Hologram calculation method

Abstract

A hologram engine for calculating a hologram of a target picture comprising a plurality of image points is provided. The hologram engine is arranged to perform a first accumulation comprising, for a first subset of image points: determining a value per nth pixel of a display device for displaying a hologram using a point cloud method; and determining values of at least some other pixels by performing the first interpolation. N is greater than 1. Each image point of the first subset has a correlation diffraction angle for a point cloud method, each diffraction angle being less than a maximum diffraction angle of the display device.

Description

Technical Field

[0001] The present disclosure relates to a hologram engine and a corresponding method for calculating a hologram. More specifically, the present disclosure relates to a hologram engine for calculating a hologram using a point cloud method. Some embodiments relate to a holographic projector, a picture generation unit, or a head-up display. Background Art

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

[0003] Computer generated holography can numerically simulate interference processes. Computer generated holograms can be calculated by techniques based on mathematical transformations such as Fresnel or Fourier transforms. These types of holograms may be referred to as Fresnel / Fourier transform holograms or simply Fresnel / Fourier holograms. Fourier holograms may be considered as Fourier domain / plane representations of objects or frequency domain / plane representations of objects. Computer generated holograms may also be calculated, for example, by coherent ray tracing or point cloud techniques.

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

[0005] A spatial light modulator typically includes a plurality of individually addressable pixels, which may also be referred to as cells or elements. The light modulation scheme may be binary, multi-level, or continuous. Alternatively, the device may be continuous (i.e., not including pixels), and thus the light modulation may be continuous across the device. A spatial light modulator may be reflective, meaning that the light is modulated to be output in reflection. A spatial light modulator may also be transmissive, meaning that the light is modulated to be output in transmission.

[0006] Using the system described here, a holographic projector can be provided. Such projectors are already used in head-up displays "HUD". Summary of the invention

[0007] Various aspects of the disclosure are defined in the accompanying independent claims.

[0008] In summary, a hologram engine for calculating a hologram of a target image in a computationally efficient manner is provided, which allows the hologram engine to include relatively low-cost and low-power hardware while still enabling substantially real-time hologram calculations. In an embodiment, the hologram engine is arranged so that a point cloud method is used to calculate the value of the hologram. However, unlike the conventional use of a point cloud method to calculate the values ​​of all pixels of a hologram, the hologram engine is arranged to undersample the hologram during the point cloud phase of the calculation. This means that the hologram engine is arranged to initially calculate only the hologram values ​​of a subset of pixels of the hologram. For example, the hologram engine may be arranged to initially calculate only the hologram values ​​of every nth pixel, such as every second, third, fourth or fifth pixel. Therefore, each pixel for which a hologram value is initially calculated (using a point cloud method) may be separated by one or more intermediate pixels for which a hologram value is not initially calculated. The hologram engine according to the present invention is then arranged to determine the values ​​of at least some other pixels (i.e., at least some intermediate pixels) by performing interpolation. The inventors have found that interpolation is much less computationally expensive than the initial hologram calculation (using a point cloud method). Therefore, the undersampling and the interpolation significantly increase the computational speed and efficiency of the hologram calculation (compared to calculating the hologram at full resolution using a point cloud approach). The memory requirements of the hologram engine are also significantly reduced. As a skilled reader will understand, it is generally desirable to reduce the computational cost of hologram calculations (or increase computational efficiency). This is particularly important for achieving real-time hologram calculations with high quality image resolution. In the case of a holographic projector, such as a head-up display in a vehicle, it is particularly advantageous to be able to achieve such real-time hologram calculations with as little computing power as possible. The hologram calculation method according to the present disclosure helps to achieve such real-time holography.

[0009] The inventors have realized that undersampling and interpolation methods are only possible when the undersampled hologram has a relatively low spatial frequency. The inventors have realized that when the spatial frequency is very high, undersampling and interpolation are not possible because the phase / complex amplitude values ​​at the display device may change so quickly that the interpolation may be (very) inaccurate and lead to (significant) aliasing problems. Therefore, the hologram engine according to the present invention is arranged so that the point cloud method is applied to the image points so that the hologram calculated in the point cloud method has a relatively low spatial frequency. In particular, the hologram engine according to the present invention is arranged so that the spatial frequency of the resulting hologram (calculated using the point cloud method) is lower than the maximum spatial frequency that can be displayed by the display device. This will be explained in more detail herein.

[0010] Conventionally, point cloud hologram computation may include virtually propagating a wave from each image point to the center of the entrance pupil of the observer (in the viewing window of the optical system including the display device). In other words, conventionally, the wave may propagate along a ray path defined between the image point and the center of the entrance pupil. The hologram computation is then based on the properties (contributions) of the wave propagated along this ray path at the display device. The propagated wave will intersect the display device at an angle that depends on the position of the center of the entrance pupil and the corresponding image point. When the computed hologram is properly illuminated, a holographic wavefront will be formed that propagates in a manner that reconstructs the simulated / propagated wave so that the corresponding image point is holographically reconstructed to appear at the expected position (defined in the original target picture). In other words, if the propagated wave intersects the display device at a particular angle, the holographic reconstruction point will appear in the field of view of the system including the display device at a position that depends on that angle, as long as that angle falls within the field of view of the display device. The field of view is typically determined by (at least) the following: a) the wavelength of the light used to illuminate the display device; and b) the pixel pitch of the display device (i.e., the distance between the centers of adjacent pixels). The smaller the pitch, the larger the field of view. The display device may only be able to holographically reconstruct image points within the angular range of the field of view.

[0011] After thorough simulations and experiments, the inventors have found that the spatial frequency of a hologram of an image point calculated using a conventional point cloud approach will generally depend on the angle between the light path along which the wave propagates and the display device. The spatial frequency may be maximum when the angle formed by the light / propagation path and the display device is equal to the maximum diffraction angle of the display device. The spatial frequency may be lowest when the angle formed by the light / propagation path and the display device is equal to zero (i.e., the propagation path is substantially orthogonal to the display device). Spatial frequency may refer to the frequency of a value (e.g., a complex amplitude) at the display device. In a pure phase hologram, a hologram of a point with a relatively high spatial frequency may have a rapidly changing phase. For example, the phase of adjacent pixels of a display device displaying the hologram may change by nearly π. A hologram of an image point with a relatively low spatial frequency may have a relatively slowly changing phase. For example, the phase of adjacent pixels of a display device displaying the hologram may change by a relatively small fraction of π. Importantly, the inventors have recognized that when a hologram has a low spatial frequency, the initial hologram calculation may be performed at a lower resolution. For example, the complex amplitude / phase at the display device may be sampled for a portion of the pixels of the display device. The inventors have realized that when the spatial frequency is relatively low, interpolation can be used to fill in the values ​​of the (intermediate) pixels between sampled pixels. The inventors have realized that when the spatial frequency is relatively high, undersampling and interpolation are not possible because the phase / complex amplitude values ​​at the display device may change so quickly that the interpolation may be (very) inaccurate and cause (significant) aliasing problems. Therefore, the hologram engine according to the present invention is arranged so that a point cloud method is applied to the image points so that the hologram calculated in the point cloud method has a relatively low spatial frequency.

[0012] The inventors have recognized that the above-described undersampling and interpolated hologram calculation can be used if image points with appropriate associated diffraction angles are selected. In particular, the inventors have found that the undersampling and interpolation can be applied to image points with associated diffraction angles that are less than the maximum diffraction angle of the display device. The associated diffraction angle here may refer to the angle used in the point cloud method. In other words, the associated diffraction angle may refer to the angle of the propagation path used in the point cloud method along which the wave propagates.

[0013] In some embodiments, the hologram engine is arranged to selectively apply undersampling and interpolation methods to image points having an (initial) position in the target picture such that the diffraction angle of the image point is less than the maximum diffraction angle of the display device. In some embodiments, the hologram engine may be arranged to process the image points to reduce the diffraction angle. This may mean translating or moving the image points such that the propagation path / light path from the translated image point forms an angle with the display device that is less than the maximum diffraction angle of the display device. Once the hologram / complex value of the translated image point has been determined (by undersampling and then interpolation as described above), the image point may be pushed back to its original intended position using one or more grating functions. The one or more grating functions may actually be high spatial frequency functions added to a low spatial frequency hologram.

[0014] In some embodiments, the hologram engine can be arranged so that the amount or degree of undersampling depends on the diffraction angle associated with the image point for which the hologram is being calculated. For example, in general, undersampling can be defined as determining the value of every nth pixel of a display device used to display the hologram, where n is an integer greater than 1. In some embodiments, n can increase as the diffraction angle of the image point for which the hologram value is calculated decreases. For example, n may be highest as the diffraction angle approaches zero (or is equal to zero).

[0015] The hologram engine according to the present invention includes additional features that may be optional and help improve computational efficiency and reduce memory usage when implementing the hologram calculation method.

[0016] For example, during a first data processing phase, which may be referred to as a first accumulation, the hologram engine may be arranged to determine the respective values ​​of the nth pixel of each image point in a first subset of image points of the target picture. Thus, for each of the nth pixels, there may be as many values ​​as there are image points in the first subset. The hologram engine may also be arranged to combine (e.g. sum) these values ​​at each of the nth pixels. This may be performed before the first interpolation. The hologram engine may be arranged to perform the first interpolation after the step of determining the combined value. In other words, the interpolation may be performed on the combined value at each pixel. The inventors have recognized that by performing the first interpolation after the combination step, even if the point cloud method has been applied to multiple image points, the first interpolation may only need to be performed once during a single iteration of the first accumulation. This advantageously reduces the computation time of the first accumulation compared to, for example, performing interpolation for each image point in the subset. The inventors recognized that this effect can be achieved because the sum of a finite number of slowly varying functions is typically another slowly varying function. Therefore, the combination of the values ​​of a finite number of holograms with low spatial frequencies (i.e. with slowly varying values) is another hologram with low spatial frequencies. Therefore, the inventors realized that after the combining step it is still possible to perform the interpolation without aliasing problems.The inventors have also developed a specific embodiment of a hologram engine comprising a second and optionally a third accumulation.

[0017] In another example, the inventors have recognized that it may be important to apply the diffraction grating after the corresponding interpolation. In more detail, a first interpolation may be performed in a first dimension / direction (filling in the intermediate pixels separating the nth pixel in the first dimension). The inventors have recognized that if a first grating function for translating light in the first dimension is to be applied, this should be done after the first interpolation. This is because the first grating function may be a relatively high frequency function and should therefore be applied after the first interpolation. Similarly, if a second grating function for translating light in a second dimension perpendicular to the first dimension is to be applied, this should be done after a second interpolation in the second dimension.

[0018] In some examples, it is desirable to apply different raster functions to different subsets of image points. The specific implementations of the first to third accumulators / accumulators described herein achieve this in a computationally efficient manner.

[0019] In a first aspect of the present disclosure, a hologram engine is provided for calculating a hologram of a target picture including a plurality of image points. The hologram can be used for display on a display device including a plurality of pixels (e.g., a pixel array). In other words, the hologram calculated by the hologram can include a plurality of pixel values, each hologram pixel value being used for display on a pixel of the display device. In some embodiments, the pixel array of the display device extends at least in a first dimension. In some embodiments, the pixel array of the display device also extends in a second dimension. The pixel array can be a regular array.

[0020] The hologram engine is arranged to perform a first processing stage, which may be referred to herein as a first accumulation. This may mean that the calculation of a hologram of a target image includes the hologram engine performing a first accumulation. The first accumulation includes determining only the value of every nth pixel of a display device (e.g., the display device described above) using a point cloud method, where n is an integer greater than 1. Therefore, the hologram may be described as undersampled during the point cloud method calculation. This is because, if n is greater than 1, a value may be determined for no more than every other pixel of the display device. The values ​​of the other / remaining pixels may not be determined using the point cloud method.

[0021] The hologram engine is also arranged to determine the values ​​of at least some other pixels by performing a first interpolation. The "other" pixels here refer to pixels whose values ​​are not determined by the point cloud method. Throughout this disclosure, these pixels may also be referred to as "intermediate" pixels. The first interpolation can be based on the values ​​determined using the point cloud method. In other words, the interpolation can include receiving the value of the nth pixel (determined using the point cloud method) and interpolating those values ​​to determine the values ​​of at least some intermediate or "other" pixels. As described above, such undersampling and interpolation can make the calculation of the hologram more efficient, for example, at least twice (or even up to five times) more efficient than determining the value of each pixel using the point cloud method.

[0022] The hologram engine is further arranged such that each image point of the first subset has an associated diffraction angle for the point cloud method that is smaller than the maximum diffraction angle of the display device. As described above, this causes the spatial frequency of the hologram of the image point to be lower than the maximum spatial frequency that can be displayed on the display device. This means that undersampling and interpolation can be performed without causing (significant) aliasing problems.

[0023] The inventors have found that the closer the diffraction angle is to zero, the greater the degree to which the hologram is undersampled when the point cloud method is applied and then interpolated without significant aliasing issues. Therefore, the efficiency gain of calculating holograms according to the present disclosure can increase as the diffraction angle decreases. For example, n can increase as the diffraction angle decreases. For example, when the diffraction angle associated with the image point is close to zero (for example, the image point is substantially orthogonal to the display device), n can be the highest, such as 3 or higher, optionally 5 or higher. This may mean that the hologram engine is arranged to determine the value of only every third or fifth pixel, respectively, using the point cloud method. For larger diffraction angles, n can be lower. For example, for an image point with a diffraction angle equal to half the maximum diffraction angle of the display, n can be equal to 2.

[0024] The hologram engine according to the first aspect has been described above with respect to a single image point. However, the first accumulation will typically be applied to multiple image points (e.g., a first subset of image points). For example, for the first subset of image points, the first accumulation may include: determining the value of each nth pixel of a display device for displaying the hologram using a point cloud method, where n is greater than 1; and determining the values ​​of at least some other pixels by performing a first interpolation. Each image point of the first subset has an associated diffraction angle for the point cloud method, each diffraction angle being less than the maximum diffraction angle of the display device.

[0025] As used herein, the values ​​determined by the hologram engine may be referred to as "complex values" or "holographic values". These values ​​may contain amplitude and / or phase information / values. These values ​​may alternatively refer to the gray level assigned to each pixel. As described above, some of these values ​​(every nth value) are determined using a point cloud method. The skilled person will be familiar with the point cloud method. In general, a hologram engine arranged to perform a point cloud method may include 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 wave propagated at the display device. Based on the contribution determined / simulated for each image point at the display device, a hologram may be calculated. For example, an array of (complex) values ​​of a wave at the intersection of a wave and a display device may be determined. Thereby, a hologram may be calculated which, when properly illuminated, spatially modulates the light incident thereon to form a holographic wavefront that may reconstruct the or each image point. In the calculation of a pure phase hologram, an array of phase values ​​for a pixel of a display device may be determined. Traditionally, in a point cloud approach, these values ​​would be calculated for all pixels of the hologram / display device. The hologram engine according to the present disclosure differs in that only the value of every nth pixel of the display device is calculated (ie, by undersampling the hologram).

