Holographic display system and method for reducing the effects of quantization noise - Patents.com

Abstract

The holographic display system (400) includes a light source (420) configured to emit at least partially coherent light, a modulator (404) arranged to generate a light field emitted by the at least partially coherent light, the light field being a quantized representation of a target light field, H, and a spatial filter defining an aperture (410) in the Fourier plane. The Fourier transform of the target light field, F(H), is defined as (i) the complex conjugate of the target light field, F(H * ), (ii) the Fourier transform of the target light field multiplied by the complex conjugate of the target light field, F(HH * ), (iii) the square Fourier transform of the target light field, F(H 2 ), and (iv) the complex conjugate square Fourier transform of the light field F(H *2 ), the aperture corresponds substantially to F(H) in the Fourier plane.

Description

[Technical field]

[0001] The present invention relates to holography and methods for producing holographic images. [Background technology]

[0002] Computer-generated holography, CGH, is known. A holographic light field is determined for a display using coherent or at least partially coherent light and is defined in terms of the amplitude and phase of each element (pixel) of the display. This combination results in a light field that is perceived by the observer with depth information. An ideal holographic display for such a light field would be capable of full complex modulation, where the amplitude and phase values ​​at each pixel of the hologram may vary to closely resemble the determined amplitude and phase of the light field. In other words, an ideal holographic display would be capable of displaying all possible combinations of phase and amplitude.

[0003] In fact, displays used for CGHs cannot achieve full complex modulation. Typical displays used for CGHs may only have very limited values ​​that they can display. For example, the displays may only have the ability to modulate either amplitude or phase. Resolution may also be limited to roughly 5-bit resolution (giving 32 or fewer displayable values), or even just binary in the case of binary display technologies.

[0004] As a result, the pixels of the full complex holographic image are quantized to values ​​that can be reproduced by the display for display. For example, in the extreme case of a binary display (Digital Micromirror Device, DMD), each pixel in the display can only be in one of two states. Every point on the full complex Argand diagram needs to be mapped to one of two states.

[0005] The process of quantization for a display reduces image quality, such that contrast and / or noise is reduced, which is visible in the perceived image.

[0006] It is known to improve the quality of quantized holograms for display through iterative methods such as the Gerchberg Saxton algorithm. However, these methods require a large number of iterations (approximately 100 or more) and therefore require significant processing resources and / or power. This is especially evident for moving holograms, where such iterative methods can reduce the frame rate and / or introduce lag.

[0007] It is desirable to improve the image quality of CGH displays with reduced requirements for processing resources and / or power. Summary of the Invention

[0008] According to a first aspect of the present invention, there is provided a holographic display system including a light source configured to emit at least partially coherent light, a modulator arranged to be illuminated by the at least partially coherent light, and a spatial filter defining an aperture in the Fourier plane. The Fourier transform of a target light field, F(H), is calculated by: (i) the complex conjugate of the target light field, F(H * ), (ii) the Fourier transform of the target light field multiplied by the complex conjugate of the target light field, F(HH * ), (iii) the square Fourier transform of the target light field, F(H 2 ), and (iv) the complex conjugate square Fourier transform of the light field F(H *2 ), and the aperture corresponds substantially to F(H) in the Fourier plane.

[0009] Such a structure can improve the image quality of the displayed hologram by a combination of restrictions on the extent of the target light field in the Fourier plane (by defining that it cannot overlap with its complex conjugate and the Fourier transform of higher order terms) and positioning of the aperture to correspond to F(H) in the Fourier plane. By F(H), it is meant the portion of the Fourier plane that has a non-zero value. It has been discovered that this arrangement prevents additional components in the Fourier plane that are introduced by quantization to the display. Furthermore, determining H in this manner is computationally simpler than previous iterative methods such as Gerchberg Saxton, reducing requirements for processing resources. This can enable higher quality holographic displays along with reduced processing and / or power requirements, allowing for one or more of the following: lower cost displays, greater portability, and, in the case of battery-powered devices, longer battery life.

[0010] As will be explained in more detail later, the inventors have realized that noise introduced by quantization to a display results in additional components in the Fourier plane that are approximated by a series expansion. By considering the additional terms in the series expansion and ensuring that they do not overlap with F(H) such that the additional components are blocked by a filter, additional image quality can be obtained. Since the energy in the series expansion tends to be concentrated in the low order terms, it is necessary to estimate at least F(H * ), and F(HH * ), F(H 2 ) and F(H *2 ) are also beneficial, but there comes a point where the impact of each term is small and imposing further constraints has little observable effect on image quality.

[0011] The light source may be, for example, a laser or other coherent or quasi-coherent light source, which may include a single emitter or multiple emitters and may emit light having a single wavelength or multiple wavelengths.

[0012] The modulator can be any modulator or modulating means suitable for modulating the amplitude and / or phase of coherent or quasi-coherent light, including Liquid Crystal on Silicon (LCoS) devices, Digital Micromirror Devices (DMDs), and liquid crystals. In one embodiment, the modulator is a spatial light modulator.

[0013] The spatial filter can be any suitable means of forming a Fourier plane and spatially filtering light within that plane. In one embodiment, the spatial filter includes a lens having a focal length and a filter that defines an aperture. The filter and the modulator are positioned on opposite sides of the lens at a distance of one focal length from the lens. The lens is preferably a Fourier lens and may be formed from multiple elements. In some embodiments, the lens may be a lens array, with the lens including the array extending across the imaging area.

[0014] The modulators, lenses, and filters may be substantially coaxial in some embodiments. Other arrangements are possible, such as a folded optical path with mirror and / or prism elements in the optical path, potentially allowing for a more compact arrangement.

[0015] The filter defines an aperture through which light can pass, and generally blocks or otherwise prevents light from passing outside the aperture (e.g., the filter may be configured to absorb light outside the aperture, or reflect it elsewhere outside the optical path).

[0016] In some embodiments, further constraints on F(H) may be placed.

[0017] Due to the presence of the filters, not all of the Fourier planes that can be generated by the SLM are actually used. This may result in a darkening of the display or a reduction in the size of the area in which the displayed hologram can be viewed. There are no specific constraints on the shape of the perimeter of F(H), but it is assumed that at least F(H * ), F(H 2 ), F(H *2 ), and F(HH * ), analysis of the behavior of the function in the Fourier plane has shown that a well-defined region can be defined. In some examples, at least a portion of the perimeter can be a straight line. This can allow for a larger display area than a curved perimeter.

[0018] The Fourier plane may be partitioned into a number of contiguous unit squares, with each unit square receiving one copy of the Fourier transform of the target light field. The aperture may then have an area that is approximately 1 / 6 of the unit square. As will be explained in more detail later, the unit square is the result of taking the Fourier transform of a discrete grid of modulators that produce a repeating pattern. The 1 / 6 area is understood to set a limit on the maximum size of the aperture that can satisfy the non-overlapping constraint.

[0019] In some embodiments, the perimeter of the aperture is a rectangle. Suitable rectangles include rectangles, squares, and trapezoids. Some embodiments use a right trapezium, and other embodiments use an isosceles trapezoid for the aperture. (Trapeziums may also be referred to as trapezoids, so a right trapezium is a right trapezoid, and an isosceles trapezium is an isosceles trapezoid.)

[0020] In some embodiments, the filter may have a single aperture, while in other embodiments, the filter may define at least two apertures, which may be non-contiguous.

