Desktop display device

Abstract

The invention relates to a desktop display device (100) arranged to generate a virtual image. The display device (100) comprises a body (50) arranged to support the desktop display device, an image source (4) provided to the body (50) and configured to emit image light forming a visual image, an optical system (3, 30, 32) provided to the body (50) and comprising a first reflector (3) having a first concavely structured reflective surface (7) configured reflect the image light emitted from the image source (4) in a viewing direction (A). The first reflector (3) is configured to generate the virtual image from the image light emitted from the image source (4) in the viewing direction (A), and the optical system (3, 30, 43) is configured to generate a folded optical path without axial symmetry from the image source (4) to the viewing direction (A).

Description

[0001] DESKTOP DISPLAY DEVICE

[0002] FIELD OF THE INVENTION

[0003] The present invention relates to a desktop display device and more particularly to a desktop display device according to preamble of claim 1.

[0004] BACKGROUND OF THE INVENTION

[0005] By the year 2024, about 25-30% of the world's population has been affected by true myopia (also called shortsightedness). This is about 2 billion people. According to the prognosis, by the year 205050% of the population will be myopic. The UN’s estimate of the world’s population in 2050 is about 9.7 billion people. This means, that in the next 26 years, true myopia will onset in 2.85 billion young people.

[0006] All myopia cases can be divided into two categories. One of them can be called “true myopia”, which is characterized by non-reversible eye deformation, and which usually has an onset in teenagers. The second one has the same effect in lowering the sight power but is reversible and is caused by an accommodation spasm, which is the consequence of prolonged focusing eyes on a close distance, e.g. when reading book or acquiring visual information from display device, for example PC display, smartphone, laptop. The exact causes of true myopia are not yet known, but one of the major causes is the necessity for a person to focus his / her eyes at a close distance while acquiring visual information. A recent (2024) metaanalysis shows a significant correlation between the time spent using display devices (so-called screen time) and the myopia development. Prolonged eye focusing on a close distance is regarded as one of the major causes of myopia onset in children and teenagers. Also prolonged eye focusing on a close distance causes eye strain in adults which leads to a temporary viewing power decrease, and often headaches.

[0007] Currently, treatment for myopia is aimed at stopping or slowing down the progression of the condition and preventing its complications. Different methods which were suggested in the last decades are divided into behavioural, drug and non-drug treatment, and surgery interventions.

[0008] In behavioural methods the following changes to behaviour were shown to be not effective in myopia prevention: prohibition on reading in dim light and of bringing a book close to the eyes, frequent breaks and limiting the time of “use” of the eyes: “less use” of the eyes will not delay the deterioration of vision.Time spent outside effectively reduces the onset of myopia but does not slow down its progression.

[0009] Concerning drug treatment, there are research results showing that the use of atropine reduces the progression of myopia in children. But the underlying mechanism is not known. It was shown that atropine drops used once a day reduce the progression of myopia by 90%. Pirenzepine (which has almost no effect on pupil size and accommodation) reduces progression by 44%. Drug treatment requires high adherence to treatment and strict medical supervision. It is not used to prevent myopia onset.

[0010] For non-drug treatment various methods were suggested in past decades. These are only the major of them: bifocal / multifocal lenses provided clinically insignificant benefit. Orthokeratology is moderately effective: reduces progression by 30-50%. Peripherally correcting soft contact lenses are moderately effective: 30% reduction in progression. Under correction was not only ineffective, but also accelerated the development of myopia. Standard glasses and soft contact lenses have no effect on progression of myopia, they just provide more or less normal vision quality. Methods that are somewhat effective (orthokeratology, peripherally correcting contact lenses) are relatively expensive, require medical follow-up and are available mostly from leading medical institutions in developed countries.

[0011] For surgical treatment various experimental treatments to strengthen sclera (including stem cell treatment and strengthening the sclera through mechanical tissue transplantation) have been tried, however, they are mostly chosen in cases of rapid myopia progression. Laser vision correction is not a treatment for myopia, but only eliminates the necessity to wear glasses or contact lenses. It can lead to complications.

[0012] BRIEF DESCRIPTION OF THE INVENTION

[0013] An object of the present invention is to provide a desktop display device so as to solve or at least alleviate the prior art disadvantages.

[0014] The objects of the invention are achieved by a desktop display device which is characterized by what is stated in the independent claim 1.

[0015] The preferred embodiments of the invention are disclosed in the dependent claims.

[0016] The invention is based on the idea of a desktop display device arrangedto generate a virtual image. The display device comprises a body arranged to support the desktop display device on a support surface, an image source provided to the body and configured to emit image light forming a visual image, an optical system provided to the body and comprising a first reflector having a first concavely structured reflective surface configured reflect the image light emitted from the image source in a viewing direction. The first concavely structured reflective surface is configured as a first non-rotationally symmetric freeform reflective surface. “Freeform surface” denotes an optical surface whose geometry is defined as a continuous mapping from a two-dimensional domain to three-dimensional space, with no requirement of rotational or translational symmetry. A freeform surface is distinguished from spherical, aspheric, toroidal, or cylindrical surfaces by the absence of a symmetry axis and by the independent variation of the surface normal orientation. The first reflector is configured to generate the virtual image from the image light emitted from the image source in the viewing direction, and the optical system is configured to generate a folded optical path without axial symmetry from the image source to the viewing direction. The optical system is configured generate an eyebox for observation of the virtual image by a user.

[0017] The desktop display device generates a virtual image from the light emitted by the image source. The generated virtual image may be observed without need to wear special eyeglasses. A user with myopia may observe the virtual image by using usual eyeglasses, which are used in normal life. A user with presbyopia does not need to use eyeglasses for near-work while using display device of the present invention.

