Holographic display system and method for reducing the effects of quantization noise

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 generating holographic images. [Background technology]

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

[0003] In reality, displays used for CGH cannot achieve full complex modulation. Typical displays used for CGH can only have very limited values ​​that they can display. For example, a display may only have the ability to modulate either amplitude or phase. Resolution can also be limited to approximately 5 bits (giving a displayable value of 32 or less), and in the case of binary display technology, even binary only.

[0004] As a result, the pixels of a fully complex holographic image are quantized to values ​​that can be reproduced by the display for display purposes. 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 a fully complex argand diagram must be mapped to one of these two states.

[0005] Quantization processing on a display reduces image quality, resulting in a decrease in contrast and / or noise, which is visible within the perceived image.

[0006] It is known that the quality of quantized holograms on displays can be improved 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 particularly 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 by reducing the requirements for processing resources and / or power. [Overview of the project]

[0008] According to a first aspect of the present invention, a holographic display system is provided comprising a light source configured to emit at least partially coherent light, modulators arranged to be emitted by at least partially coherent light, and a spatial filter that divides an aperture in the Fourier plane. The Fourier transform of the target light field, F(H), is (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) Target light field squared The Fourier transform of F(H 2 ), and (iv) the complex conjugate of the Light field F squared The Fourier transform F(H *2 ), and does not substantially overlap with, the opening substantially corresponds to F(H) in the Fourier plane.

[0009] Such a structure can improve the image quality of the displayed hologram through a combination of restrictions on the range of the target light field within the Fourier plane (by defining that it cannot overlap with its complex conjugate and higher-order Fourier transforms) and the positioning of the aperture to correspond to F(H) within the Fourier plane. By F(H), it signifies a portion of the Fourier plane that has non-zero values. This arrangement has been found to prevent additional components in the Fourier plane introduced into the display by quantization. Furthermore, determining H in this way is computationally simpler than previous iterative methods such as Gerchberg-Saxton, reducing the requirements for processing resources. This can lead to lower processing and / or power requirements, as well as enabling higher-quality holographic displays, which can result in one or more of the following: lower display costs, increased portability, and, in the case of battery-powered devices, extended battery life.

[0010] As will be explained in more detail later, the inventors have realized that the noise introduced to the display by quantization results in additional components in the Fourier plane, which are approximated by a series expansion. Additional image quality can be obtained by considering the additional terms in the series expansion and ensuring that they do not overlap with F(H) so that the additional components are filtered out. Since the energy in the series expansion tends to be concentrated in the lower-order terms, at least F(H) * It is beneficial to ensure that it does not overlap with F(HH * ), F(H 2 ) and F(H *2 While higher-order terms such as ) are also beneficial, the influence of each term is small, and we reach a point where 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. It 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 modulation means suitable for modulating the amplitude and / or phase of coherent or quasi-coherent light. This includes Liquid Crystal on Silicon (LCoS) devices, digital micromirror devices (DMDs), and liquid crystals. In one embodiment, the modulator is a spatial light modulator.

[0013] A spatial filter can be any suitable means of forming a Fourier plane and means of spatially filtering light within that plane. In one embodiment, the spatial filter includes a lens having a focal length and a filter that divides an aperture. The filter and modulator are positioned on the opposite side 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, and the lens including the array extends across the imaging area.

[0014] The modulator, lens, and filter may be substantially coaxial in some embodiments. Other arrangements are also possible, such as a folded optical path having mirrors and / or prism elements in the optical path, which may allow for a more compact arrangement in some cases.

[0015] A filter separates an aperture through which light can pass, completely blocking or otherwise preventing light from passing outside the aperture (for example, a filter may be configured to absorb light outside the aperture or reflect it elsewhere outside the optical path).

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

[0017] Due to the presence of the filter, a Fourier plane that cannot be generated by the SLM is actually used. This can result in a darker display or a reduction in the size of the area where the displayed hologram can be viewed. Although there are no specific constraints on the shape of the perimeter of F(H), at least F(H * ), F(H 2 ), F(H *2 ), and F(HH * ). By analyzing the operation of the function in the Fourier plane, it has been shown that a well-defined region can be defined when the non-overlapping requirement is satisfied. In some embodiments, 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 can be partitioned into a plurality of contiguous unit squares, and each unit square receives one copy of the Fourier transform of the target light field. The aperture can then have an area of approximately 1 / 6 of the unit square. As will be described in more detail later, the unit square is the result of taking the Fourier transform of a discrete grid of modulators that produces 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 quadrilateral. Suitable quadrilaterals include rectangles, squares, and trapezoids. Some embodiments use a right trapezoid, and other embodiments use an isosceles trapezoid for the aperture. (Trapeziums can also be referred to as trapezoids, so a right trapezium is a right trapezoid, and an isosceles trapezium is an isosceles trapezoid.)

[0020] Some embodiments can have a single aperture, and in other embodiments, the filter can separate at least two apertures. At least two apertures cannot be contiguous.

[0021] In some embodiments, the filter comprises multiple parts, which 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 through, thereby forming an aperture formed by the part 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 target light fields at different positions can be displayed rapidly and sequentially in time. This can expand the range of positions in which the displayed hologram can be seen, 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 can provide a significant improvement in image quality of DMDs due to their binary characteristics. In other embodiments, the spatial light modulator is a Liquid Crystal on Silicon (LCoS) device. LCoS devices may have more quantization states than DMDs, but a beneficial improvement in image quality is also achieved. When the spatial light modulator is an amplitude-only SLM such as a DMD, the display systems and methods described herein can enable the display of holograms with an improved (darker) black level.

