target image on which a hologram is calculated. Four image points are shown in FIG. 6: a first image point 610, a second image point 612, a third image point 614, and a fourth image point 616. The first through fourth image points are distributed throughout point cloud 604. This is merely a representative example. It should be understood that typically the point cloud of a point cloud hologram will consist of thousands or millions of image points that represent an image.

[0140] Conventionally, a method for computing a point cloud hologram consists of simulating the propagation of light waves (or wavelets) along propagation paths from each image point of the point cloud 604 towards the center of the entrance pupil 606. The propagation paths from the first to fourth image points 610 to 614 are represented by dashed lines in FIG. 6. A first propagation path 620 extends from the first image point 610 to the entrance pupil 606, a second propagation path 622 extends from the second image point 612 to the entrance pupil 606, a third propagation path 624 extends from the third image point 614 to the entrance pupil 606, and a fourth propagation path 626 extends from the fourth image point 616 to the entrance pupil 606. The skilled reader will be familiar with suitable approaches and algorithms for performing this propagation of light waves.

[0141] It should be noted that the optical system in FIG. 6 is simplified. In most examples, one or more optical components are placed between the point cloud 602 / display device 604 and the observer. The propagation path may pass through one or more of these optical components. For example, the one or more optical components may include one or more lenses, one or more mirrors, and / or wave guides, as previously described. The calculation of the point cloud hologram must take each of these optical components into account when virtually calculating the propagating wave from the image point. Furthermore, FIG. 6 is not drawn to scale. For example, in a head-up display for a vehicle, the distance between the display device 604 and the observer may be one meter or more. The distance from the observer to the point cloud 602 may be even longer.

[0142] After simulating the propagation of the light waves, the next step in the method is to obtain complex values ​​at each point on the (virtual) display device 604 or hologram plane. The display device 604 is pixelated. Conventionally, this step of the method involves determining a complex value for each pixel of the display device 604. In this example, a phase-only hologram is determined and a phase value is extracted from the complex value of each pixel. The skilled reader will be familiar with determining these values. This example is iterative, iterating through each image point. In particular, in each iteration, a light wave is propagated from each image point, a complex value is determined for each pixel of the display device 604, and then a phase value is determined. The phase values ​​for each image point are summed, superimposed, accumulated, or otherwise combined to output a hologram of the target image.

[0143] Improved point cloud hologram calculation method It would be desirable to be able to compute point cloud holograms in real time, such that a sequence of holograms for different target images can be computed and displayed successively at a relatively high frame rate (e.g., at least 30 frames / s) and at a high enough resolution that the holographic reconstructions appear of high quality. It would also be desirable to achieve this with relatively limited computational resources. Vehicle head-up displays may have relatively limited on-board computational resources.

[0144] However, the point cloud hologram computation method described in connection with Figure 6 is computationally very expensive and impractical for real-time computation, especially at high resolutions, and is impractical for devices with relatively limited on-board computational resources. Therefore, the inventors have devised an improved point cloud hologram computation method described herein.

[0145] The inventors have recognized that the spatial frequency of a hologram of an image point depends on the location of that image point within the point cloud hologram. In general, spatial frequency refers to the change in phase and / or intensity of a wavefront / hologram across different locations within a hologram. In this example, the hologram is a phase-only hologram, so spatial frequency refers to the change in phase.

[0146] FIG. 7A shows the hologram of the first image point 610 of FIG. 6 in isolation. FIG. 7B shows the hologram of the third image point 614 of FIG. 6 in isolation. The top pane 702 of FIG. 7A shows the complete hologram of the first image point 610. The bottom pane 704 of FIG. 7A shows a close-up of a portion of the complete hologram of the first image point 610. The top pane 712 of FIG. 7B shows the complete hologram of the third image point 614. The bottom pane 714 of FIG. 7B shows a close-up of a portion of the complete hologram of the third image point 614. Both FIGS. 7A and 7B are in grayscale, and both show how the phase delay applied to a hologram varies spatially. In this example, the phase varies from dark (black), which represents a phase delay of 0, to light (white), which represents a phase delay of 2π.