[0018] The desktop display device is configured to be observed from a distance. Accordingly, the desktop display device may replace conventional monitors or display screens, such as computer screens and televisions.

[0019] The optical system is configured to generate the folded optical path without axial symmetry from the image source to the viewing direction. This enables shortening the optical path and decreasing the size of the desktop display device. Further, the viewing direction may be provided free of obstacles disturbing viewing the virtual image.

[0020] The folded optical path means an optical path in which the light beam is bent in a way to make the optical path much longer than the overall length of the optical device.

[0021] On optical system without axial symmetry, an unsymmetric optical system, means an optical system in which the optical elements such as mirrors andlenses, are arranged without having an axis of rotational symmetry.

[0022] The display device and the optical system thereof is designed to meet one or more pre-determined characteristics enabling functionality of the display device and the optical system thereof. The one or more pre-determined characteristics of the display device and the optical system thereof comprise:

[0023] A) The device must have an eyebox of a size in at least one of the directions transversal to its optical axis enough for the user to perceive the virtual image with both eyes simultaneously. For instance, for a child it must be not less than 45-50 mm, and for an adult not less than 65 mm. Larger eyebox transversal size is preferable for more natural and comfortable user experience.

[0024] B) The worst-case resolving power of the display device, measured across the whole light emitting surface of the image source for an aperture of the transversal size as shown above, must be higher than the inverse value to a pixel size of the image source, to ensure that both left and right eyes of the user perceive the same image without image doubling or blur. For instance, for a typical LCD display used as the image source, the resolving power must be not less than 10 cycles / mm.

[0025] C) To ensure the relaxation of the user’s eyes, the distance between the user’s eyes and the virtual image must be not less than the distance called ‘optical infinity’ in ophthalmology. This ‘optical infinity’ distance is considered to be between 5 and 6 m, according to different references. For instance, the distance between the user and the virtual image must be 10 m.

[0026] D) In order to be usable in everyday educational or work tasks, the virtual image, produced by the display device, must have sufficient angular size in both dimensions, to ensure that a reasonable amount of visual content (number of text lines, images, interface elements, etc.) can be displayed simultaneously, with no need for scrolling or virtual page turning. A minimal comfortable text line angular height is known to be around 0.3 degrees, and for low visual fatigue and prolonged usage, the comfortable text line angular height is known to be above 0.5 degrees. For instance, a reasonable vertical angular size of the virtual image must be 10 degrees or more.

[0027] E) A general display system must not introduce severe geometrical distortions into the displayed content to avoid development of fatigue and headache in user. This is, for instance, required by ISO 9241-303:2011 standards. The display device must create a virtual image with acceptable level of geometrical distortion. If this level cannot be achieved solely by an optimization of opticalsystem, a distortion correction scheme, described below, must be applied as well. In some embodiments, the image source comprises a planar or curved surface configured to emit image light.

[0028] The desktop display device enables generating the virtual image based on light emitted from a planar or curved light emitting surface of the image source.

[0029] In some embodiments, the image source is a display screen. Display screen provides simple image source for generating the virtual image.

[0030] In some embodiments, the first reflector comprises a concave mirror surface configured to provide the first concavely structured reflective surface.

[0031] The concave mirror surface provides structurally simple and efficient mirror surface for generating the virtual image.

[0032] In some other embodiments, the first reflector comprises a Fresnel reflector surface configured to provide the first concavely structured reflective surface.

[0033] The Fresnel reflector enables decreasing the size and weight of the desktop display device as the Fresnel reflector enables providing the first reflector with a thin structure.

[0034] In some further embodiments, the first reflector comprises a diffractive reflector surface configured to provide the first concavely structured reflective surface.

[0035] Also, the diffractive reflector enables decreasing the size and weight of the desktop display device as the diffractive reflector enables providing the first reflector with a thin structure.

[0036] In some embodiments, the optical system comprises one or more premodifying lenses arranged to face the image source, the image light from the image source is incident on the one or more pre-modifying lenses.

[0037] Accordingly, the one or more pre-modifying lenses are provided between the image source and the first reflector. Alternatively, the one or more pre-modifying lenses are provided downstream of the image source and arranged receive the image light from the image source.

[0038] The one or more pre-modifying lenses may be configured to provide predistortions for compensating distortions of the first reflector or other optical elements, such a second reflector.

[0039] Alternatively or additionally, the one or more pre-modifying lenses may be configured to provide optical transformations or modification to the virtualimage.

[0040] In some embodiments, the one or more pre-modifying lenses comprise a Fresnel lens and / or diffractive lens.

[0041] Utilizing the Fresnel lenses and / or diffractive lenses enables decreasing the size and weight of the desktop display device.

[0042] In some embodiments, the one or more pre-modifying lenses comprise a plane-convex lens.

[0043] In some embodiments, the optical system comprises a second reflector having a second concavely structured reflective surface configured reflect the image light emitted from the image source or from the one or more pre-modifying lenses to the first reflector.

[0044] The second reflector provides further freedom in positioning the image source in relation to the first reflector in the desktop display device.

[0045] In some embodiments, the second reflector comprises a concave mirror surface configured to provide the second concavely structured reflective surface.

[0046] The concave mirror surface provides structurally simple and efficient mirror surface for generating the virtual image.

[0047] In some other embodiments the second reflector comprises a Fresnel reflector surface configured to provide the second concavely structured reflective surface.

