Computer-generated holographic display system

Abstract

A computer-generated holographic display system is described to have improved image quality when used with an illumination source other than a single-mode laser, such as a broadband light source including LEDs and multimode lasers. In one example, the computer-generated holographic display system has angular resolution and an angular field of view at a viewing position. The computer-generated holographic display system includes an illumination system comprising an LED or a multimode laser, a spatial light modulator (SLM) illuminated by the illumination system, and an optical system configured to re-image the SLM at a predetermined distance from the viewing position. The illumination system has an étendue at the SLM that is less than or equal to the value obtained by dividing the product of the angular resolution at the viewing position and the angular field of view at the viewing position by the maximum focusing power of the virtual image points with respect to the re-imaged SLM. The angular resolution is less than about 1 milliradian. In another example, the computer-generated holographic display system has an angular resolution and a restricted aperture width at the viewing position. The computer-generated holographic display system includes an illumination system comprising an LED or a multimode laser and having a spectral bandwidth and a nominal wavelength, a spatial light modulator (SLM) illuminated by the illumination system, and an optical system configured to re-image the SLM at a predetermined distance from the viewing position. The spectral bandwidth divided by the nominal wavelength is less than or equal to the value obtained by dividing the angular resolution by the product of the restricted aperture width and the maximum focusing power of the virtual image points with respect to the re-imaged SLM, and the angular resolution is less than about 1 milliradian.

Description

Technical Field

[0001] The present invention relates to a holographic display system.

Background Art

[0002] A holographic display system, also called a computer-generated hologram (CGH) display system, for example, by retaining wavefront information, includes depth information when displaying an image and brings many advantages. For example, the conflict of convergence adjustment in a conventional display is reduced or eliminated, and a viewer can naturally focus on a CGH image or a part of the CGH image in the perceived depth.

[0003] A CGH display needs to use at least a partially coherent light source. Although it is known that the coherence of the light source affects the resulting image quality, such as the sharpness of the image, this relationship is not well understood.

[0004] Generally, when using a broadband light source such as a light-emitting diode (LED) in a CGH display, it is assumed that the resolution of the displayed image is lost. The paper Y., Chu, D. “Coherence properties of different light sources and their effect on the image sharpness and speckle of holographic displays.” Sci Rep 7, 5893 (2017) is available from https: / / doi.org / 10.1038 / s41598-017-06215-x, which discusses how the temporal coherence of the light source affects the speckle of the image and how the spatial coherence of the light source affects the sharpness of the image. Simulations and experimental results of different light sources are presented. A single-mode laser light source has high spatial coherence for good image sharpness but also high temporal coherence that causes unwanted speckle in the image. Deng et al. conclude that a light source with high spatial coherence (for good sharpness) and low temporal coherence (for low speckle) is ideal for a holographic display. They suggest the use of a superluminescent light-emitting diode (SLED or SLD) or a micro light-emitting diode (mLed) as a suitable light source, but do not suggest the characteristics of other light sources.

[0005] Deng et al. state that spatial filtering such as using a pinhole between the light source and the SLM can improve the spatial coherence of the LED, but explain that this reduces efficiency. This paper concludes with a note that future research is needed to improve the spatial coherence of the LED while maintaining good optical efficiency.

[0006] When used with a light source other than a single-mode laser, such as a broadband light source including an LED or a multimode laser, it is desirable to improve at least one aspect of the image quality of the CGH display. SUMMARY OF THE INVENTION

[0007] The inventors have a new approach for quantifying the impact of a broader-band light source on image quality. By considering the contribution to the point spread function (PSF) of the CGH display after the SLM, more specifically, it is possible to define the limitations on the illumination system characteristics for improving image quality, particularly the sharpness of the image. The general result of this analysis is that the acceptable source bandwidth emitted from the illumination system (both spatial things such as the source emission area or étendue and temporal things such as the wavelength range present in the output) is inversely proportional to the distance between the re-imaged SLM viewed by the viewer and the virtual image point perceived by viewing the re-imaged SLM. For example, in a plane separated from the image content viewed at a low dioptric number such as 4 diopters or less, 3 diopters or less, or 2 diopters or less, it may be beneficial to design a holographic display system to re-image the SLM at a certain distance from the viewer. Once this relationship is established, then the characteristics of the illumination source and / or the optical system can be defined so as to give acceptable resolution and / or improved efficiency when used with a broadband light source such as an LED or a multimode laser. For example, the limitations on the illumination source étendue and / or the spectral bandwidth are specified in a way that was not previously understood and can then be used to select a particular illumination source and / or optimize the system design for improving efficiency. Deng et al did not consider or recognize how re-imaging the SLM at the distance from the viewer can affect image quality, and their proposed system re-images the SLM such that it substantially coincides with the pupil plane of the viewer, i.e., the distance from the viewer is zero.

[0008] According to a first aspect, a computer-generated hologram display system, also simply referred to as a holographic display system, a computer-generated holographic (CGH) display system has an angular resolution and an angular field of view at a viewing position. The CGH display system includes an illumination system including an LED or a multimode laser, a spatial light modulator (SLM) illuminated by the illumination system, and an optical system configured to reimage the SLM at a predetermined distance from the viewing position. The illumination system has an étendue that is less than or equal to a value obtained by dividing the product of the angular resolution and the angular field of view by the maximum focusing power of virtual image points with respect to the reimaged SLM at the SLM. The angular resolution is less than about 1 milliradian. Mathematically expressed, θ resolution <≒ 1 mrad. Pixelation is seen, but this may be acceptable depending on some applications. As the numerical value of the angular resolution becomes smaller, the pixelation becomes less noticeable and the image quality improves. In other words, the angular resolution can be better / equivalent than about 1 milliradian, which corresponds to about 17.5 pixels per degree. In other systems, the angular resolution may be less than 0.9 milliradian, less than 0.7 milliradian, less than 0.6 milliradian, less than 0.5 milliradian, less than 0.4 milliradian, and less than 0.3 milliradian.

[0009] In this way, the characteristics of the CGH display system can provide information to the characteristics of the illumination system and enable a selection based on the information of the illumination source without degrading the angular resolution. Similarly, the characteristics of the illumination system can provide information to the characteristics of the optical system to improve the efficiency of a specific illumination system.

[0010] It should be understood that in some embodiments, the illumination system may include a plurality of LEDs and / or a plurality of multimode lasers.