[0026] As used herein, accumulation refers to an iterative process as part of a hologram calculation in which multiple values ​​are calculated and combined. For example, a first accumulation may iterate over a first subset of image points. Specifically, for each image point in the first subset of image points, the first accumulation may include calculating a value for each of the nth pixels of the display device. The values ​​calculated in a particular iteration may be combined (e.g., added) with the values ​​calculated in the previous iteration. Thus, at the end of the last iteration, a combined value for each of the nth pixels of the display device may be output. Each combined value (for each pixel) may represent a combination / sum of all values ​​determined at that corresponding pixel of the display device for each image point of the first subset. The hologram may be arranged to perform further accumulations (e.g., second and third accumulations), which will be described in more detail below. The terms accumulation and data processing stage may be used interchangeably. In particular, the first accumulation may be referred to as the first data processing stage. The second accumulation may be referred to as the second data processing stage. The third accumulation may be referred to as the third data processing stage.

[0027] As used herein, the diffraction angle associated with one / each image point refers to the angle made by the propagation path used in the point cloud method and the display device for the image point. In particular, the angle may be the angle between the propagation path and the normal of the display device. As described above, the point cloud method includes determining the contribution of the wave propagating along the propagation path. The determined values ​​(for each of the nth pixels) each represent the contribution of the wave propagating at the pixel. The diffraction angle is less than the maximum diffraction angle of the display device. In some embodiments, the propagation path used in the point cloud method follows the path of the light from the image point. In such an embodiment, a diffraction angle less than the maximum diffraction angle can be achieved by selectively applying the method only to a first subset of pixels, which are positioned at such an angle to the display device. In some embodiments, the hologram engine is arranged to translate or move the starting point of the propagation path to reduce the angle (so that the angle is less than or much less than the maximum angle). This may have the effect of moving the image point. As described above, when the angle is less than the maximum diffraction angle, the spatial frequency of the hologram / determined value will be relatively low, advantageously allowing undersampling and interpolation to have significant aliasing problems. In some embodiments, the diffraction angle may be less than half of the maximum diffraction angle of the display device, optionally less than one quarter of the maximum diffraction angle of the display device, and optionally substantially equal to zero.

[0028] The maximum diffraction angle of the display device may depend on the pixel pitch of the display device. In some embodiments, the maximum diffraction angle may be 2 degrees or greater, optionally 3 degrees or greater. As described above, the maximum diffraction angle may be defined relative to the normal of the display device. This may mean that a display device with a maximum diffraction angle of 2 degrees may have a field of view of 4 degrees. In some embodiments, the diffraction angle associated with the image points of the first subset may be 50% or less of the maximum diffraction angle. For example, the diffraction angle associated with the image points of the first subset may be no greater than 0.5 degrees.

[0029] As used herein, the maximum diffraction angle of a display device refers to the maximum angle at which light can be diffracted or deviate from its original path after interacting with the display device. Therefore, the maximum diffraction angle of a display device can define the size of the field of view and the playback field of the system. The display device may only be able to reconstruct image points within the maximum diffraction angle range. The maximum diffraction angle depends on the wavelength of the incident light (incident on the display device) and the pixel spacing of the display device. As the pixel spacing decreases, the maximum diffraction angle increases. In an embodiment, the pixel spacing of the display device is equal in the first and second dimensions, so the maximum diffraction angles in the first and second dimensions can be substantially equal. Throughout this disclosure, the maximum diffraction angle is defined relative to the normal of the display device. In this way, light can be emitted from the display device within an angle range equal to + / - the maximum diffraction angle.

[0030] In some embodiments, the display device is a spatial light modulator. In some embodiments, the display device is a liquid crystal on silicon spatial light modulator.

[0031] In some embodiments, the hologram engine is arranged so that determining the value of each nth pixel includes: for each image point of the first subset, determining the value of the nth pixel of the display device using a point cloud method; and combining the determined values ​​at each of the nth pixels. In such an embodiment, the first interpolation is based on the combined value determined for each nth pixel. Therefore, the first interpolation can be performed after the step of combining the determined values ​​at each of the nth pixels. As described above, it may be advantageous to perform the first interpolation after the (multiple) values ​​determined for each (hologram) pixel (one value for each image pixel of the first subset) have been combined. This may be because only one interpolation needs to be performed for multiple image points. The inventors have recognized that this is possible because the holographic value for each image point has a low spatial frequency and is therefore a slowly varying function. The combination of a finite number of slowly varying functions can be another slowly varying function. Therefore, the combined value also represents a slowly varying function with a low spatial frequency and may therefore be suitable for performing interpolation without the risk of aliasing problems.

[0032] In some embodiments, the value determined for each image point using the point cloud method is a value representing the contribution of a wave propagating along a path that makes an angle with the display device equal to the associated diffraction angle of the corresponding image point. In other words, the angle formed by the propagation path with the display device is less than the maximum diffraction angle of the display device.

[0033] In some embodiments, the diffraction angle associated with each image point of the first subset is defined by a first path from the image point to an entrance pupil of an observer. This may be the case when using conventional point cloud methods without pre-processing the image points. In such embodiments, the image points of the first subset may be selected so as to be positioned in the target image such that the first path forms an angle less than a maximum diffraction angle of the display device. In other words, the image points of the first subset may not be substantially at the edge of the playback field / field of view. For example, the image points of the first subset may be closer to the center of the target image than to the edge of the target image.

[0034] In some embodiments, the diffraction angle associated with each image point of the first subset is defined by a second path arranged as if the corresponding image point had been moved within the target image closer to the center of the target image. In such embodiments, some pre-processing of the target image may be performed to move the image point closer to the center of the target image. This may cause the angle formed by the second path with the display device to be reduced relative to the angle formed by the corresponding first path for the image point (and less than the maximum diffraction angle of the display device).

[0035] In some embodiments, the maximum diffraction angle of the display device defines a replay field including a central portion surrounded by an outer portion. The central portion may include the center of the replay field. The center of the replay field may be concentric with the center of the central portion. In some embodiments, the central portion occupies less than 75% of the replay field, optionally less than 50% of the replay field, optionally less than 25% of the replay field. The central portion may represent a portion of the replay field where a hologram of a point anywhere in the central portion has a sufficiently low spatial frequency that the hologram values ​​may be initially undersampled and then interpolated without causing significant aliasing issues.

[0036] In some embodiments, the first subset of image points is contained only in a central portion of the replay field. In such embodiments, the diffraction angle associated with each image point of the first subset may be defined by a first path from the image point to an entrance pupil of the observer. In other words, the image points in the central portion of the replay field may not require preprocessing in order to implement undersampling and interpolation methods without significant aliasing issues.

[0037] In some embodiments, the point cloud method is arranged so that it appears as if the first subset of image points have been moved from an outer portion to a central portion of the playback plane. In such an embodiment, the diffraction angle associated with each image point of the first subset may be defined by a path according to the second path described above. In other words, the hologram engine may be arranged to pre-process the first subset of image points so that they are translated or otherwise moved from the outer portion to the central portion (i.e., closer to the center of the playback field). This reduces the angle formed by the second path and the display device relative to the angle formed when the image points were in their original positions. This may result in a corresponding reduction in the spatial frequency of the hologram calculated using the point cloud method.

[0038] In some embodiments, the hologram engine is arranged so that at least some of the pixels whose values ​​are determined using the point cloud method are separated in a first dimension by one or more first intermediate pixels. In such embodiments, the display device may include a pixel array extending in at least the first dimension. In some embodiments, a first interpolation is performed in the first dimension to determine the value of the first intermediate pixel.

[0039] In some embodiments, the first accumulation further comprises applying a first grating function arranged to translate light incident thereon in a first direction parallel to the first dimension. The hologram engine may be arranged such that the first accumulation comprises applying the grating function after performing the first interpolation. In some embodiments, the hologram engine is arranged such that the first grating function is applied to the nth pixel (of the hologram) and the first intermediate pixel.

[0040] In some embodiments, the hologram is for a display device comprising an array of pixels extending in a first dimension and a second dimension different from the first dimension. In some embodiments, the first dimension is perpendicular to the second dimension. In some embodiments, the hologram engine is arranged so that at least some of the pixels whose values ​​are determined using the point cloud method are separated by one or more second intermediate pixels in the second dimension. In some embodiments, the hologram engine is arranged to determine the value of the second intermediate pixels by performing a second interpolation in the second dimension, the hologram engine being arranged to perform the second interpolation after the first interpolation.

[0041] In some embodiments, the hologram engine is arranged to perform a second accumulation. The second accumulation may include receiving the value determined in the first accumulation. When the first accumulation includes a combined value at each pixel, the received value may be the combined value.

[0042] In some embodiments, the hologram engine is arranged to perform a second accumulation comprising repeating the first accumulation for k subset image points of the target image. The second accumulation may also include receiving a corresponding value for each of the k subset image points from the first accumulation. In some embodiments, each of the k subset image points falls within a discrete angle range defined by a first angle in a first dimension and a second angle in a second dimension. The second angle may be the same for each of the k subsets. In other words, each of the k subset image points may together form a row or column. In the same manner as the first subset image points, each image point of the k subset has an associated diffraction angle for the point cloud method, each diffraction angle being less than the maximum diffraction angle of the display device.

[0043] In some embodiments the hologram engine is further arranged to combine the values ​​determined for each of the nth pixel and the first intermediate pixels during the second accumulation period (if any).

[0044] In some embodiments, the second accumulation comprises a second interpolation. The hologram engine may be arranged such that the second interpolation is performed after the step of combining the values ​​determined during the second accumulation. The advantages of this approach are similar to the description of the first accumulation. In particular, this arrangement may advantageously mean that, despite the presence of k subset image points, the second interpolation only needs to be performed once.

[0045] The second accumulation may further comprise applying a second grating function arranged to translate light incident thereon in a second direction parallel to the second dimension.The hologram engine may be arranged such that the second accumulation comprises applying the second grating function after performing the second interpolation.

[0046] The hologram engine may be arranged such that a second grating function is applied to the nth pixel (of the hologram) and to the first and second intermediate pixels.

[0047] In some embodiments, the hologram engine is arranged to perform a third accumulation. The third accumulation may include receiving the value determined in the second accumulation. This may be performed after the combining and interpolation steps.

[0048] In some embodiments, the third accumulation includes repeating the second accumulation for l subset image points of the target image and receiving corresponding values. For each of the l subset image points corresponding to a discrete angle range defined by a first angle in the first dimension and a second angle in the second dimension, the third accumulation also includes, wherein the second angle is different at each repetition of the second accumulation. In the same manner as the first subset image points, each image point of the l subset has an associated diffraction angle for the point cloud method, each diffraction angle being less than a maximum diffraction angle of the display device.

[0049] In some embodiments, the hologram engine is arranged to divide the target picture into a plurality of subset image points by dividing the target picture into a plurality of discrete angular ranges in a first dimension and a second dimension.

[0050] In some embodiments, the hologram engine is arranged to divide the target image into an array of cells. Each cell may contain a subset of image points. For example, each cell may be defined by an angular range in a first and a second dimension. The cell array may extend in a first dimension and a second dimension. In some embodiments, a first accumulation is initially performed on the image points of a first cell of the cell array. A second accumulation may include repeating the first accumulation for each cell in a cell column or row of the cell array including the first cell. A third accumulation may include repeating the first and second accumulations for another of each row or column cells of the cell array.

[0051] The first accumulation may require storing data in a relatively smaller memory than the memory required for the third accumulation (and the second accumulation). However, the memory used in the first accumulation may need to be accessed relatively frequently (e.g., more frequently than the memory used in the third accumulation). Therefore, the inventors have found that it may be beneficial for the hologram engine to use different memories in different accumulations. For example, the first and / or second accumulations may be implemented using registers, while the third accumulation may be implemented using VRAM.

[0052] In a second aspect, a hologram engine for calculating a hologram of a target picture including a plurality of image points is provided. The hologram is for display on a display device including an array of pixels extending in at least a first dimension. The display device has a maximum diffraction angle defined relative to a normal to the display device. This may refer to the maximum diffraction angle in the first dimension.

[0053] The hologram engine is arranged to perform a first accumulation. For each image point in a first subset of image points of the target picture, a value is determined (only) at a first subset of pixels of the display device. In other words, the hologram is undersampled. These values ​​represent the contribution of waves propagating along a path that makes an angle with the display device that is less than a maximum diffraction angle, optionally less than half the maximum diffraction angle.

[0054] At least some of the pixels of the first subset are separated in the first dimension by one or more first intermediate pixels. The first intermediate pixels are complex values ​​of the propagating wave that are initially undetermined. The first accumulation also includes: for each pixel of the first subset, combining the values ​​determined for each image point (if any) at the pixel. Combining may mean superimposing, summing these values. If the value is a complex value, including an imaginary part and a real part, these parts can be combined separately. The first accumulation also includes determining the value of the first intermediate pixel by performing a first interpolation in the first dimension based on the combined values ​​of the first accumulation (for the first subset of pixels).

[0055] In a third aspect, a method for calculating a hologram of a target picture including a plurality of image points is provided. The method comprises performing a first accumulation. For a first subset of image points, the first accumulation comprises: determining a value of each nth pixel of a display device for displaying the hologram using a point cloud method, where n is greater than 1. The first accumulation also comprises determining values ​​of at least some other pixels (whose values ​​are not determined by the point cloud method) by performing a first interpolation (based on the hologram values ​​determined using the point cloud method). Each image point of the first subset has an associated diffraction angle for the point cloud method, each diffraction angle being less than a maximum diffraction angle of the display device (defined relative to a normal of the display device) (optionally, less than half of the maximum diffraction angle of the display device).

[0056] The method is such that determining the value of every nth pixel comprises: for each image point of the first subset, determining the value of the nth pixel of the display device using a point cloud method; and combining the determined values ​​at each of the nth pixels.

[0057] In some embodiments, the first interpolation is based on a combined value determined for every nth pixel.

[0058] In some embodiments, the value determined for each image point using the point cloud method is a value representing the contribution of a wave propagating along a path that makes an angle with the display device equal to the associated diffraction angle of the corresponding image point (i.e., an angle less than the maximum diffraction angle of the display device).

[0059] In some embodiments, the diffraction angle associated with each image point of the first subset is defined as follows: through a first path from the image point to an entrance pupil of an observer; or through a second path arranged as if the corresponding image point had been moved within the target image closer to the center of the target image, so that the angle formed by the second path with the display device is reduced relative to the angle formed by the corresponding first path with the image point (and is less than the maximum diffraction angle of the display device).

[0060] In some embodiments, the maximum diffraction angle of the display device defines a playback field including a central portion surrounded by an outer portion. The central portion may include a center of the playback field. The center of the playback field may be concentric with a center of the central portion. The central portion may occupy less than 75% of the playback field, optionally less than 50% of the playback field, optionally less than 25% of the playback field.

[0061] In some embodiments, the first subset of image points may be contained in a central part of the replay field.In some embodiments, the point cloud method is arranged as if the first subset of image points had been moved from an outer part to a central part of the replay plane.

[0062] In some embodiments, the first accumulation is such that at least some of the pixels whose values ​​are determined using the point cloud method are separated in a first dimension by one or more first intermediate pixels (where the display device includes an array of pixels extending in at least the first dimension). The step of performing the first interpolation can be performed in the first dimension to determine the values ​​of the first intermediate pixels.