[0147] As can be seen from Figures 7A and 7B, the spatial frequency of the hologram of the first image point 610 (see Figure 7A) is much higher than the spatial frequency of the third image point 614 (see Figure 7B). In other words, the phase of the hologram of Figure 7A changes much more rapidly than the phase of the hologram of Figure 7B. This difference in spatial frequency is particularly evident when comparing the bottom panes 704, 714 of Figures 7A and 7B. In the bottom pane 704 of Figure 7A, the phase changes by approximately π between adjacent pixel columns. See, for example, the difference in darkness between the first pixel column 706 and the second pixel column 707 of Figure 7A. However, in the bottom pane 714 of Figure 7B (same scale as the bottom pane 704 of Figure 7A), the change in phase is much more gradual. The phase changes very smoothly from approximately 0 to 2π along the entire length of the bottom panel 714.

[0148] The field of view of a pixelated display device (such as display device 604) is limited by the wavelength of light and, more importantly in the context of this disclosure, by the pixel pitch (or pixel size) of the display device. The smaller the pixel pitch, the larger the field of view. Display device 604 can holographically reconstruct only points within its field of view (corresponding to the maximum diffraction angle of the display device). The hologram of the first image point 610 has a very high spatial frequency. This is because the first image point 610 is toward the edge of the point cloud 602. In this example, this corresponds to being near the edge of the field of view of the display device 604, and the propagation axis 620 passes through the display device 604 at an angle close to the diffraction limit of the display device 604. The high spatial frequency is necessary to diffract the light incident thereon to form the reconstructed first image point 610 that is near the edge of the field of view (i.e., close to the diffraction limit of the display device 604). Conversely, the image point 610 is toward the center of the point cloud 602, and the associated wave propagates nearly perpendicular to the display device 604. This means that the spatial frequency is relatively very low (when compared to the hologram of the first image point 610).

[0149] The inventors have recognized that if the spatial frequency of a hologram is low, the hologram can be calculated at a lower resolution than the native resolution of the display device 604. In other words, a hologram with a low spatial frequency may be undersampled with only a portion of the calculated phase values. For example, there may be one or more empty pixel values ​​between each phase value. The inventors have recognized that since the phase of such a hologram varies slowly and smoothly, it is possible to accurately interpolate between the calculated phase values ​​(without aliasing problems) and upscale the hologram to the full resolution of the display device 604. The inventors have utilized this concept in the proposed improved method for computing point cloud holograms, providing a method that is counterintuitive but computationally very efficient.

[0150] The core idea of ​​the method according to the present disclosure is that the propagation path is changed (at least for image points that have a high spatial frequency associated with them). In particular, instead of propagating the wave along the propagation path from the image point towards the entrance (where the propagation path forms a relatively large angle with the display device), a different propagation path is used. The actual propagation path is arranged to form a small angle with the display device 804. This means that the start of the propagation path is not the image point in the target image. Another way to explain this is that the image point is effectively moved in the target image. Figures 8A and 8B show this for a single image point.

[0151] Both Fig. 8A and 8B represent a point cloud hologram calculation for a single image point. Both Fig. 8A and 8B are composed of a point cloud 802 and a display device 804. The entrance pupil is not shown in Fig. 8A and 8B. The point cloud in Fig. 8A is composed of the first image point 610 in Fig. 6, from which ray path 820 extends. Ray path 820 corresponds to the propagation path 620 in Fig. 6, which in this example is a path determined using ray tracing through the display device 804 from the first image point 610 to the entrance aperture (not shown in Fig. 8A). The hologram wave does not propagate along ray path 820. Fig. 8A shows an angle 822 formed by ray path 820 and the normal to the display device 804. The angle 822 is exaggerated in Fig. 8A. The point is that the angle is not zero, but is approaching the diffraction limit of the display device 804.