[0011] When referring to the characteristics of the illumination system, it refers to the light emitted from the illumination system incident on the SLM, and does not necessarily have to be the same as the characteristics of the illumination source forming part of the illumination system. The illumination system may comprise at least one illumination source. In some examples, the illumination system may consist of at least one illumination source used directly. What is important is the étendue at the SLM, or the étendue incident on the SLM. Other examples of the illumination system may include components in addition to at least one illumination source. The components may include filters such as a spatial filter, an angular filter, and a spectral filter, as well as fibers such as a multimode fiber that at least partially modifies the emission of the illumination system. For example, the emission area of the illumination source may be reduced by a spatial filter, the emission spectrum of the illumination source may be reduced by a spectral filter, the emission cone of the illumination source may be reduced by an angular filter, and a single-mode illumination source may be converted into a multimode illumination source by an optical fiber. Additional components may be combined, for example, to define the emission area and the emission cone.

[0012] The viewing position may be the position of the pupil of the viewer in use, and thus both the angular resolution and the angular field of view may be represented at the position of the pupil of the viewer. The angular resolution may be represented as the angular range of the smallest details from the viewing position.

[0013] Etendue is a property known to those skilled in the art. For simplicity, in this disclosure, this term is used to refer to the etendue in one dimension (i.e., the product of length and angle). A similar analysis may be continued in two dimensions, and when considering the range of the light source in x and y, the etendue is defined as the product of area and solid angle. The etendue of an illumination system can be calculated by multiplying the width of the SLM by the angular subtense of the illumination light source at the SLM. The angular subtense can be calculated from knowledge of the emission characteristics obtained directly from, for example, the data sheet of the illumination light source, or by measurement using, for example, a camera with an entrance pupil placed at the position of the SLM. Deng et al. recognize that spatial filtering of an extended light source such as an LED can improve image quality, but have not identified a more quantifiable relationship. Deng's spatial filtering reduces the area but does not consider the etendue. A quantifiable limit on the etendue of the illumination system can be set by shifting the position of the re-imaged SLM away from the viewer's pupil. In contrast, Deng et al. teach that the SLM should be re-imaged at the pupil (sometimes referred to as a "pupil plane" architecture).

[0014] The etendue of a broadband light source such as an LED can be reduced by filtering. The filtering may be one or both of spatial filtering (reducing the effective emission area of the illumination light source) and angular filtering (reducing the effective emission cone angle of the illumination light source). Knowledge of the maximum etendue makes it possible to improve the efficiency of the system while minimizing the impact on resolution. For example, the filtering may be selected to reduce the etendue of the illumination system incident on the SLM, and as a result, the etendue is substantially equal to 100% of the value obtained by dividing the product of the angular resolution (θ resolution ) and the angular field of view (θ FOV ) by the maximum focusing power (D max ) of the virtual image point with respect to the re-imaged SLM. ((θ resolution θ FOV ) / D max) is substantially equal to 100%. This can improve the efficiency without adversely affecting the resolution.

[0015] The étendue of the illumination system is (θ resolution θ FOV ) / D max and may be at least 2%, at least 5%, at least 10%, at least 20%, or at least 50%.

[0016] The focusing power is well-known. The maximum focusing power D max for the CGH display system can be calculated as (d SLM - d obj ) / (d obj d SLM ), where d SLM is the distance from the viewer to the re-imaged SLM, and d obj is the distance to the virtual object closest to the viewer.

[0017] In some examples, the illumination system includes a light-emitting diode LED, a superluminescent light-emitting diode sLED, or a micro light-emitting diode mLED.

[0018] The predetermined distance may be set to be greater than the minimum distance from the viewing position to the virtual image point. This places the re-imaged SLM farther from the viewing position than the closest virtual image point, helping to reduce the required maximum focusing power. For example, the SLM may be re-imaged at least 1 m, or at least 0.5 m, from the viewing position. In some examples, the predetermined distance may be negative, corresponding to the position of the re-imaged SLM behind the viewer, as may occur when the SLM is re-imaged "beyond infinity".

[0019] In some cases, the maximum focusing power corresponds to a virtual image point about 1 m or less from the viewing position. For example, the maximum focusing power may correspond to the virtual image point closest to the viewing position displayed by the CGH display in use.

[0020] In some examples, the maximum focusing power corresponds to a virtual image point about 0.25 m from the viewing position. Since 0.25 m is generally accepted as the closest focal distance of the human eye, this is useful for headset-based displays such as virtual reality or augmented reality.

[0021] The maximum focusing power may be about 4 diopters or less, about 3 diopters or less, about 2 diopters or less, or about 1 diopter or less. The inventors have discovered that the maximum acceptable étendue of an illumination system for a given angular resolution is inversely proportional to the maximum focusing power. The smaller the maximum focusing power, the more advantageously a larger étendue is allowed, thus allowing a wider range of possible choices of illumination sources and / or allowing a reduction in filtering in the illumination system, which can improve efficiency.

[0022] The angular resolution may be greater than about 0.15 milliradians. Mathematically expressed, θ resolution >≒0.15 mrad. As the value of θ resolution increases, the size of the dots / pixels increases, pixelation increases, and image quality decreases. In other words, the angular resolution can be worse than or equivalent to about 0.15 milliradians, corresponding to about 6,700 dots per radian, and generally corresponding to the resolution limit of the human eye. Since the acceptable étendue is proportional to the angular resolution, setting the value of the angular resolution greater than about 0.15 milliradians means that the acceptable étendue can be maximized without providing a system with a pixel size smaller than what the human eye can resolve. Other systems may have a higher angular resolution, e.g., greater than 0.2 milliradians, greater than 0.3 milliradians, greater than 0.4 milliradians, greater than 0.5 milliradians, greater than 0.6 milliradians, greater than 0.7 milliradians, greater than 0.8 milliradians, and greater than 1 milliradian.

[0023] So far, only the étendue of the illumination system has been considered. Broadband light sources also typically have a spectral bandwidth, in other words, they emit over a range of wavelengths rather than a single wavelength. This also affects image quality. In some embodiments, the CGH display system has a restricted aperture width, the illumination system has a spectral bandwidth Δλ and a nominal wavelength λ, and the spectral bandwidth divided by the nominal wavelength is the angular resolution θ resolution is at most the product of the maximum focusing power D max and the restricted aperture width w eyebox and is less than or equal to the value obtained by dividing by the product of. In other words, Δλ / λ is θ resolution / (D max w eyebox ). This provides a limit on the spectral bandwidth, maintaining a reasonable image resolution and making it possible to use light sources such as LEDs.

[0024] As Deng et al. have stated, speckle noise can be reduced by light sources with a high spectral bandwidth (low temporal bandwidth) such as LEDs. However, Deng does not provide any limits on acceptable image quality beyond the general observation that as the spectral bandwidth increases, speckle noise decreases while image sharpness decreases. By shifting the re-imaged SLM away from the viewing position, it is possible to quantify the acceptable spectral bandwidth for a given resolution of the display without unduly affecting the angular resolution.