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

[0024] The light source may be configured to emit light that is at least partially coherent 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 the axis defining the unit square of the Fourier plane. Conjugate, F(H * This can be beneficial because the aperture can be positioned so that it does not overlap with any wavelength.

[0025] The light source may include at least two emitters positioned such that the zero-order Fourier plane is at a different position relative to each of the at least two emitters, with at least one aperture for every at least two emitters, and the filter partitions at least two apertures. This allows for covering a larger portion of the Fourier plane by tiling the apertures relative to different emitters. Each emitter may have its own aperture(s) partitioned by the filter, independently of any other aperture(s) relative to other emitters. The apertures may at least partially overlap such that the aperture for one emitter shares at least a portion of its open area with respect to the aperture for another emitter. At least two emitters may operate in time series by their respective apertures. For example, the first emitter and first aperture may be activated, followed in time by the second emitter and second aperture.

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

[0027] In another embodiment, a filter is provided that separates the aperture corresponding to the Fourier transform of the target light field H in the Fourier plane, F(H), and the Fourier transform F(H) is (i) its complex conjugate, F(H * ), (ii) Target light field, F(HH * (iii) The Fourier transform of the target light field multiplied by the complex conjugate of (H), (iii) the target light field, F(H 2 )of squared The Fourier transform of and the light field F(H) in the Fourier plane. *2 The complex conjugate of ) squaredThe Fourier transform of does not overlap. Positioning such a filter within a holographic display, when combined with controlling the display to show the corresponding target light field H, may allow the display to obtain the benefits of the image quality improvements discussed herein. The filter and aperture may have any of the features discussed above.

[0028] During use, the filter can be positioned at different locations in the optical path, such as occupying the "pupil plane" or the "image plane." The pupil plane is the plane corresponding to the modulator image as reproduced on the observer's movement, and allows for further flexibility in aperture design. The pupil plane, and pupil-like planes, have the characteristic that gaps can exist in the aperture without significantly altering the viewed image. When the filter is not positioned in the pupil plane or pupil-like plane, it is considered to be in the image plane. When the filter is positioned in the image plane, gaps in the aperture may be visible to the observer, and therefore it is preferable to avoid such gaps in the aperture. Examples will be described later with reference to Figures 3 and 8.

[0029] In a further embodiment, the target light field H for quantization is determined by (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) Target light field squared The Fourier transform of F(H 2 ), and (iv) the complex conjugate of the Light field squared The Fourier transform F(H *2 ), and so that they do not overlap, the Fourier transform has F(H), and it is determined that F(H) is the result of quantization. * ), F(HH * ), F(H 2 ), and F(H *2A method is provided which includes displaying a quantized version of the target light field through a filter that divides an aperture corresponding to a range of F(H) in the Fourier plane such that the component corresponding to ) is 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 reduced display area, but this constraint means that components introduced by quantization are filtered out and do not reach the observer's eye, thus improving image quality.

[0031] In addition, F(H) stands for Target Light Field, F(HH) * The Fourier transform of the target light field multiplied by the complex conjugate of ) cannot overlap. In further embodiments, F(H) is also (i) the target light field, F(H 2 )of squared Fourier transform and light field F(H *2 The complex conjugate of ) squared It does not overlap with at least one of the Fourier transforms of the following:

[0032] The shape or range of F(H) in the Fourier plane can be any that satisfies the constraints, but in some embodiments, the range of F(H) in the Fourier plane has at least one linear perimeter. The range of F(H) in the Fourier plane may have a quadrilateral perimeter. The range of F(H) in the Fourier plane may include at least two non-contiguous regions.

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

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

[0035] The advantage of the present invention is that, through filter positioning and F(H) constraints, the processing can be designed to reduce computational requirements and ensure that noise does not enter the blind's "don't care" area. In other words, aperture design ensures noise reduction without the need to evaluate the exact noise field. This differs from iterative Fourier transform algorithms (IFTAs) such as Gerchberg-Saxton (GS), where the image replay field must be computationally reconstructed and iteratively improved, requiring significant processing resources. Some embodiments may use IFTA in combination with apertures. Due to the reduced iterations required resulting from the filter's action to reduce noise, this can enable improved image quality with reduced processing.

[0036] Therefore, any suitable quantization method and resolution can be used, quantized in phase and / or amplitude. For example, the quantization may be the nearest value that can be reproduced by the display, the nearest value that can be reproduced by the display without increasing the amplitude, the nearest value that can be reproduced by the display without increasing the phase, etc. In some embodiments, a real offset may be applied to a masked light field, etc., before quantization. The real offset may be based on the average amplitude of the values ​​before quantization, such as the root mean square (rms) amplitude. In another embodiment, |H+c|^2 may be quantized. In such embodiments, the preferred quantization cannot be a quantization scheme that minimizes the total quantization factor in the SLM. The quantized version of H is H Q When expressed as such, the quantization error is the additional noise field, E Q =H Q -It can be written as H. Typically, the total quantization factor in F(H) can be achieved by quantizing each pixel to the most recent available value, E Q It is minimized by minimizing F(H * ), F(H 2 ), F(H *2 ), and F(HH * A specific quantization scheme may be used that increases the combined noise multiplier at ) but decreases the noise multiplier at F(H). Such a quantization scheme, compared to nearest neighbor quantization, increases the noise multiplier E Q This can increase the noise factor while still reducing the noise multiplier 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 which has the property that the range of its Fourier transform does not overlap with the range of its complex conjugate Fourier transform, and rapidly displaying quantized versions of each of the multiple target light fields in time-sequentially through respective filters that demarcate apertures corresponding to the ranges of their Fourier transforms in the Fourier plane. This can increase the area over which the hologram can be viewed.