[0021] In some embodiments, the filter includes multiple portions that can be selectively controlled to have a first state in which light is blocked, or a second state in which light is allowed to pass, whereby an aperture is formed by the portions in the second state. This allows the position and range of the aperture to be controlled as needed. For example, with a suitable responsive display, holograms with different positions of the target light field can be displayed in rapid temporal succession. This can expand the range of positions from which the displayed hologram can be viewed, or increase the perceived image quality.

[0022] As discussed above, the spatial light modulator may be a digital micromirror device (DMD). The display systems and methods discussed herein may provide significant improvements to the image quality of a DMD due to its binary nature. In another embodiment, the spatial light modulator is a Liquid Crystal on Silicon, LCoS, device. LCoS devices may have more quantized states than a DMD, but beneficial improvements in image quality are also achieved. When the spatial light modulator is an amplitude-only SLM such as a DMD, the display systems and methods described herein may enable the display of holograms with improved (darker) black levels.

[0023] The position and size of the aperture is determined with reference to a square having dimensions based on the wavelength of light from the light source. Some embodiments may use a single wavelength for a monochrome display. In other embodiments, the light source is configured to emit at least partially coherent light at two or more different wavelengths for a range of colors, such as red, green, and blue, that can be switched in series for a color display. In one embodiment, the light source is configured to emit at least partially coherent light at multiple wavelengths, including green light, and the aperture corresponds to a position of F(H) for the green light. The green light may have a wavelength in the range of 495 to 570 nanometers, or in the range of 520 to 560 nanometers, such as 530 nanometers. In another embodiment, the aperture corresponds to a portion of F(H) that has at least partially coherent light at the smallest wavelength of the two different wavelengths. In that case, the aperture may be optimized for only one wavelength. Some embodiments may adjust the size of the aperture to correspond to the wavelength, for example, using an aperture with a selectively controllable portion as discussed above. In another embodiment, the lens has optical properties configured such that the aperture corresponds to F(H) having light that is at least partially coherent at both wavelengths. The optical properties include at least one of a shape and a refractive index.

[0024] The light source may be configured to emit at least partially coherent light at multiple wavelengths, and one side of the aperture may be angled at 45 degrees. For example, at least one side may be angled with respect to an axis that defines a unit square of the Fourier plane. * This can be beneficial because the apertures can be positioned such that the λ / 2, λ / 3, λ / 4, λ / 5, λ / 6, λ / 7, λ / 8, λ / 9, λ / 10, λ / 11, λ / 22, λ / 23, λ / 34, λ / 15, λ / 26, λ / 36, λ / 14, λ / 27, λ / 28, λ / 38,

[0025] The light source may include at least two emitters positioned such that the zero-order Fourier plane is at a different location for each of the at least two emitters, with at least one aperture for each of the at least two emitters, and a filter separating the at least two apertures. This may allow a larger portion of the Fourier plane to be covered by tiling the apertures for the different emitters. Each emitter may have its own respective aperture(s) separated by a filter, independent of the other aperture(s) for the other emitters. The apertures may at least partially overlap such that an aperture for one emitter shares at least a portion of its open area with an aperture for another emitter. The at least two emitters may be operated in a time sequence with their respective apertures. For example, a first emitter and a first aperture are activated, followed in time by activating a second emitter and a second aperture.

[0026] The light source may include a first emitter having a first wavelength and a second emitter having a second wavelength, the first emitter and the second emitter positioned such that the F(H) of one of the first emitter and the second emitter is contained within the F(H) of the other of the first emitter and the second emitter, which may mean that the same aperture is appropriate for both emitters.

[0027] According to another aspect, a filter is provided that defines an aperture corresponding to a Fourier transform, F(H), of a target light field in the Fourier plane, H, where the Fourier transform F(H) is: (i) its complex conjugate, F(H * ), (ii) the target light field, F(HH * ), (iii) the Fourier transform of the target light field, F(H 2 ) square Fourier transform, and the light field F(H *2), does not overlap with. Locating such a filter within a holographic display, when combined with controlling the display to display a corresponding target light field H, may enable the display to benefit from the image quality improvements discussed herein. The filters and apertures may have any of the characteristics discussed above for filters and apertures.

[0028] In use, the filter can be positioned at different positions in the optical path, such as occupying a "pupil plane" or an "image plane". The pupil plane is the plane that corresponds to the image of the modulator as reproduced on the observer's movement, and may allow for additional freedom in the design of the aperture. Pupil planes, and planes such as the pupil, have the property that there may be gaps in the aperture without significantly altering the image seen. When the filter is not positioned at the pupil plane or a pupil-like plane, it is considered to be in the image plane. When the filter is positioned at the image plane, gaps in the aperture may be visible to the observer, and as a result, it is preferable to avoid such gaps in the aperture. Examples are described below with reference to Figures 3 and 8.

[0029] According to a further aspect, a target light field, H, for quantization is determined, the target light field being (i) its complex conjugate, F(H * ), (ii) the Fourier transform of the target light field multiplied by the complex conjugate of the target light field, F(HH * ), (iii) the square Fourier transform of the target light field, F(H 2 ), and (iv) the square Fourier transform of the complex conjugate of the light field F(H *2 ), and determine the Fourier transform, F(H), such that it does not overlap with the F(H * ), F(HH * ), F(H 2 ), and F(H *2and displaying a quantized version of the target light field through a filter that bounds an aperture corresponding to a range of F(H) in the Fourier plane such that components corresponding to F(H) are substantially blocked by the filter.

[0030] Therefore, the Fourier transform of the target light field, F(H), is limited in range and occupies only a portion of the Fourier plane. This may result in a darker image and / or a smaller viewing area, but this constraint means that components introduced by quantization are filtered out and do not reach the observer's eye, improving image quality.

[0031] In addition, F(H) is the target light field, F(HH * ) may not overlap with the Fourier transform of the target light field multiplied by the complex conjugate of F(H). 2 ) square Fourier transform and light field F(H *2 ) the Fourier transform of the complex conjugate square of

[0032] The shape or extent of F(H) in the Fourier plane can be any that satisfies the constraints, but in some embodiments, the extent of F(H) in the Fourier plane has at least one rectilinear perimeter. The extent of F(H) in the Fourier plane may have a rectangular perimeter. The extent of F(H) in the Fourier plane may include at least two disjoint regions.

[0033] The target light field having F(H) within a precise region of the Fourier plane can be determined in any suitable manner. For example, it can be determined by applying a mask to the initial light field in the Fourier plane. In this way, the range of the target light field is limited in the Fourier plane. The initial light field can be a full complex representation of the target light filter that occupies the entire addressable range of the Fourier plane. The mask can be applied in the Fourier domain by setting values ​​below the mask to zero or a predefined value.

[0034] Display of the quantized image can be done in any suitable manner, for example by illuminating a spatial light modulator with coherent or quasi-coherent light and controlling the SLM to adapt the inverse Fourier transform of the masked light field.

[0035] The advantage of the method of the present invention is that through the positioning of the filter and the limitation of F(H), the process can be considered to reduce the computational requirements and allow the noise not to enter the blind "don't care" areas. In other words, the aperture design ensures that the noise is reduced without the need to evaluate the exact noise field. This is different from iterative Fourier transform algorithms (IFTA) such as Gerchberg Saxton (GS). In GS and other IFTAs, the replay field of the image must be computationally reconstructed and iteratively improved, requiring significant processing resources. Some embodiments may use IFTA in combination with an aperture. This may allow improved image quality with reduced processing because fewer iterations are required due to the action of the filter to reduce noise.