[0025] Some examples may apply stricter limits to the light source spectral bandwidth divided by the nominal wavelength (Δλ / λ). For example, if the value of Δλ / λ is less than 100%, 90%, 75%, or 50% of θresolution / (D max w eyebox ), the impact on the angular resolution gradually decreases. In some examples, θresolution / (D max w eyebox) can have Δλ / λ at about 100% thereof. This can be advantageous when designing an optical system to use the spectral bandwidth to the maximum extent, for example, to improve efficiency and / or reduce speckle noise.

[0026] The light source spectral bandwidth can be measured in the manner of the conventional full width at half maximum (FWHM) method, whereby the spectral bandwidth is measured between the wavelengths of the points having the intensity half of the wavelength with the maximum intensity.

[0027] It is possible to directly use the illumination light source without adjusting the spectral bandwidth, but in some examples, it may include a spectral filter that limits the spectral bandwidth, such as a spectral filter that allows only limited wavelengths to pass through. Spectral filters having defined nominal characteristics and FWHM characteristics are commercially available from, for example, Thor Labs. The spectral filter can enable the use of a light source with a wide spectral bandwidth that otherwise could not be used. The spectral filter may be provided as part of the illumination system, may filter the optical spectral bandwidth before the light is incident on the SLM, or may be provided separately after the SLM.

[0028] The limiting aperture is the smallest pupil aperture in the system. This may be the exit pupil of the display itself. The inventors have shown that the acceptable spectral bandwidth is inversely proportional to the size of the limiting aperture, and thus it may be advantageous to keep the limiting aperture small. In some examples, the limiting aperture width is less than about 7 mm. 7 mm is approximately the diameter of the human pupil. When the display system itself has a larger limiting aperture, in some examples, 7 mm may be used instead of the limiting aperture because the viewer's pupil can form the limiting aperture.

[0029] As described above, the spectral bandwidth limitation is provided in combination with the étendue limitation. The spectral bandwidth limitation may also be applied independently of the étendue limitation. In another aspect, the CGH display system has an angular resolution at the viewing position and a limited aperture width. The CGH display system includes an illumination system having an LED or a multimode laser and having a spectral bandwidth and a nominal wavelength, a spatial light modulator (SLM) illuminated by the illumination system, and an optical system configured to re-image the SLM at a predetermined distance from the viewing position. The spectral bandwidth divided by the nominal wavelength is less than or equal to a value obtained by dividing the angular resolution by the product of the limited aperture width and the maximum focusing power of the virtual image points with respect to the re-imaged SLM. The angular resolution is less than about 1 milliradian.

[0030] In another aspect, the CGH display system has an angular resolution at the viewing position. The CGH display system includes an illumination system having an LED or a multimode laser and having a light source spectral bandwidth and a nominal wavelength, a spatial light modulator (SLM) illuminated by the illumination system, and an optical system configured to re-image the SLM at a predetermined distance from the viewing position. The light source spectral bandwidth divided by the nominal wavelength is less than or equal to a value obtained by dividing the angular resolution by the product of 7 mm and the maximum focusing power of the virtual image points with respect to the re-imaged SLM. The angular resolution is less than about 1 milliradian.

[0031] In a further aspect, the contribution to the PSF by one, some, or all of (i) the spectral bandwidth of the illumination system, (ii) the angular subtense of the light incident on the SLM, and (iii) the dimensions of the light source such as the diameter, is kept smaller than the contribution by the intrinsic resolution of the SLM up to a predetermined maximum distance from the SLM. There are many design solutions regarding these constraints, and it will be understood that this can lead to various different ways of defining and / or restricting the characteristics of the illumination system in order to meet this solution. However, one of ordinary skill in the art will be able to easily determine these various designs from the knowledge of how each component affects the PSF, as will be described in more detail later. The predetermined maximum distance imposes constraints so that the contributions can be determined. For example, by determining the contribution to the PSF from the SLM at the predetermined maximum distance and then deriving the constraints on the illumination system to ensure that the contributions from the spectral bandwidth, angular subtense, and dimensions of the light source at the maximum distance do not substantially exceed the contribution from the SLM.

[0032] When further constraints are applied to the characteristics, various effects on the sharpness of the image can be controlled. There are also advantages in constraining only one of the spectral bandwidth, angular subtense, or the dimensions of the light source. These advantages are improved when multiple ones are applied, and a good balance is obtained by applying constraints to the spectral bandwidth and angular subtense, but the present invention is not limited to this combination.

[0033] According to one aspect, a CGH display system is provided, the CGH display system comprising an illumination system comprising a light emitting diode, an LED, or a multimode laser, and a spatial light modulator SLM illuminated by the illumination system. The CGH display system is configured to display an image within a certain focal power of an image of the SLM relayed to a viewer. This corresponds to displaying the image within a predetermined maximum distance from the SLM that is less than about 50 mm. Up to the predetermined maximum distance, (i) the spectral bandwidth and (ii) the angular subtense of the light incident on the SLM each have respective contributions to the composite point spread function of the light exiting the SLM, and this contribution is below the contribution due to the intrinsic resolution of the SLM. In other examples, less stringent criteria may be applied, for example, up to the predetermined maximum distance, (i) the spectral bandwidth and (ii) the angular subtense of the light incident on the SLM each have respective contributions to the composite point spread function of the light exiting the SLM, and this contribution is within 2 times or 4 times the contribution due to the intrinsic resolution of the SLM.

[0034] This utilizes the fact that the contributions from the intrinsic resolution, spectral bandwidth, and angular subtense of the SLM to the PSF are orthogonally added. It has been found that good image quality can be obtained by keeping the contributions from the spectral bandwidth and angular subtense below the contribution from the intrinsic resolution of the SLM. All of these quantities can be readily determined by one of ordinary skill in the art for a particular display configuration. In this way, good image quality can be obtained while using an illumination source other than a single mode laser such as an LED or a multimode laser. (Of course, a multimode laser can itself comprise a single mode laser, and the single mode laser can be converted to multimode using an additional device, for example, by passing through an optical fiber. In this case, the illumination system includes this multimode laser due to this conversion of the single mode laser.)

[0035] By specifying a predetermined maximum distance for imaging from the SLM, it becomes possible to define the qualitative characteristics of the illumination system in a way that was not previously possible. More specifically, limitations on the characteristics of the illumination system can be defined before the light source becomes a significant limiting factor for resolution. This does not mean that it can be used with any multimode laser or LED light source, but it will be understood that the acceptable range is such that more light sources can be used.