[0038] In another embodiment, a computer-readable medium, such as a non-temporary computer-readable medium, is provided, which, when executed by a processor, includes instructions causing the holographic display system discussed above to display a holographic image in the manner discussed above.

[0039] Further features and advantages of the present invention will become apparent from the following description of preferred embodiments of the invention, which are given only as examples and are made with reference to the accompanying drawings. [Brief explanation of the drawing]

[0040] [Figure 1A] This shows an example of the location of the Fourier transform of a hologram F(H) in the Fourier plane. [Figure 1B] The location of F(H*) in the Fourier plane according to the embodiment is shown. [Figure 1C] The location of F(HH*) in the Fourier plane according to the embodiment is shown. [Figure 1D] The location of F(H2) in the Fourier plane according to the embodiment is shown. [Figure 1E] The location of F(H*2) in the Fourier plane according to the embodiment is shown. [Figure 1F] Figures 1A to 1E illustrate the complex, illustrating all the components in the same figure. [Figure 1G] This shows all the locations of the components and all of their copies. [Figure 2A] An example of a filter for partitioning an opening is shown. [Figure 2B] An example of a filter for partitioning an opening is shown. [Figure 2C] An example of a filter for partitioning an opening is shown. [Figure 2D] An example of a filter for partitioning an opening is shown. [Figure 2E] An example of a filter for partitioning an opening is shown. [Figure 2F] An example of a filter for partitioning an opening is shown. [Figure 3] A filter including multiple parts relating to the embodiment is shown. [Figure 4] This is a schematic diagram showing a holographic display system according to an embodiment. [Figure 5] The method according to the example is shown below. [Figure 6] This document describes a method for calculating the hologram targeted for display according to the embodiment. [Figure 7A] The simulated results of the method shown in Figure 6 are presented. [Figure 7B] The simulated results of displaying a quantized hologram without using the method in Figure 6 are shown. [Figure 8] This example demonstrates the use of multiple light sources to position apertures at different locations within the Fourier plane. [Figure 9] An example of the Fourier plane for two light sources with different wavelengths is shown. [Modes for carrying out the invention]

[0041] A holographic image is an image that contains depth information, giving the observer a sense of depth, and can be generated by utilizing the electromagnetic wave properties of light. The term "image" as used herein is understood to include both static images and moving holographic images, which include sequences of rapidly displayed holographic frames. Furthermore, this disclosure relates to both two-dimensional and three-dimensional holograms.

[0042] A two-dimensional hologram occupies essentially a single image plane, but the image plane can be positioned at a depth perceived by the user. This can allow for more comfortable focusing on the observer's eye, particularly in augmented reality situations, where the hologram can be given a depth corresponding to the point of interest. A three-dimensional hologram provides the observer's eye with an appropriate depth cue for a three-dimensional scene or object.

[0043] In CGH, the hologram for display is typically first calculated as a “fully 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 a hologram, each pixel in the fully 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 having the ability to produce an image containing pixels that take one of two possible amplitude or phase values. The binary amplitude display in this embodiment is a digital micromirror device (DMD) containing an array of microscope-operated mirrors. When illuminated by a light source, each mirror can direct the light to the next component in the optical system, representing the pixel “on” state, or to another location, such as towards a heatsink, representing the “off” state. Each mirror can be operated between the two states as needed to produce 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 a continuum of modulated values ​​of all complex numbers to quantized amplitude and / or phase values ​​requires the use of a specific quantization method. A simple embodiment of a binary amplitude quantization scheme is as follows: If a value has a negative or zero real part (the point is in the second or third quadrant on the Algando diagram), the point is mapped to the point (0,0) on the Algando diagram. If a value has a positive real component, the point is mapped to the point (0,1) on the Algando diagram. Those skilled in the art will recognize that many alternative quantization methods can be used and that this disclosure is not limited to any particular quantization method. However, this embodiment highlights the loss in phase and amplitude information resulting from quantizing points for display on a DMD. Other display techniques may supply more values, but the number of available finite states is still low, perhaps 5 bits (32 values). It is evident that any quantization will result in a loss in amplitude and phase information, reducing image quality.

[0045] The inventors have shown that noise introduced by quantization can be reduced by using physical filters in a display device to selectively filter out undesirable noise components within a quantized hologram. (Quantized representation of target light field, H) Q By approximating it as a series expansion, the quantized field can be determined, and in the quantized field, additional undesirable components introduced by quantization can be filtered out within the Fourier domain / Fourier plane, enabling a much improved approximation of the full complex target field regardless of the quantization that occurs in the display system. The display systems and methods discussed may provide computationally inexpensive techniques for achieving full complex modulation using conventional display devices, in particular, compared to previous iterative software-based techniques such as Gercberg-Saxton.

number

[0046] Quantized hologram, H Q The image is displayed by quantizing an initial all-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 may be, for example, a DMD, LCD, amplitude LCoS, or phase LCoS. The light source may be configured to produce at least partially coherent light modulated by the SLM, and may be, for example, a laser or a light-emitting diode (LED).

[0047] An SLM generates a light field, which, when observed by an observer through an optical system, generates another light field, thus perceiving an image. Conventional systems include a lens that produces a Fourier transform of the image displayed on the SLM, which is then produced by the observer's eye, which produces an inverse Fourier transform. Without applying further steps such as iterative techniques that consider quantized values ​​reproducible by the SLM, the image quality is low due to errors introduced by quantization.