[0036] Thus, any suitable quantization method and resolution can be used, quantized in phase and / or amplitude. For example, the quantization may be the closest value that can be reproduced by the display, the closest value that can be reproduced by the display without increasing the amplitude, the closest value that can be reproduced by the display without increasing the phase, etc. Some embodiments may apply a real offset, such as to the masked light field, before quantizing. The real offset may be based on the average amplitude of the values ​​before quantization, such as the root mean square (rms) amplitude. Another embodiment may quantize |H+c|^2. In such embodiments, the preferred quantization may not be the quantization scheme that minimizes the total quantization scale in the SLM. The quantized version of H may be expressed as H Q When expressed as Q =H Q −H. Usually, the total quantization factor in F(H) can be achieved by quantizing each pixel to the nearest available value, E Q However, F(H * ), F(H 2 ), F(H *2 ), and F(HH * A particular quantization scheme may be used that increases the combined noise factor in F(H) but reduces the noise factor in F(H). Such a quantization scheme reduces the noise factor E Q while still reducing the noise factor in F(H) transmitted through the aperture.

[0037] The method may include generating multiple target light fields in different regions of the Fourier domain, each of the multiple target light fields having the property that the range of their Fourier transform does not overlap with the range of the Fourier transform of their complex conjugate, and displaying a quantized version of each of the multiple target light fields in rapid temporal succession through a respective filter that bounds an aperture corresponding to the range of their Fourier transform in the Fourier plane, which may increase the area in which the hologram can be viewed.

[0038] According to another aspect, a computer readable medium, such as a non-transitory computer readable medium, is provided that includes instructions that, when executed by a processor, cause the holographic display system discussed above to display a holographic image according to the method discussed above.

[0039] Further features and advantages of the invention will become apparent from the following description of preferred embodiments of the invention, given by way of example only, made with reference to the accompanying drawings, in which: [Brief description of the drawings]

[0040] [Figure 1A] 1 shows an example of the location of the Fourier transform of a hologram, F(H), in the Fourier plane. [Figure 1B] 1 illustrates the location of F(H*) in the Fourier plane according to an embodiment. [Figure 1C] 1 illustrates the location of F(HH*) in the Fourier plane according to an embodiment. [Figure 1D] 1 illustrates the location of F(H2) in the Fourier plane according to an embodiment. [Figure 1E] 1 illustrates the location of F(H*2) in the Fourier plane according to an embodiment. [Figure 1F] FIG. 1A shows the composite of FIGS. 1A-1E illustrating all of the components in the same figure. [Figure 1G] Shows the locations of all of the components and all of the component copies. [Figure 2A] 1 shows an embodiment of a filter that delimits an aperture. [Figure 2B] 1 shows an embodiment of a filter that delimits an aperture. [Figure 2C] 1 shows an embodiment of a filter that delimits an aperture. [Figure 2D] 1 shows an embodiment of a filter that delimits an aperture. [Figure 2E] 1 shows an embodiment of a filter that delimits an aperture. [Figure 2F] 1 shows an embodiment of a filter that delimits an aperture. [Diagram 3] 1 illustrates a filter including multiple sections according to an embodiment. [Figure 4] FIG. 1 is a schematic diagram illustrating a holographic display system according to an embodiment. [Diagram 5] 1 shows a method according to an embodiment. [Figure 6] 1 illustrates a method for computing a targeted hologram for display according to an embodiment. [Figure 7A] 7 shows simulated results of the method of FIG. 6. [Figure 7B] 7 shows simulated results of displaying a quantized hologram without using the method of FIG. [Figure 8] An embodiment is shown that uses multiple light sources to position the aperture at different locations in the Fourier plane. [Figure 9] 1 shows an example of a Fourier plane for two light sources with different wavelengths. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0041] A holographic image is an image that has depth information that gives the viewer a perception of depth and can be generated by utilizing the electromagnetic properties of light. The term image as used herein is understood to include static images as well as moving holographic images, including a sequence of holographic frames displayed in rapid succession. Furthermore, the present disclosure relates to both two-dimensional and three-dimensional holograms.

[0042] A two-dimensional hologram is one that occupies substantially a single image plane, but the image plane can be positioned at a perceived depth from the user. This can allow a more comfortable focus for the observer's eyes, especially in augmented reality situations, where the hologram can be given a depth that matches the point of interest. A three-dimensional hologram gives the appearance of a three-dimensional scene or object with the appropriate depth cues for the observer's eyes.

[0043] In a CGH, a hologram for display is typically first calculated as a "full complex" hologram, containing an array of values ​​corresponding to each element (pixel) of the display. Each value is a complex number with its own phase and amplitude. However, many display systems used for CGH images, such as DMDs and LCoS spatial light modulators, have a finite range of values ​​that they can reproduce. To display the hologram, each pixel in the full complex modulated holographic image needs to be mapped or quantized to a value that can be reproduced by the display. In one embodiment, the display is a binary display, capable of generating images with pixels that take on one of two possible amplitude or phase values. An example binary amplitude display is a digital micromirror device (DMD), which contains an array of microscopically actuated mirrors. When illuminated by a light source, each mirror can direct light to the next component in the optical system, representing the pixel "on" state, or direct light elsewhere, such as towards a heat sink, representing an "off" state. Each mirror can be actuated between two states as needed to generate the desired hologram. Similarly, in a binary phase display, each pixel has the ability to emit light in one of two discrete phases.

[0044] Mapping the continuum of full complex modulated values ​​to quantized amplitude and / or phase values ​​requires that a particular quantization method be used. A simple example of a binary amplitude quantization scheme is as follows: If the value has a negative or zero real part (the point is in the second or third quadrant on the Argand diagram), the point is mapped to point (0,0) on the Argand diagram. If the value has a positive real component, the point is mapped to point (0,1) on the Argand diagram. Those skilled in the art will recognize that many alternative quantization methods can be used and this disclosure is not limited to any particular quantization method. However, this example highlights the loss in phase and amplitude information that results from quantizing points for display on the DMD. Other display technologies may provide more values, but the number of finite states available is still low, perhaps 5 bits (32 values). It is clear that any quantization results in a loss in amplitude and phase information, reducing image quality.

[0045] The inventors have shown that the noise introduced by quantization can be reduced by selectively filtering out undesired noise components in the quantized hologram using physical filters in the display device. Q By approximating as a series expansion, a quantized field can be determined in which additional undesirable components introduced by quantization can be filtered out in the Fourier domain / Fourier plane, allowing a much improved approximation of the full complex target field, regardless of the quantization that occurred in the display system. The display systems and methods discussed may provide a computationally less expensive technique to achieve full complex modulation using conventional display devices, particularly compared to previous iterative software-based techniques such as Gerchberg Saxton.

number

[0046] Quantized hologram, H Q is displayed by quantizing the initial full complex hologram, which is calculated or determined by known techniques for display. Any suitable display device can be used, including a spatial light modulator (SLM). The SLM can be, for example, a DMD, LCD, amplitude LCoS, or phase LCoS. The light source can be configured to generate at least partially coherent light that is modulated by the SLM, and can be, for example, a laser or light emitting diode (LED).

[0047] The SLM generates a light field, which when viewed by an observer through an optical system recreates the light field, and thus an image is perceived. Conventional systems include a lens that generates a Fourier transform of the image displayed on the SLM, which is then processed by the observer's eye, which generates an inverse Fourier transform. Without applying further steps, such as an iterative technique that takes into account the quantized values ​​reproducible by the SLM, the image quality is poor due to the errors introduced by the quantization.