[0036] Several potential advantages can result, including the ability to use higher power and / or lower cost multimode laser light sources, the ability to use less expensive LED light sources, and the reduction of laser safety risks for a given optical output.

[0037] In some examples, the spectral bandwidth is greater than 1 nm. Additionally, or alternatively, the spectral bandwidth may be substantially unconstrained. This allows the use of light sources with a wider bandwidth than single-mode lasers in the illumination system, thereby reducing costs. When an upper limit is used, the effect of the spectral bandwidth on the sharpness degradation of the image is controlled to be less noticeable.

[0038] The predetermined maximum distance may be less than about 50 mm, less than about 25 mm, or less than about 10 mm. By setting a smaller value for the maximum distance, the allowable spectral bandwidth of the illumination system increases, and a wider range of illumination light sources can be used.

[0039] In some examples, the illumination system comprises a light-emitting diode (LED), a superluminescent light-emitting diode (sLED), or a micro light-emitting diode (mLED).

[0040] The spectral bandwidth Δλ of the illumination system can be limited according to the following equation.

Equation

[0041] The illumination system can be configured such that light diverges from the SLM at an angular subtense θ.

Equation

[0042] The system can include a collimating lens having a focal length f disposed between the illumination system and the SLM, and the illumination system is configured as follows. c

Equation

Equation

[0043] The system may include a lens having a focal length after the SLM, and the predetermined maximum distance is based on the focal length of the lens.

[0044] According to a further aspect of the present invention, a head-mounted display is provided, which comprises a CGH display system according to any of the above aspects, with or without any features.

[0045] Further features and advantages of the present invention will become apparent from the following description of the preferred embodiments of the present invention, which is given by way of example only and made with reference to the accompanying drawings.

Brief Description of the Drawings

[0046]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Modes for Carrying Out the Invention

[0047] This disclosure enables understanding of the impact of a broadband light source (e.g., in terms of spectral bandwidth and étendue) on the image resolution of a computer-generated hologram display (hereinafter also referred to as a "holographic display") by considering the contribution to the point spread function (PSF) at the viewing position. From this analysis, various relationships can be determined to improve the design of the CGH display.

[0048] Figure 1 shows a general viewing scheme of a CGH display, including the image 102 of the SLM, a virtual image point that is viewed as part of the displayed image and is in the plane 104, and a viewer viewing from the plane 106. The image of the SLM is at a distance d from the viewer shown as 108, SLM and the virtual image point is at a distance d from the viewer shown as 110. obj The distance Δd between the re-imaged SLM and the virtual object is also shown and is shown as 112.

[0049] The position of the virtual object is described as being at a position separated from the plane of the SLM by a certain focusing power, where the focusing power D is given by D = (d SLM - d obj ) / (d SLM d obj ) and is in diopters.

[0050] Note in Figure 1 that, for simplicity, the image of the SLM is shown as being at a finite distance in front of the viewer. However, the SLM can be re-imaged at infinity or "beyond infinity", which means that the position of the virtual image wraps around to be behind the viewer and d SLM is negative. Even in such cases, the following analysis still applies.

[0051] Due to the extended nature of the light source, the light in the image of the SLM has an angular subtense θ shown as 114. SLM As a result, the PSF in the plane of the object has a width w shown as 116.spatial It has. Using the small angle approximation, it becomes as follows. w spatial ≈Δd·θ SLM Thus, a PSF visible to a viewer having a certain angular width θ shown as 118 spatial is obtained. θ spatial represents the contribution to the overall angular psf due to the limited spatial coherence of the light source.

[0052] Also, the width w of the SLM image shown as 120 SLM , and the angular field of view θ shown as 122 fov are also shown. In other words, w SLM is the apparent width of the SLM as viewed from plane 106, for example, the width of the SLM image when viewing the SLM through an optical system arranged between the SLM and plane 106.

[0053] The conservation law of étendue from the light source to the SLM is that the product of θ SLM and w SLM is the same as the product of the angular width θ source of the light source and the width w source of the light source. In other words, it becomes as follows. w SLM =(θ SLM ·w source ) / θ source Note that the range of the light source here is defined as the range of the light incident on the SLM. For example, if the light source is spatially or angularly filtered, their dimensions define the range of the light source. For simplicity, in this description, G represents the étendue in one dimension (i.e., the product of length and angle). A similar analysis may be continued in two dimensions, and when considering the range of the light source in x and y, G is defined as the product of area and solid angle.

[0054] Next, the étendue G of the light source is θ spatial , θ fovand can be specified from the perspective of D. That is, for a display specified to have a given angular resolution and field of view, with the object displayed within a certain focal power of the SLM, the maximum allowable source étendue can be specified.

[0055] In the small angle approximation (sinx≒tanx≒x), the following equation can be described. θ spatial =w spatial / d obj and w spatial =Δd.θ SLM =(d SLM -d obj )θ SLM Also, θ SLM =G / w SLM =G / (d SLM .θ fov ) Summarizing this, the following equation is obtained. θ spatial =(d SLM -d obj )θ SLM / d obj =G(d SLM -d obj ) / (d obj .d SLM .θ fov )=G.D / θ fov Therefore, expressing this in terms of the source étendue for a given θ spatial , the following equation is obtained. G=θ spatial θ fov / D (1)

[0056] Contribution θ temporal to the angular PSF due to a finite source bandwidth ΔλThe analysis regarding this is the same. Figure 2 shows a general viewing scheme of a CGH display. According to the time bandwidth analysis, the display includes the image 202 of the SLM, a virtual image point that is viewed as part of the displayed image and is in the plane 204, and a viewer viewing from the plane 206. The image of the SLM is at a distance d SLM from the viewer shown as 208, and the virtual image point is at a distance d obj from the viewer shown as 210. The distance Δd between the re-imaged SLM and the virtual object is also shown and is shown as 212.

[0057] For the image point at the distance d obj from the viewer, a ray 214 drawn as a solid line is shown at the nominal design wavelength λ. The ray 214 converges on the plane 204. A second set of rays 216 drawn as dashed lines corresponds to light that undergoes the same phase modulation at the SLM but has a different wavelength λ’ = λ + Δλ. Due to the wavelength difference, the rays 216 converge on a different plane shown as 218. Note that the scale has been adjusted for clarity. In reality, the distance 210 of the virtual image point from the viewer can be at least 100 times larger than the distance 220, which means that the rays 214 and 216 are nearly coincident.

[0058] The range of rays at the design wavelength is defined by the width of the limited aperture w eyebox shown as 220. This aperture is likely an image of a spatial filter within the display device rather than a physical aperture in the plane of the eye. However, if the eye box (the position where the image can be viewed) is larger than the viewer's pupil, the width of the pupil may be considered as the limited aperture.