[0048] However, this disclosure states that if a lens having a focal length, f is positioned in front of the SLM at one focal length such that light modulated by the SLM is incident on the lens, H Q The Fourier transform of F(H Q This utilizes the observation that a region occurs behind the lens at one focal length. This position is called the Fourier plane of the SLM. This is the plane in which the complex amplitude is explained by the Fourier transform of the complex amplitude in the SLM, which scales or includes a modulo that multiplies the spherical phase term. In this case, H Q The Fourier transform of can be described 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 Equation 2 below. 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 * These are referred to herein as noise components because they relate to undesirable components generated by quantizing the target field, H. The effect of these components is visible as classical "noise," but is also a reduction in image contrast and is generally understood to result in reduced image quality.

[0050] The Fourier transform of a spatial function (for example, a target light field, H, is a spatial function H≡H(x,y)) is its respective frequency component, k x and k y The function is decomposed into the following: The Fourier transform of the constant a in Equation 1 is expressed by the term aF(1) in Equation 2, which is sometimes known as the zero-order diffraction peak, multiplied by a and kx =k y This is a delta function centered at =0. The location of each upper right component of Equation 2 in the Fourier plane can be determined from knowledge of the location of F(H), as described here with reference to Figures 1A-1G. Figures 1A-1G are intended to illustrate the overall principle used in this disclosure and the locations of the noise components involved.

[0051] An example of F(H)102 being targeted in any area within the Fourier plane is illustrated in Figure 1A. Figure 1A shows the spatial frequency k x The central horizontal line 110 represents the axis, and the spatial frequency k y Figure 1A is a plot of the Fourier transform of H in spatial frequency space, with a central vertical line 120 representing the axis. Similarly, Figure 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 Figure 1A is a square with side dimensions 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. Figure 1A represents four cells centered at the origin to show how tiling of unit squares affects the aperture design. For example, for illumination with wavelength λ = 520 nanometers, f = 60 millimeters, and p = 5 micrometers, the dimensions of the square in the Fourier plane are 6.24 millimeters, which is the size of the filter.

[0052] If the position of F(H) in the Fourier plane is known, then H * , F(H * The position of the Fourier transform of ) can be determined from the position of F(H). In the Fourier plane, this is the position of line k y =-k x This is a reflection in that region. The result is shown in Figure 1B as region 104.

[0053] Similar spatial plots in the Fourier plane can be created for higher-order components of the expansion. Figure 1C shows F(HH) in the Fourier plane.* ) Indicates the position of 106. F(HH * ) is its complex conjugate, H * This is the Fourier transform of the target light field, H, multiplied by F(HH). * ) is at the center of the Fourier plane, k x and k y H and H in * This is a range twice that of F(H)102 and F(H * It is also in a range twice the size of 104, and is located at the center, twice the distance from the origin F(H)102, within the Fourier plane 100. 2 Figure 1E shows the position of F(H) in the Fourier plane. *2 ) indicates the position of 110. Similarly, F(H *2 )110 is F(H)102 and F(H * ) is also in a range twice that of 104, and F(H * It is located at a distance of twice 104 units from the center.

[0054] Figure 1F is a composite of Figures 1A-1E, illustrating the relative positions of components 102, 104, 106, 108, and 110 within the Fourier plane 100. Because the target light field, H, is sampled on a pixel grid, the field in the Fourier plane repeats on a square grid that forms a repeating pattern of components 102, 104, 106, 108, and 110. Figure 1G shows each of the components represented in Figure 1F, along with each of the duplicates of the components in the Fourier plane. Regarding the location of F(H)102, the noise components introduced by the quantization considered in Figures 1B-1E do not overlap with F(H). Furthermore, none of the other duplicates of those additional components resulting from sampling on the grid overlap with F(H).

[0055] It will become clear 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 will cause the noise components to grow accordingly. When F(H) reaches a sufficient range, it will begin to overlap with one or more of the noise components. Furthermore, translating and / or rotating F(H) with respect to the origin in the Fourier plane will result in corresponding translations and / or rotations of the noise components.

[0056] As can be seen from Figure 1G, the effects of the noise components under consideration can be removed by a spatial filter in the Fourier plane. The resulting inverse Fourier transform of the filtered Fourier plane is more similar to the original total complex function H than the Fourier transform of the unfiltered Fourier plane. Such filtering can be performed physically as part of the hologram display, rather than requiring additional computational steps such as multiple iterations of the Gercberg-Saxton. Referring to Figure 6, as will be explained in more detail below, a CGH targeting a specific region of the Fourier plane is relatively easy to determine, for example, by applying a mask function. This requires significantly less processing resources and / or power than the previous iterative method.

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

[0058] As discussed above, once the location of F(H) in the Fourier plane is determined, the location of the noise component can also be determined, for example, using the methods shown in Figures 1A-1G. Many possible locations for F(H) that do not overlap with the noise component under consideration are also possible. Some embodiments can maximize the region in the Fourier plane that satisfies the condition that the noise component under consideration does not overlap with F(H). Maximizing the region covered by F(H) maximizes the amount of light passing through the filter and increases the brightness of the hologram in the target plane. This also maximizes the area of ​​the hologram in the Fourier plane and increases 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 condition of no overlap of noise components related to ) is 1 / 6 of the total area of ​​the filter. Furthermore, the shape of the aperture is constrained by the no-overlap condition described above. Figures 2A-2E show filters 200, 210, 220, 230, 240, and 250 that demarcate apertures 202, 212, 222, 232, 242, and 252 in embodiments that satisfy the maximum area condition. It can be seen that none of the apertures 202, 212, 222, 232, 242, and 252 are circular. This may be because circles cannot satisfy the maximum area condition since they cannot perfectly tile a flat two-dimensional space.