[0048] The Fresnel reflector enables decreasing the size and weight of the desktop display device as the Fresnel reflector enables providing the first reflector with a thin structure.

[0049] In some further embodiments, the second reflector comprises a diffractive reflector surface configured to provide the second concavely structured reflective surface.

[0050] Also, the diffractive reflector enables decreasing the size and weight of the desktop display device as the diffractive reflector enables providing the first reflector with a thin structure.

[0051] In some embodiments, the second concavely structured reflective surface is configured as a second non-rotationally symmetric freeform reflective surface.

[0052] In some embodiments, the image source is arranged as an integral image source to the body.

[0053] Thus, the desktop display device is an integral unit.

[0054] In some other embodiments, the image source is provided as adetachable image source to the body.

[0055] In this embodiment, a separate image source, such as mobile phone, tablet computer or the like may be connected to the body of the desktop display device.

[0056] The desktop display device may comprise an image source connection arrangement to which the image source is connected detachably.

[0057] In some embodiments, the image source is fixedly arranged to the body. Accordingly, the position of the image source cannot be adjusted. Thus, the image source is pre-aligned towards the optical system.

[0058] In some other embodiments, the image source is arranged adjustably to the body.

[0059] Accordingly, the position of the image source is adjustable. Thus, the direction of the light emitted from the image source may be adjusted.

[0060] The distance between the user and the virtual image can be adjusted as well.

[0061] In some embodiments, the first reflector is fixedly arranged to the body. Accordingly, the position of the first reflector cannot be adjusted. Thus, the first reflector is pre-aligned to generate the virtual image in the fixed viewing direction.

[0062] In some other embodiments, the first reflector is adjustably arranged to the body.

[0063] Thus, the viewing direction may be adjusted.

[0064] In some further embodiments, the first reflector and the second reflector are fixedly arranged to the body.

[0065] The first and second reflectors are pre-aligned to generate the virtual image in the fixed viewing direction.

[0066] In some yest further embodiments, the first reflector and the second reflector are arranged adjustably arranged to the body.

[0067] Thus, the viewing direction may be adjusted by adjusting the position of the first and second reflectors.

[0068] In some embodiments, the desktop display device comprises adjustment system configured to adjust position of one or more of the following: the image source, the first reflector, the second reflector, and the one or more premodifying lenses.

[0069] The adjustment system is provided as manual and / or mechanical adjustment system configured adjust the position of the one or more mentionedcomponents for adjusting the viewing direction of the virtual image.

[0070] Alternatively, the adjustment system is provided as an automatic adjustment system configured to detect position of the user head or eyes and adjust the position of the one or more mentioned components for adjusting the viewing direction of the virtual image based on the detected position of the user head or eyes.

[0071] In some embodiments, the adjustment system is arranged to adjust position such that the relative position of at least two of the following is not changed: the image source, the first reflector, the second reflector, and the one or more pre-modifying lenses.

[0072] Keeping the relative position of the image source and the optical components fixed during adjusting the positions enables maintaining good quality virtual image. Thus, the adjustment is configured to adjust the viewing direction, not the virtual image.

[0073] Adjusting the position of the image source and the optical components comprises at least adjusting the orientation of the image source and the optical components.

[0074] In some embodiments, the body comprises a support element arranged to support the display device on a planar surface.

[0075] The support element is provided as a stand for supporting the desktop display device on the planar surface such as table top.

[0076] In some embodiments, the first non-rotationally symmetric freeform reflective surface, or the second non-rotationally symmetric freeform reflective surface, or the first and second non-rotationally symmetric freeform reflective surfaces are configured comprise locally varying principal curvatures in two orthogonal directions.

[0077] In some other embodiments, the first non-rotationally symmetric freeform reflective surface, or the second non-rotationally symmetric freeform reflective surface, or the first and second non-rotationally symmetric freeform reflective surfaces are configured comprise locally varying principal curvatures in two orthogonal directions and characterized by an offset (wj from a base plane with local coordinates (u, v] defined by a polynomial function of order N > 2, w = Si.fc ci:kulvk, 1 < i + k < N, where at least one coefficient c_(i, k] is non-zero.

[0078] In some embodiments, the first reflector, or the second reflector, or the first and second reflectors are configured based on computer-based numerical optimization comprising ray-tracing method of the polynomial coefficients c_(i, k]to form the magnified virtual image.

[0079] In some embodiments, the eyebox is configured to have an eyebox dimension of at least 45 mm in at least one direction transversal to the viewing direction of the folded optical path.

[0080] In some other embodiments, the eyebox is configured to have an eyebox dimension of at least 65 mm in at least one direction transversal to the viewing direction of the folded optical path.

[0081] In some embodiments, the optical system is configured generate the magnified virtual image at an optical infinity distance from the eyebox, the optical infinity distance being at least 5 m.

[0082] In some other embodiments, the optical system is configured generate the magnified virtual image at an optical infinity distance from the eyebox, the optical infinity distance being at least 6 m.

[0083] In some further embodiments, the optical system is configured generate the magnified virtual image at an optical infinity distance from the eyebox, the optical infinity distance being at least 10 m.

[0084] In some embodiments, the magnified virtual image generated by the optical system has angular size of at least 20 degrees.

[0085] In some other embodiments, the magnified virtual image generated by the optical system has angular size of at least 25 degrees.

[0086] In some embodiments, the optical system is configured provide resolving power of the image source in the eyebox at least 5 cycles / mm; or

[0087] - the optical system is configured provide resolving power of the image source in the eyebox at least 10 cycles / mm.