[0059] In the plane of the object 204, the rays 216 define a certain width w temporal shown as 222. This in turn defines the contribution θ temporal to the overall angular PSF due to the limited temporal coherence of the light source shown as 224.

[0060] 226 and 228 indicate construction lines for calculating θ temporal 226 is a line from the center of the eye box to the image of the SLM, and 228 is a ray passing through the image point in the plane 204. 226 represents a ray with zero focusing power from the SLM (i.e., the image point in the plane of the SLM), and 228 indicates a ray starting from the same point of the SLM but deflected to contribute to the object point in the plane 204. The angular deflection at the design wavelength Δθ is shown as 230. At a different wavelength λ’, the deflection angle Δθ’ shown as 232 is changed. The difference in deflection angle δθ = Δθ’ - Δθ due to the spectral bandwidth is shown as 234. When the angle is small, the diffraction angle is proportional to the wavelength, so δθ = ΔθΔλ / λ. Also, at the limit of 214 and 216 approaching coincidence, Δθ = w eyebox / (2d SLM ), and thus δθ = w eyebox Δλ / (2d SLM λ), which can be seen.

[0061] Here, the calculation of θ temporal can proceed. Using the small-angle approximation again, it can be described as follows. θ temporal = w temporal / d obj Substituting the above δθ into the formula of the inventors, w temporal = 2δθΔd obj = w eyebox Δd obj Δλ / (d SLM λ) Therefore, θ temporal = w eyebox Δd obj Δλ / (d obj d SLM λ)= w eyebox DΔλ / λ Expressing this from the perspective of the spectral bandwidth of a given θ temporal , the following is obtained. Δλ / λ = θ temporal / (D.w eyebox ) (2) System design example

[0062] The above analysis is performed without particularly referring to SLM characteristics such as the number of pixels or pixel pitch. This enables an effective and easy analysis of the design based on user specifications such as angular resolution, field of view, and iBox size (dimensions of the region where the image can be visually recognized).

[0063] In one example, the image points are within the maximum absolute focus power D of the image of the SLM, and further, both θ max and θ spatial are required to be smaller than a certain target angular resolution θ temporal . θ resolution can be considered as the maximum value of the angular resolution that satisfies the design requirements of the display, i.e., the worst angular resolution. In the display, θ resolution corresponds to, for example, the resolution that can be measured during use at the viewing position. resolution

[0064] Thus, (1) and (2) can be rewritten as the following inequalities. G ≦ θ resolution θ fov / D max (3) and Δλ / λ ≦ θ resolution / (D max w eyebox )(4) Examples 1 to 3 - Specification of illumination source

[0065] The following practical examples show the source coherence requirements for various display specifications according to the above analysis. These examples start from the user-oriented characteristics of the CGH display and use this to show guidelines for the selection of an appropriate illumination source (or a method of filtering the illumination source for acceptable performance). Example 1

[0066] ​In the first embodiment, the CGH display has the following characteristics. · The SLM is re-imaged at 0.5 m from the viewer. · The virtual content is represented in the range from 0.25 m to infinity (+-2 diopters), and D max = 2 diopters. · The resolution θ resolution is 0.4 mrad (points per degree of 44 ppd). · The width of the eye box is 2.5 mm. · The horizontal field of view is 0.4 rad (23 degrees).

[0067] Applying this to the above inequalities (3) and (4), we get G≦80μm.rad and Δλ / λ≦0.08. In this case, the LED is likely to be appropriate, but it is necessary to supply an LED with a relatively small emission area. For example, when collimating the central 0.4 rad (full width) emission cone, a phosphor width of 200 μm becomes possible. Due to the requirements of the spectral bandwidth, wide LED emission becomes possible, but it may be necessary to avoid LEDs with a very wide spectrum centered on the phosphor. RGB LEDs are suitable candidates and can enable the display of color images through sequential display of component images. Exemplary suitable RGB LEDs are DISPLIX® P3333 and KRTBLSLPS1.32 commercially available from Osram Opto Semiconductors. Embodiment 2

[0068] In the second embodiment, the CGH display has a smaller horizontal field of view, and the eye box is limited by the maximum size of the viewer's pupil. This has the following characteristics. · The SLM is re-imaged at infinity. · The virtual content is represented in the range from 0.25 m to infinity, and D max = 4 diopters. · The resolution θ resolution is set for typical human vision and is about 0.15 mrad (116 ppd). · The width of the eye box is 7 mm (limited by the maximum size of the viewer's pupil). · The horizontal field of view is 0.17 rad (10 degrees).

[0069] Applying this to the above inequalities (3) and (4), we get G ≤ 6 μm·rad and Δλ / λ ≤ 0.005. In this case, in order to provide a sufficiently low étendue and a sufficiently small spectral bandwidth, it is necessary to significantly filter the LED, and the resulting efficiency is likely to be too low. However, a multimode laser can still be used and may be coupled, for example, into a 25-μm, 0.1-NA multimode fiber. Example 3

[0070] In the third example, a small eye box and a relatively low resolution are required with a wide horizontal field of view. This has the following characteristics. · The SLM is re-imaged at 1 m from the viewer. · The virtual content is displayed in the range from 0.5 m to infinity (+-1 diopter), Dmax = 1 diopter. · The resolution θ resolution is approximately 0.6 mrad (29 ppd). · The eye box has a width of 1 mm. · The horizontal field of view is 1.0 rad (57 degrees).

[0071] Applying this to the above inequalities (3) and (4), we get G ≤ 600 μm·rad and Δλ / λ ≤ 0.6. In this case, an LED with a relatively large (about 1 mm) emission area may be used in combination with a low-f condenser lens (or in some cases without a condenser lens) that combines a large emission angle. The requirements for the spectral bandwidth do not pose a practical limitation, and a broadband LED based on a phosphor can be used. Examples 4 to 7 - Design of a CGH display for a specific illumination source

[0072] A person skilled in the art can design a CGH display system to provide a pre-defined user specification as defined by the above equations (3) and (4). This presents an alternative way of using the present disclosure, namely, a method for designing a CGH display system starting from a selected illumination light source. For example, a particular illumination light source may have a particular desired wavelength(s), or it may be desirable to increase efficiency by reducing the level of filtering without unduly degrading the resolution. Example 4 - Compact RGB LED

[0073] Osram OSIRE® E3323, KRTBDWLM32.32, commercially available from Osram Opto Semiconductors, has individually controllable RGB dies in a compact package. Its form factor, luminous flux, and power consumption are suitable for a non-connected head-mounted device (HMD) (about 1 lumen at about 100 mW). From the datasheet (English version 1.1 2020 - 11 - 25), the parameters λ peak = 635 nm, 526 nm, 456 nm, Δλ = 20 nm, 31 nm, 26 nm (FWHM), emission surface size of about 0.25 mm × 0.25 mm (separate die for each color, each approximately this size), approximately Lambertian emitter, are obtained. Assuming that the full-width cone of 1 radian at the center is collimated for illuminating the SLM. This results in G = 250 μm.rad and Δλ / λ = 0.031, 0.059, 0.057 (R, G, B).