[0063] In some embodiments, the first accumulation further comprises the step of applying a first grating function arranged to translate light incident thereon in a first direction parallel to the first dimension. In some embodiments, the method comprises applying the grating function after performing the first interpolation.

[0064] In some embodiments, the hologram engine is arranged such that a first grating function is applied to the nth pixel (of the hologram) and to the first intermediate pixels.

[0065] In some embodiments, the hologram is for a display device comprising an array of pixels extending in a first dimension and a second dimension different from the first dimension (optionally, vertically). In some embodiments, the method is such that at least some of the pixels whose values ​​are determined using the point cloud method are separated by one or more second intermediate pixels in the second dimension. In some embodiments, the method further comprises determining the values ​​of the second intermediate pixels by performing a second interpolation in the second dimension, the hologram engine being arranged to perform the second interpolation after the first interpolation.

[0066] In some embodiments, the method further includes performing a second accumulation. This may be after performing the first accumulation (for the first time). The second accumulation may include receiving the values ​​determined in the first accumulation. This may be after the combining and / or interpolation steps. The second accumulation may further include repeating the first accumulation for a subset of m image points of the target image and receiving corresponding (complex) values. Each of the m subset image points may correspond to a discrete angle range defined by a first angle in the first dimension and a second angle in the second dimension. The second angle may be the same for each of the m subsets, so that the m subsets together form a column or row extending in the first dimension. The method may further include combining the values ​​determined for each of the nth pixel and the first intermediate pixel during the second accumulation. The second accumulation may include a second interpolation.

[0067] The method may be such that the second interpolation is performed after the step of combining the values ​​determined during the second accumulation.The second accumulation may further comprise applying a second grating function arranged to translate light incident thereon in a second direction parallel to the second dimension.

[0068] In some embodiments, the method further comprises performing a third accumulation. The third accumulation may comprise receiving the value determined in the second accumulation. This may be after the combining step of the second accumulation and / or after the second interpolation.

[0069] The third accumulation may include repeating the second accumulation for l subset image points of the target picture. The third accumulation may include receiving a corresponding value for each of the l subsets. Each of the l subset image points may correspond to an image point contained in a discrete angle range defined by a first angle in the first dimension and a second angle in the second dimension. Each time the second accumulation is repeated, the second angle is different.

[0070] The method may include dividing the target image into a plurality of subsets of image points by dividing the target image into a plurality of discrete angular ranges in a first dimension and a second dimension.

[0071] In some embodiments, the method may include dividing the target picture into an array of cells. Each cell may contain a subset of image points. The array of cells may include cells extending in a first dimension and a second dimension. The method may include initially performing a first accumulation on the image points of a first cell of the array of cells. The second accumulation may include repeating the first accumulation for each cell in a cell column or row of the array of cells that includes the first cell. The third accumulation may include repeating the first and second accumulations for each of another of the cell rows or columns of the array of cells.

[0072] In the present disclosure, the term "replica" is used only to reflect that the spatially modulated light is split so that 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 of a pupil expander. Each replica propagates 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 - that is, light that is spatially modulated with a hologram of an image rather than the image itself. Therefore, it can be said that multiple replicas of the hologram are formed. Those skilled in the art of holography will understand that the composite light field associated with the propagation of light encoded with a hologram will vary with the propagation distance. The term "replica" as used herein is independent of the propagation distance, so two light branches or paths associated with a replication event are still referred to as "replicas" of each other, even if the branches have different lengths, so that the composite light field evolves differently along each path. That is, according to the present disclosure, even if two composite light fields are associated with different propagation distances, they are still considered "replicas" - assuming that they originate from the same replication event or series of replication events.

[0073] According to the present disclosure, a "diffraction light field" is a light field formed by diffraction. A diffraction light field can 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 diffraction light field is a holographic light field or a light field of a holographic reconstruction that forms an image. The holographic light field forms a (holographic) reconstruction of an image on a playback plane. The holographic light field propagated from the hologram to the reproduction plane can be said to include light encoded with the hologram or light in the holographic domain. The diffraction light field is characterized by a diffraction angle determined by the minimum characteristic size of the diffraction structure and the wavelength of the light (of the diffraction light field). According to the present disclosure, it can also be said that the "diffraction light field" is a reconstructed light field formed on a plane spatially separated from the corresponding diffraction structure. An optical system for propagating a diffraction light field from a diffraction structure to an observer is disclosed herein. The diffraction light field can form an image.

[0074] The term "hologram" is used to refer to a record containing amplitude information or phase information or some combination thereof about an object. The term "holographic reconstruction" is used to refer to the optical reconstruction of an object formed by illuminating a hologram. The system disclosed herein is described as a "holographic projector" 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 area in which the holographic reconstruction is formed and is fully focused. If the hologram is displayed on a spatial light modulator including pixels, the replay field will be repeated in the form of multiple diffraction orders, each of which is a replica of the zero-order replay field. The zero-order replay field usually corresponds to the preferred or main replay field because it is the brightest replay field. Unless otherwise explicitly stated, the term "replay field" should be considered to refer to the zero-order replay field. The term "replay plane" is used to refer to a plane in space that contains all replay fields. The terms "image", "replay image" and "image area" refer to the area of ​​the replay field illuminated by the light of the holographic reconstruction. In some embodiments, an "image" may include discrete points, which may be referred to as "image points," or, for convenience only, "image pixels."

[0075] The terms "encoding", "writing" and "addressing" are used to describe the process of providing a plurality of pixels of the SLM with a corresponding plurality of control values ​​that respectively determine the modulation level of each pixel. It can be said that the pixels of the SLM are configured to "display" a light modulation distribution in response to receiving the plurality of control values. Thus, the SLM can be said to "display" a hologram, and a hologram can be considered to be an array of light modulation values ​​or levels.

[0076] 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 may be referred to as phase-only holograms. The embodiments relate to phase-only holograms, but the disclosure is equally applicable to amplitude-only holography.

[0077] The present disclosure is also equally applicable to forming a holographic reconstruction using amplitude and phase information related to the Fourier transform of the original object. In some embodiments, this is achieved by using complex modulation of a so-called fully complex hologram that contains amplitude and phase information related to the original object. Because the value (gray level) assigned to each pixel of the hologram has an amplitude and a phase component, such a hologram may be referred to as a fully complex hologram. The value (gray level) assigned to each pixel can be represented as a complex number with an amplitude and a phase component. In some embodiments, a fully complex computer-generated hologram is calculated.

[0078] Reference may be made to the phase value, phase component, phase information, or simply phase, of a pixel of a computer-generated hologram or spatial light modulator as shorthand for "phase delay". That is, any phase value described is actually a number (e.g., in the range of 0 to 2π) representing 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 will delay the phase of the received light by π / 2 radians. In some embodiments, each pixel of the spatial light modulator may be operated at one of a plurality of possible modulation values ​​(e.g., phase delay values). The term "grayscale" may be used to refer to a plurality of available modulation levels. For example, the term "grayscale" may be used for convenience to refer to a plurality of available phase levels in a phase modulator alone, even if the different phase levels do not provide different shades of gray. For convenience, the term "grayscale" may also be used to refer to a plurality of available complex modulation levels in a complex modulator.

[0079] Thus, a hologram comprises an array of gray levels, i.e. an array of light modulation values, such as phase delay values ​​or an array of complex modulation values. A hologram is also considered to be a diffraction pattern, since it is a pattern that causes diffraction when displayed on a spatial light modulator and illuminated with light of a wavelength relative to (usually less than) the pixel pitch of the spatial light modulator. Reference is made herein to combining a hologram with other diffraction patterns, such as a diffraction pattern used as a lens or a grating. For example, a diffraction pattern used as a grating may be combined with a hologram to shift the replay field on the replay plane, or a diffraction pattern used as a lens may be combined with a hologram to focus the holographic reconstruction on the replay plane in the near field.

[0080] Although different embodiments and embodiment groups may be disclosed separately in the following detailed description, any feature of any embodiment or embodiment group may be combined with any other feature or combination of features of any embodiment or embodiment group. That is, all possible combinations and permutations of the features disclosed in this disclosure are contemplated. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Specific embodiments are described by way of example only with reference to the following drawings:

[0082] Figure 1is a schematic diagram showing a reflective SLM producing a holographic reconstruction on a screen;

[0083] Figure 2 An image for projection is shown, comprising eight image regions / components V1 to V8, and corresponding cross-sections of hologram channels H1-H8;

[0084] Figure 3 shows a hologram displayed on an LCOS that directs light to multiple discrete areas;

[0085] Figure 4 Shown includes display such as Figure 2 and 3 A system for displaying a computer generated hologram as shown;

[0086] Figure 5A shows a perspective view of a first example two-dimensional pupil expander comprising two replicators, each replicator comprising a pair of stacked surfaces;

[0087] Figure 5B shows a perspective view of a first example two-dimensional pupil expander comprising two replicators, each in the form of a solid waveguide;

[0088] Figure 6 A schematic diagram representing a conventional point cloud hologram method is shown;

[0089] Fig. 7A Shown separately Figure 6 A hologram of a first image point of a point cloud;

[0090] Figure 7B Shown separately Figure 6 a hologram of another image point different from the first image point in the point cloud;

[0091] Figure 8 An undersampled sub-hologram is shown, where every fifth pixel is sampled;

[0092] Fig. 9 A target picture is shown;

[0093] Fig.10 shows the unit divided into multiple units Fig. 9 Target image;

[0094] Fig.11 The central and outer parts of the target image are shown, where the cells in the central part are shaded gray;

[0095] Fig.12 Another example is shown, which shows a target picture having an outer part and first to third central parts, wherein the grayscale of a cell in the central part is darker as it is closer to the center of the target picture;

[0096] Fig.13A shows a portion of an undersampled sub-hologram, where every other pixel is sampled;

[0097] Fig. 13B shows a portion of an undersampled sub-hologram, where every third pixel is sampled;

[0098] Fig. 13C shows a portion of an undersampled sub-hologram, where every fourth pixel is sampled;

[0099] Fig.14A showing a first image point of a point cloud in a point cloud hologram, including a ray path extending from the first image point;

[0100] Fig. 14B shows the propagation path of the wave propagation used to calculate the contribution of the first image point to the hologram, which is different from Fig.14A The light path of

[0101] Fig.15 A flow chart representing a first accumulation of a single unit applied to a target picture is shown;

[0102] Fig.16A A picture of a target divided into cells is shown, with the first accumulated cell highlighted in grey;

[0103] Fig. 16B shows a portion of an undersampled hologram, where every fifth pixel is sampled;

[0104] Fig. 16C shows that after applying the first interpolation in the x direction Fig. 16B A portion of an undersampled hologram of ;

[0105] Fig.16D Shown by Fig. 16B Holographic reconstruction formed by a hologram of (or 16C);

[0106] Fig.17 A flow chart showing a second accumulation of a row of cells applied to a target picture is shown;

[0107] Fig.18 A flow chart representing a third accumulation applied to an array of rows of cells of a target picture (i.e., applied to multiple rows of cells) is shown;

[0108] Fig.19A shows a target picture divided into units, where Fig.17 The second cumulative cell row is highlighted in grey;

[0109] Fig.19Bshows a portion of an undersampled hologram in which the values ​​of a row of pixels have been determined;

[0110] Fig.19C shows that by interpolating in the y direction Fig.19B A portion of a full-resolution hologram formed by a hologram of

[0111] Fig.19D Shown by Fig.19B Holographic reconstruction formed by a hologram of (or 19C);

[0112] Fig. 20A A picture of the target divided into cells is shown, with the 2D array of cells of the third accumulation highlighted in grey;

[0113] Fig. 20B showing a portion of a full resolution hologram in which values ​​of adjacent pixel blocks have been determined; and

[0114] Fig. 20C Shows Fig. 20B Reconstruction of the hologram.

[0115] The same reference numbers will be used throughout the drawings to refer to the same or like parts. DETAILED DESCRIPTION

[0116] The present invention is not limited to the embodiments described below, but extends to the full scope of the appended claims. That is, the present invention can be implemented in different forms and should not be construed as limited to the described embodiments, which are set forth for illustrative purposes.

[0117] Unless otherwise stated, terms in the singular may include plural forms.

[0118] A structure described as being formed on / under another structure or above / below another structure should be construed to include the case where the structures are in contact with each other and, further, also include the case where a third structure is provided therebetween.

[0119] When describing a temporal relationship, for example, when the temporal order of events is described as "after," "subsequently," "next," "before," etc., the present disclosure should be considered to include both sequential and non-sequential events unless otherwise specified. For example, unless terms such as "just," "immediately," or "directly" are used, the description should be considered to include non-sequential situations.

[0120] Although the terms "first", "second", etc. may be used herein to describe various elements, these elements are not limited by these terms. These terms are only used to distinguish between various elements. For example, a first element may be referred to as a second element, and similarly, a second element may be referred to as a first element without departing from the scope of the appended claims.

[0121] The features of different embodiments may be coupled or combined with each other in part or in whole, and may interoperate with each other in different ways. Some embodiments may be performed independently of each other, or may be performed together in a mutually dependent relationship.

[0122] In the present disclosure, the term "substantially" when applied to a structural unit of a device may be interpreted as a technical feature of the structural unit produced within the technical tolerance of a method for manufacturing it.

[0123] Traditional optical configuration for holographic projection

[0124] Figure 1 An embodiment is shown in which a computer generated hologram is encoded on a single spatial light modulator. The computer generated hologram is a Fourier transform of the object used for reconstruction. Therefore, it can be said that the hologram is a Fourier domain or 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 on the spatial light modulator and a holographic reconstruction is formed at a playback field, such as a light receiving surface such as a screen or diffuser.

[0125] A light source 110, such as a laser or laser diode, is arranged to illuminate the SLM 140 via a collimating lens 111. The collimating lens causes a substantially planar wavefront of light to be incident on the SLM. Figure 1 In some embodiments, the direction of the wavefront is off-normal (e.g., two or three degrees from a plane that is truly normal to the transparent layer). However, in other embodiments, a substantially planar wavefront is provided at normal incidence and a beam splitter arrangement is used to separate the input and output optical paths. Figure 1 In the embodiment shown, the arrangement is such that light from the light source reflects from the mirrored rear surface of the SLM and interacts with the light modulating layer to form an exit wavefront 112. The exit wavefront 112 is applied to an optical device including a Fourier transform lens 120, the focus of which is located at a screen 125. More specifically, the Fourier transform lens 120 receives the modulated light beam from the SLM 140 and performs a frequency-space transform to produce a holographic reconstruction at the screen 125.

[0126] It is important to note that in this type of hologram, every pixel of the hologram contributes to the entire reconstruction. There is no one-to-one correlation between a specific point on the replay field (or image pixel) and a specific light modulation element (or hologram pixel). In other words, the modulated light leaving the light modulation layer is distributed over the entire replay field.

[0127] In these embodiments, the position of the holographic reconstruction in space is determined by the power (focus) of the Fourier transform lens. Figure 1In the illustrated embodiments, the Fourier transform lens is a physical lens. That is, the Fourier transform lens is an optical Fourier transform lens and performs a Fourier transform optically. Any lens can act as a Fourier transform lens, but the performance of the lens will limit the accuracy of the Fourier transform it performs. The skilled person understands how to use a lens to perform an optical Fourier transform. In some embodiments of the present disclosure, the lens of the observer's eye performs the conversion of the hologram to the image.