[0088] BRIEF DESCRIPTION OF THE DRAWINGS

[0089] The invention is described in detail by means of specific embodiments with reference to the enclosed drawings, in which

[0090] Figures 1 to 4 show schematically operation of display device according the present invention;

[0091] Figure 5 shows schematically one embodiment ofthe present invention; Figure 6 shows schematically one embodiment of the display device according to the present invention;

[0092] Figure 7 is a schematic illustration of mathematical parametrical description of a curved surface;Figure 8 is a schematic illustration of mathematical description of a curved surface based on spline functions;

[0093] Figure 9 is a schematic illustration of a method of optimization of normal directions of a Fresnel reflector;

[0094] Figure 10 is a schematic illustration of a method of providing a surface of a Fresnel reflector;

[0095] Figure 11 shows schematically another embodiment of the present invention;

[0096] Figure 12 shows schematically another embodiment of the display device according to the present invention;

[0097] Figures 13, 13a and 13b show schematically yet another embodiment of the present invention;

[0098] Figure 14 shows schematically a further embodiment of the display device according to the present invention;

[0099] Figure 15 shows schematically a further embodiment of the present invention;

[0100] Figure 16 shows schematically yet another embodiment of the display device according to the present invention;

[0101] Figure 17 shows schematically a curved image source for the display device; and

[0102] Figure 18 shows schematically adjustment of the image source in the display device.

[0103] DETAILED DESCRIPTION OF THE INVENTION

[0104] The present invention provides a display device which is not mounted on a head of a user nor attached to his body by any other means. The display device is located at a distance from the user (e.g. tens of centimeters) and it creates a virtual image, that is located at greater distance from the user compared to the distance between eyes of the user and the display device itself. The display device is based on the optical system with folded optical path comprising curved freeform mirrors. The optical system may comprise one or more flat Fresnel reflectors or one or more diffractive reflectors, and one or more lenses. One or more of the lenses may be flat Fresnel lenses or diffractive lenses. The lenses may be obtained by means of computer-aided numerical optimization. The virtual image, created by the display device, can be observed by the user with both eyes simultaneously,without an accommodation-vergence conflict, without any additional wearable devices (except for eyeglasses or contact lens, in the case when the user has to wear them in everyday life), preventing the user from prolonged focusing eyes on a close distance, and thus preventing eyestrain and accommodation spasm on adults and myopia onset on children and teenagers.

[0105] The display device provides for the user with presbyopia (also called farsightedness) the ability to acquire visual information without using an eyeglasses, which a presbyopic person would normally need to read.

[0106] The display device comprises an image source, an optical system with folded optical path comprising one or more curved freeform mirrors and lenses, a mounting system for the image source and mirrors.

[0107] The optical system is arranged to provide no rotational symmetry. In some embodiments, the display device further comprises an image processing unit for image distortion correction, and / or an optical unit for image distortion correction, and / or a case enclosing the parts mentioned above.

[0108] The surfaces of the curved mirrors and lenses are provided, or described mathematically, as analytical parametric polynomial surfaces with the order of polynomials equal or greater than two.

[0109] The coefficients of the polynomials, which define the exact geometric form for each mirror and lens surface, as well as the parameters which define the position and the tilt of each mirror in space, may be obtained by the computer-aided numerical optimization, where the goal function on each step of the optimization process is calculated by the backward optical ray propagation from an eyebox to the surface, which in normal operation acts as the source of the image, with the goal function proportional to the spot size on that surface.

[0110] Alternatively, the geometric form of the curved mirrors’ surfaces can be defined by two-dimensional spline functions, for instance, by the NURBS splines. In this case, during the computer-aided optimization process, the positions of control points of the splines are optimized.

[0111] In some embodiments, the curved mirrors are replaced by the flat non-symmetric Fresnel reflectors, and lenses with the flat non-symmetric Fresnel lenses. The exact form of the reflectors and lenses may be obtained by means of the computer-aided numerical optimization of their local normal directions.

[0112] In some other embodiments, the mirrors and lenses are replaced by the flat diffractive optical elements.

[0113] In some further embodiments, the optical system of the display deviceis configured to carry out correction of the geometrical distortion of the image provided by the optical system. In some embodiments, the correction is caried out numerically, by the additional image processing unit configured to carry out predistortion of the image data before displaying it on the image source, or an optical module, attached to the image source.

[0114] The method of operation of the display device comprises of receiving the necessary information, or input data, from an external data source for creating a visual image, optionally introducing pre-distortion to compensate the geometrical distortion caused by the optical system, and creating a magnified virtual copy of the image at a large distance from the eyes of the viewer, where the virtual image is viewed by the user without any additional wearable head-mounted devices. The image is hereafter defined as a spatial distribution of zones of varying brightness and color on a two-dimensional surface, whether flat or curved, or combination of both, either light-emitting or light-reflecting, which is intended to be perceived by the human visual system.

[0115] The distance between the virtual image and the eyes of the viewer is understood in the sense of an optical system. This means that when the eyes of the viewer are focused on the virtual image located a given distance, the accommodation system of the viewer adjusts the optical power of eyes exactly as if the user was looking at some real object located at the same given distance from the eyes of the viewer, which is, in turn, in the agreement with the vergence of optical axes of the eyes of the viewer. The ratio of magnification and distance between the virtual image and the eyes of the viewer is chosen in such a way that for the viewer the angular size of the virtual image is of the order of the angular size of commonly used office or mobile display devices, when viewed from the typical distance. The distance between the virtual image and the eyes of the viewer is chosen to be greater than the typical distance between the common display device, which creates a real image (in the sense described above) on its physical surface, flat or curved. The distance between the virtual image and the eyes of the viewer can be fixed to any given values, or to the distance of the eye accommodation relaxation, or to the infinite distance. The distance between the virtual image and the eyes of the viewer can be set to some fixed value to provide maximal viewing comfort for the viewer or to vary slowly in time to provide additional accommodation training to the eyes of the viewer. The virtual image is created in such a way that perception of this image does not cause a vergenceaccommodation conflict in the vision of the viewer, when observed by both eyessimultaneously. The virtual image is created in such a way, that it can be observed by both eyes of the viewer from different head positions at least within some interval in all the three dimensions (the interval is commonly called an eyebox) or / and when the head of the viewer is tilted at the angle within certain limits.