[0074] Through the above inequalities (3) and (4), it is now possible to set the other parameters of the system to be compatible with this light source. For example, · D max ≒ 1.5 diopters (re-images the SLM at about 67 cm from the eye. The content is displayed between about 33 cm and infinity) · FoV ≒ 50 degrees · Resolution ≒ 40 ppd (points per degree), θ resolution≈0.4 mrad · Eyebox ≈ 5 mm Example 5 - High - output, high - bandwidth LED

[0075] M565D2 commercially available from Thorlabs is a high - brightness, high - output green LED. It may use a fluorescent phosphor (where a UV LED emits light to a green phosphor) to achieve high output in the desired color, and as a result, the spectral bandwidth is very wide. This is suitable for a connected head - mounted display (HMD) that requires high brightness with a large FoV and limited depth of focus (e.g., an aerospace HMD). From the datasheet (September 27, 2019, MTN003919 - S01, RevD), information such as λ = 565 nm, Δλ = 104 nm (FWHM), and a light - emitting surface size of 1 mm × 1 mm (assuming approximately a Lambertian emitter) can be obtained.

[0076] Similar to Example 4, assume that the full - width cone of 1 radian at the center is collimated for the illumination of the SLM. Here, G = 1000 μm·rad and Δλ / λ = 0.18 are obtained.

[0077] Through the above inequalities (3) and (4), it is possible here to set the other parameters of the system to be compatible with this light source. For example, · D max ≈1 diopter (re - imaging the SLM at about 1 m from the eye. The content is displayed between about 50 cm and infinity) · FoV ≈ 100 degrees · Resolution ≈ 30 ppd, θ resolution ≈0.6 mrad · Eyebox ≈ 3 mm Example 6 - Multi - mode fiber pigtail laser diode

[0078] The PL52E0252FCB-T commercially available from MKS Newport is believed to be formed from a single lateral mode emitter coupled to a multimode fiber to improve efficiency (compared to coupling to a single mode fiber). In a CGH display, this is believed to be used with a de-speckler to function as a more uniform multimode light source. In this example, it is assumed that the spectral bandwidth is not a limiting factor (since the light source is a laser, it can be assumed to be narrow to satisfy Equation (2)). However, according to Equation (1), a relatively small source étendue can be used for high resolution even for a small field of view (FoV). This can be useful for providing a high-quality display that occupies only a small part of the overall field of view of an HMD, just as a watch or smartwatch can provide useful information by forming only a small part of the FoV. It can display time, status, or other data. The status or other data may include motion data such as heart rate and step count, as well as motion data such as current speed and average speed. From the data sheet (DS-072002_08 / 20), it can be seen that λ = 520 nm, Δλ = ~1 nm (although not specified, it is assumed to be common for this type of laser), and a 50 μm 0.2NA fiber. Here, G = 20 μm.rad and Δλ / λ = 0.002 are obtained.

[0079] Through the above inequalities (3) and (4), it is now possible to set the other parameters of the system to match this light source. For example, · D max ≒2 diopters (re-images the SLM at approximately 50 cm from the eye. The content is displayed between approximately 25 cm and infinity) · FoV ≒ 10 degrees · Resolution ≒ 80 ppd, θ resolution ≒ 0.2 mrad · Eye box ≒ N / A (no limitation due to spectral bandwidth) Example 7 - Superluminescent LED (SLED or SLD)

[0080] The EXS210115-00, commercially available from Exalos AG Switzerland, is a single transverse mode light source with a broad spectral emission (compared to a laser). Similar to the laser of Example 6, this laser can also be coupled to a multimode fiber, but due to its broad spectral bandwidth, the need for additional spectral filtering is avoided. From Exalos' website (https: / / www.exalos.com / sled-modules / ), it has the characteristics of λ = 510 nm, Δλ = 10 nm, and single transverse mode. This results in G = λ = 0.51 μm·rad (single transverse mode) and Δλ / λ = 0.02.

[0081] Through the above equations (1) and (2), it is now possible to set the other parameters of the system to be compatible with this light source. For example, · D max ≒ 1.5 diopters (re-images the SLM at about 67 cm from the eye. The content is displayed between about 33 cm and infinity) · FoV ≒ N / A (unrestricted due to single transverse mode) · Resolution ≒ 80 ppd, θ resolution ≒ 0.2 mrad · Eye box ≒ 7 mm (i.e., matching the maximum expected pupil size) Example Computer-Generated Hologram Display System

[0082] An exemplary computer-generated hologram (CGH) display system that can be used in the principles of the present disclosure is shown in schematic form in FIG. 3.

[0083] The CGH display system includes an illumination system 300 and an SLM 306. The illumination system 300 includes an illumination light source 302 and an illumination optical system 304, which in this case includes a collimating lens.

[0084] Light from the illumination light source 302 illuminates the spatial light modulator (SLM) 306 after passing through the illumination optical system 304. The light incident on the SLM has an étendue G, a spectral bandwidth Δλ, and a nominal wavelength λ. After the SLM 306, the light forms an image plane 310 at a distance from the viewing position of the viewer's eye 312. A feature of such a display system is that the SLM is re-imaged on the image plane 310 at a distance from the viewer's pupil, and the maximum focusing power of the virtual points displayed on the image plane 310 limits the allowable characteristics of the illumination system.