[0152] FIG. 8B shows the actual propagation path 830 (not the ray path 820) used in the point cloud hologram calculation. The propagation path 830 is positioned to be nearly perpendicular to the display device 804. In other words, the angle 822 is reduced (to nearly zero). This means that the propagation path 830 does not extend from the first image point 610. Instead, the propagation path 830 has a starting point 832, shown by the dashed line in FIG. 8B. As the wave propagates along the propagation path 830, complex and phase values ​​are determined on the display device 604 or in the hologram plane, in a manner familiar to the skilled reader. The calculated complex / phase values ​​are in fact the values ​​of the hologram of the image point at the starting point 832 of the propagation path 830, not the values ​​of the image point at the location of the first image point 610. It can therefore be said that the first image point 610 is effectively moved to the starting point 832 as part of the hologram calculation method. This movement is represented by the arrow 834 in FIG. 8B. The hologram of the image point at starting point 832 will have a comparatively very low spatial frequency and will in fact look similar to the hologram of FIG. 7B.

[0153] Because the hologram calculated in Figure 8B (by propagating waves along propagation path 830) has a low spatial frequency, the calculation of the hologram can undersample the complex / phase values ​​as described above. A portion of the undersampled hologram displayed on display device 804 is shown in Figure 9.

[0154] The grid in FIG. 9 represents pixels of a pixelated display device 804. Each square in the array represents a pixel. The black / filled squares 904 in the array represent pixels for which a complex / phase value has been determined in the initial hologram calculation (following the wave's propagation along the propagation path 830). The white / blank squares 906 represent pixels for which a complex / phase value has not been determined. Each black square 904 is separated from its nearest neighboring black square by four white (blank) squares 906. Thus, FIG. 9 illustrates how undersampling can be used to significantly reduce the number of pixels for which complex / phase values ​​need to be determined during the initial hologram calculation. This saves significant computation time and greatly increases the efficiency of the hologram calculation.

[0155] As mentioned above, the hologram determined in FIG. 8B has a very low spatial frequency. Therefore, using interpolation, the values ​​of the empty squares / pixels 906 can be accurately determined based on the known values ​​of the black squares 904. For example, a bicubic interpolation scheme can be used for the interpolation. This would not be possible if the hologram calculation waves were propagated along ray path 820 instead of propagation path 830, because the high spatial frequency of such a hologram would cause significant aliasing that would make interpolation impractical.

[0156] Without further processing, a properly illuminated hologram calculated as described in connection with FIG. 8B and displayed on a display device will form a reconstruction of a first image point 810 approximately in the center of the system's field of view. This does not coincide with the location of the first image point 810 in the target image, which is located toward the edge of the point cloud 802 (as shown in FIGS. 8A and 8B). The inventors recognize that the original or intended location in the point cloud 802 can be recovered by further processing the hologram to move the reconstructed point. For example, one or more grating functions or phase ramp functions can be added to the hologram. In some examples, a first grating function can be added to the hologram to move the reconstructed point in a first dimension (e.g., in the x-direction) and a second grating function can be added to the hologram to move the reconstructed point in a second dimension (e.g., in the y-direction). The use of phase ramp functions to transform an image point will be familiar to the skilled reader. Since the angular falloff is already known from the hologram calculation process, it is straightforward to select a gradient function or phase ramp function that compensates for the angular falloff of the propagation path 830. Therefore, a phase ramp function that counteracts the falloff can be easily determined / selected.