[0116] The illustration of the method of operation of the disclosed display device is presented in Fig. 1 - 4. In Fig. 1 (not to scale) the viewer 1 is looking at, but not focusing eyes on the disclosed display device, denoted by 3, and is observing the virtual image 2, with focusing eyes on it, which has the larger dimensions than the physical display device, and is located at the larger distance from the eyes of the viewer, than the physical display device. The angular size of the virtual image is close to the angular size of the conventional display, observed from the usual distance. The display device 3 is to produce in its output plane the same optical ray distribution, as the large conventional display whose position coincides with the position of the virtual image 2. To illustrate this, three arbitrary points on the virtual image 2 are chosen (denoted by A, B and C), and the optical paths from these point sources to the pupils of the eyes of the viewer are shown by thin lines. The virtual part of the paths is shown in dashed lines, and the real part of the paths, created by the display device 3, are shown in solid lines.

[0117] The display device, from the point of view of the viewer, as it is illustrated in Figure 2 (not to scale), acts like a relatively small window 3 in an opaque wall 4, through which the user looks inside the hall at the big screen 2, where this screen displays the image according to the data provided by a user device, such as PC, laptop, smartphone, tablet PC, etc. In this illustration, the optical paths from points A, B, C to the user’s eyes are real and are shown in solid thin lines.

[0118] In Figure 3 (not to scale), the schematic illustration of the method of operation of the display device for the binocular view is presented. User’s eyes, denoted as l.L and l.R, are focused on the virtual image 2, while their optical axis, displayed by bold dashed lines, converges at the same virtual image 2, with the convergence angle a corresponding to the focusing distance, so no vergenceaccommodation conflict occurs. The display device 3 by some means produces the same optical ray distribution in its output plane, as the large conventional display whose position coincides with the position of the virtual image 2 could produce in the same plane. To illustrate this, three arbitrary points on the virtual image 2 are chosen (denoted by A, B and C), and the optical paths from these point sources to the pupils of the user’s eyes are shown by thin lines. The virtual part of the paths is shown in dashed lines, and the real part of the paths are shown in solid lines. Fromthe point of view of the viewer, the disclosed device , as it is illustrated in Figure 4 (not to scale), acts like a relatively small window 3 in the opaque wall 4 through which the viewer looks inside the hall at the big screen 2 where this screen displays the image according to the data provided by user device, such as PC, laptop, smartphone, tablet PC, etc. In this illustration, the optical paths from points A, B, C to the user’s eyes are real and are shown in solid thin lines.

[0119] Figure 5 shows one embodiment of the display device. The display device comprises an image source 4 and an optical system 3 configured to provide a folded optical path without axial symmetry. The optical system 3 comprises at least one curved mirror. The image source 4 is a light-emitting or light-reflecting flat or curved image-forming system, based on any available conventional technology, for instance, but not limited to, the one based on liquid crystal matrix with coherent or non-coherent backlight, or on an array of light- emitting diodes, or on reflecting array of e-paper elements, or a combination of a projection screen and a projector. The source of the visual content for the image source 4 may be any external device capable of creating visual content. The source of the visual content may be for example PC, laptop, media player, etc., connected to the image source by a cable or by a wireless connection. The image source 4 may comprise a display screen or a projector based on one or more of the above technologies.

[0120] The image source 4, meaning for example the display screen or the projector, is an integral part or component of the external device or alternatively a separate image source 4 arranged in data transfer communication with the external device. Accordingly, in some embodiments the image source 4 is a user device, such a PC, laptop, tablet computer, mobile phone, projector or the like, comprising the display screen or the projector.

[0121] Here the “image”, created by the image source 4, means the spatial distribution of local primary or secondary light sources with varying intensity and color, on a two-dimensional physical surface of image source 4. The image, formed by the image source 4, is then transformed by the optical system 3 in such a way that the viewer 1 of the display device observes a virtual image 2, curved or flat virtual image, with the same visual content as provided by the image source 4. To illustrate this, three arbitrary points A’, B’, C are chosen on the surface of the image source 4, and the mapping of these points into the three points A, B, C of the virtual image 2 is shown in Figure 5. According to the definition of the image source 4 presented above, each point of the image source is considered as the light point source of color and intensity varying from one point to another. The real opticalray paths for these points are shown as thin solid lines, and the virtual paths as they are perceived by the user are shown as thin dashed lines. The virtual image 2 formed by the display device is located at a distance from the eyes of the viewer 1. The distance is greater than the physical distance between the eyes of the viewer and the actual display device, and may be less than or equal to infinity. The distance between the eyes of the viewer 1 and the virtual image 2 or the shape of the virtual image 2 surface may be either fixed or varied to provide the best user experience for the viewer 1 and to lower eye strain of the viewer. The distant virtual image 2 formed by the display device is magnified compared to the original image of the image source 4. Therefore, for the viewer 1 the angular size of the virtual image 2 is comparable to the angular size of the image, formed by a conventional display device when observed from the normal distance.