[0085] FIG. 3 is a simplified representation and may have additional components such as relay lenses, which are described in more detail below with reference to FIG. 6. FIG. 3 shows a transmissive SLM for clarity, but the present disclosure applies equally to reflective SLMs. Further, those skilled in the art will understand that the present disclosure can be generally applied to CGH displays that re-image the SLM at a distance from the viewing position and is not limited to the specific form of FIG. 3. Relationship with SLM parameters

[0086] The previous descriptions have not been related to the SLM. In many cases, but not necessarily, the target resolution is related to the field of view or the eye box size. When the resolution of the display matches the pixel size of the SLM, it can be described as follows. θ resolution =θ fov / n where n is the number of pixels in the entire SLM. θ resolution is equated to θ spatial and substituting into Equation (1), it can be described as follows. G≦nθ resolution 2 / D max

[0087] Furthermore, when the SLM is relayed to the eye by a lens with a focal length f r , θ resolution =p / f rand where p is the pixel pitch of the SLM and is as follows: G≦np 2 / (D max f r 2 )

[0088] When the light source is an extended light source of width φ collimated by a lens having a focal length f, the angular range of the light source required to satisfy the SLM is given by np / f c . Substituting G = φnp / f c gives the following: c Substituting gives the following: φ / f c ≦p / (D max f r 2 )

[0089] 1 / f r >>D max Assuming that max d max f r 2 it can be described as d max is the maximum distance from the SLM at which the image point is formed, and thus can be described as follows: θ s ≦p / d max (5) where θ s =φ / f c is the angular subtense of the light source at the SLM.

[0090] Similar to the case of temporal coherence, in many cases, the target resolution of the display is determined by the diffraction-limited resolution of a given eye box size and follows the following relationship: θ resolution =λ / w eyebox θ resolution Setting θ spatial equal to θ Δλ≦θ resolution 2 / D max Here too, substituting θ resolution=p / f r and d max =D max f r 2 Using them, it can be described as follows. Δλ≦p 2 / d max (6) Further Considerations Considering SLM Characteristics

[0091] In the following section, additional analysis considering the contribution to the point spread function (PSF) of the display system is presented. From this, constraints on the characteristics of the illumination system can be qualitatively defined to assist in the selection of the illumination source within the illumination system. The width of the synthesized point spread function (w PSF ) of the display system has contributions from the angular subtense of the light source (w spatial ), the spectral bandwidth of the light source (w temporal ), and the inherent SLM resolution (w SLM ). These contributions to the width are added according to the following relationship.

Equation

[0092] In the display system described here, since the illumination system is designed so that neither of the coherence-related coefficients (w spatial and w temporal ) has a major impact on the resolution represented by w PSF , the following constraints are used. w spatial ≦w SLM w temporal ≦w SLM (8)

[0093] The inherent SLM resolution w SLM depends on the nature of the display system. When the entire range of the SLM is directly used, w SLMcan be approximated to the pixel pitch p of the SLM. In other cases, the spatial filtering after the SLM may reduce the intrinsic resolution, for example, it may be reduced to twice the pixel pitch, 2p. From the inequality in (8), w SLM The larger the value of, the greater the contribution from the illumination system characteristics. Two constraints can be applied to the illumination system, but in other examples, it will be understood that other numbers of constraints, such as a single constraint, can be applied. The lateral coherence width (w spatial )

[0094] Referring to FIG. 4, the elements of the display system design contributing to w spatial are shown. The illumination system 402 has a light source diameter φ and a numerical aperture NA. (The numerical aperture is a measure of the divergence of the light source). The light from the illumination system 402 passes through a collimating lens 404 having a focal length f c so that the light is substantially collimated when it is incident on the SLM 406. As can be seen in FIG. 4, the collimating lens does not have to make the light exactly parallel, but can be slightly converging (as shown) or slightly diverging so that the light from the light source minimizes the "wasteful" light outside the SLM and substantially illuminates the SLM, thereby improving the efficiency.

[0095] The light incident on the SLM 406 has an angular subtension θ s which is not necessarily the same as the numerical aperture NA of the light source 402. Using the small angle approximation,

Equation

Equation

[0096] Referring to FIG. 5, the elements of the display system design contributing to the temporal coherence width w temporal are shown. The light emerging from the SLM506 is limited in terms of the amount that can be brought to a single focus by the spectral band of the illumination system.

[0097] The temporal coherence of the illumination system determines the degree to which the spectral band (Δλ centered on λ) from the light source can be brought to a single focus at the axial distance (d) from the SLM.

[0098] This is limited by the standard equation of the blazed grating according to the maximum diffraction angle achievable from the SLM (β) and the pixel pitch (p). p(sinα + sinβ)=mλ (10) Where α is the angle of incidence, which can be assumed to be zero since the light incident on the SLM is generally collimated, m is the diffraction order, which is 1 in this case. Applying the small angle approximation, it becomes as follows.

Equation

[0099] From this, the value of w temporal is obtained.

Equation

[0100] Figure 6 is an illustrative operation of a relay lens. The output relay lens 608 (having a focal length f r ) maps the object space to the image space, thereby scaling the axial distance from the SLM 606. In some embodiments, the relay lens may be omitted, but if a relay lens is included, it can be useful to ensure that the content (imaged at an actual distance d max from the SLM) is not placed within the near point of the viewer (z min , the closest point at which the eye can focus, typically within about 25 cm). The relay lens can impose a limit on d max for the design of the system, but the calculation is offset by the characteristics of the lens itself. Nevertheless, the relay lens enables d max to be made smaller, which is beneficial for the system because a wider range of light sources can be used since a smaller value of d max allows a wider spectral bandwidth and angular subtension in the light exiting the SLM. [Number] (13) where f r is the focal length of the relay lens, z min is the minimum focal distance of the viewer, u is the distance from the viewer to the re-imaged SLM, n is the number of pixels / dots within a given axis (e.g., for a 1080p display, the horizontal axis is 1920), and θ FOV is the field of view of the viewer. System Design Using SLM Characteristics

[0101] Here, the constraints on the system can be determined as follows. [Number] and / or [Number] Spatial coherence limit-(14) [Number] Temporal coherence limit-(15)

[0102] Using this set of equations, with reference to the characteristics of the CGH display system and the SLM, it becomes possible to determine the quantitative characteristics of the spectral bandwidth, diameter, and / or angular subtense of the illumination system in ways that were previously impossible. An appropriate illumination source can be selected based on cost, luminance, efficiency, or other factors, understanding that an acceptable image sharpness is achieved. For example, while it remains true that not all LEDs are suitable, it is possible to reliably select an appropriate LED for a particular system design. Method for defining an appropriate light source considering SLM characteristics

[0103] FIG. 7 shows a method for selecting an appropriate light source for a computer-generated hologram display system according to an embodiment using the above-described analysis considering SLM characteristics. Although the blocks in FIG. 7 are shown sequentially, the method is not limited to this order, and the blocks can be executed in a different order and / or in parallel in other embodiments.

[0104] First, the optical system is designed or the parameters of an existing CGH display system are collected. At 702, details of a spatial light modulator (SLM) having a pixel pitch are specified or collected from the SLM's data sheet. At 704, a predetermined maximum distance at which the SLM is re-imaged during use is specified. Other features of the design may also be specified, such as the focal length of a collimating lens and / or the focal length of a relay lens, if included.