[0048] However, this disclosure provides that if a lens having a focal length, f, is positioned one focal length in front of the SLM such that the light modulated by the SLM is incident on the lens, then H Q The Fourier transform of F(H Q ) occurs one focal length behind the lens. This position is called the Fourier plane of the SLM. This is the plane in which the complex amplitude is described by the Fourier transform of the complex amplitude at the SLM, modulo potentially scaling or including a multiplicative spherical phase term. In this case, H Q can be written in terms of the Fourier transform of the series expansion of Equation 1 above. Using the linearity of the Fourier transform and Equation 1, F(H Q ) can be expressed as the following Equation 2: F(H Q )=aF(1)+bF(H)+cF(H * )+dF(H 2 )+eF(H *2 )+fF(HH * )+… Formula 2

[0049] Component F(H * ), F(H 2 ), F(H *2 ), and F(HH * ) are referred to herein as noise components because they relate to undesirable components produced by quantizing the target field, H. It will be appreciated that the effect of those components is visible as classical "noise", but is also a reduction in image contrast, generally resulting in reduced image quality.

[0050] The Fourier transform of a spatial function (e.g., the target light field, H, is a spatial function H≡H(x,y)) is expressed as its respective frequency components, k x and k y The Fourier transform of the constant, a, in Equation 1 is represented by the term aF(1) in Equation 2, sometimes known as the zeroth diffraction peak, multiplied by a, kx =k y = 0. The location of each of the components on the right hand side of Equation 2 in the Fourier plane can be determined from knowledge of the location of F(H), as described herein with reference to Figures 1A-1G. Figures 1A-1G are intended to illustrate the overall principles used in this disclosure and the relative locations of the noise components.

[0051] An example of F(H) 102 targeted at an arbitrary area in the Fourier plane is illustrated in FIG. 1A. FIG. 1A shows the F(H) 102 signal at spatial frequency k x A central horizontal line 110 representing the axis, and a spatial frequency k y FIG. 1A is a plot of the Fourier transform of H in spatial frequency space, with a central vertical line 120 representing the spatial x-axis. Equivalently, FIG. 1A is a plot of the Fourier plane, with a horizontal line 110 representing the spatial x-axis, and a central vertical line 120 representing the spatial y-axis. By this definition, each cell in FIG. 1A is a square with sides of dimension λf / p, where λ is the wavelength of light illuminating the SLM, f is the focal length of the lens, and p is the pixel pitch of the display. FIG. 1A represents four cells, centered at the origin, to show how tiling of the unit square affects the aperture design. For example, for illumination with a wavelength λ=520 nanometers, f=60 millimeters, and p=5 micrometers, the dimension of the square in the Fourier plane is 6.24 millimeters, which is the size of the filter.

[0052] Once the location of F(H) in the Fourier plane is known, H * , F(H * ) can be determined from the location of F(H). In the Fourier plane, this corresponds to the position of the line k y =-k x The result is shown in FIG.

[0053] Similar spatial plots in the Fourier plane can be made for higher order components of the expansion. FIG. 1C shows the relationship between F(HH* )106 position. F(HH * ) is its complex conjugate, H * is the Fourier transform of the target light field, H, multiplied by F(HH * ) is at the center of the Fourier plane, and k x and k y H and H in * FIG 1D shows the relationship between F(H)102 and F(H * ) 104 in the Fourier plane 100, centered twice as far from the origin as F(H) 102. 2 1E shows the location of F(H *2 ) 110. Similarly, F(H *2 ) 110 is F(H) 102 and F(H * )104, and F(H * )104 twice as far apart in the center.

[0054] FIG. 1F is a composite of FIGS. 1A-1E and illustrates the relative location of each of the components 102, 104, 106, 108, 110 in the Fourier plane 100. Because the target light field, H, is sampled on a grid of pixels, the field in the Fourier plane repeats on a square grid forming a repeating pattern of the components 102, 104, 106, 108, 110. FIG. 1G shows each of the components represented in FIG. 1F as well as each of the replicas of the components in the Fourier plane. For the location of F(H) 102, the noise components introduced by quantization considered in FIGS. 1B-1E do not overlap with F(H). Furthermore, none of the other replicas of those additional components resulting from sampling on a grid overlap with F(H).

[0055] It will be appreciated how varying the area occupied by F(H) affects the area occupied by each of the noise components. For example, expanding the area of ​​F(H) in the Fourier plane causes the noise components to correspondingly grow. When F(H) reaches sufficient range, it begins to overlap one or more of the noise components. Furthermore, translating and / or rotating F(H) relative to the origin in the Fourier plane causes corresponding translation and / or rotation of the noise components.

[0056] As can be seen from FIG. 1G, the effect of the considered noise components can be removed by a spatial filter in the Fourier plane. The resulting inverse Fourier transform of the filtered Fourier plane resembles the original full complex function H more closely than the Fourier transform of the unfiltered Fourier plane. Such filtering can be physically performed as part of the display of the hologram, rather than requiring additional computational steps, such as multiple iterations of Gerchberg Saxton. As will be explained in more detail below, with reference to FIG. 6, CGHs that target specific regions of the Fourier plane are relatively easy to determine, such as by applying a mask function. This requires significantly less processing resources and / or power than previous iterative methods.

[0057] In an embodiment, filtering is performed by positioning a filter that delimits an aperture corresponding to a region in the Fourier plane where F(H) is targeted. The filter is located in the Fourier plane of the lens (e.g., if the lens is one focal length from the SLM, the Fourier plane of the lens is one focal length on the opposite side), so the filter can physically block the noise components. The aperture allows the light corresponding to F(H) to pass through the filter and thus reach the target plane where the hologram can be viewed. Selecting the position of F(H) such that there is no overlap of F(H) with the considered noise components ensures that the light corresponding to F(H) reaches the target plane while blocking the noise components.

[0058] Once the location of F(H) in the Fourier plane is determined, as discussed above, the location of the noise component can also be determined, for example, using the method of FIGS. 1A-1G. Many possible locations of F(H) that do not overlap the considered noise component are also possible. Some embodiments may maximize the area in the Fourier plane that obeys the condition that the considered noise component does not overlap with F(H). Maximizing the area covered by F(H) maximizes the amount of light that passes through the filter, increasing the brightness of the hologram at the target plane. This also maximizes the area of ​​the hologram in the Fourier plane, increasing the area in which the hologram can be viewed. The area of ​​the Fourier plane occupied by the hologram coincides with the "eyebox" of the holographic display system, where the observer's pupil can be positioned to view the hologram.

[0059] F(H) can occupy the Fourier plane and F(H * ), F(HH * ), F(H *2 ), and F(H 2 It follows that the maximum area F(H) that satisfies the non-overlapping condition of noise components related to 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 55, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 12

[0060] Filters 200, 210, 220, 230, 240, 250 are shown as unit squares with relative side lengths of 1 for illustrative purposes, but in practice have lengths equal to λf / p. Figures 2A-2F delineate filters including apertures that satisfy the condition that when F(H) is targeted at the aperture, at least the noise components considered above for Figures 1A-1G are blocked by the non-aperture portion of the filter, and 1 / 6 of the area of ​​the unit square is used. Figures 2A-2F show only some of the possible filters that satisfy the above condition, thus illustrating that the filters described herein are not limited to the filters represented in Figures 2A-2F. Similarly, in some embodiments, the filters may not attempt to occupy the maximum area, but may occupy a smaller area that still satisfies the non-overlapping condition. This allows for a "buffer" area between F(H) and its noise components to more effectively filter and avoid diffraction effects at the aperture boundary perimeter, or to allow for increased tolerance for filter alignment, in some cases.