[0122] The viewer 1 can observe the virtual image 2 by both eyes simultaneously without accommodation-convergence conflict and without any additional device-specific wearable devices. However, if the viewer has myopia, he / she may have to use the same eyeglasses or contact lenses as he / she uses in everyday life. The volume with the cross-section, denoted with dashed lines and marked as 5 is usually called an eyebox. For any position of the eyes of the viewer 1 inside this volume, the virtual image 2 is perceived correctly by both the eyes simultaneously. A larger volume of the eyebox 5 is usually desirable to improve the comfort of using the display device, since it allows the head movements and tilts of the viewer 1 without destroying the perception of the virtual image 2.

[0123] The exact surface of the mirror 3 is described mathematically as parametrical analytic two-dimensional surface, where the displacement of the surface from its base plane is presented as a finite sum of some mathematical basis functions with corresponding weight coefficients.

[0124] Figure 6 shows schematically one embodiment of the desktop display device 100. The desktop display device 100 comprises a body 50 comprising a support element 59, or stand, arranged to support the desktop display device 100 on a planar surface such as a table top.

[0125] The body 50 further comprises an image source connection arrangement 52, 54 arranged to support the image source 4. The image source connection arrangement comprises an image source support element 52 and an image source connector 54. The image source 4 is fixedly or detachably connected to the image source connector 54. The image source 4 is connected to the image source connector 54 is configured to emit image light in the emit direction B.The image source connection arrangement is provided with first adjustment arrangement arranged to adjust position of the image source 4 or the image source connector 54 for adjusting the position of the image source 4. The first adjustment arrangement is arranged to adjust the orientation of the image source 4 or the image source connector 54 for adjusting the emit direction B in which the image source 4 is configured to emit image light.

[0126] In some embodiments, the image source connection arrangement or the first adjustment arrangement is arranged to adjust position of the image source 4 in the body 50 in the direction or along the emit direction B. This enables adjusting the distance between the user 1 and the virtual image 2.

[0127] The body 50 further comprises a first reflector connection arrangement 56 arranged to support the first reflector 3 having a fist reflective surface 7. The first reflector connection arrangement comprises a first reflector support element 56. The first reflector 3 is fixedly or detachably connected to the first reflector support element 56. The first reflector 3 connected to the first reflector support element 56 is generate the virtual image 2 in the viewing direction A.

[0128] The first reflector connection arrangement is provided with second adjustment arrangement arranged to adjust position of the first reflector 3 for adjusting the position of the first reflector 3. The second adjustment arrangement is arranged to adjust the orientation of the first reflector 3 for adjusting the viewing direction A.

[0129] The first and second adjustment arrangements are arranged to form the adjustment system. The first and second adjustment arrangements are interconnected in the adjustment system such that the position or orientation of the image source 4 and the first reflector 3 are adjusted together maintaining the relative orientation of the image source 4 and the first reflector 3 fixed.

[0130] In Figure 7, an illustrative example of mirror surface 7 as well as its base plane 8 is presented. The exact geometrical form of the curved surface 7 is fixed as the analytical function w(u,v] defined in the local coordinates (u,vj on the base plane, where w in each point (u,vj within some fixed region (1, which can be rectangular or of more complex form, defines the distance between the base plane and the curved surface 7, as illustrated in Figure 7. The set of the basis functions of the displacement decomposition can be chosen in any convenient way, for example, but not limiting to, as simple polynomials of the base plane local coordinates, Zernike polynomials, trigonometrical functions and other. After the set of the basis functions is fixed, the exact shape of the mirror is completelydetermined by the set of the weight coefficients. For instance, when the polynomials of order up to 3 are chosen as the basis functions, the displacement w of the mirror surface in the point corresponding to the point on the basis plane with the local coordinates (u,vj

[0131]

[0132] In this example, the shape of the mirror surface 7 is completely determined by the 9 weight coefficients c_l...c_9. The weight coefficients of the mirror are determined within the two-stage process of the computer-aided numerical optimization. Main design objectives of the optical system, such as the desired angular size of the virtual image, desired eyebox size, desired overall display device assembly volume and the actual size of the image source are taken as the input data for the optimization. These design objectives are configured to satisfy the one or more characteristics A) - E), disclosed above. The whole design process has two stages: the initial stage and the main stage. On the initial stage, the preliminary design of display device based on spherical mirror with the layout of the optical components presented in Figure 5, is obtained by using any of the known suitable optical design process. This optical system will have the folded optical path and without axial symmetry due to the tilt of the mirror 3 and image source 4, although the mirror 3 itself will be axially symmetric. The optical system designed at this stage will have completely unsatisfactory performance, in terms of the optical quality of the virtual image. However, the spatial position of the base plane for the spherical mirror 3 as well as its focal distance are then used as the starting point for the main stage of the optimization process. The shape of the spherical mirror, obtained on the initial stage of the design process, is approximated in terms of the mathematical basis functions, selected for the analytical description of the surface of the curved mirror 3. The weight coefficients, obtained by this approximation, are used as the starting point for the main computer-based numerical optimization stage. During this process, the shape of the mirror 3, as well as its position and tilt are changed. In each step of the optimization process simulation of backpropagation of the optical rays is performed. During this simulation, the spot sizes, formed by the rays, on the surface of the image source are calculated, when the rays are launched from the eyebox 5 of the system in such a way that without the optical system these rays would converge to the points on the distant virtual image, or these rays form parallel ray bundles at different angles, if an infinite distance to the virtual imageis chosen. The goal function of the optimization is chosen to be dependent on the spot sizes obtained by means of the simulation of the backpropagation. For example, this function may be chosen to be equal to the average spot size on the image plane. Additionally, geometric distortion of the image, obtained by means of backpropagation, may also be considered in the goal function. The optimization process is carried out with any known suitable numerical optimization algorithm, with the goal of minimizing the spot sizes on the image plane and, possibly, to minimize the geometrical distortion of the image. During the optimization, the weight coefficients of mirror, as well as position and tilt of its base plane and image source are changed by the selected optimization algorithm to minimize the goal function. At some step the process stops, and the resulting values are taken for manufacturing the mirror as well as for building the mounting system for the optical components. The mirror 3 can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from metal or any suitable plastic with mirror coating.