[0060] Filters 200, 210, 220, 230, 240, 250 are shown as unit squares having a relative side length of 1 for illustrative purposes, but in reality, they have a length equal to λf / p. FIGS. 2A-2F depict filters delimiting an aperture, where the aperture satisfies the condition that when F(H) is targeted at the aperture, at least the noise components considered above for FIGS. 1A-1G are blocked by the non-aperture portions of the filter, and 1 / 6 of the area of the unit square is used. FIGS. 2A-2F show only some of the possible filters satisfying the above conditions, thus indicating that the filters described herein are not limited to the filters represented in FIGS. 2A-2F. Similarly, in some embodiments, the filters may not attempt to occupy the maximum area and may occupy a smaller area while still satisfying the non-overlapping condition. This may, in some cases, enable a "buffer" area between F(H) and its noise components in order to more effectively filter and avoid diffraction effects at the perimeter of the aperture boundary or to increase the tolerance for filter alignment.

[0061] FIG. 2A shows a filter 200 of an embodiment delimiting a rectangular aperture 202 according to an embodiment. The rectangular aperture 202 extends from the side of the filter, in this case from the vertical side, and has a width of 1 / 2 the width of the filter and a height of 1 / 3 the width of the filter. More specifically, the region is centered on the vertical axis and is located on the left side. The rectangular aperture 202 is positioned such that F(H * ), F(H 2 ), F(H *2 ), and F(HH * ) are blocked by the filter. In particular, F(H * ]>) occupies a region 203 adjacent to the aperture 202 along the horizontal axis and occupying the same range on the vertical axis. F(HH * ), F(H 2 ), and F(H *2 ) occupy a region 204 extending across the full width of the filter 200 above and below the aperture 202.

[0062] Reflections of filter 200 around vertical lines extending through the center of the filter, reflections around horizontal lines extending through the center of the filter, 90-degree rotations around the center of the filter, reflections around axes extending through the origin of the Fourier plane, and reflections around the origin are also possible and satisfy the constraint of non-overlapping noise components. For example, as shown in Figure 2A, an alternative form may have a region 203 as an aperture and region 202 that are blocked off.

[0063] Figure 2B shows a filter 210 of another embodiment that demarcates a rectangular aperture 212. In this case, the height of the 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 the aperture 212 is equal to the total width of the filter 210. Further shown in the filter 210 is a portion or region 214 indicated by a solid line in the filter 210. The portion 214 represents a region where the aperture 212 is instead positioned to produce the same effect. The portion 214 is the reflection and rotation of the aperture 212, as discussed above with respect to Figure 2A.

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

[0065] Figure 2D shows a side view of the filter, in this case, of the filter 230 that demarcates a single trapezoidal opening 232 extending from the base axis or horizontal axis. More specifically, the opening 232 is a right trapezoid. The base of the opening 232 is centered midway along the base or horizontal axis of the filter 230. The base has a width of 1 / 3 the length of the filter 230. The left edge of the opening 232 is a straight line perpendicular to the base and has a length of 1 / 3 the width of the filter 230. The right edge of the opening 232 is a straight line perpendicular to the base and has a length of 2 / 3 the width of the filter. The upper ends of the two edges are connected by a further straight line. The portion of the filter 234, shown by a solid line, indicates the region that is instead demarcated as an opening to achieve the same effect related to region 232 by rotation and / or reflection.

[0066] Figure 2E shows a filter 240 that separates two openings 242 and 244 extending between two vertical sides of the filter. Each opening 242, 244 has a trapezoidal, more specifically, isosceles trapezoidal shape. Opening 244 has a base that is 1 / 6 the width of the filter 240 and is 1 / 4 center along the base of the filter 240. Opening 244 has a left edge that is 1 / 6 the length of the filter and is 1 / 4 center along the left edge of the filter 240. The lower corner of the left edge is connected to the left edge of the base by a straight line, and the upper corner of the left edge is connected to the right edge of the base by a further straight line.

[0067] The opening 242 is 3 / 4 centered along the base of the filter 240 and has a base that is 1 / 6 the width of the filter 240. The opening 242 further has a left edge 3 / 4 centered upward along the left edge of the filter and has a left edge that is 1 / 6 the width of the filter 240. The lower corner of the left edge of the opening 242 is connected by a straight line to the left corner of the base of the opening 242, and the upper corner of the left edge is connected by a further straight line to the right edge of the base.

[0068] The portions of filters 246 and 248, shown as solid lines in filter 240, indicate where the filters instead divide the apertures to achieve the same effect through rotation and reflection of apertures 242 and 244.

[0069] Figure 2F shows a filter that demarcates a single opening 252 having a trapezoidal, more specifically, isosceles trapezoidal shape. The opening 252 extends between two vertical sides. It has a base that is one-third the width of the filter 250 and centered on the base of the filter. The left edge, which is one-third the width of the filter 250, is centered on the left edge of the filter 250. The left corner of the base is connected by a straight line to the lower corner of the left edge, and the right corner of the base is connected by a straight line to the upper corner of the left edge. The portion of the filter 254, designated by a solid line in the filter 250, indicates where the filter 250 would instead demarcate the opening to achieve the same effect. The portion 254 is related to the opening 252 by rotation and / or reflection of the opening 252.