[0061] 2A illustrates an example filter 200 that defines a rectangular aperture 202 according to an example embodiment. The rectangular aperture 202 extends from a side of the filter, in this case a vertical side, and has a width that is ½ the width of the filter 200, and a height that is ⅓ the width of the filter. More specifically, the region is centered on the vertical axis and located on the left side. The rectangular aperture 202 defines a region F(H * ), F(H 2 ), F(H *2 ), and F(HH * ) is positioned so that it is blocked by the filter. In particular, F(H * ) occupies an area 203 adjacent to the aperture 202 along the horizontal axis and occupies the same area on the vertical axis. * ), F(H 2 ), and F(H *2 ) occupies an area 204 that extends the entire width of the filter 200 above and below the opening 202 .

[0062] It will be appreciated that reflection of filter 200 about a vertical line extending through the center of the filter, reflection about a horizontal line extending through the center of the filter, a 90 degree rotation about the center of the filter, reflection about an axis extending through the origin of the Fourier plane, and reflection about the origin are also possible and satisfy the constraint of non-overlapping noise components. For example, as shown in FIG. 2A, an alternative format may have region 203 as the aperture and region 202 blocked.

[0063] 2B shows another embodiment of filter 210 that defines a rectangular aperture 212. In this case, the height of aperture 212 is 1 / 6 the height of the filter, and the aperture occupies a position from 2 / 3 to 5 / 6 on the vertical axis. The width of aperture 212 is equal to the overall width of filter 210. Also shown in filter 210 is a portion or area 214, indicated by a solid line in filter 210. Portion 214 represents an area where aperture 212 could be alternatively positioned to provide the same effect. Portion 214 is a reflection and rotation of aperture 212, as discussed above with respect to FIG. 2A.

[0064] FIG. 2C shows a filter 220 that delimits two apertures 222, 224, each of which has a trapezoidal shape and extends from the same side of the filter. More specifically, in this embodiment, the apertures 222, 224 are right trapezoids. The aperture 222 extends from the base or horizontal axis and is centered 1 / 4 along the base of the filter 220 with the base having a length 1 / 6 of the length of the base of the filter 220. The top of the aperture 222 corresponds to a line connecting the lower left corner of the filter 220 to the upper right corner of the filter 220. The top and base of the aperture 222 are connected by two straight lines perpendicular to the base. Similarly, the aperture 224 is centered 3 / 4 along the base of the filter 220. A central vertical dotted line is shown to indicate the middle along the filter 220, and a diagonal dotted line connecting the lower left and upper right corners of the filter 220 is shown to indicate the top location of the apertures 222, 224. The filter 220 still satisfies the condition that the range of F(H) is maximized without any overlap with noise components when F(H) is targeted simultaneously at the apertures 222, 224. As in Figure 2B, Figure 2C also shows portions of the filters 226, 228 that are instead partitioned as apertures to provide the same effect as the apertures 222, 224 through rotation and / or reflection of the apertures 222, 224. Those portions 226, 228 are again shown by solid lines in the filter 220.

[0065] FIG. 2D shows a filter 230 that defines a single trapezoid-shaped aperture 232 that extends from the side of the filter, in this case the base or horizontal axis. More specifically, the aperture 232 is a right trapezoid. The base of the aperture 232 is centered midway along the base or horizontal axis of the filter 230. The base has a width that is 1 / 3 the length of the filter 230. The left edge of the aperture 232 is a straight line that is perpendicular to the base and has a length that is 1 / 3 the width of the filter 230. The right edge of the aperture 232 is a straight line that is perpendicular to the base and has a length that is 2 / 3 the width of the filter. The tops of the two edges are connected by a further straight line. The portion of the filter 234 shown by the solid line indicates an area that is instead defined as an aperture to achieve the same effect associated with the area 232 by rotation and / or reflection.

[0066] 2E shows a filter 240 that defines two apertures 242 and 244 that extend between two perpendicular sides of the filter. Each aperture 242, 244 has the shape of a trapezoid, more specifically, an isosceles trapezoid. Aperture 244 has a base that is 1 / 6 the width of filter 240 and is centered 1 / 4 along the base of filter 240. Aperture 244 has a left edge that has a length that is 1 / 6 the width of the filter and is centered 1 / 4 along the left edge of filter 240. The bottom corner of the left edge is connected to the left edge of the base by a straight line, and the top corner of the left edge is connected to the right edge of the base by a further straight line.

[0067] Aperture 242 has a base that is centered 3 / 4 of the way along the base of filter 240 and has a length 1 / 6 the width of filter 240. Aperture 242 also has a left edge that is centered 3 / 4 of the way up along the left edge of the filter and has a length 1 / 6 the width of filter 240. The bottom corner of the left edge of aperture 242 is connected to the left corner of the base of aperture 242 by a straight line, and the top corner of the left edge is connected to the right edge of the base by an additional straight line.

[0068] The portions of filters 246, 248 shown as solid lines in filter 240 indicate where the filters would alternatively delimit apertures 242, 244 to achieve the same effect by rotating and reflecting the apertures.

[0069] FIG. 2F shows a filter that defines a single aperture 252 having the shape of a trapezoid, more specifically, an isosceles trapezoid. The aperture 252 extends between two vertical sides. It has a base with a length that is 1 / 3 the width of the filter 250, which is centered on the base of the filter. The left edge with a length that is 1 / 3 the width of the filter 250, is centered on the left edge of the filter 250. The left corner of the base is connected to the bottom corner of the left edge by a straight line, and the right corner of the base is connected to the top corner of the left edge by a straight line. The portion of the filter 254, designated by a solid line in the filter 250, indicates where the filter 250 would define an aperture instead to achieve the same effect. The portion 254 is related to the aperture 252 by a rotation and / or reflection of the aperture 252.

[0070] It will be appreciated that these are merely examples of aperture shapes that can satisfy the requirement that F(H) does not overlap with any components of its series expansion in the Fourier plane, and that the disclosure is not limited to any particular form. For example, it will be appreciated that while the filters described above all have straight sides, which can be useful for maximizing usable area, other embodiments may use curved sides, or may choose not to maximize the usable area of ​​the filter.

[0071] Although the above discussion has considered maximizing the area of ​​the aperture so that all undesired components are blocked, some embodiments may still use a larger aperture. In general, higher order noise components are not evenly distributed in the Fourier plane and tend to have lower power and / or amplitude at their periphery than at the center. Thus, the size of the aperture may be increased slightly beyond the 1 / 6 criterion described above without introducing much more noise. For example, the aperture may have an area of ​​1 / 5 to 1 / 6 of a unit square in the Fourier plane and still show improved performance with a hologram targeting the aperture compared to a hologram not targeting and having no aperture.

[0072] The discussion so far has considered apertures that are static in that their position within the filter does not change over time. In those examples, the maximum area of ​​the filter that bounds the aperture is 1 / 6 of the total area. This has the advantages discussed above in terms of improved image quality, but means that the area in which the hologram can be viewed is reduced. In further examples, the effectively observable area in which the hologram can be perceived (sometimes referred to as the "eyebox") can be increased using multiple portions that are selectively controlled to either allow light to pass through or block light from reaching the viewer. The aperture then includes the portion of the filter that allows light to pass through. The portions can be configured to allow at least two of the apertures 202, 212, 222, 232, 242, 252 shown in Figures 2A-2F to be used in succession. In this way, the position of F(H) in the Fourier plane can be variable over time. Assuming a suitably fast display such as a DMD, the display can then be rapidly switched between different positions within a single frame period. Through visual persistence, an observer perceives a series of such rapidly displayed holograms as a single hologram.