[0133] Alternatively, the surface of the curved mirror 3 can be described mathematically with the help of spline functions, for instance, with two-dimensional NURBS surface. In the case of the spline functions, the surface is determined by the rectangular matrix of NxM control points, and, possibly, with the set of knot vectors. The geometrical surface is fully controlled by this set of parameters. An illustration is presented in Figure 8, where the surface 10 is determined by the set of control points 11, which are defined in the local coordinates (u,v,wj around base plane 12, defined by an equation w=0. In Figure 8, a cross-section of the two-dimensional surface 10 is presented. The exact shape of the surface 10 in the local coordinates is described as the function of positions of the control points 11. For this mathematical description of the mirror surface, a method of optimization, similar to the one described above is applied. At the first stage, a design based on the spherical mirror is obtained. Then for the spherical mirror the positions of the control points 11 are determined. On the second stage, these positions are modified by a computer-aided numerical optimization, carried out analogously to the one described above. Then the resulting surface 10 is used for manufacturing of the mirror 3, as described above.

[0134] Alternatively, the curved mirror 3 can be replaced with a thin Fresnel reflector, for example, to reduce the overall size and weight of the system. The exact shape of the Fresnel reflector can be obtained numerically by the two-step optimization method described below. At the first stage, an initial design of thesystem with the spherical mirror is obtained by any known suitable method of designing of the optical systems with the principal layout of the optical elements as shown in Figure 5. Then, on the second stage, a flat Fresnel reflector is designed. To do this, the whole base plane of the mirror, obtained on the previous stage, is divided into a two-dimensional array of small zones, for instance, of square or rectangular shape. The size of each zone has to be small, but much larger than the maximum wavelength of the visible light, for instance, 50 micrometers for the side of square-shaped zone, so the simple law of reflection of light from the geometrical optics can be applied instead of diffraction-based approach. For each zone, a certain geometrical normal direction is assigned. The geometrical normal for each zone is a direction, specified by pair of angles (cp,d). For the whole base plane, divided into NxM zones, where will be NxM pairs of geometrical normal angles. The initial direction of normal for each of NxM zones is determined by the spherical surface, obtained in the initial part of the optimization method. To do this, a geometrical center (u,vj of each zone is calculated on the base plane, and the direction of the normal of the spherical surface is calculated for this point. Then this direction is used as the initial value for the corresponding zone of the Fresnel reflector. After all the initial values are fixed, a computer-aided numerical optimization of the direction of normal for each zone is performed. On each step of the optimization process the simulation of the backpropagation of the optical rays is performed. For each zone of the Fresnel reflector, all the light rays impinging on this zone are reflected in accordance with the normal direction, associated with this zone, by the law of reflection of geometrical optics, stating that the angle of reflection is equal to the angle of incidence, where these two angles are measured with respect to the direction of the normal.

[0135] To illustrate the above, a two-dimensional cross-section of the reflection is presented in Figure 9. In figure 9, the base plane is denoted by 20, and the four zones are denoted as cl, c2, c3 and c4, with their borders displayed by the dotted lines. For each zone, a normal direction nl, n2, n3 and n4 are defined by the angles <p2, <P3> (p^, respectively. Incident parallel rays 22, impinging on each zone, are reflected 24 in different directions, depending on the zone and its normal direction.

[0136] During the simulation, the spot sizes, formed by the rays, on the surface of the image source are calculated, when the rays are launched from the eyebox of the system in such a way that without the optical system these rays would converge to the points on the distant virtual image, or these rays form parallel ray bundlesat different angles, if an infinite distance to the virtual image is chosen. The goal function of the optimization is chosen to be dependent on the spot sizes obtained by means of the simulation of the backpropagation. For example, this function may be chosen to be equal to the average spot size on the image plane. Additionally, geometric distortion of the image, obtained by means of backpropagation, may also be considered in the goal function. The optimization process is carried out with any known suitable numerical optimization algorithm, with the goal of minimizing the spot sizes on the image plane and, possibly, to minimize the geometrical distortion of the image.

[0137] On each step of this optimization process, the normal directions for each zone, as well as the position of the base plane and the position of the image source, are changed by the selected optimization algorithm to minimize the goal function. At some step the process of numerical optimization stops. The normal directions for each zone are then converted to the Fresnel reflector, as illustrated in Figure 10. For each zone on the base plane 20 of the reflector, a piece of three-dimensional plane is created. The projection of this piece on the base plane 20 coincides with the corresponding zone. The normal to the piece of plane coincides with the normal direction associated with the zone. The position of this piece of plane with respect to the base plane 20 is chosen in such a way that the central point of the corresponding zone on the base plane lies on the line of intersection of the piece of plane and the corresponding zone on the base plane. Then the edges of all the pieces of planes are connected to the edges of neighboring pieces of planes to form the continuous surface. This surface is considered as the working surface of the designed Fresnel reflector, as it is shown in Figure 10. The rays incident 22 on this surface are reflected in the same manner as the rays in the numerical model in the end of the main optimization process. The designed Fresnel reflector can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from metal or any suitable plastic with mirror coating. Additionally, to simplify the manufacturing process, a threshold may be introduced, and if the maximal vertical distance between the edges of the two neighboring pieces of planes is below threshold, these pieces may be considered for the manufacturing purpose as the single piece of double size.