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

[0071] While the above discussion has considered maximizing the aperture area so that all undesirable components are blocked, some embodiments may still utilize larger apertures. Generally, higher-order noise components are not evenly distributed within the Fourier plane and tend to have lower output and / or amplitude around them than at the center. Therefore, the aperture size can be increased slightly beyond the 1 / 6 criterion described above without introducing much more noise. For example, an aperture may have an area of ​​1 / 5 to 1 / 6 of a unit square in the Fourier plane and may still demonstrate improved performance with a hologram that targets an aperture compared to one without an aperture and without targeting the hologram.

[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 embodiments, the maximum area of ​​the filter that demarcates the aperture is 1 / 6 of the total area. This has the advantages discussed above in terms of improved image quality, but it means that the area in which the hologram can be seen is reduced. In further embodiments, the effectively observable area in which the hologram can be perceived (sometimes referred to as the "eyebox") can be increased by using multiple portions that are selectively controlled to either allow light to pass through or block light from reaching the observer. The aperture then includes portions of the filter that allow light to pass through. The portions may be configured to allow at least two of the apertures 202, 212, 222, 232, 242, and 252 shown in Figures 2A–2F to be used consecutively. In this way, the position of F(H) in the Fourier plane can be variable over time. Assuming a reasonably fast display such as a DMD, the display can then be rapidly switched between different positions within a single frame period. Through visual persistence, the observer perceives such a series of rapidly displayed holograms as a single hologram.

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

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

[0075] While the One-Step Phase Search (OSPR) algorithm also leverages visual persistence, the method disclosed herein can provide higher quality results with lower computational resource usage. OSPR utilizes the entire Fourier plane, but multiple holograms with different random phase patterns are displayed rapidly in time, and the observer's eye combines them to perceive a single hologram through overall noise reduction (noise leveling). The concept here is to use the same visual persistence effect rather than leveling the noise effect, and averaging is used to increase the portion of the Fourier plane used, and thus the observable area. Furthermore, instead of 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 may use different random phase patterns for each displayed hologram, effectively applying the apertures disclosed herein to OSPR.

[0076] In some embodiments, apertures and OSPR described herein can be combined. In such cases, OSPR can utilize a lower bit depth due to the noise reduction provided by the aperture. Frames can be processed more immediately so that OSPR becomes less computationally intensive and / or to reduce noise in OSPR by maximizing the benefits of time-averaging effects.

[0077] The portions can be tiled within each unit cell of the filter, resulting in multiple portions for each unit cell, i.e., a portion of the filter having dimensions λf / p. The SLM may then be configured to generate a holographic light field, H, so that F(H) is targeted in one or more deactivated portions of the filter. Synchronizing the deactivated portions of the filter with the holographic light field generated by the SLM targeting those portions allows for an increase in the effective area of ​​the hologram generated in the target plane. If the portions of the filter are activated and deactivated at a sufficiently fast rate, such as greater than or equal to 100 Hz or 200 Hz or more, the observer may not perceive the switching. This allows for a further effective increase in the size of the eyebox. As discussed above with reference to Figure 1C, the central zero-order mode is formed from the constant term in Equation 2 above and is therefore always blocked so as to constrain the maximum output of the noise period. However, in some embodiments, the "zero-order" may be located in a different position (when an Echelle diffraction grating is used), and in those embodiments, a portion of the Fourier plane encompassing the highest output noise period is blocked.

[0078] Figure 3 shows an embodiment of filter 300, which includes multiple sections corresponding to areas that can be controlled to allow or block light from passing through. These are labeled 301–316. The sections of filter 300 correspond to apertures similar to those illustrated in Figures 2C and 2D, which include rotation and reflection. More specifically, sections 301, 302, 303, 304, 305, 306, 307, and 308 each include a single trapezoidal region as shown in Figure 2D, while sections 309, 310, 311, 312, 313, 314, 315, and 316 each include two trapezoidal regions. At any given time, one of the apertures 301–316 (which may include more than one region) is in a state that allows light to pass through, while all the other sections are in a state that blocks light from passing through. Accordingly, the holographic light field, H, can be targeted such that F(H) corresponds to the portion(s) through which light can pass. During use, the controller can supply the SLM with the appropriate hologram and control the filter so that the relevant portion(s) can pass through. Some SLMs can operate quickly enough so that all 16 apertures 301-316 can be displayed within a single frame period. Any sequence of operations can be used, including incrementing from apertures 301-316 so that they can be labeled, and decrementing from apertures 316-301 so that they can be labeled.

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

[0080] The controllable portion of Figure 3 can be manufactured in various ways. For example, the filter 300 may be manufactured from liquid crystal and may operate to either substantially allow light to pass through or substantially block light. The liquid crystal may have high switching speeds, such as a pi cell or a ferroelectric LCD (FLCD). Another embodiment may use a DMD as the filter, which is controlled not to modulate the light field but to control which portion of the modulated light is allowed to pass through. Yet another embodiment may use a rotating chopper wheel, which rotates to define each of a plurality of apertures and lasers synchronized to the chopper wheel. The chopper wheel may use a stepping motor or similar to control its rotational position, for example. Of course, the filter 300 may utilize any suitable example of shutter technology, including molecular-based shutters, quantum optical shutters, and plasmonic metamaterial shutters.

[0081] The filter 300 in Figure 3 includes regions that are always blocked, but other embodiments may also allow control over those blocked regions. Such embodiments may allow spatial filtering to be completely disabled if necessary. This may allow the user to choose between operation with spatial filtering or alternative image processing such as Gercberg-Saxton iterative processing. Alternatively, or in addition, filters may be selectively placed in the optical path, for example, by providing a mechanism to remove the filter from the optical path when not needed and to place the filter in the optical path when used by the methods of the present disclosure.