[0128] Hologram computing

[0129] In some embodiments, the computer generated hologram is a Fourier transform hologram, or simply a Fourier hologram or a Fourier-based hologram, where the image is reconstructed in the far field by utilizing the Fourier transform properties of a positive lens. The Fourier hologram is calculated by Fourier transforming the desired light field in the replay plane back to the lens plane. The computer generated Fourier hologram can be calculated using the Fourier transform. By way of example only, the embodiments relate to Fourier holography and Gerchberg-Saxton type algorithms. The present disclosure is equally applicable to Fresnel holography and Fresnel holograms that can be calculated by similar methods. In some embodiments, the hologram is a phase or pure phase hologram. However, the present disclosure is also applicable to holograms calculated by other techniques, such as techniques based on point cloud methods.

[0130] In some embodiments, the hologram engine is arranged to exclude from the hologram calculation the contribution of light blocked by the limiting aperture of the display system. UK patent application 2101666.2, filed on February 5, 2021 and incorporated herein by reference, discloses a first hologram calculation method in which eye tracking and ray tracing are used to identify sub-areas of a display device for calculating a point cloud hologram that eliminates ghost images. The sub-areas of the display device correspond to the aperture 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, which includes a step of performing light field clipping according to the pupil of the optical system during the hologram calculation. The clipping of the light field corresponds to the determination of the limiting aperture of the present disclosure. UK patent application 2118911.3, filed on 23 December 2021 and also incorporated herein by reference, discloses a third method of computing a hologram, the method comprising the step of determining the area of ​​a so-called extended modulator formed by a hologram replicator. According to the present disclosure, the area of ​​the extended modulator is also the aperture.

[0131] In some embodiments, a real-time engine is provided that is arranged to receive image data and calculate a hologram in real time using an algorithm. In some embodiments, the image data is a video comprising a sequence of image frames. In other embodiments, the hologram is pre-calculated, stored in a computer memory and called up as needed for display on the SLM. That is, in some embodiments, a repository of predetermined holograms is provided.

[0132] Large field of view using a small display

[0133] In general, the present disclosure relates to image projection. It relates to a method of image projection and an image projector including a display device. The present disclosure also relates to a projection system including an image projector and an observation system, wherein the image projector projects or relays light from the display device to the observation system. The present disclosure is equally applicable to monocular and binocular observation systems. The observation system may include one or more eyes of an observer. The observation system includes an optical element with optical focal length (e.g., a lens of a human eye) and an observation plane (e.g., a retina of 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 observer forms or perceives the image on the display plane. In some embodiments, the image is a virtual image, and the display plane may be referred to as a virtual image plane. In other examples, the image is a real image formed by holographic reconstruction, and the image is projected or relayed to the observation plane. In these other examples, the spatially modulated light of the 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 diffraction pattern (eg a hologram or kinoform) displayed on a display device.

[0134] The display device includes pixels. The pixels of the display can display a diffraction pattern or structure of diffracted light. The diffracted light can form an image on a plane that is spatially separated from the display device. According to well-known optical principles, the magnitude of the maximum diffraction angle is determined by the size of the pixel and other factors such as the wavelength of the light.

[0135] 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 to a viewing entity / system such as a camera or eye within a range of diffraction angles (e.g., from zero to a maximum diffraction angle). In some embodiments, amplification techniques may be used to increase the range of available diffraction angles beyond the conventional maximum diffraction angle of the LCOS.

[0136] 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 to a holographic reconstruction, i.e., an image) - which can be informally referred to as being "encoded" with / by the hologram - is transmitted directly to the eye of the observer. The observer can perceive a real or virtual image. In these embodiments, no intermediate holographic reconstruction / image is formed between the display device and the observer. It is sometimes said that in these embodiments, the lens of the eye performs the conversion or transformation of the hologram to the image. The projection system or light engine can be configured so that the observer effectively looks directly into the display device.

[0137] The "light field" mentioned here is a "composite light field". The term "light field" simply means a light pattern with finite size in at least two orthogonal spatial directions, such as x and y. The term "light field" simply means a light pattern with finite size in at least two orthogonal spatial directions (x and y). The word "complex" used here simply means that the light at each point in the light field can be defined by an amplitude value and a phase value, and can therefore be represented by a complex number or a pair of values. For the purpose of hologram calculation, the composite light field can be a two-dimensional array of complex numbers, where the complex numbers define the intensity and phase of light at multiple discrete locations within the light field.

[0138] According to well-known optical principles, the angular range of light propagating from a display device that can be observed by an eye or other viewing entity / system varies with the distance between the display device and the viewing entity. For example, at a viewing distance of 1 meter, only a small range of angles from the LCOS can propagate through the pupil of the eye to form an image on the retina at a given eye position. The angular range of light propagating from the display device that can successfully propagate through the pupil of the eye to form an image on the retina at a given eye position determines the portion of the image that is "visible" to the observer. In other words, not all portions of the image are visible from any point on the viewing plane (e.g., any one eye position within an viewing window such as an eye box).

[0139] In some embodiments, the image perceived by the observer is a virtual image that appears upstream of the display device, that is, the observer perceives the image as being farther away from them than the display device. Thus, conceptually, the observer can be thought of as observing the virtual image through a "window the size of the display device," which can be very small, such as 1 cm in diameter, and at a relatively large distance, such as 1 meter. And the user will be observing the display device-sized window through the pupil of their eye, which can also be very small. Thus, at any given time, the field of view becomes smaller, and the specific range of angles that can be seen depends heavily on the eye position.

[0140] Pupil expanders address how to increase the angular range of light propagating from a display device and that can successfully propagate through the pupil of the eye to form an image. Display devices are typically (relatively) small and have (relatively) large projection distances. In some embodiments, the projection distance is at least one order of magnitude, such as 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).

[0141] The use of a pupil expander increases the viewing area (i.e., the user's eye box) laterally, thereby enabling some eye movement while still enabling the user to see the image. As will be appreciated by the skilled artisan, in an imaging system, the viewing area (the user's eye box) is the area where the viewer's eye can perceive the image. The present disclosure encompasses non-infinite virtual image distances - i.e., near-field virtual images.

[0142] Traditionally, a two-dimensional pupil expander comprises one or more one-dimensional optical waveguides, each formed using a pair of opposing reflective surfaces, wherein the output light from the surfaces forms an observation window or eye box. Light received from a display device (e.g., spatially modulated light from an LCOS) is replicated by the or each waveguide to increase the field of view (or observation area) in at least one dimension. In particular, the waveguide enlarges the observation window due to the generation of additional light rays or "copies" by dividing the amplitude of the incident wavefront.

[0143] The display device may have an active or pixel display area having a first dimension of less than 10 cm, such as less than 5 cm or less than 2 cm. The propagation distance between the display device and the viewing system may be greater than 1 m, such as greater than 1.5 m or greater than 2 m. The optical propagation distance within the waveguide may be up to 2 m, such as up to 1.5 m or up to 1 m. The method is capable of receiving an image and determining a corresponding hologram of sufficient quality in less than 20 ms, such as less than 15 ms or less than 10 ms.

[0144] In some embodiments described only by examples of diffraction 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-region) of the image. The channels formed by the diffraction structure are referred to here as "hologram channels" simply to reflect that they are light channels encoded by holograms with image information. It can be said that the light of each channel is in the holographic domain, rather than in the image or spatial domain. In some embodiments, the hologram is a Fourier or Fourier transform hologram, so the hologram domain is the Fourier or frequency domain. The hologram can also be a Fresnel or Fresnel transform hologram. The hologram can also be a point cloud hologram. The hologram is described herein as routing light into multiple hologram channels 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-regions, where each hologram channel will correspond to each image sub-region. Importantly, the hologram of this example is characterized by how it distributes the image content when it is illuminated. Specifically and uniquely, the hologram divides the image content by angle. That is, every point on the image is associated with a unique ray angle in the spatially modulated light formed by the hologram when illuminated - at least a unique pair of angles, since the hologram is two-dimensional. For the avoidance of doubt, this holographic behavior is not conventional. When illuminated, the spatially modulated light formed by this particular type of hologram can be separated into multiple hologram channels, each of which is defined by a range of ray angles (in two dimensions). It will be understood from the above that any hologram channel (i.e., a sub-range of ray angles) that can be considered in the spatially modulated light will be associated with a corresponding portion or sub-region of the image. That is, all of the information required to reconstruct that portion or sub-region of the image is contained within the angular sub-range of the spatially modulated light formed by the hologram of the image. When the spatially modulated light is observed as a whole, there is not necessarily any evidence of multiple discrete light channels.

[0145] Nevertheless, the hologram can still be recognized. For example, if only continuous portions or sub-regions of the spatially modulated light formed by the hologram are reconstructed, only sub-regions of the image should be visible. If different continuous portions or sub-regions of the spatially modulated light are reconstructed, different sub-regions of the image should be visible. Another identifying feature of this type of hologram is that the shape of the cross-section of any hologram channel substantially corresponds to the shape of the entrance pupil (i.e., substantially the same), although the size may be different—at least at the correct plane where the hologram is calculated. Each light / hologram channel propagates from the hologram at a different angle or range of angles. Although these are example ways to characterize or identify this type of hologram, other ways may also be used. In summary, the holograms disclosed herein are characterized and identified by how the image content is distributed within the light encoded by the hologram. In addition, to avoid any doubt, references herein to holograms configured to guide light or to angularly divide an image into multiple hologram channels are only by way of example, and the present disclosure is equally applicable to any type of holographic light field or even any type of diffraction or pupil expansion of a diffracted light field.

[0146] The system can be provided in a compact and streamlined physical form. This makes the system suitable for a wide range of practical applications, including those where space is limited and asset value is high. For example, it can be implemented in a head-up display (HUD), such as a vehicle or automotive HUD.

[0147] According to the present disclosure, a pupil expansion is provided for diffracted light, which may include a diverging bundle of light rays. The diffracted light field may be defined by a "light cone". Thus, the size of the diffracted light field (as defined in a two-dimensional plane) increases with propagation distance from the corresponding diffractive structure (i.e., the display device). It can be said that the pupil expander replicates the hologram or forms at least one replica of the hologram to convey that the light transmitted to the observer is spatially modulated according to the hologram.

[0148] In some embodiments, two one-dimensional waveguide pupil expanders are provided, each of which is arranged to effectively increase the size of the exit pupil of the system by forming multiple copies or replicas of the exit pupil (or the light of the exit pupil) of the spatial light modulator. The exit pupil can be understood as the physical area where the system outputs light. It can also be said that each waveguide pupil expander is arranged to expand the size of the exit pupil of the system. It can also be said that each waveguide pupil expander is arranged to expand / increase the size of the eye box in which the observer's eyes can be located in order to see / receive the light output by the system.

[0149] Optical Channel

[0150] Holograms formed in accordance with some embodiments angularly divide the image content to provide multiple hologram channels that may have a cross-sectional shape defined by the aperture of the optical system. The hologram is calculated to provide this guidance of the diffracted light field. In some embodiments, this is achieved by taking into account the aperture (virtual or real) of the optical system during the calculation of the hologram, as described above.

[0151] Figure 2 and 3 An example of this type of hologram is shown, which can be used in conjunction with the pupil expander disclosed herein. However, this example should not be viewed as limiting the present disclosure.

[0152] Figure 2 An image 252 is shown for projection, comprising eight image regions / components V1 to V8. By way of example only, Figure 2 Eight image components are shown, and image 252 may be separated into any number of components. Figure 2 Also shown is a coded light pattern 254 (ie, a hologram) that can reconstruct the image 252—for example, when transformed by a lens of a suitable viewing system. The coded light pattern 454 includes first to eighth sub-holograms or components H1 to H8, corresponding to first to eighth image components / regions V1 to V8. Figure 2 It further shows how a hologram breaks down the image content by angle. Therefore, a hologram is characterized by its guidance of light. Figure 3 Specifically, the hologram in this example directs light into multiple discrete regions. In the example shown, the discrete regions are disks, but other shapes are also contemplated. After propagation through the waveguide, the size and shape of the optimal disk can be related to the size and shape of the aperture of the optical system (e.g., the entrance pupil of the observation system).

[0153] Figure 4 A system 400 is shown, including a display such as Figure 2 and 3 A display device for a computed hologram is shown.

[0154] The system 400 comprises a display device which in this arrangement comprises an LCOS 402. The LCOS 402 is arranged to display a modulation pattern (or "diffraction pattern") comprising a hologram and projects light which has been holographically encoded to an eye 405 which comprises a pupil acting as an aperture 404, a lens 409 and a retina (not shown) acting as an observation plane. There is a light source (not shown) arranged to illuminate the LCOS 402. The lens 409 of the eye 405 performs the conversion of the hologram to an image. The light source may be of any suitable type. For example, it may comprise a laser source.

[0155] The viewing system 400 also includes a waveguide 408 located between the LCOS 402 and the eye 405. The presence of the waveguide 408 enables all angular content from the LCOS 402 to be received by the eye, even at the relatively large projection distance shown. This is because the waveguide 408 acts as a pupil expander in a well-known manner and is therefore only briefly described here.

[0156] in short, Figure 4 The waveguide 408 shown comprises a substantially elongated structure. In this example, the waveguide 408 comprises an optical plate of a refractive material, but other types of waveguides are also well known and can be used. The waveguide 408 is positioned to intersect the light cone (i.e., the diffracted light field) projected from the LCOS 402, for example, at an oblique angle. In this example, the size, position, and positioning of the waveguide 408 are configured to ensure that light from each of the eight light beams within the light cone enters the waveguide 408. The light from the light cone enters the waveguide 408 via a first planar surface of the waveguide 408 (positioned closest to the LCOS 402) and is guided at least partially along the length of the waveguide 408 before being emitted via a second planar surface of the waveguide 408 that is substantially opposite to the first surface (positioned closest to the eye). It is easy to understand that the second planar surface is partially reflective and partially transmissive. In other words, when each light ray propagates from the first planar surface within the waveguide 408 and strikes the second planar surface, some of the light will be transmitted out of the waveguide 408 and some of the light will be reflected back to the first planar surface by the second planar surface. The first planar surface is reflective so that all light striking it from within the waveguide 408 will be reflected back toward the second planar surface. Thus, some light may simply be refracted between the two planar surfaces of the waveguide 408 before being transmitted, while other light may be reflected and may therefore experience one or more reflections (or "bounces") between the planar surfaces of the waveguide 408 before being transmitted.

[0157] Figure 4 A total of nine "bounce" points B0 to B8 are shown along the length of waveguide 408. Figure 2 As shown, light associated with all points of the image (V1-V8) is transmitted out of the waveguide at each "bounce" from the second planar surface of the waveguide 408, but only light from one angular portion of the image (e.g., light from one of V1 to V8) has a trajectory that enables it to reach the eye 405 from each corresponding "bounce" point B0 to B8. In addition, light from different angular portions of the image (V1 to V8) reaches the eye 405 from each corresponding "bounce" point. Therefore, at Figure 4 In the example of FIG. 4 , each angular channel of coded light reaches the eye from waveguide 408 only once.