[0073] However, the present disclosure is not limited to the above discussed time multiplexing techniques or / and quantization schemes used in combination with the above aperture conditions. Other algorithmic methods, such as windowed IFTA, may use partitioned apertures that are less than a unit square area in the Fourier plane (i.e., each subaperture spans less than one diffraction order) as a means to enhance image quality. That is, in some embodiments, windowed IFTA, such as windowed GS, may be utilized to constrain only a subregion of the Fourier plane to have a "don't care region" or "noise region" blocked by a filter, thereby improving image quality in the selected subregion but reducing either the field of view (when the filter is in the image plane) or eyebox (when the filter is in the pupil plane). The full field of view or eyebox can be recreated by time multiplexing each subregion and blocking the "don't care" regions, so that the observer perceives a single hologram through visual persistence. Although this may increase requirements for processing resources, when computational power is available to apply such an iterative method, it may have advantages over other methods known in the art.

[0074] When the spatial filtering is in the image plane, if the combination of all apertures of the spatial filter has any gaps or irregular shapes etc. that are visible in the image, this constrains the set of apertures that can be used, and the specification of the actual physically switchable apertures. However, when the spatial filtering is in the pupil plane, any gaps or irregular shapes are not apparent to the observer (if gaps, irregularities or shapes exist, they are only visible as slight differences to the blur and point spread function that the observer is unlikely to notice).

[0075] The one step phase retrieval (OSPR) algorithm also exploits visual persistence, but the method of the present disclosure can give higher quality results with lower computational resource usage. In OSPR, the entire Fourier plane is used, but many holograms with different random phase patterns are displayed in rapid temporal succession, and the observer's eye combines them to perceive a single hologram with an overall reduced noise (noise smoothing). The concept here uses the same visual persistence effect, rather than smoothing the effect of noise, and averaging is used to increase the portion of the Fourier plane used, and thus the observable area. Furthermore, rather than computing multiple holograms with different random phase patterns, as in OSPR, the method here can simply mask the holograms with the same random phase pattern, which is less computationally intensive. Nevertheless, other embodiments can use different random phase patterns for each displayed hologram, effectively applying the apertures disclosed herein to OSPR.

[0076] Some embodiments may combine OSPR with apertures as described herein, in which case OSPR may utilize a lower bit depth because of the noise reduction provided by apertures, and OSPR may process frames more quickly to become less computationally intensive and / or maximize the benefit of the time averaging effect to reduce noise in OSPR.

[0077] The sections can be tiled within each unit cell of the filter, so that there are multiple sections per unit cell, i.e., section of the filter with dimension λf / p. The SLM can then be configured to generate a holographic light field, H, such that F(H) is targeted at one or more deactivated sections of the filter. Synchronizing the deactivated sections of the filter with the holographic light field generated by the SLM targeting those sections allows an increase in the effective area of ​​the hologram generated at the target plane. If the sections of the filter are activated and deactivated at a sufficient rate, such as greater than or equal to 100 Hertz or 200 Hertz or more, the observer may not perceive the switching. This effectively allows a further increase in the size of the eyebox. As discussed above with reference to FIG. 1C, the central zeroth order mode is formed from the constant term in Equation 2 above, and is therefore always blocked so that it constrains the maximum output of the noise term. However, in some embodiments, the "zeroth order" may be located at a different location (when an echelle grating is used), and in those embodiments, the portion of the Fourier plane encompassing the highest output noise term is blocked.

[0078] FIG. 3 shows an embodiment of a filter 300 that includes multiple portions corresponding to areas that can be controlled to allow light to pass or not. They are labeled 301-316. The portions of filter 300 correspond to apertures similar to those illustrated in FIGS. 2C and 2D, where rotation and reflection are included. More specifically, portions 301, 302, 303, 304, 305, 306, 307, 308 each include a single trapezoidal shaped region as in FIG. 2D, and portions 309, 310, 311, 312, 313, 314, 315, and 316 each include two trapezoidal shaped regions. At any one time, a single one of apertures 301-316 (which may include more than one region) is in a state that allows light to pass, and all other portions are in a state that does not allow light to pass. Correspondingly, the holographic light field, H, may be targeted such that F(H) corresponds to the portion(s) that allow light to pass through. In use, a controller may supply the SLM with the appropriate hologram and control the filters so that the relevant portions allow light to pass through. Some SLMs may operate instantaneously enough that all 16 apertures 301-316 can be displayed within a single frame period. Any sequence of operations may be used, including incrementing from apertures 301-316 as labeled and decrementing from apertures 316-301 as labeled.

[0079] The central portion 317 of the filter 300, which corresponds to the zeroth mode, is F(HH *) and the zeroth order are always blocked to prevent light corresponding to the zeroth order from passing through the filter 300. Furthermore, due to this particular arrangement of portions, the outer region 318 of the filter 300 is always blocked. The filter 300 provides a larger eyebox than is possible with filters 200, 210, 220, 230, 240, 250 that include static apertures 202, 212, 222, 232, 242, 252. The presence of the central portion 317, which is always blocked, makes this filter well suited to be used in a position in the pupil plane, in which case the blocked central portion does not significantly affect the perceived image. Filters positioned in the image plane could also be used, but the blocked central portion may be more visible in that case.

[0080] The controllable portion of FIG. 3 can be fabricated in a variety of ways. For example, filter 300 can be fabricated from liquid crystals and can operate to either substantially allow light to pass through or substantially block light. The liquid crystals can have high switching speeds, such as pi-cells or ferroelectric LCDs (FLCDs). Other embodiments can use a DMD as the filter, where the DMD is controlled not to modulate the light field, but controls which portions of the modulated light are allowed to pass through. Another embodiment can use a rotating chopper wheel, which rotates to define a number of apertures and each of the lasers is synchronized to the chopper wheel. The chopper wheel can use, for example, a stepper motor or the like to control the rotational position. Of course, filter 300 can utilize embodiments of any suitable shutter technology, including molecular-based shutters, quantum optical shutters, plasmonic metamaterial shutters.

[0081] Although the filter 300 of FIG. 3 includes regions that are always blocked, other embodiments may allow those blocked regions to be controllable. Such embodiments may allow spatial filtering to be completely disabled if desired. This may allow a user to choose between spatial filtering or alternative image processing operations such as Gerchberg Saxton iterative processing. Alternatively, or in addition, a filter may be selectively placed in the optical path, such as by providing a mechanism that removes the filter from the optical path when not needed and places the filter in the optical path when used with the methods of the present disclosure.

[0082] In the previous discussion of Figures 2A-2F and 3, F(H) has been discussed as being generated by light of a single illumination wavelength. However, the principles described herein can be extended to cover light of multiple illumination wavelengths. Such light may be generated by multiple light sources, such as multiple single mode lasers, or a single light source operating at multiple wavelengths. In the case of multiple illumination wavelengths, the aperture(s) may be selected such that the condition of no overlap of F(H) with the noise component is exact for light of a first wavelength, but approximates only for light of a second wavelength. This allows for an approximate full complex modulation of a multi-color hologram.

[0083] 4 generally illustrates a holographic optical system 400. System 400 includes a light source 402 configured to generate at least partially coherent light. System 400 further includes a spatial light modulator (SLM) 404 arranged to be illuminated by the at least partially coherent light. System 400 further includes a lens 406. Lens 406 has a focal length, f, and is positioned one focal length from SLM 404. System 400 further includes a filter 408 defining an aperture 410. Filter 408 is positioned one focal length from lens 406, on the opposite side of lens 406 from SLM 404.