[0082] In the preceding discussions in Figures 2A-2F and 3, F(H) was discussed assuming it was generated by light of a single irradiation wavelength. However, the principle described herein can be extended to cover light of multiple irradiation wavelengths. Such light is 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 irradiation wavelengths, the aperture(s) can be selected such that the condition of no overlap of F(H) with noise components is strict for light of the first wavelength, but approximates it only for light of the second wavelength. This enables the approximation of total complex modulation in multicolor holograms.

[0083] Figure 4 generally shows a holographic optical system 400. The system 400 includes a light source 402 configured to produce at least partially coherent light. The system 400 further includes a spatial light modulator (SLM) 404 arranged to be illuminated by at least partially coherent light. The system 400 further includes a lens 406. The lens 406 has a focal length, f, and is positioned at one focal length from the SLM 404. The system 400 further includes a filter 408 that divides the aperture 410. The filter 408 is located on the opposite side of the lens 406 from the SLM 404 and is positioned at one focal length from the lens 406.

[0084] SLM404 is configured to generate a light field, which is a quantized representation of the target light field, H, as discussed above. The array of holographic optical systems 400 is such that the Fourier transform of the light field, F(H), is formed in a plane coinciding with the position of the filter 408. This plane is the Fourier plane of SLM404 as imaged by lens 406. The Fourier transform of the target light field, F(H), is then converted to the complex conjugate of the target light field, F(H * The target light field is determined such that it does not overlap with at least the Fourier transform of and the quadratic component in the Fourier plane of SLM404. Furthermore, the aperture in filter 408 corresponds to F(H) in the Fourier plane, and as a result, the portion of the target light field outside of F(H) is blocked.

[0085] The light source 402 may include, for example, a laser module or an LED. The light source 402 is configured to produce light that is at least partially coherent at one or more wavelengths (for example, corresponding to red, green, and blue).

[0086] The SLM404 can be configured to modulate at least one of the phase, amplitude, binary phase, and binary amplitude of light. The SLM404 may be, for example, a DMD, LCD, amplitude LCoS, or phase LCoS.

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

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

[0089] Since the theory and overall structure of the holographic display according to the present disclosure have been described, the method of its operation is described herein. FIG. 5 shows a method 500 for reducing quantization noise in a holographic image. The method 500 can be executed, for example, by a controller of the holographic optical system 400 shown in FIG. 4. At 502, the method 500 includes generating a target light field, H, for quantization. The target light field has a Fourier transform, F(H), that does not overlap with its complex conjugate, F(H * ) and the quadratic component in the Fourier plane. F(H) can be predetermined as occupying a region having those characteristics, as discussed, for example, in reference to FIGS. 2 and 3. The method of targeting the hologram in this region is described below in reference to FIG. 6.

[0090] Next, at 504, the quantized version of the target light field is displayed through a filter that delimits an aperture corresponding to the extent of F(H) in the Fourier plane, such that at least the Fourier transform of its complex conjugate, F(H * ) and the quadratic component are blocked by the filter.

[0091] FIG. 6 shows an exemplary method 600 for calculating a hologram targeted in a predefined region of the Fourier plane, along with a representation of an example of an image at each step showing the effect of the processing. The method 600 can be executed by a processing system that can be local or remote from the holographic display system. The holographic frame determined by the method 600 is output to an SLM such as the SLM 404.

[0092] Method 600 begins in block 602 by receiving a target light field. The target light field is a two-dimensional array representing a single image layer to be displayed by the holographic optical system. The target light field is transformed into a complex target light field 602 by applying a 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 variance across the light field. Each random phase factor e iθ This may include a matrix of random numbers applied to the target light field, which contains a matrix of pixels.

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

[0094] Previously, images were perceived as being infinitely positionable, and therefore, in block 608, the defocus Zernike polynomial is applied to the output of block 606, resulting in a defocused image at a target depth on a plane coinciding with the SLM. Generally, the properties 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 a focal length f is positioned at one focal length from the SLM, and the SLM is illuminated with light of a single wavelength, λ. For the layer at depth d and the SLM in optical infinity, the opening pupil 606 is multiplied by the defocus Zernike polynomial: exp(2πi(2r 2 (-1) / 4dλ), where r is the radial distance (in meters) from the center of the aperture region to each sample point. Spatial sampling of the pupil determines the value of r for each point, fλ / pN in the x-direction and fλ / pM in the y-direction. The method is not limited to the use of Zernike polynomials, and other methods such as parabolic phase functions may be used.

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

[0096] The out-of-focus aperture pupil from block 608 undergoes an inverse Fourier transform in block 610, resulting in the light field at the depth of the SLM. Although the aperture is restricted to the Fourier plane, it can be observed that the inverse Fourier transform means that the entire range of the SLM is still used to display the image. (Just as filtering a time-variable waveform within the Fourier domain still results in a time-domain waveform of the same temporal length, filtering the Fourier plane still results in the entire range of the SLM 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. Any suitable quantization scheme can be applied as discussed above. Process 600 determines the holographic light field formed by an SLM such as SLM404, and consequently, the Fourier transform of the light field is formed within an area of ​​the Fourier plane corresponding to a predefined aperture in the filter.

[0098] Figure 6 shows that the image in block 610 appears to be of lower quality than the image in block 602. This is due to several reasons. Firstly, the image in block 602 is ideal, and therefore the image in block 610 cannot be of higher quality. Secondly, the image in block 610 exhibits the effect of the defocus Zernike polynomial. If no aperture were present, the image in block 610 would be of lower quality than represented.