[0158] The waveguide 408 forms multiple copies of the hologram at corresponding "bounce" points B1 to B8 along its length, corresponding to the direction of pupil expansion. As shown in Figure 5, the multiple copies can be linearly extrapolated back to the corresponding multiple copies or virtual display device 402'. This process corresponds to the step of "expanding" the light path within the waveguide so that the light of the replica is extrapolated back to the "virtual surface" without internal reflection within the waveguide. Therefore, the light of the expanded exit pupil can be considered to originate from the virtual surface (also referred to herein as the "expansion modulator") including the display device 402 and the replica display device 402'.

[0159] Although virtual images have been discussed generally herein, which require the eye to convert received modulated light to form a perceived image, the methods and apparatus described herein can be applied to real images.

[0160] 2D pupil expansion

[0161] Although Figure 4 The arrangement shown includes a single waveguide that provides pupil expansion in one dimension, but pupil expansion may be provided in more than one dimension, for example in two dimensions. Figure 4 The examples in use a hologram that has been calculated to create channels of light, each corresponding to a different portion of an image, but the present disclosure and the systems described below are not limited to this type of hologram.

[0162] Figure 5A A perspective view of a system 500 is shown, the system comprising two replicators 504, 506 arranged to expand a light beam 502 in two dimensions.

[0163] exist Figure 5A In the system 500, the first replicator 504 includes a first pair of surfaces stacked parallel to each other, which are arranged in a manner similar to Figure 4 The first pair of surfaces are similar in size and shape to each other (in some cases identical) and are substantially elongated in one direction. The collimated beam 502 is directed to the input of the first replicator 504. Due to internal reflection processes between the two surfaces, as well as from one of the surfaces (the upper surface, such as Figure 5A As will be familiar to the skilled reader, light from beam 502 is replicated in a first direction along the length of first replicator 504. Thus, a first plurality of replica beams 508 are emitted from first replicator 504 toward second replicator 506.

[0164] The second replicator 506 includes a second pair of surfaces stacked parallel to one another, arranged to receive each collimated beam of the first plurality of beams 508, and further arranged to provide replication or pupil expansion by expanding each of these beams in a second direction that is substantially orthogonal to the first direction. The size and shape of the first pair of surfaces are similar to one another (in some cases identical), and are substantially rectangular. The rectangular shape is implemented for the second replicator so that it has a length along the first direction so as to receive the first plurality of beams 508, and has a length along the second orthogonal direction so as to provide replication in the second direction. Due to internal reflection processes between the two surfaces, and from one of the surfaces (such as Figure 5A The light of each of the first plurality of light beams 508 is replicated in the second direction by partial transmission of light from each of the plurality of output points on the upper surface (as shown in FIG. 1 ), and the light of each light beam within the first plurality of light beams 508 is replicated in the second direction. Thus, a second plurality of light beams 510 is emitted from the second replicator 506, wherein the second plurality of light beams 510 includes a replica of the input light beam 502 along each of the first direction and the second direction. Thus, the second plurality of light beams 510 can be viewed as a two-dimensional grid or array including replica light beams.

[0165] Therefore, it can be said that Figure 5A The first and second replicators 504, 505 are combined to provide a two-dimensional replicator (or "two-dimensional pupil expander"). Thus, the replicated light beam 510 can be emitted along an optical path to an expanded eye box of a display system, such as a head-up display.

[0166] exist Figure 5A In the system, the first replicator 504 is a waveguide comprising a pair of elongated rectilinear reflective surfaces stacked parallel to each other, and similarly, the second replicator 504 is a waveguide comprising a pair of rectangular reflective surfaces stacked parallel to each other. In other systems, the first replicator can be a solid elongated rectilinear waveguide and the second replicator can be a solid planar rectangular waveguide, wherein each waveguide comprises an optically transparent solid material, such as glass. In this case, the pair of parallel reflective surfaces are formed by a pair of opposing major side walls, optionally including respective reflective and reflective-transmissive surface coatings, which will be familiar to the skilled reader.

[0167] Figure 5B A perspective view of a system 500 is shown, the system comprising two replicators 520 , 540 arranged for replicating a light beam 522 in two dimensions, wherein the first replicator is a solid elongated waveguide 520 and the second replicator is a solid planar waveguide 540 .

[0168] exist Figure 5BIn the system of FIG. 5 , the first replicator / waveguide 520 is arranged 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 arranged to couple light from the output port of the first replicator 520 to the input port of the second replicator 540. In the arrangement shown, the optical coupler is a plane / folding mirror 530 arranged to fold or redirect the optical path of the light to achieve the desired optical coupling from the first replicator to the second replicator. Figure 5B As shown, a mirror 530 is arranged to receive light from the output port / reflection-transmission surface 524a of the first replicator / waveguide 520, comprising a one-dimensional array of replicas extending in a first dimension. The mirror 530 is tilted so as to redirect the received light at an angle into the optical path of the input port in the (totally) reflective surface of the second replicator 540 to provide waveguide and replica formation along its length in the second dimension. It should be understood that the mirror 530 is one example of an optical element capable of redirecting light in the manner shown, and one or more other elements may alternatively be used to perform this task.

[0169] In the arrangement shown, the (partial) reflection-transmission surface 524a of the first replicator 520 is adjacent to an input port of the first replicator / waveguide 520 that receives the input light beam 522 at an angle to provide waveguide and replica formation along its length in the first dimension. Thus, the input port of the first replicator / waveguide 520 is located at its input end, on the same surface as the reflection-transmission surface 524a. The technical reader will appreciate that the input port of the first replicator / waveguide 520 may be at any other suitable location.

[0170] therefore, Figure 5B The arrangement enables the first replicator 520 and the mirror 530 to be provided as part of a first relatively thin layer in a first and third dimensional plane (illustrated as the xz plane). Specifically, the size or "height" of the first planar layer (in which the first replicator 520 is located) in the second dimension (illustrated as the y dimension) is reduced. The mirror 530 is configured to direct light away from the first layer / plane (i.e., the "first planar layer") where the first replicator 520 is located, and direct it to the second layer / plane (i.e., the "second planar layer") where the second replicator 540 is located, which is located above the first layer / plane and substantially parallel thereto. Therefore, the overall size or "height" of the system - including the first and second replicators 520, 540 and the mirror 530 in the first and third dimensions (illustrated as the xz plane) - in the second dimension (illustrated as the y dimension) - located in the stacked first and second planar layers - is compact. Technical readers will appreciate that the invention can be used to implement the present disclosure. Figure 5B Many variations of the arrangements are possible and contemplated.

[0171] The image projector can be arranged to project a divergent or diffracted light field. In some embodiments, the light field is encoded with a hologram. In some embodiments, the diffracted light field includes a divergent beam of light rays. In some embodiments, the image formed by the diffracted light field is a virtual image.

[0172] In some embodiments, the first pair of parallel / complementary surfaces are elongated or slender surfaces, relatively long along a first dimension, relatively short along a second dimension, for example relatively short along each of two other dimensions, each dimension being substantially orthogonal to each of the respective other dimensions. The process of light reflecting / transmitting between / from the first pair of parallel surfaces is arranged such that the light propagates within the first waveguide pupil expander, and the general direction of light propagation is the direction in which the first waveguide pupil expander is relatively long (i.e., in its "elongated" direction).

[0173] A system is disclosed herein that uses diffracted light to form an image and provides an eyebox size and field of view suitable for real world applications - for example in the automotive industry via heads-up displays. Diffracted light is light that forms a holographic reconstruction of an image from a diffractive structure - for example a hologram such as a Fourier or Fresnel hologram. The use of diffraction and diffractive structures requires a high density of display devices with very small pixels (e.g. 1 micron) - which in practice means small display devices (e.g. 1 cm). The inventors have solved the problem of how to provide a diffracted light field for 2D pupil expansion, for example diffracted light comprising a divergent (non-collimated) beam of light rays.

[0174] In some embodiments, a display system includes a display device—such as a pixelated display device, such as a spatial light modulator (SLM) or a liquid crystal on silicon (LCoS) SLM—that is arranged to provide or form diffracted or divergent light. In these aspects, 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 defines the array of light modulating pixels contained within the SLM—determines the size (e.g., spatial extent) of the bundle of light rays that can exit the system. According to the present disclosure, it is stated that by using at least one pupil expander, the exit pupil of the system is expanded to reflect that the exit pupil of the system (which is limited by the small display device having a pixel size for light diffraction) becomes larger in spatial extension.

[0175] A diffracted or divergent light field may be referred to as having a "light field size," which is defined in a direction substantially orthogonal to the direction of propagation of the light field. Because the light is diffracted / diverged, the light field size increases with propagation distance.

[0176] In some embodiments, the diffracted light field is spatially modulated according to the hologram. In other words, in these aspects, the diffracted light field comprises a "holographic light field". The hologram can be displayed on a pixelated display device. The hologram can be a computer generated hologram (CGH). It can be a Fourier hologram or a Fresnel hologram or a point cloud hologram or any other suitable type of hologram. Optionally, the hologram can be calculated so as to form channels of holographic light, each channel corresponding to a different part of the image that the observer wants to observe (or perceive, if it is a virtual image). The pixelated display device can be configured to display multiple different holograms continuously or sequentially. Each of the aspects and embodiments disclosed herein can be applied to the display of multiple holograms.

[0177] The output port of the first waveguide pupil expander may be coupled to the input port of the second waveguide pupil expander. The second waveguide pupil expander may be arranged to guide the diffracted light field (including some, preferably most, preferably all copies of the light field output by the first waveguide pupil expander) from its input port to the corresponding output port by internal reflection between a third pair of parallel surfaces of the second waveguide pupil expander.

[0178] The first waveguide pupil expander may be arranged to provide pupil expansion or replication in a first direction, and the second waveguide pupil expander may be arranged to provide pupil expansion or replication in a second, different direction. The second direction may be substantially orthogonal to the first direction. The second waveguide pupil expander may be arranged to maintain the pupil expansion already provided by the first waveguide pupil expander in the first direction, and expand (or replicate) some, preferably most, preferably all of the copies it receives from the first waveguide pupil expander in a second, different direction. The second waveguide pupil expander may be arranged to receive the light field from the first waveguide pupil expander directly or indirectly. One or more other elements may be provided along the propagation path of the light field between the first and second waveguide pupil expanders.

[0179] The first waveguide pupil expander may be substantially elongated and the second waveguide pupil expander may be substantially planar. The elongated shape of the first waveguide pupil expander may be defined by a length along a first dimension. The planar or rectangular shape of the second waveguide pupil expander may be defined by a length along the first dimension and a width or breadth along a second dimension substantially orthogonal to the first dimension. The size or length of the first waveguide pupil expander along its first dimension may correspond to the length or width of the second waveguide pupil expander along its first dimension or second dimension, respectively. A first surface of a pair of parallel surfaces of the second waveguide pupil expander including its input port may be shaped, sized and / or positioned to correspond to an area defined by an output port on a first surface of a pair of parallel surfaces on the first waveguide pupil expander, such that the second waveguide pupil expander is arranged to receive each copy output by the first waveguide pupil expander.

[0180] The first and second waveguide pupil expanders may jointly provide pupil expansion in a first direction and in a second direction perpendicular to the first direction, optionally wherein a plane containing the first and second directions is substantially parallel to a plane of the second waveguide pupil expander. In other words, first and second dimensions defining the length and width, respectively, of the second waveguide pupil expander may be parallel to the first and second directions, respectively (or to the second and first directions, respectively), wherein the waveguide pupil expander provides pupil expansion. The combination of the first waveguide pupil expander and the second waveguide pupil expander may generally be referred to as a "pupil expander".

[0181] It can be said that the expansion / replication provided by the first and second waveguide expanders has the effect of expanding the exit pupil of the display system in each of two directions. The area defined by the expanded exit pupil can in turn define an expanded eyebox area from which an observer can receive light of the input diffracted or divergent light field. The eyebox area can be said to be located in or define an observation plane.

[0182] The two directions of exit pupil expansion may be coplanar or parallel to the first and second directions in which the first and second waveguide pupil expanders provide replication / expansion. Alternatively, in an arrangement including other elements such as an optical combiner, such as a windshield of a vehicle, the exit pupil may be considered to be an exit pupil from the other element, such as from the windshield. In such an arrangement, the exit pupil may be non-coplanar and non-parallel to the first and second directions in which the first and second waveguide pupil expanders provide replication / expansion. 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 replication / expansion.

[0183] The observation plane and / or the eye box region may be non-coplanar or non-parallel to the first and second directions in which the first and second waveguide pupil expanders provide replication / expansion. For example, the observation plane may be substantially perpendicular to the first and second directions in which the first and second waveguide pupil expanders provide replication / expansion.

[0184] In order to provide suitable launch conditions to achieve internal reflections 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.

[0185] Combiner shape compensation

[0186] An advantage of projecting a hologram to the eyebox is that optical compensation can be encoded in the hologram (e.g., see European Patent 2936252, incorporated herein by reference). 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 windshield of a vehicle. Full details of this approach are provided in European Patent 2936252 and are not repeated here because the detailed features of these systems and methods are not essential to the novel teachings of this disclosure herein and are merely examples of configurations that benefit from the teachings of the present disclosure.

[0187] Controls

[0188] The present disclosure is also compatible with an optical configuration including a control device (e.g., an optical shutter device) to control the delivery of light from the optical channel hologram to the observer. The holographic projector may also include a control device arranged to control the delivery of the angular channel to the eye box position. British patent application 2108456.1, filed on June 14, 2021 and incorporated herein by reference, discloses at least one waveguide 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 substantially based on the user's eye box position and is compatible with any hologram calculation method for implementing the optical channel described herein. It can be said that the control device is an optical shutter or aperture device. The optical shutter device may include a 1D array aperture or window, each of which can be independently switched between a light-transmitting and a light-impermeable state to control the delivery of the hologram optical channel and its replica to the eye box. Each aperture or window may include a plurality of liquid crystal cells or pixels.

[0189] Point cloud hologram calculation

[0190] Figure 6 A schematic diagram representing the point cloud hologram method is shown. Figure 6 The method described here is performed virtually (i.e., simulated). Therefore, Figure 6is merely a representation of what is computationally performed during the point cloud hologram calculation. Furthermore, each step of the method is performed virtually. For example, where wave propagation is described, the waves are not physically propagated through a physical system. Instead, virtual waves propagate virtually in a virtual system. The display device 604 in this example represents the plane on which the hologram will be displayed once the hologram is calculated. As described in more detail below, the purpose of the point cloud hologram calculation is to determine a hologram that can be (physically) displayed on the display device 604, so that when the hologram is appropriately (physically) illuminated with coherent light, a (physical) holographic wavefront is formed, which is relayed to the observer's real entrance pupil, giving the appearance of a holographic reconstruction of the three-dimensional point cloud.

[0191] In this example, point cloud 602 is a three-dimensional point cloud, where the points represent an object or scene. Specifically, point cloud 602 represents a target image based on which a hologram is calculated. Figure 6 Four image points are shown: a first image point 610, a second image point 612, a third image point 614, and a fourth image point 616. The first to fourth image points are distributed throughout the point cloud 604. This is merely representative. It should be understood that, typically, the point cloud of a point cloud hologram will include thousands or millions of image points that together represent a picture.