[0105] In a known system design, at 706, the contribution to the point spread function (PSF) by SLM at a predetermined maximum distance is determined. For example, this can simply be the pixel pitch that assumes that the incident light is substantially collimated when irradiating the SLM and thus generally remains substantially collimated even after exiting the SLM. This contribution to the PSF is used as a constraint for determining the maximum spectral bandwidth of the illumination system based on the predetermined maximum distance at 708, such as by applying the above formula (15). Based on the predetermined maximum distance and using the contribution to the point spread function by the SLM at the predetermined maximum distance as a constraint, the maximum angular subtense exiting the SLM is determined at 710, for example, by applying the above formula (14) to θ s at 710. At 712, the maximum diameter of the light source is determined, such as by applying the above formula 8 for Φ. In some examples, one, two, or all three of the determinations at 708, 710, and 712 can be used, and the more they are used, the stricter the criteria for the light source and the better the image quality. Specifying the angular subtense θ s and Φ can be useful when the angular subtense after the SLM is not the same as the numerical aperture of the light source.

[0106] Finally, at 714, a light source is selected for the illumination system based on the determined characteristics.

[0107] It can be understood that the method of FIG. 7 can be used to qualitatively obtain the selection of a light source for good image quality. In other examples, the design of the CGH display system itself can be affected, such as enabling a wider selection of light sources or allowing the use of specific light sources. For example, it may be desired to use a superluminescent LED to achieve high brightness, and knowledge of the spectral bandwidth can affect other variables of the display system, such as determining the value of d max that allows a sufficient spectral bandwidth for the light source to be used.

[0108] In other examples, other design methods may be used. For example, the design of the CGH display system in the above Examples 1 to 7 was started based on the characteristics of the user specifications of the CGH system that has nothing to do with the SLM, or the characteristics of the illumination system from the viewpoint of étendue and / or spectral bandwidth.

[0109] The above embodiments are to be understood as exemplary embodiments of the present invention. Further embodiments of the present invention are envisioned. For example, although the present system includes a collimating lens, this may not be necessary when the numerical aperture of the light source is sufficiently small. It should be understood that any feature described in connection with any one embodiment may be used alone or in combination with other features described, and may also be used in combination with one or more features of any other embodiment, or any combination of any other embodiments. Furthermore, equivalents and modifications not described above may be used without departing from the scope of the present invention as defined in the appended claims.

Claims

1. A computer-generated holographic display system having angular resolution and angular field of view at a viewing position, wherein the computer-generated holographic display system comprises: An illumination system comprising an LED or a multimode laser; An SLM illuminated by the illumination system; An optical system configured to re-image the SLM at a predetermined distance from the viewing position; Comprising; The illumination system has an étendue such that, at the SLM, a value obtained by dividing a product of the angular resolution and the angular field of view at the viewing position by a maximum focusing power of a virtual image point with respect to the re-imaged SLM is less than or equal to the étendue; A computer-generated holographic display system, wherein the angular resolution is less than about 1 milliradian.

2. The computer-generated holographic display system according to claim 1, wherein the viewing position is a position of a pupil of a viewer in use.

3. The computer-generated holographic display system according to claim 1 or 2, wherein the illumination system has an étendue exceeding 2% of a value obtained by dividing a product of the angular resolution and the angular field of view by a maximum focusing power of a virtual image point with respect to the re-imaged SLM.

4. The computer-generated holographic display system according to claim 1, 2, or 3, wherein the illumination system comprises an angular filter that at least partially sets a source étendue of the illumination system.

5. The computer-generated holographic display system according to any one of claims 1 to 4, wherein the illumination system comprises a spatial filter that at least partially sets the source étendue of the illumination system.

6. The computer-generated holographic display system according to any one of claims 1 to 5, wherein the predetermined distance at which the SLM is re-imaged is greater than a minimum distance of a virtual image point from the viewing position.

7. The computer-generated holographic display system according to any one of claims 1 to 6, wherein the maximum focusing power corresponds to a virtual image point at about 1 m or less from the viewing position.

8. The computer-generated holographic display system according to any one of claims 1 to 6, wherein the maximum focusing power corresponds to a virtual image point at about 0.25 m away from the viewing position.

9. The computer-generated holographic display system according to any one of claims 1 to 8, wherein the maximum focusing power is about 3 diopters or less. **Claim 10** The computer-generated holographic display system according to any one of claims 1 to 9, wherein the angular resolution is greater than about 0.15 milliradians. **Claim 11** The computer-generated holographic display system has a restricted aperture width, The illumination system has a spectral bandwidth and a nominal wavelength, The computer-generated holographic display system according to any one of claims 1 to 10, wherein the spectral bandwidth divided by the nominal wavelength is less than or equal to a value obtained by dividing the angular resolution by the product of the maximum focusing power and the restricted aperture width. **Claim 12** The computer-generated holographic display system according to claim 11, wherein the restricted aperture width is less than about 7 mm. **Claim 13** The illumination system has a spectral bandwidth and a nominal wavelength, The computer-generated holographic display system according to any one of claims 1 to 10, wherein the spectral bandwidth divided by the nominal wavelength is less than or equal to a value obtained by dividing the angular resolution by the product of the maximum focusing power and 7 mm. **Claim 14** A computer-generated holographic display system having an angular resolution and a restricted aperture width at a viewing position, wherein the computer-generated holographic display system Comprises an LED or a multimode laser and an illumination system having a spectral bandwidth and a nominal wavelength, An SLM illuminated by the illumination system, An optical system configured to re-image the SLM at a predetermined distance from the viewing position, Comprising, The spectral bandwidth divided by the nominal wavelength is less than or equal to a value obtained by dividing the angular resolution by the product of the restricted aperture width and the maximum focusing power of a virtual image point with respect to the re-imaged SLM, The computer-generated holographic display system, wherein the angular resolution is less than about 1 milliradian. **Claim 15** A computer-generated holographic display system having an angular resolution at a viewing position, wherein the computer-generated holographic display system Comprises an LED or a multimode laser and an illumination system having a spectral bandwidth and a nominal wavelength, the SLM illuminated by the illumination system, an optical system configured to re-image the SLM at a predetermined distance from the viewing position, comprising, the spectral bandwidth divided by the nominal wavelength is less than or equal to a value obtained by dividing the angular resolution by the product of the maximum focusing power of the virtual image point with respect to the re-imaged SLM and 7 mm, a computer-generated holographic display system, wherein the angular resolution is less than about 1 milliradian. **Claim 16** A head-mounted display comprising the computer-generated holographic display system according to any one of Claims 1 to 15.

Images