[0084] SLM 404 is configured to generate a light field that is a quantized representation of a target light field, H, as discussed above. The arrangement of holographic optical system 400 is such that the Fourier transform of the light field, F(H), is formed in a plane that coincides with the location of filter 408. This plane is the Fourier plane of SLM 404 as imaged by lens 406. The Fourier transform of the target light field, F(H), is the complex conjugate of the target light field, F(H * The target light field is determined so that it does not overlap with at least the Fourier transform of F(H) and the second order component in the Fourier plane of SLM 404. Additionally, an aperture in filter 408 corresponds to F(H) in the Fourier plane such that portions of the target light field outside of F(H) are blocked.

[0085] The light source 402 may include, for example, a laser module or an LED. The light source 402 is configured to generate at least partially coherent light at one wavelength or multiple wavelengths (e.g., corresponding to red, green, and blue colors).

[0086] The SLM 404 may be configured to modulate at least one of the phase, amplitude, binary phase, and binary amplitude of light. The SLM 404 may be, for example, a DMD, an LCD, an amplitude LCoS, or a phase LCoS.

[0087] Filter 408 corresponds to the area targeted by F(H) and can be any of the filters shown in Figures 2A-2F and 3 with the configuration as discussed above. As shown, SLM 404, lens 406, and filter 408 are coaxial. Other configurations such as a folded optical path can be used, which may allow for a more compact display.

[0088] For clarity, Figure 4 represents a transmissive SLM, it will be understood that the principles discussed here are not limited thereto and can be equally applied to reflective SLMs, and similarly the same principles apply to other types of modulators other than SLMs.

[0089] Having described the theory and overall structure of a holographic display according to the present disclosure, its method of operation will now be described. FIG. 5 illustrates a method 500 for reducing quantization noise in a holographic image. Method 500 can be performed, for example, by a controller of the holographic optical system 400 shown in FIG. 4. At 502, method 500 includes generating a target light field, H, for quantization. The target light field is expressed as a complex conjugate, F(H * ) and has a Fourier transform, F(H), that has the property of not overlapping with the second order components in the Fourier plane. F(H) can be predetermined as occupying a region having those properties, for example, as discussed with reference to Figures 2 and 3. A method for targeting a hologram in this region is described below with reference to Figure 6.

[0090] Next, at 504, the quantized version of the target light field is filtered through a filter that defines an aperture corresponding to the extent of F(H) in the Fourier plane, resulting in at least its complex conjugate, F(H * ) and the second order components are blocked by a filter.

[0091] 6 shows an example method 600 for computing a targeted hologram in a predefined region of the Fourier plane, along with example representations of images at each step showing the effect of the processing. Method 600 may be performed by a processing system, which may be local or remote from the holographic display system. The holographic frame determined by method 600 is output to an SLM, such as SLM 404.

[0092] The method 600 begins at block 602 by receiving a target light field. The target light field is a two-dimensional array representing one image layer to be displayed by a holographic optical system. The target light field is transformed into a complex target light field 602 by applying a respective random phase factor to each pixel. This acts to rotate each pixel value in the complex plane, giving each pixel an imaginary component. The phase values ​​have a statistically uniform distribution across the light field. Each random phase factor e iθ may include a matrix of random numbers to be applied to a target light field that includes a matrix of pixels.

[0093] In block 604, the complex target light field undergoes a Fourier transformation (such as a fast Fourier transform, FFT, etc.) to stimulate a light field at the observer's pupil. The simulated pupil is then masked in block 606 to form an aperture pupil. Applying the mask sets the amplitude to zero for all portions of the simulated light field outside the aperture. The aperture pupil is a subregion less than the entire field from block 604, and the shape of the subregion is dictated by the particular mask used. In practice, the particular mask used corresponds to the aperture selected in the filter of the holographic optical system. For example, as shown in FIG. 6, the mask in block 606 used to form the aperture pupil corresponds to the aperture 202 shown in FIG. 2A. In method 600, the resulting F(H) is targeted at an area in the Fourier plane that corresponds to the aperture 202.

[0094] So far, the image has been perceived as being located at infinity, so in block 608 a defocus Zernike polynomial is applied to the output of block 606 resulting in a defocused image at the target depth on a plane coincident with the SLM. In general, the characteristics of the defocus Zernike polynomial are determined by the parameters of the holographic optical system. For example, the SLM has N×M pixels and a pixel pitch p. A lens with focal length, f, is positioned one focal length from the SLM, and the SLM is illuminated with light of a single wavelength, λ. For a layer at depth d, and an SLM at optical infinity, the aperture pupil 606 is multiplied by the defocus Zernike polynomial: exp(2πi(2r 2 -1) / 4dλ), where r is the radial distance (in meters) of each sample point from the center of the aperture region. Spatial sampling of the pupil determines fλ / pN in the x-direction and fλ / pM in the y-direction, from which the value of r for each point can be determined. The method is not limited to the use of Zernike polynomials, other methods such as a parabolic phase function could be used.

[0095] By applying the defocus Zernike polynomials after the masking in block 606, the processing required may be reduced because the range of the field is smaller than if the polynomials were applied after block 604. However, block 608 may occur after block 604 and before block 606 in some embodiments.

[0096] The defocus aperture pupil from block 608 is subjected to an inverse Fourier transform in block 610, resulting in a light field at the depth of the SLM. It can be observed that although the aperture is limited to the Fourier plane, the inverse Fourier transform means that the full extent of the SLM is still used to display the image. (Just as filtering a time-varying waveform in the Fourier domain still results in a time-domain waveform of the same length in time, filtering the Fourier plane still results in the full extent of the SLM being used for display.)

[0097] The resulting light field from block 610 can then be quantized to form a quantized representation of the resulting light field. As discussed above, any suitable quantization scheme can be applied. Process 600 determines a holographic light field formed by an SLM, such as SLM 404, such that a Fourier transform of the light field is formed within an area of ​​the Fourier plane that corresponds to a predefined aperture in the filter.

[0098] 6, it appears that the image in block 610 is of lower quality than in block 602. This is for several reasons. First, the image in block 602 is ideal, and therefore the image in block 610 cannot be of higher quality. Second, the image in block 610 shows the effect of the defocus Zernike polynomials. If the aperture were not present, the image in block 610 would be of lower quality than is shown.

[0099] Figure 7A shows simulated results of the method of Figure 6 using the aperture described above together with targeting F(H) to the aperture. Figure 7B shows simulated results of displaying the quantized field H without using an aperture and targeting F(H) to the aperture. Figure 7B is of noticeably lower quality than Figure 7A.

[0100] As previously discussed, Fig. 6 considers a single image layer, which can provide a holographic image with accurate depth of focus cues for the observer's eye. Those skilled in the art will know that the process of Fig. 6 can be repeated for multiple layers at different distances (with corresponding defocus Zernike polynomials), each layer calculated independently and summed together to generate a three-dimensional scene.

[0101] In some embodiments, the filter includes multiple portions that can be selectively controlled to pass or block light, such as filter 300 shown in FIG. 3. In this case, different portions can be activated and deactivated to expand the effective eyebox of the resulting hologram. Using process 600, it is clear that targeting F(H) at different regions of the Fourier plane can be achieved simply by applying a corresponding mask to the simulated pupil determined in block 604 to generate the appropriate aperture pupil in block 606. Thus, similar to the embodiment of FIG. 3, if there are 16 regions to target, blocks 606, 608, and 610 are repeated for each aperture. The holographic display is then controlled to display the resulting complex field while the corresponding aperture allows light to pass through the filter.