[0192] The point cloud hologram calculation method generally includes simulating the propagation of a light wave (or wavelet) from each image point of the point cloud 604 along a propagation path toward the center of the entrance pupil 606. The propagation paths of the first to fourth image points 610 to 614 are given by Figure 6 The first propagation path 620 extends from the first image point 610 to the entrance pupil 606; the second propagation path 622 extends from the second image point 612 to the entrance pupil 606; the third propagation path 624 extends from the third image point 614 to the entrance pupil 606; and the fourth propagation path 626 extends from the fourth image point 616 to the entrance pupil 606. The skilled reader will be familiar with suitable methods and algorithms for performing such light wave propagation.

[0193] It should be noted that Figure 6 The optical system is simplified. In most examples, one or more optical components will be located between the point cloud 602 / display device 604 and the observer. The propagation path can pass through these one or more optical components. For example, as described above, the one or more optical components may include one or more lenses, one or more mirrors, and / or waveguides. When virtually propagating waves from the image points, the point cloud hologram calculation will need to take into account each of these optical components. In addition, Figure 6 Not drawn to scale. For example, in a head-up display of a vehicle, the distance between display device 604 and the observer may be 1 meter or more. The distance from the observer to point cloud 602 may be greater.

[0194] After simulating the propagation of the light wave, the next step of the method is to obtain a complex value at each point on the (virtual) display device 604 or holographic plane. The display device 604 is pixelated. Traditionally, this step of the method includes determining a complex value for each pixel at the display device 604 (or at least each pixel of the display device that the wave is incident on). In this example, a pure phase hologram is determined so that a phase value is extracted from the complex value of each pixel. A skilled reader will be familiar with how to determine these values. The example is iterative, iterating for each image point. Specifically, in each iteration, the light wave propagates from the corresponding image point, and a complex value for each pixel at the display device 604 is determined, followed by a phase value. The phase values ​​for each image point are added, superimposed, accumulated or otherwise combined to output a hologram of the target picture.

[0195] The inventors have found that the spatial frequency of an image point hologram depends on the position of the image point in the target image. In general, spatial frequency refers to the change in phase and / or intensity of the wavefront / hologram at different positions within the hologram. In this example, the hologram is a pure phase hologram, so the spatial frequency refers to the phase change.

[0196] Fig. 7A Shown separately Figure 6 610 of the first image point 610 . Figure 7B Shown separately Figure 6 A hologram of the third image point 614. Fig. 7A The upper diagram 702 of shows the complete hologram of the first image point 610 . Fig. 7A The lower image 704 shows a close-up of a portion of the complete hologram of the first image point 610 . Figure 7B The upper diagram 712 shows the complete hologram of the third image point 614 . Figure 7B The lower image 714 shows a close-up of a portion of the complete hologram of the third image point 614 . Fig. 7A and 7B Both are greyscale images, and both represent how the phase delay applied to the hologram varies spatially. In this example, the phase varies from dark (black), representing a phase delay of 0, to light (white), representing a phase delay of 2π.

[0197] like Fig. 7A and 7B As shown, the spatial frequency of the hologram of the first image point 610 (eg Fig. 7A ) is greater than the spatial frequency of the third pixel 614 (as shown Figure 7B In other words, Fig. 7A The phase ratio of the hologram Figure 7B The phase of the hologram changes much faster. Fig. 7A and 7BThis difference in spatial frequency becomes particularly evident in the following figures 704 and 714. Fig. 7A In the following figure 704 of FIG. , the phase variation between adjacent pixel columns is approximately π. For example, see Fig. 7A The difference in darkness between the first column of pixels 706 and the second column of pixels 707 in FIG. Figure 7B The following figure 714 (with Fig. 7A In the lower figure 704 (of the same scale), the phase changes more gradually. Along the entire length of the lower figure 714, the phase changes very smoothly from about 0 to 2π.

[0198] A pixelated display device, such as display device 604, has a field of view that is limited by the wavelength of light and, more importantly for the context of the present disclosure, by the pixel pitch (or pixel size) of the display device. As the pixel pitch decreases, the field of view increases. Display device 604 can only holographically reconstruct points within the 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 because the first image point 610 is toward the edge of the point cloud 602, which in this example corresponds to an edge close to the field of view of the display device 604, and causes the propagation axis 620 to pass through the display device 604 at an angle close to the diffraction limit of the display device 604. The high spatial frequency is required to diffract the light incident thereon to form the reconstructed first image point 610 close to the edge of the field of view (i.e., close to the diffraction limit of the display device 604). In contrast, the image point 610 is toward the center of the point cloud 602, and the associated waves propagate substantially orthogonally to the display device 604. Therefore, the spatial frequency is relatively very low (when compared to the hologram of the first image point 610).

[0199] The inventors have recognized that when the spatial frequency of the hologram is low, the hologram may be computed at a resolution lower than the native resolution of the display device 604. In other words, a hologram of low spatial frequency may be undersampled, with only a portion of the phase values ​​being computed. For example, there may be one or more empty pixel values ​​between each phase value. The inventors have recognized that due to the slowly and smoothly changing nature of the phase of such a hologram, it is possible to accurately interpolate (without aliasing issues) between the computed phase values ​​to upgrade the hologram to the full resolution of the display device 604. The inventors have exploited this concept in an improved method for computing point cloud holograms disclosed below.

[0200] Improved point cloud hologram calculation method

[0201] It is desirable to be able to compute point cloud holograms in real time, so that a sequence of holograms of different target pictures can be computed and displayed sequentially at a relatively high frame rate (e.g., at least 30 frames per second) and at a sufficiently high resolution that the reconstruction of the hologram appears to be of good quality. It is also desirable to achieve this with relatively limited computing resources. For example, a vehicle's head-up display may have relatively limited on-board computing resources. This was not previously possible using conventional point cloud hologram calculation methods. This is because it is computationally very expensive to calculate hologram values ​​at high resolution using a point cloud approach. This means that such real-time calculations are not practical, certainly not at high resolutions and using devices with relatively limited on-board computing resources. Therefore, the inventors have designed the improved point cloud hologram calculation method described herein.

[0202] The method proposed by the inventors includes, for a first subset of image points, determining a hologram value using a point cloud method only for every nth pixel, where n is greater than 1 (e.g., every second, third, fourth, or fifth pixel). Because the point cloud method (including the propagation of wavelets and the determination of values) is computationally very expensive, reducing the number of sampling points (i.e., the number of pixel values ​​to be determined) significantly reduces the computational burden of determining values ​​at each pixel of the display device. Interpolation can be used to fill in pixels between nth pixels based on the determined (nth) pixels.

[0203] The first subset of image points is arranged / selected so that each image point of the first subset has an associated diffraction angle for the point cloud method, each diffraction angle being smaller than the maximum diffraction angle of the display device. As described above, this allows the hologram to be undersampled and interpolated without aliasing problems. Here, two examples of image points forming such a first subset are described.

[0204] First example

[0205] In a first example, a first subset of image points is achieved simply by selecting a first subset of pixels as pixels that are relatively close to the center of the field of view / the center of the target image, and applying the improved method only to those pixels, each image point having an associated diffraction for the point cloud method, resulting in a relatively low spatial frequency. For example, the first subset of image points may include image point 614, but not image points 610 or 616. Because the first subset of image points is selected in this manner, the hologram to be calculated has a low spatial frequency and can be undersampled as described above. A portion of the undersampled hologram displayed on a display device such as Figure 8 shown.

[0206] Figure 8The grid represents the pixels of a pixelated display device. Each square of the array represents a pixel. The black / solid squares 804 of the array represent pixels for which complex / phase values ​​have been determined in the initial hologram calculation (after the wave has propagated along the propagation path). The white / empty squares 806 represent pixels for which complex / phase values ​​have not yet been determined. In this example, each black square 804 is separated from its nearest neighboring black square by four white (empty) squares 806 in the x-direction and the y-direction. In other words, the pixel value has been determined for every 5th pixel. Therefore, Figure 8 It was shown 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 a lot of computation time and makes the calculation of the hologram much more efficient. As mentioned above, Figure 8 The hologram determined in has very low spatial frequencies. Therefore, interpolation can be used to accurately determine the value of the empty square / pixel 806 based on the known value in the black square 804. For example, a bicubic interpolation scheme can be used for interpolation.

[0207] To further describe the improved method for calculating the hologram of the target image, Figures 9 to 11 Indicates a specific target image (rather than Figure 6 The steps for calculating the hologram of a general single point 610). Fig. 9 A target picture 900 of this example is shown. Figure 6 The point cloud is shown in the yz plane. Fig. 9 The target image 900 is instead located on the xy plane. Therefore, Fig. 9 The view of the target image 900 in is actually a front view (not a side view) of the target image 900 from the perspective of the observation system. Fig. 9 The target image 900 in the image 900 appears to be two-dimensional. In some examples, the target image 900 may also have depth in the z direction and thus may be three-dimensional.

[0208] Fig. 9 The target image 900 is used for the head-up display of the vehicle and therefore includes information useful to the vehicle driver. This includes speed information, the vehicle's charging status and direction information. The target image 900 is a cloud of points (or point cloud). However, because the target image 900 is high resolution, it is not possible to obtain a high resolution image of the target image 900 in the vehicle. Fig. 9 At the scale of the target image 900 shown, individual image points cannot be distinguished.

[0209] In this example, an initial step of the method for computing a hologram includes dividing a target picture into a plurality of parts or cells. Fig.10A target image 900 is shown divided into a cell array 1000. In this example, the cell array 1000 includes 12×9 cells extending in the x and y directions, respectively. In this example, dividing the target image into a plurality of cells includes defining an angular range from an observer to the target image (using ray tracing). This step is performed virtually. Adjacent angular ranges are adjacent to each other (adjacent to each other) and do not overlap. In this example, the range of each angular range in the x and y directions is equal to each other angular range. In other words, the size of each cell is substantially equal.

[0210] The method also includes identifying which image points of the target image 900 fall into which cell. In this example, some cells (e.g., cell 1002) do not contain any image points. Other cells (e.g., cell 1004) contain image points. In this method, cells that do not contain any image points can be effectively ignored. The image points contained in a single cell can be referred to as an image point subset.

[0211] In this example, the method of calculating a hologram includes calculating a sub-hologram for each cell (or at least each cell containing an image point). In other words, the method includes calculating a sub-hologram for each subset of image points. In this example, different methods will be used to calculate sub-holograms for different cells / subsets of image points. Specifically, the sub-holograms of the cells in the central portion 1104 of the target image are calculated using the improved method of the present disclosure, while the sub-holograms of the cells in the outer portion of the target image are calculated using the traditional point cloud method.

[0212] Fig.11 An outer portion 1102 and a central portion 1104 are shown. The boundary 1100 between the outer portion 1102 and the central portion 1104 is represented by a broken / dashed line. For illustrative purposes, cells in the central portion 1104 are shaded grey to distinguish between cells of the inner and outer portions 1102, 1104.

[0213] The image points in the cells of the central portion 1104 are closer to the center of the target image 900 than the image points in the cells of the outer portion 1102. Therefore, the angle formed by the propagation paths of the image points in the cells of the central portion 1104 will be closer to zero than the angle formed by the propagation paths of the image points in the cells of the outer portion 1102 (instead, it will be closer to the maximum diffraction angle of the display device that displays / can display the hologram). This means that the spatial frequency of the sub-hologram of the cells in the central portion 1104 is lower than the spatial frequency of the sub-hologram of the cells in the outer portion 1102. Therefore, the sub-hologram of the cells in the central portion 1104 can be calculated according to the method of the present disclosure (including undersampling and then interpolation) because the spatial frequency can be low enough so that interpolation does not cause significant aliasing problems. In contrast, the spatial frequency of the sub-hologram of the cells in the outer portion 1102 may be too high to use interpolation without causing significant aliasing problems.

[0214] In short, Fig.11 In the example of , different image points of the target image are treated differently in the hologram calculation, depending on how close these image points are to the center of the target image. In particular, the inventors have realized that for points closer to the center of the target image, it is possible to initially undersample the values ​​of the sub-hologram. Fig.12 and 13A 13C shows an extension of this idea. In particular, the inventors have recognized that a balance must generally be struck between maximizing initial undersampling (for computational efficiency) and not causing aliasing problems. The inventors have recognized that this balance can change on a cell-by-cell basis, depending on how close the cell is to the center of the target image. Fig.12 and 13A In the example shown in FIG13C , there are three different undersampled regions using this effect. The sub-holograms of the cells in different regions or parts are undersampled to different degrees.

[0215] In more detail, Fig.12 Examples of include an outer portion 1202, a first center portion 1204, a second center portion 1206, and a third center portion 1208. Each portion is concentric with each other portion and is concentric with the center of the target image. A first boundary exists between the outer portion 1202 and the first center portion 1204. A second boundary exists between the first center portion 1204 and the second center portion 1206. A third boundary exists between the second center portion 1206 and the third center portion 1208. The first, second, and third center portions are represented by gray shading, with the portion being darker the closer to the center of the target image. Such shading is for illustration purposes only.

[0216] As previously described, the calculation of the hologram of the target image includes calculating a sub-hologram of the image point of each cell. As in the previous example, the sub-hologram of the cell in the outer portion 1202 is calculated using conventional point cloud techniques at full resolution (i.e., without undersampling and subsequent interpolation to achieve full resolution). The sub-hologram of the cell in each of the first to third central portions 1204 to 1208 is calculated using a method according to the present disclosure (including initial undersampling and subsequent interpolation). For each consecutive central portion, the degree of interpolation increases.

[0217] In one example, determining a sub-hologram of the image points of the cells in the first central portion 1204 includes initially using a point cloud method to determine the value of every other pixel (i.e., every second pixel). Determining a sub-hologram of the image points of the cells in the second central portion 1206 includes initially using a point cloud method to determine the value of every third pixel. Determining a sub-hologram of the image points of the cells in the third central portion 1208 includes initially using a point cloud method to determine the value of every fourth pixel. Such sub-holograms (before interpolation) are Figures 13A to 13C Specifically, Fig.13A A portion of a sub-hologram 1302 is shown for a cell in the first central portion 1204, wherein a sub-hologram value 1304 is determined for every other cell. Between each value 1304 are undetermined or intermediate pixels 1306 (in both the x-direction and the y-direction). Fig. 13B A portion of a sub-hologram 1312 for a cell in the second central portion 1206 is shown, wherein for every third cell a sub-hologram value 1314 is determined. Between each value 1314 are two non-determined or intermediate pixels 1316 (in the x-direction and the y-direction). Fig. 13C A portion of a sub-hologram 1322 is shown for a cell in the third central portion 1208, wherein a sub-hologram value 1324 is determined for every fourth pixel. Between each value 1324 are three indeterminate or intermediate pixels 1326 (in the x-direction and the y-direction).

[0218] More generally, determining a sub-hologram of an image point of a cell can be described as comprising the step of determining the value of every nth pixel of the hologram using a point cloud approach. In the above example, for the first central portion 1204, n is 2; for the second central portion 1206, n is 3; and for the third central portion 1208, n is 4. It should be understood that these values ​​of n are merely exemplary. Furthermore, having three central portions is also exemplary. There can be any number of central portions and any number of values ​​for n.

[0219] In conclusion, Fig.12 and 13A 13C show an example where the value of n depends on the location of the cell. Specifically, n increases for cells closer to the center of the target picture.