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

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

[0101] In some embodiments, the filter includes multiple parts that can be selectively controlled to allow or block light, such as filter 300 shown in Figure 3. In this case, the different parts can be activated and deactivated to enlarge the effective eyebox of the resulting hologram. It is evident that targeting F(H) in different regions of the Fourier plane can be simply achieved by using process 600 to apply a corresponding mask to the simulated pupil determined in block 604, thereby generating the appropriate aperture pupil in block 606. Thus, as in the embodiment of Figure 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 allow the corresponding aperture to pass light through the filter while simultaneously displaying the resulting complex field.

[0102] Figure 8 illustrates another method by which a larger area of ​​the Fourier plane can 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 in a different position, effectively translating the zero-order position in the Fourier plane. Figure 8 schematically shows this effect with three light sources resulting in a Fourier plane with zero order located at positions 802a, 802b, and 802c, respectively. Using the aperture discussed above with reference to Figure 2A, the aperture is accordingly positioned at 804a, 804b, and 804c in the Fourier plane. During use, the light sources operate in a time series, and the position of the aperture is synchronized with the light sources. From Figure 8, it can be seen how this covers a larger area of ​​the Fourier plane. Throughout this process, the data displayed by the modulator also operates in a corresponding time series synchronized with the light sources, and the change in the position of the aperture is due to the different angles of the light sources.

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

[0104] As shown in Figure 8, there is a single aperture 804a, 804b, 804c for each light source, but multiple apertures for each light source can be time-multiplexed for each light source to fill an even larger area. For example, the offset light source in Figure 8 is combined with multiple aperture positions of a single light source in Figure 3. Similarly, other shapes of apertures can be used as described above.

[0105] Figure 9 shows an embodiment of the Fourier planes 906a and 906b for two light sources having different wavelengths. In this embodiment, the light sources are physically separated and therefore located at different zero-order positions 902a and 902b. In addition, as described above, the different colors of the light sources mean that the Fourier plane is scaled by the different wavelengths, and the dimensions of the unit square change. In this embodiment, the angle and / or position of the light sources with respect to the modulator is chosen so that aperture 904b is located within aperture 904a, and in this case, it is located entirely within aperture 904a. Without shifting the angle or position of the light sources, apertures 904a and 904b do not completely overlap, which may reduce 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 entire range of aperture 904a is not used.

[0106] As shown in Figure 9, there are single apertures 904a and 904b for each light source, but multiple apertures for each light source can be time-multiplexed for each light source to fill a larger area. For example, the offset light source in Figure 9 can be combined with multiple aperture positions of a single light source in Figure 3. Similarly, other shapes of apertures can be used as described above.

[0107] The above embodiments are to be understood as exemplary embodiments of the present invention. Further embodiments of the present invention are conceivable. It is to be understood that any feature described in relation to any one embodiment may be used alone or in combination with other features described, or in combination with one or more other features of any embodiment, or in any other combination of any embodiment. Furthermore, equivalents and modifications not described above may be adopted without departing from the scope of the present invention, as defined in the appended claims.

Claims

1. A holographic display system, A light source configured to emit at least partially coherent light, A modulator, which is emitted by at least partially coherent light and arranged to generate a light field that is a quantized representation of a target light field, H, It comprises a spatial filter that divides an aperture in the Fourier plane, The aperture substantially corresponds to the Fourier transform of the target light field, F(H), in the Fourier plane, where F(H) is (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) Fourier transform of the square of the target light field, F(H ２ (iv) the Fourier transform F(H) of the square of the complex conjugate of the light field. ＊２ ), which does not substantially overlap with, The aforementioned holographic display system.

2. The aforementioned spatial filter is A lens having a focal length, Includes a filter that partitions the opening, The filter and the modulator are positioned on the opposite side of the lens at a distance of one focal length from the lens. The holographic display system according to claim 1.

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

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

5. The holographic display system according to claim 1, wherein the perimeter of the opening is rectangular.

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

7. The holographic display system according to 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 through, thereby forming an aperture by a portion in the second state.

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

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

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

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

12. The holographic display system according to 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. The holographic display system according to 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 one F(H) of the first emitter and the second emitter is contained within the other F(H) of the first emitter and the second emitter.

14. A method for displaying holographic images, The process involves determining the target light field H for quantization, wherein the target light field is (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) Fourier transform of the square of the target light field, F(H ２ (iv) the Fourier transform F(H) of the square of the complex conjugate of the light field. ＊２ ), and to determine that they do not overlap, the Fourier transform has F(H), The quantized version of the target light field is displayed through the filter that demarcates an aperture corresponding to the range of F(H) in the Fourier plane such that the components corresponding to F(H ＊ ), F(HH ＊ ), F(H ２ ), and F(H ＊２ ) are substantially blocked by the filter. The method, including the method described above.

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

16. The method according to claim 14, wherein the range of F(H) in the Fourier plane has the perimeter of a quadrilateral.

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

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

19. The process involves generating multiple target light fields within different regions of the Fourier domain, wherein each of the multiple target light fields has the characteristic that the range of its Fourier transform does not overlap with the range of its complex conjugate Fourier transform. Through each filter that demarcates the aperture corresponding to the range of those Fourier transforms in the Fourier plane, the quantized versions of each of the multiple target light fields are displayed in time continuously at a speed sufficient to allow the observer to perceive the multiple holograms displayed in time continuously as a single hologram through visual persistence, The method according to claim 14, including the method described in claim 14.

20. A computer-readable medium that, when executed by a processor, includes instructions causing the holographic display system according to any one of claims 1 to 13 to display a holographic image in the manner described in any one of claims 14 to 19.

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