[0102] FIG. 8 illustrates another way in which a larger area of ​​the Fourier plane can then be covered by using multiple light sources, each illuminating the modulator from a different angle. The change in angle means that the Fourier plane of each light source is located at a different position, effectively translating the position of the zeroth order in the Fourier plane. FIG. 8 illustrates this effect diagrammatically, with three light sources resulting in a Fourier plane with the zeroth order located at respective positions 802a, 802b, and 802c. Using the apertures discussed above with reference to FIG. 2A, the apertures are accordingly positioned at 804a, 804b, and 804c in the Fourier plane. In use, the light sources are operated in a time sequence, and the position of the apertures is synchronized to the light sources. From FIG. 8 it can be seen how this allows a larger area of ​​the Fourier plane to be covered. Throughout this process, the data displayed by the modulator also operates in a corresponding time sequence synchronized to the light sources, with the change in the position of the apertures being due to the different angles of the light sources.

[0103] The aperture of Figure 8 allows for substantially uniform coverage of the Fourier plane, avoiding, for example, the central blocked portion 317 of Figure 3. This makes it suitable for use at any position of the filter, but can be beneficial when the filter is positioned in the image plane.

[0104] As shown in Figure 8, there is a single aperture 804a, 804b, 804c per light source, however multiple apertures per light source can be added and time multiplexed per light source to fill an even larger area. For example, the offset light sources of Figure 8 are combined with the single light source multiple aperture positions of Figure 3. Similarly, other shapes of apertures can be used, as explained above.

[0105] FIG. 9 shows an example of Fourier planes 906a, 906b for two light sources with different wavelengths. In this example, the light sources are physically separated, so the zeroth order is located at different positions 902a, 902b. In addition, as explained above, the different colors of the light sources mean that the Fourier plane is scaled and the dimensions of the unit square change with different wavelengths. In this example, the angle and / or position of the light source relative to the modulator is chosen such that aperture 904b is located within aperture 904a, which in this case is located entirely within aperture 904a. Without a shift in the light source angle or position, apertures 904a, 904b may not completely overlap, potentially reducing performance. In use, using aperture 904b for both light sources provides the benefit of noise reduction for both light sources, but slightly reduces the brightness for one light source because the full extent of aperture 904a is not used.

[0106] As shown in Figure 9, there is a single aperture 904a, 904b per light source, however multiple apertures per light source can additionally be time multiplexed per light source to fill a larger area. For example, the offset light sources of Figure 9 can be combined with the single light source multiple aperture positions of Figure 3. Similarly, other shapes of apertures can be used, as explained above.

[0107] The above-described embodiments are to be understood as illustrative examples of the present invention. Further embodiments of the present invention are envisioned. It is to be understood that any feature described in connection with any one of the embodiments may be used alone or in combination with other features described, and may also be used in combination with one or more other features of any of the embodiments, or in any other combination of any of the embodiments. Moreover, equivalents and modifications not described above may also be employed without departing from the scope of the present invention, as defined in the appended claims.

Claims

1. 1. A holographic display system, comprising: a light source configured to emit at least partially coherent light; a modulator emitted by the at least partially coherent light and arranged to generate a light field that is a quantized representation of a target light field, H; a spatial filter defining the aperture in the Fourier plane; The aperture substantially corresponds in the Fourier plane to a Fourier transform of the target light field, F(H), where F(H) is a complex conjugate of the target light field, F(H ＊ ), (ii) the Fourier transform of the target light field multiplied by the complex conjugate of the target light field, F(HH ＊ ), (iii) the squared Fourier transform of the target light field, F(H ２ ), and (iv) the Fourier transform F(H ＊２ ), which does not substantially overlap with The holographic display system.

2. The spatial filter is a lens having a focal length; a filter defining the aperture; the filter and the modulator are positioned on opposite sides of the lens at a distance of one focal length from the lens; The holographic display system of claim 1 .

3. The holographic display system of claim 1 , wherein at least a portion of the perimeter of the aperture is a straight line.

4. 10. The holographic display system of claim 1, wherein the Fourier plane is partitioned into a plurality of contiguous unit squares, each unit square receiving one copy of the Fourier transform of the target light field, and the aperture has an area approximately 1 / 6 of a unit square.

5. The holographic display system of claim 1 , wherein the perimeter of the aperture is rectangular.

6. The holographic display system of claim 1 , wherein the filter separates at least two apertures.

7. 10. The holographic display system of claim 1, wherein the filter includes a plurality of portions that can be selectively controlled to have a first state in which light is blocked and a second state in which light is allowed to pass, whereby an aperture is formed by the portions in the second state.

8. The holographic display system of claim 1 , wherein the modulator is a digital micromirror device.

9. The holographic display system of claim 1 , wherein the modulator is a Liquid Crystal on Silicon (LCoS) device.

10. 10. The holographic display system of claim 1, wherein the light source is configured to emit at least partially coherent light at multiple wavelengths including green light, and the aperture corresponds to a position of F(H) for green light.

11. The holographic display system of claim 1 , wherein the light source is configured to emit at least partially coherent light at multiple wavelengths, and at least one side of the aperture is angled at 45 degrees.

12. 10. The holographic display system of claim 1, wherein the light source includes at least two emitters positioned such that the zeroth order of the Fourier plane is at a different position for each of the at least two emitters, and the filter has at least one aperture for each of the at least two emitters and separates at least two apertures.

13. 2. The holographic display system of claim 1, wherein the light source includes a first emitter having a first wavelength and a second emitter having a second wavelength, and the first emitter and the second emitter are positioned such that F(H) of one of the first emitter and the second emitter is contained within F(H) of the other of the first emitter and the second emitter.

14. 1. A method for displaying a holographic image, comprising: determining a target light field, H, for quantization, the target light field being (i) its complex conjugate, F(H ＊ ), (ii) the Fourier transform of the target light field multiplied by the complex conjugate of the target light field, F(HH ＊ ), (iii) the square Fourier transform of the target light field, F(H ２ ), and (iv) the Fourier transform F(H ＊２ ), and determining the Fourier transform, F(H), such that it does not overlap; The resulting F(H ＊ ), F(HH ＊ ), F(H ２ ), and F(H ＊２ displaying a quantized version of the target light field through a filter that defines an aperture corresponding to a range of F(H) in the Fourier plane such that components corresponding to F(H) are substantially blocked by the filter; The method comprising:

15. The method of claim 14 , wherein the extent of F(H) in the Fourier plane has at least one linear perimeter.

16. The method of claim 14 , wherein the extent of F(H) in the Fourier plane has a rectangular perimeter.

17. The method of claim 14 , wherein the range of F(H) in the Fourier plane includes at least two non-contiguous regions.

18. The method of claim 14 , wherein generating the target light field comprises applying a mask to an initial light field.

19. generating a plurality of target light fields in different regions of the Fourier domain, each of the plurality of target light fields having the property that the range of their Fourier transform does not overlap the range of the Fourier transform of their complex conjugate; displaying quantized versions of each of the plurality of target light fields in temporal succession through respective filters that delimit apertures corresponding to the range of their Fourier transforms in the Fourier plane at a rate sufficient to allow an observer to perceive the temporally displayed multiple holograms as a single hologram through visual persistence; 15. The method of claim 14, comprising:

20. A computer readable medium comprising instructions which, when executed by a processor, cause a holographic display system according to any one of claims 1 to 13 to display a holographic image according to a method according to any one of claims 14 to 19.

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