[0220] Second example

[0221] In a second example, a first subset of image points, each with an associated diffraction resulting in a relatively low spatial frequency used in a point cloud method, is achieved by processing the first image points to reduce the angle of the propagation path. In particular, instead of propagating the wave from the image point along the propagation path to the incident aperture of the observer (so that the propagation path forms a relatively large angle with the display device), a different propagation path is used. The propagation path used in the point cloud method is arranged to form a reduced angle with the display device. This means that the starting point of the propagation path is not an image point in the target image. Another way to describe this is that the image points of the first subset are effectively moved in the target image. Fig.14A and 14B This is shown to be related to a single image point.

[0222] Fig.14A and 14B Both represent point cloud hologram calculations of a single image point. Fig.14A and 14B Both include a point cloud 1402 and a display device 1404 . Fig.14A and 14B The entrance pupil is not shown. Fig.14A The point cloud includes Figure 6 , which has a ray path 1420 extending therefrom. The ray path 1420 corresponds to Figure 6 The propagation path 1420 of , and in this example, has been traced using rays from the first image point 710 to the entrance aperture ( Fig.14A 1420) through the path determined by the display device 1404. The waves of the hologram do not propagate along the light path 1420. Fig.14A An angle 1422 is shown between the ray path 1420 and the normal of the display device 1404. The angle 1422 is Fig.14A The key is that this angle is non-zero and close to the diffraction limit of the display device 1404.

[0223] Fig. 14B The actual propagation path 830 (rather than the ray path 1420) used in the point cloud hologram calculation is shown. The propagation path 1430 is arranged substantially orthogonal to the display device 1404. In other words, the angle 1422 has been reduced (to substantially zero). This means that the propagation path 1430 does not extend from the first image point 610. Instead, the propagation path 1430 has a starting point 1432, which is determined by Fig. 14BOnce the wave has propagated along the propagation path 1430, the complex value and phase value are determined on the display device 1404 or the holographic plane in a manner familiar to the skilled reader. The complex / phase value to be calculated is the effective value of the hologram for the image point at the starting point 1432 of the propagation path 1430, rather than the effective value of the image point at the location of the first image point 610. Therefore, it can be said that as part of the hologram calculation method, the first image point 610 is effectively moved to the starting point 1432. This movement is determined by Fig. 14B The hologram at the image point at the starting point 1432 will have a relatively very low spatial frequency and will actually look similar to Figure 7B A hologram instead of Fig. 7A hologram.

[0224] Without further processing, as in reference Fig. 14B The hologram calculated and displayed on the display device and properly illuminated will form a reconstruction of the first image point 610 at the substantial center of the system's field of view. This does not coincide with the position of the first image point 610 in the target image, which (e.g. Figure 6 and 14A 1402). The inventors have recognized that the original or intended position in the point cloud 1402 can be restored by further processing the hologram to translate the reconstructed points. 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 translate the reconstructed points in a first dimension (e.g., the x-direction), and a second grating function can be added to the hologram to translate the reconstructed points in a second dimension (e.g., the y-direction). The skilled reader will be familiar with the use of phase ramp functions to translate image points. Selecting a gradient or phase ramp function that compensates for the reduction in angle of the propagation path 1430 is simple because the reduction in angle is already known from the hologram calculation process. Therefore, a phase ramp function that reverses / compensates for the reduction can be easily determined / selected.

[0225] The second example can be used to Fig. 9 and 10The sub-holograms of the cells of the target image are calculated in the described manner. In particular, the method includes an initial step of dividing the target image into a plurality of parts or cells. In this example, dividing the target image into a plurality of cells includes defining an angular range from an observer to the target image (using ray tracing). This step is performed virtually. Adjacent angular ranges are adjacent to each other (adjacent to each other) and do not overlap. In this example, the range of each angular range in the x and y directions is equal to each other angular range. In other words, the size of each cell is substantially equal. In this example, the method also includes identifying which image points of the target image 900 fall into which cell. In this example, some cells (e.g., cell 1002) do not contain any image points. Other cells (e.g., cell 1004) contain image points. In this method, cells that do not contain any image points can be effectively ignored. The image points contained in a single cell can be referred to as an image point subset.

[0226] In some examples, the method of computing a hologram includes computing a sub-hologram for each cell (or at least each cell containing an image point). In other words, the method includes computing a sub-hologram for each subset of image points. In some examples, the method of the second example is applied to multiple cells. In some examples, the method of the second example is applied to substantially all cells (perhaps with the exception of the cell in the exact center of the target image, which is as close to the center as possible).

[0227] The benefit of the second example over the first example is that the second example can be used to calculate holograms or sub-holograms at low spatial frequencies for all image points of the target picture. In particular, the second example can be applied to image points appearing in the outermost part of the target picture so that the holograms of these points have the same spatial frequency as the holograms of image points closer to the center. Figure 1 Another benefit of the second example over the first example is that the degree of undersampling can always be maximized. For example, as described above with respect to the first example, a balance is struck between maximizing interpolation without causing aliasing problems. "n" (i.e., the parameter defining the proportion of pixels computed in the point cloud method) can be increased as the image point gets closer to the center (hence Fig.12 ). However, in the second example, the point cloud method can be performed as if the image point is substantially in the center of the target image, regardless of where the image point is actually in the target image. In other words, any image point can be arbitrarily moved closer to the center of the target image before the point cloud method is applied. Thus, in the second example, n can be maximized for all image points.

[0228] In some examples, the hologram calculation may include a combination of the two examples above. For example, the first example may be applied to a subset of image points closer to the center of the target image, while the second example may be applied to a subset of image points closer to the periphery of the target image. Fig.11 , the first example may be applied to a subset of image points in cells of the central portion 1104 , and the second example may be applied to a subset of image points in cells of the outer portion 1102 .

[0229] Implementation of the improved point cloud method

[0230] So far, examples of the improved point cloud method have been described in relatively general terms. Specifically, several examples of computing a hologram (or sub-hologram) of a first subset of image points of a target picture have been described, wherein the first subset of image points has an associated diffraction angle that is less than the maximum diffraction angle of a display device, such that the hologram has a sufficiently low spatial frequency that the hologram can be initially undersampled and then interpolated to full resolution. Here, specific details of examples of implementing the improved point cloud method will be described. These examples are particularly advantageous. The inventors have developed these computationally efficient methods.

[0231] An exemplary embodiment of an improved point cloud hologram includes three accumulators or accumulations. Each accumulator is used to perform an iterative process involved in the calculation of a hologram. As described above, the first step of the method for calculating a hologram includes dividing a target image into a cell array, each cell including a plurality of image points. In general, a first accumulator is arranged to iterate all image points in a subset of image points (e.g., iterate all image points in a first cell in the cell array). The first accumulator thus determines the value of the hologram for a corresponding subset or cell of the image points. In this example, the hologram determined by the first accumulator (using point cloud technology) is undersampled in both the first and second directions (e.g., the x and y directions). In this example, the first accumulator is arranged to interpolate in the first direction but not in the second direction. The second accumulator is arranged to repeat the first accumulation for each cell in the cell array extending in the first direction (i.e., each cell in a cell row or column). The second accumulator is arranged to receive and combine the hologram values ​​determined in each iteration of the first accumulator. Then, the second accumulator is arranged to interpolate these values ​​in the second direction. The third accumulator is arranged to repeat the second accumulation for a cell set extending in the first direction of the cell array. Thus, if the second accumulator is arranged to repeat the first accumulation for the first row unit, the third accumulator repeats the second accumulation for each remaining row unit, and vice versa.After the third accumulation, a full resolution hologram of the full object picture is output.

[0232] The above embodiment is computationally efficient. It minimizes the number of interpolation steps that need to be performed to achieve a full-resolution hologram, thereby effectively implementing the above improved hologram calculation method (including undersampling and interpolation).

[0233] Furthermore, this embodiment allows a grating function (or phase ramp function) to be applied to a hologram while minimizing the number of interpolation steps to be performed. In particular, this embodiment allows different grating functions to be applied to sub-holograms of different cells or parts of a target image. As the skilled reader will be familiar with, it may be desirable to apply a grating function to a hologram in order to achieve a beam steering effect. This may be to move the content within the playback field of a holographic projector as required. For example, such movement may be based on instructions from a user. The movement may compensate for or calibrate for physical changes in the holographic projector, such as those caused by temperature changes of the holographic projector or distortions of the optical combiner. This may require applying different grating functions to (sub-)holograms of image points contained in different cells (for example because the distortion may be non-uniform). Another example where it may be desirable to apply different grating functions to different cells is to use a grating function in a point cloud approach to compensate for movements of image points of a target image (such as Fig.14A and 14B In this case, the image points in different cells may be moved by different amounts so that they are substantially located in the center of the target image. In any case, the inventors have realized that it is not possible to simply add a raster function at the end.

[0234] In any case, the inventors have realized that the required movement can be divided into an x-direction and a y-direction. A first raster function can be used to achieve the required movement in the x-direction. A second raster function can be used to achieve the required movement in the y-direction. The inventors have developed a method to achieve this in a computationally efficient manner.

[0235] Now refer to Fig.15 This embodiment (including three accumulators) is described in more detail.

[0236] First accumulator

[0237] Fig.15 1 is a flow chart showing the first accumulation 1500 of a single unit applied to a target picture. In the following description, Fig.16A As shown, the first accumulation 1500 is applied to a cell 1602 of the target picture 900. For illustrative purposes, the cell 1602 is shaded grey in FIG16. The cell 1602 includes an image point that forms a portion of the number nine.

[0238] The step 1502 of the first accumulation 1500 comprises setting a counter j to zero. The counter is stored in a memory of a hologram engine arranged to execute a hologram calculation method (not shown in the figure).

[0239] Step 1504 of the first accumulation 1500 comprises comparing the current value of the counter j with the number x of image points contained in the cell 1602. Optionally, the first accumulation comprises determining the number x of image points. Alternatively, the number x of image points of the cell 1602 may have been previously determined or identified and may be contained in a memory of the hologram engine. For example, when the target image is divided into an array of cells, the number of image points in each cell may have been previously identified. The hologram engine may be arranged to count the number of image points in each cell and store the count in a memory.

[0240] If j is less than x, the first accumulation moves to step 1506. If j is equal to or greater than x, the first accumulation moves to step 1512.

[0241] Step 1506 of the first accumulation 1500 includes using a point cloud method to (virtually) propagate a wave along a propagation path associated with the j-th image point of the first unit 1602. In some examples, the propagation path is defined as from the j-th image point of the first unit 1602 to the aperture of the viewing system, which may have been determined using an eye tracker. This is similar to Figure 6 In other examples, some processing may have been applied so that the angle between the propagation path and the display device is reduced. In fact, the jth image point may have been moved closer to the center of the target image 900 or substantially at the center of the target image 900. This is consistent with the description of Fig.14A and 14B The example described is consistent. The processing of the jth image point and / or the associated propagation path may have been performed before the first accumulation or during step 1506 of the first accumulation. In other examples, each propagation path associated with the jth image point used in the point cloud method is such that the angle formed by it with the display device 604, 1404 is less than, optionally much less than, the maximum diffraction angle of the display device 604, 1404. The maximum diffraction angle of the display device 604, 1404 is determined by the pixel pitch of the display device and is defined relative to the normal of the display device. Optionally, the angle of each propagation path with the display device can be substantially zero. In any case, the angle of the propagation path associated with the jth image point is such that the hologram value has a relatively low spatial frequency. In this example, a hologram value is then determined for every 5th pixel of the display device in the x-direction and the y-direction. In other words, the hologram value determined in step 1506 is determined in the x-direction and the y-direction at a resolution reduced relative to the inherent resolution of the display device 604, 1604. In other words, the hologram value is undersampled.

[0242] Fig. 16B The output of step 1506 is shown. Fig. 16B A portion of a hologram is shown, wherein a hologram value has been determined for every 5th pixel. The pixels 1614 whose hologram values ​​have been determined in step 1506 are represented by Fig. 16B The black square in FIG. 1506 indicates that the pixel 1616 whose holographic value is not determined in step 1506 is Fig. 16B Indicated by white squares.

[0243] Step 1508 of the first accumulation 1500 includes storing the hologram values ​​output in step 1506 in a memory of the hologram engine. If the hologram values ​​for the respective pixels are already stored in the memory (because an iteration of the first accumulation has been performed for the previous image point 1614), then step 1508 includes adding (i.e., accumulating or summing or superimposing) the hologram value for each pixel 1614 of the j-th image point to the currently stored hologram value for that pixel. Thus, each value for each pixel may actually be an accumulated value combining the values ​​calculated for that pixel for each image point.

[0244] The step 1510 of the first accumulation includes increasing the counter j by 1. Then, the first accumulation returns to the step 1504.

[0245] For each image point j of the first cell 1602, steps 1504 to 1510 of the first accumulation 1500 are repeated. For each iteration, the wave is propagated along the propagation axis of the j-th image point using the point cloud method and a hologram value is determined for this j-th image point with a reduced resolution in the x and y directions. In each iteration, new hologram values ​​are determined in step 1506. In step 1508, these are added to the hologram values ​​already stored in the memory. Thus, the hologram values ​​for the pixel 1614 are accumulated in the memory over time (hence the term "accumulator").

[0246] The first accumulator continues to iterate steps 1504 to 1510 for each image point until j equals x. When j equals x, the first accumulator moves to step 1512 instead of step 1506.

[0247] In this example, step 1512 of the first accumulator 1500 includes performing interpolation in the x-direction only. In an example, a bicubic interpolation scheme may be used for interpolation. Interpolation is used to determine the hologram value of the pixel 1616 in the x-direction between the pixels 1614. The result is Fig. 16C , where pixels 1614 for which holographic values ​​have been determined extend in consecutive rows. In other examples, step 1512 of the first accumulator 1500 comprises performing interpolation in the y direction only.

[0248] In this example, step 1514 of the first accumulator 1500 includes applying the first raster function to Fig. 16C of pixels 1614 (but not between rows of pixels 1614 Fig. 16C Pixels 1616). It is important that the interpolation of step 1512 is performed before applying the first raster function of step 1514. This is because the first raster function is actually a high frequency function. Therefore, if the first raster function is applied before interpolation, the high frequency of the first raster function may cause aliasing problems in the interpolation.

[0249] At step 1516 of the first accumulator 1500, the hologram values ​​of step 1514 are output to the second accumulator and the memory used by the first accumulator is cleared. The hologram values ​​output in step 1516 are substantially full resolution in the x-direction (because interpolation has been performed in the x-direction), but are reduced resolution in the y-direction. The hologram values ​​also include the first grating function.

[0250] If the output of step 1516 is displayed on a display device (e.g., a liquid crystal on silicon spatial light modulator) and properly illuminated, a holographic reconstruction of the image point of cell 1602 will be formed. Fig.16D The situation shown.

[0251] In step 1518 of the first accumulation 1500, the memory used in the first accumulation is cleared.

[0252] Second accumulator

[0253] Fig.17 1 is a flow chart showing the second accumulation 1700 applied to the unit row of the target image. In the following description, the second accumulation 1700 is applied to the unit row 1902 of the target image 900, as shown in FIG. Fig.19A For illustration purposes, cell row 1902 is shaded grey in FIG19. Cell row 1902 includes image points that form the top of the number 9 and the tops of two boundary graphics.