[0157] To further illustrate the improved method of computing a hologram of a target image, FIGS. 10 through 12 represent the steps of hologram computation for a specific target image (rather than the general single point 610 of FIG. 8B). FIG. 10 shows the target image 1000 of this example. The point clouds of FIGS. 6, 8A, and 8B were shown in the yz plane. This target image 1000 of FIG. 10 is instead in the xy plane. Thus, the view of the target image 1000 of FIG. 10 is effectively a front view of the target image 1000 from the perspective of the viewing system (rather than a side view). Thus, the target image 1000 of FIG. 10 is displayed in two dimensions. However, in some examples, the target image 1000 may have depth in the z direction and therefore may be three-dimensional.

[0158] The target image 1000 in FIG. 10 is for a vehicle head-up display and consists of information useful to the vehicle driver. This includes speed information, the vehicle's state of charge, direction information, etc. The target image 1000 is a point cloud. However, because the target image 1000 is high resolution, the scale of the target image 1000 shown in FIG. 10 does not allow individual image points to be distinguished.

[0159] In this example, the first step in computing a hologram is to divide the target image into multiple parts or cells. Figure 11 shows a target image 1000 divided into an array of cells 1100. In this example, the array of cells 1100 consists of 12x9 cells extending in the x and y directions. In this example, dividing the target image into multiple cells involves defining the angular ranges from the observer to the target image (using ray tracing). Obviously, this step is performed virtually. Adjacent angular ranges are adjacent to each other (touching each other) and do not overlap. In this example, each angular range has equal extent in both the x and y directions.

[0160] The method further includes identifying which image points of the target image 1000 correspond to which cells. In this example, some cells (such as cell 1102) do not contain image points. Other cells (such as cell 1104) do contain image points. The cells that do not contain image points can be effectively ignored in this method. The image points contained in each cell may be referred to as a subset of the image points.

[0161] In this example, the method of computing a hologram includes computing a sub-hologram for each cell (or at least each cell that includes an image point). In other words, the method includes computing a sub-hologram for a subset of image points. Here, the computation of a first sub-hologram for a first cell 1106 is described. The first cell 1106 in FIG. 11 is shaded gray simply to highlight the cell. As can be seen in FIG. 11, the first cell 1106 includes an image point that forms part of a shape that outlines directional information in the target image.

[0162] Calculating or determining a first sub-hologram for a first subset of image points included in the first cell 1106 includes, for each image point of the first subset, propagating a wave along a propagation path that forms a relatively small angle with respect to the display device with respect to the angle made by the respective ray path, and determining a contribution of the wave at the display device for each image point of the first subset.

[0163] This is the same as described in connection with FIG. 8B. Thus, each propagation path does not start from the position of the image point in the first cell 1106, but from a position closer to the center of the target image 1000. In this particular example, the angle of each propagation path is reduced by the same amount. The amount of reduction is selected so that the propagation path of the central image point of the first cell 1106 has a starting point at the center of the target image 1000. As a result of reducing the angle of the propagation path of the image point of the first cell 1106 in this way, the first cell 1106 effectively moves to the center of the target image 1000. In other words, the first sub-hologram determined is a hologram of the first cell 1106 as if the first cell 1106 were located at the center of the target image 1000. Thus, without further processing, when the first sub-hologram is displayed on a display device and properly illuminated, the holographic reconstruction of the first cell 1106 will be located in the center of the field of view, rather than at the position indicated in the target image 1000. This is illustrated in FIG. 12, which shows that the contents of the first cell 1106 are substantially centered.

[0164] As mentioned above, the smaller the angle of the propagation path used in the calculation of the hologram (or sub-hologram) (e.g., substantially equal to zero), the lower the spatial frequency of the hologram. In this example, the sub-hologram is a hologram of a plurality of image points (i.e., the image points that make up the first cell 1106). Thus, the sub-hologram effectively constitutes a superposition of a plurality of individual holograms of each individual point. The hologram of each individual point resembles that shown in FIG. 7B (low spatial frequency), but differs slightly due to the slightly different propagation path of each point (due to the slightly different angles of the different points in the cell). In other words, the hologram of each individual point varies slowly and has a low spatial frequency. As the skilled reader will appreciate, the sum or superposition of multiple slowly varying functions is also a slowly varying function. Thus, the sub-hologram of the plurality of image points of the first cell 1106 also has a low spatial frequency. This means that the sub-holograms can be undersampled and interpolated, as explained in relation to FIG. 9.

[0165] Once the sub-holograms are interpolated, two grating functions are added to the sub-holograms to compensate for the reduced angle of the propagation path. In this example, a first grating function is added to the first sub-hologram to compensate for the reduced angle in the x-direction, and a second grating function is added to the first sub-hologram to compensate for the reduced angle in the y-direction. The influence of the first and second grating functions on the reconstruction of the first sub-hologram (the combination of the first and second grating functions) is represented by the arrows in FIG. 12. In particular, the first arrow 1202 in FIG. 12 represents the translation or shift caused by the first grating function, and the second arrow 1204 in FIG. 12 represents the translation or shift caused by the second grating function. If the original reduction amount (angle of the propagation path during the hologram calculation) was known and was the same for all image points in the first cell 1106, it would be easy to select the first and second grating functions that compensate for this known amount. Furthermore, the first and second grating functions can be applied to the entire sub-hologram of the first cell 1106 (ie, only once) rather than having to apply the grating functions individually to the image points.

[0166] The output of the above description is a sub-hologram of the first cell 1106 in combination with one or more diffraction grating features. It will be apparent to the skilled reader that this process is repeated for each cell (or each cell that contains at least one image point). At each iteration a sub-hologram (in combination with a respective diffraction grating feature) is determined. Said sub-holograms can be combined (or accumulated) to form a hologram of the complete target image. This hologram can be said to contain the information of the sub-hologram of each cell (in combination with the appropriate diffraction grating feature).

[0167] Additional Features The methods and processes described herein may be embodied in a computer-readable storage medium. The term "computer-readable storage medium" includes media configured to store data temporarily or permanently, such as random access memory (RAM), read-only memory (ROM), buffer memory, flash memory, cache memory, etc. The term "computer-readable storage medium" is also intended to include any medium, or combination of media, capable of storing instructions for execution by a machine, which, when executed by one or more processors, cause the machine to perform, in whole or in part, one or more of the methods described herein.

[0168] The term "computer-readable storage medium" also includes cloud-based storage systems. The term "computer-readable storage medium" includes, but is not limited to, one or more tangible, non-transitory data repositories (e.g., data volumes) in the form of, such as, a solid-state memory chip, an optical disk, a magnetic disk, or any suitable combination thereof. In some embodiments, the execution instructions may be carried by a carrier medium. Examples of such carrier media include transitory media (e.g., a propagated signal carrying the instructions).

[0169] It will be apparent to one skilled in the art that various modifications and variations can be made without departing from the scope of the appended claims. This disclosure covers all modifications and variations that come within the scope of the appended claims and their equivalents.

Claims

1. 1. A hologram engine for computing a hologram of a target image for display on a display device of an optical system, the target image comprising a plurality of image points, each image point being defined by a first path therefrom to an entrance pupil of an observer, each first path being at an angle with respect to the display device; The hologram engine, for each image point of a first subset, generates a first sub-hologram of the first subset of image points of the target image: propagating waves along second paths that form a relatively small angle with respect to the angle of each of the first paths relative to the display device; determining, for each image point of the first subset, a contribution of the wave at the display device. Hologram engine.

2. the hologram engine is configured to add one or more diffraction grating features to the first sub-hologram, the one or more diffraction grating features being configured to compensate for a reduced angle of a second path of each of the image points of the first subset. The hologram engine of claim 1 .

3. reducing the angle between the second path associated with each image point in the first subset and the display device by substantially the same amount; 3. The hologram engine according to claim 1 or 2.

4. the second paths for at least some of the image points of the first subset do not pass through the entrance pupil. The hologram engine according to any one of claims 1 to 3.