[0254] The step 1702 of the second accumulation 1700 comprises setting a counter k to zero. The counter is stored in a memory of a hologram engine arranged to execute a hologram calculation method (not shown in the figure).

[0255] Step 1704 of the second accumulation 1700 comprises comparing the current value of the counter k with the number of cells y in the cell row 1902. In this example, there are 8 individual cells in the cell row 1902. Therefore, y=8 in this example.

[0256] If k is less than y, the second accumulation 1700 moves to step 1706. If k is equal to or greater than y, the second accumulation 1700 moves to step 1712.

[0257] The step 1706 of the second accumulation includes performing the first accumulation 1500 on the k-th cell of the cell row 1902. Thus, the second accumulation 1700 actually includes performing the first accumulation 1500 (optionally, multiple iterations).

[0258] According to step 1516 of the first accumulation 1500, the hologram value determined in the first accumulation 1500 is output to the second accumulator. Therefore, step 1708 of the second accumulation 1700 includes receiving the hologram value determined in the first accumulation. Step 1708 of the second accumulation 1700 also includes storing the hologram value in a memory of the hologram engine. If the hologram value of each pixel is already stored in the memory (because the first accumulation has been performed on the previous cell in the cell row 1902), step 1708 includes adding (i.e., accumulating or summing or superimposing) the hologram value of each pixel 1614 to the currently stored hologram value of the pixel. Therefore, each value of each pixel can effectively be a cumulative value that combines the values ​​calculated for that pixel for each cell in the cell row.

[0259] The step 1710 of the second accumulation comprises increasing the counter k by 1. The second accumulation then returns to the step 1704 .

[0260] Steps 1704 to 1710 of the second accumulation 1700 are repeated for each cell k of the cell row 1902. For each iteration, a first accumulation is performed for the kth cell and a new hologram value is determined in the first accumulation which is added to the hologram values ​​already stored in the memory of the hologram engine for the second accumulation.

[0261] The hologram value at the second accumulation step 1708 is Fig.19B Because the hologram value determined in step 1708 corresponds to the first accumulated output, Fig.19B Corresponds to Fig. 16B .in other words, Fig.19B A portion of a hologram is shown, wherein a hologram value has been determined for every 5th pixel. Pixel 1914 whose hologram value has been determined in step 1708 is represented by Fig.19B The black square in . The pixel 1916 whose hologram value has not yet been determined is represented by Fig.19B The white square in the figure indicates.

[0262] The second accumulator continues to repeat steps 1704 to 1710 for each cell until k equals y. When k equals y, the second accumulator moves to step 1712 instead of step 1706.

[0263] In this example, step 1712 of the second accumulation 1700 includes performing interpolation in the opposite direction to that performed in the first accumulator. Since the interpolation of the first accumulation in this example is only in the x direction, the interpolation performed by the second accumulation in this example is only in the y direction. In an example, a bicubic interpolation scheme may be used for interpolation. Interpolation is used to determine the hologram value of the pixel 1616 in the y direction between the rows of pixels 1614. The result is Fig.19C , where the pixels 1614 for which the holographic values ​​have been determined extend in a continuous two-dimensional block. In other examples, step 1712 of the second accumulation 1700 comprises performing interpolation only in the y direction (if the interpolation performed in the first accumulation was only in the x direction).

[0264] In this example, step 1714 of the second accumulation 1700 includes Fig.19C The second raster function is applied to the pixels 1614 of step 1712. It is important that the interpolation of step 1712 is performed before the second raster function of step 1714 is applied. This is because the second raster function may actually be a high frequency function. Therefore, if the second raster function is applied before the interpolation, the high frequency of the second raster function may cause aliasing problems in the interpolation.

[0265] At step 1716 of the second accumulator 1700, the hologram values ​​of step 1714 are output to the third accumulator and the memory used by the second accumulator is cleared. The hologram values ​​output in step 1516 are substantially full resolution in the x and y directions (because interpolation has been performed in the x and y directions in the first and second accumulations, respectively). The hologram values ​​also include one or more grating functions.

[0266] If the output of step 1716 is displayed on a display device (e.g., a liquid crystal on silicon spatial light modulator) and illuminated appropriately, a holographic reconstruction of cell row 1702 will be formed. Fig.19D The situation shown.

[0267] In step 1718 of the second accumulation 1700, the memory for the second accumulation is cleared.

[0268] Third accumulator

[0269] Fig.18 1 is a flow chart showing the third accumulation 1800 applied to the 2D cell array of the target image. In the following description, the third accumulation 1800 is applied to the 2D cell array 2002 of the target image 900, as shown in FIG. Fig. 20A For the purpose of illustration, the 2D cell array 2002 is Fig. 20A The 2D array of unit 2002 corresponds to Fig.11 The center portion 1104 of the unit.

[0270] The step 1802 of the third accumulation 1800 comprises setting a counter 1 to zero. The counter is stored in a memory of a hologram engine arranged to execute a hologram calculation method (not shown in the figure).

[0271] Step 1804 of the third accumulation 1800 includes comparing the current value of the counter 1 with the number of rows of cells z in the 2D array 2002. In this example, there are 4 individual rows of cells in the array 2002. So z=4 in this example.

[0272] If l is less than z, the third accumulation 1800 moves to step 1806. If l is equal to or greater than z, the third accumulation 1800 moves to step 1812.

[0273] Step 1806 of the third accumulation 1800 includes executing the second accumulation 1700 on the lth row of cells in 2002. Thus, the third accumulation 1800 actually includes executing the second accumulation 1700 (optionally, multiple iterations).

[0274] According to step 1716 of the second accumulation 1700, the hologram value determined in the second accumulation 1700 is output to the third accumulator. Therefore, step 1808 of the third accumulation 1800 includes receiving the hologram value determined in the second accumulation. Step 1808 of the third accumulation 1800 also includes storing the hologram value in a memory of the hologram engine. If the hologram values ​​of the individual pixels are already stored in the memory (because the second accumulation has been performed on the previous row of cells in the array 2002), step 1808 includes adding (i.e., accumulating or summing or superimposing) the hologram value of each pixel 1614 to the currently stored hologram value of the pixel. Therefore, each value of each pixel can effectively be a cumulative value that combines the values ​​calculated for the pixel of each cell in the row of cells.

[0275] The second accumulation step 1810 includes increasing the counter 1 by 1. The third accumulation 1800 then returns to step 1804.

[0276] Steps 1804 to 1810 of the third accumulation 1800 are repeated for each cell l of the cell row 2002. For each iteration, a second accumulation is performed for the lth row of cells and a new hologram value is determined in the second accumulation which is added to the hologram values ​​already stored in the memory of the hologram engine for the third accumulation.

[0277] The hologram value at the third accumulation step 1808 is Fig. 20B Because the hologram value determined in step 1808 corresponds to the second accumulated output, Fig. 20B Corresponds to Fig.19C .

[0278] The third accumulation continues to repeat steps 1804 to 1810 for each cell until l equals z. When l equals z, the third accumulation 1800 moves to step 1812 instead of step 1806.

[0279] Step 1812 of the third accumulation 1800 includes outputting a hologram. The hologram is full resolution in the x and y directions. The hologram value also includes one or more grating functions.

[0280] If the output of step 1812 is displayed on a display device (e.g., a liquid crystal on silicon spatial light modulator) and properly illuminated, a holographic reconstruction of the image points of the element array 1902 will be formed. Fig. 20C The situation shown.

[0281] Step 1814 of the third accumulation 1800 includes clearing the memory for the third accumulation.

[0282] Among the three accumulators mentioned above, the allowed values ​​are those corresponding to Fig.11 The center portion shown Fig. 20A The cell array 1802 shown determines the hologram. This is the portion where an image point may have an associated hologram value that has a sufficiently low spatial frequency that the hologram value may initially be undersampled. In the example, the hologram corresponding to Fig.11 The hologram values ​​for the remaining cells of the outer portion shown can be calculated using the point cloud hologram in a conventional manner (eg without undersampling and interpolation). These values ​​can be added to the hologram output in the third accumulated step 1812.

[0283] In some examples, the cell array may include all cells of the target image. Thus, the first accumulator may be iteratively applied (via the second and third accumulators) to each cell of the cell array. In such an embodiment, the image point of each cell may be moved or otherwise processed to be closer to the center of the target image before the accumulation is applied. The first and second raster functions may then be used to compensate for this processing. A skilled reader will appreciate that it may be desirable to apply different first and second raster functions to each cell (in the first and second interpolations) to push cells and / or cell rows back to their respective original positions.

[0284] In some examples, according to Fig.12 For different units, undersampling may be different.

[0285] Additional Features

[0286] The methods and processes described herein may be embodied on a computer-readable medium. The term "computer-readable medium" includes media arranged to store data temporarily or permanently, such as random access memory (RAM), read-only memory (ROM), buffer memory, flash memory, and cache memory. The term "computer-readable medium" should also be considered to include any medium or combination of media capable of storing instructions for execution by a machine, so that when the instructions are executed by one or more processors, the machine performs, in whole or in part, any one or more of the methods described herein.

[0287] The term "computer-readable medium" also encompasses cloud-based storage systems. The term "computer-readable medium" includes, but is not limited to, one or more tangible and non-transitory data storage repositories (e.g., data volumes) in the example form of solid-state memory chips, optical disks, magnetic disks, or any suitable combination thereof. In some example embodiments, instructions for execution may be conveyed by a carrier medium. Examples of such carrier media include transient media (e.g., propagated signals conveying instructions).

[0288] It will be apparent to those skilled in the art that various modifications and variations can be made without departing from the scope of the appended claims. The present disclosure covers all modifications and variations within the scope of the appended claims and their equivalents.

Claims

1. A hologram engine for calculating a hologram of a target image comprising a plurality of image points, the hologram engine being arranged to perform a first data processing stage, for a first subset of image points, the first data processing stage comprising: Determining a value of every nth pixel of a display device for displaying a hologram using a point cloud method, where n is greater than 1; and determining values ​​of at least some other pixels by performing a first interpolation; Therein, each image point of the first subset has an associated diffraction angle for the point cloud method, each diffraction angle being smaller than a maximum diffraction angle of the display device.

2. The hologram engine of claim 1, wherein: The hologram engine is arranged such that determining the value of each nth pixel comprises: For each image point of the first subset, determining a value of an nth pixel of the display device using a point cloud method; and The values ​​determined for each image point at each of the nth pixels are combined.

3. The hologram engine of claim 2, wherein: The first interpolation is based on a combined value determined for each nth pixel.

4. A hologram engine as claimed in any preceding claim, wherein: The value determined for each image point using the point cloud method is a value representing the contribution of a wave propagating along a path at an angle to the display device that is equal to the associated diffraction angle of the corresponding image point.

5. A hologram engine as claimed in any preceding claim, wherein: The diffraction angle associated with each image point of the first subset is defined as follows: through a first path from the image point to the observer's entrance pupil; or Through the second path, the second path is arranged as if the corresponding image point has been translated closer to the center of the target picture, so that the second path is at an angle with the display device that is reduced relative to the angle made by the corresponding first path for the image point.

6. A hologram engine as claimed in any preceding claim, wherein: The maximum diffraction angle of the display device defines a replay field including a central portion surrounded by an outer portion, the central portion including a center of the replay field, wherein the central portion occupies an area less than 50% of the replay field.

7. The hologram engine of claim 6, wherein: The first subset of image points is contained in a central portion of the playback field; Or wherein the point cloud method is arranged as if the first subset of image points had been translated from an outer part to a central part of the replay plane.

8. A hologram engine as claimed in any preceding claim, wherein: The hologram engine is arranged such that at least some of the pixels whose values ​​are determined using the point cloud method are separated by one or more first intermediate pixels in a first dimension, and wherein the first interpolation is performed in the first dimension to determine the values ​​of the first intermediate pixels.

9. The hologram engine of claim 8, wherein: The first data processing stage further comprises applying a first grating function arranged to translate light incident thereon in a first direction parallel to the first dimension and applying the grating function after the first interpolation.

10. A hologram engine as claimed in any preceding claim, wherein: The hologram is for use in a display device comprising an array of pixels extending in the first dimension and in a second dimension perpendicular to the first dimension, and Therein, the hologram engine is arranged such that at least some of the pixels whose values ​​are determined using the point cloud method are separated in the second dimension by one or more second intermediate pixels.

11. The hologram engine of claim 10, wherein: The hologram engine is arranged to determine the value of the second intermediate pixel by performing a second interpolation in the second dimension, the hologram engine being arranged to perform the second interpolation after the first interpolation.

12. A hologram engine as claimed in any preceding claim, wherein: The hologram engine is arranged to perform a second data processing stage, wherein the second data processing stage comprises: receiving a value determined in said first data processing stage; and Repeating the first data processing stage for k subset image points of the target image and receiving corresponding values, each of the k subset image points corresponds to a discrete angle range defined by a first angle in the first dimension and a second angle in the second dimension, the second angle being the same for each of the k subsets.

13. The hologram engine of claim 12, wherein: The hologram engine is further arranged to combine, during the second data processing stage, values ​​determined for each of the nth pixel and the first intermediate pixels.

14. A hologram engine as claimed in claim 12 when dependent on claim 11, wherein: The second data processing stage comprises a second interpolation, and wherein the hologram engine is arranged such that the second interpolation is performed after the step of combining values ​​determined during the second data processing stage.

15. The hologram engine according to any one of claims 12 to 14, wherein: The second data processing stage further comprises applying a second grating function arranged to translate light incident thereon in a second direction parallel to the second dimension.

16. A hologram engine as claimed in claim 15 when dependent on claim 14, wherein: The hologram engine is arranged such that the second data processing stage comprises applying the second grating function after performing the second interpolation.

17. The hologram engine according to any one of claims 12 to 16, wherein: The hologram engine is arranged to perform a third data processing stage, wherein the third data processing stage comprises: receiving a value determined in the second data processing stage; The second data processing stage is repeated for l subset image points of the target image and corresponding values ​​are received, each of the l subset image points corresponds to a discrete angle range defined by a first angle in the first dimension and a second angle in the second dimension, wherein the second angle is different each time the second data processing stage is repeated.

18. A hologram engine as claimed in any preceding claim, wherein: The hologram engine is arranged to divide the target picture into an array of cells, each cell containing a subset of image points.

19. The hologram engine of claim 18, wherein: The first data processing stage is initially performed on image points of a first cell in the array of cells.

20. A hologram engine as claimed in claim 18 or 19 when dependent on claim 12, wherein: The second data processing stage includes repeating the first data processing stage for each cell in a cell column or row of a cell array that includes the first cell.

21. A hologram engine as claimed in claim 20 when dependent on claim 17, wherein: The third data processing stage includes repeating the first and second data processing stages for each column or row cell of the cell array.

22. A method for calculating a hologram of a target picture comprising a plurality of image points, the method comprising performing a first data processing stage, for a first subset of image points, the first data processing stage comprising: Determining a value of every nth pixel of a display device for displaying a hologram using a point cloud method, where n is greater than 1; and determining values ​​of at least some other pixels by performing a first interpolation; Therein, each image point of the first subset has an associated diffraction angle for the point cloud method, each diffraction angle being smaller than a maximum diffraction angle of the display device.

Images