5. each second path for the image points of the first subset is arranged such that each wave does not pass through each image point; The hologram engine according to any one of claims 1 to 4.

6. each second path for the image points of the first subset passes through a first portion of the target image, the distance between the first portion and a center of the target image being less than a distance between at least one image point of the first subset and the center; The hologram engine according to any one of claims 1 to 5.

7. each second path for the image points of the first subset is arranged as if each of the image points had moved within the target image toward a center of the target image; The hologram engine according to any one of claims 1 to 6.

8. at least one reduced angle of the second path is substantially equal to zero; The hologram engine according to any one of claims 1 to 7.

9. the hologram engine is configured to initially undersample the first sub-hologram such that values ​​of the first sub-hologram are initially determined for a subset of pixels of the display device that includes one or more undetermined pixels between each determined sub-hologram pixel. The hologram engine according to any one of claims 1 to 8.

10. the hologram engine is configured to interpolate the undersampled first sub-hologram in at least a first dimension of the display device to determine values ​​for at least some of the undetermined values ​​of the first sub-hologram. The hologram engine of claim 9.

11. the hologram engine is configured to divide the target image into at least n subsets of image points, n being 10 or greater; The hologram engine according to any one of claims 1 to 10.

12. arranged to determine, for each of said n subsets of image points, an nth sub-hologram for said nth subset by determining a wave contribution at said display device for each image point of said nth subset, wherein each wave propagates along a second path that makes a relatively small angle with respect to a normal to the display device with respect to the angle made by each said first path; The hologram engine of claim 11.

13. reducing the angle between the second path associated with each image point in the nth subset and the display device by substantially the same amount; The hologram engine of claim 12.

14. the hologram engine is configured to add one or more diffraction grating features to the sub-holograms of each of the n subsets, the one or more diffraction grating features being configured to compensate for the reduced angle of the second path for the nth subset. The hologram engine according to claim 12 or 13.

15. the amount by which the angle of each second path is reduced is different for different subsets; The hologram engine according to any one of claims 12 to 14.

16. the hologram engine for dividing the target image into at least n subsets of image points comprises a hologram engine for dividing the target image into a plurality of angular ranges; The hologram engine according to any one of claims 12 to 15.

17. 1. A method of computing a hologram of a target image for display on a display device of an optical system, the target image comprising a plurality of image points, each image point defined by a first path therefrom to an entrance pupil of an observer, each first path forming an angle with respect to the display device; The method includes determining a first sub-hologram of a first subset of the image points of the target image; Determining the first sub-hologram comprises, for each image point of the first subset: propagating waves along second paths that form a relatively small angle with respect to the angle of each of the first paths relative to the display device; and determining, for each image point of the first subset, a contribution of the wave at the display device. method.

18. The method is a computer-implemented method.

20. The method of claim 17.

19. adding one or more diffraction grating features to the first sub-hologram, the one or more diffraction grating features being configured to compensate for the reduced angle of the second path of the image points of the first subset.

19. The method of claim 17 or 18.

20. The method includes dividing the target image into at least n subsets of image points, where n is 10 or greater; For each of the n subsets of image points, the method includes determining an nth sub-hologram for the nth subset; Determining each of the n sub-holograms includes, for each image point of the nth subset: propagating waves along second paths that form a relatively small angle with respect to a normal to the display device with respect to the angle of each of the first paths; determining a contribution of the wave at the display device.

20. The method according to any one of claims 17 to 19.

21. A method for displaying a hologram comprising: a display device for displaying a hologram; and a processor configured to perform the steps of the method according to any one of claims 19 to 20. optical system.

22. A computer program comprising instructions which, when said program is executed by a computer, cause the computer to carry out the steps of the method according to any one of claims 19 to 20. Computer program.

23. comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the method according to any one of claims 19 to 20, A computer-readable storage medium.

Images