[0138] Another possible way to construct the Fresnel reflector is based on dividing the base plane of the mirror to very small zones, with the number of zones greater than in the previous method. The two-stage optimization process is done in the same way as for the previous case. During the backpropagation simulation,all the rays are reflected according to the law of reflection of the geometrical optics, regardless of the size of each zone in terms of the wavelength of the incident light. After the second stage of optimization stops, the small zones are merged into the larger groups of NxM zones, in such way that the size of each large zone is much greater than the wavelength of the field generated by the image source. For each larger zone, an analytical smooth curved surface piece w=w(u,v) is built in such a way that for each center of the small zone (u_nm,v nm) the direction of the normal to the surface piece w coincides with the direction of the normal of the zone (n,m), which was previously obtained by the optimization process, and between these points the normal direction to the surface piece is interpolated. The edges of the neighboring surface pieces are then connected to each other to form the continuous surface. This surface is considered as the working surface of the designed Fresnel reflector. The designed Fresnel reflector can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from metal or any suitable plastic with mirror coating. The manufacturing of this reflector is possibly more difficult compared to the previous surface, since it is necessary to manufacture curved surfaces instead of flat surfaces. However, better image quality can be obtained in this way.

[0139] Alternatively, the curved mirror can be replaced with a diffractive reflector, which has the microrelief numerically optimized to provide the desired ray reflections in the same way as described above. Since diffractive optical elements have optical properties highly dependent on the wavelength of the incident field, a three-band operation of the diffractive reflector is required to provide user with the full-color virtual image. This means that the diffractive reflector must provide the same behaviour for three different wavelengths of incident light, corresponding to red, green and blue colors in human perception. Design of three-band diffractive reflector can be done with any known suitable numerical algorithm of diffractive optical element design. The image source in this case has three wavelength monochromatic backlights for red, green and blue colors, where the wavelength of each component coincides with the wavelength of the corresponding band of the diffractive reflector. The monochromatic backlight is implemented with laser diodes. The three components may provide backlight for the image source simultaneously or in alternating order fast enough that the human eye can’t see the blinking of the image.

[0140] In the case when the level of the geometrical distortion of the virtual image provided with the display device, when comparing to the original image,after the optimization process is considered as not satisfactory, additional means of reducing it may be implemented. In the proposed system, due to its folded optical path and absence of rotational symmetry, geometrical distortion cannot be presented in terms of well-known distortion types of barrel, pincushion and mustache distortions. One of the ways to decrease the level of the geometrical distortion of the virtual image is to introduce geometrical predistortion to the initial image data, in such a way that the predistortion, introduced by the numerical preprocessing into the image, after the image is displayed by the image source will be compensated by the distortion introduced by the optical system itself, so the final virtual image will be free of any geometrical distortions. The predistortion, which is unique to each specific realization of the proposed display system, can be determined by numerical simulation of ray propagation for the final design of the display device optical system with the test image, comprised of a rectangular grid. Then for the simulated virtual image, the position of each grid knot of the image is compared to its ideal position, and the displacement for each knot is determined. The mathematical description of predistortion, which is necessary to compensate for the distortion introduced by the optical system can be calculated by any known suitable method of distortion correction. A special digital image processing unit is then introduced into the system. This unit takes the digital image from the external image data source, applies to this data the predistortion procedure with the parameters determined on the previous stage, and then transfers the data to the image source module to be used as the initial image of the system, so the user will see an undistorted virtual image. In the case, when a mobile phone is used as the physical image source, the predistortion can be introduced by a special software, installed to the mobile phone.

[0141] Another way to mitigate the geometrical distortion of the virtual image is to introduce into the proposed display device a bent waveguide array slab, attached to the image source, which pixel-by-pixel transfers the initial image from a first plane to a second plane. The first or the second plane of the bent waveguide array slab is a curved surface, or both the first and second planes of the bent waveguide array slab are curved surfaces. The bent waveguide array slab, or the first and second plane thereof, deliberately introduces the geometrical predistortion, which will be then compensated by the distortion introduced by the optical system, and thus producing a final virtual image free of geometrical distortion. In addition, both methods of mitigating the geometrical distortion, described above, may be used in the disclosed display device simultaneously.A variation of the distance from the eyes of the viewer to the virtual image can be introduced by a precise variation of the position of the image source along the folded optical axis of the display device. The variation of the position of the image source may be done by numerically controlled motors, which mechanically move the image source unit and thus the image source plane in the direction perpendicular to the optical axis of the display device around its ideal position, obtained by the numerical optimization on the previous step. The movement may be user-controlled, to provide the best viewing experience, or automatic, to provide an additional stimulation of user’s accommodation system, or both.

[0142] Another embodiment of the display device is shown in Figure 11 (not to scale). The display device comprises the optical system with the folded optical path without axial symmetry. The optical system comprises the curved mirror 3 and a freeform lens 30, or system of two or more lenses 30. The image source 4 is a lightemitting or light-reflecting flat or curved image-forming system. The image source 4 is based on any available conventional technology, for instance, but not limited to, the one based on liquid crystal matrix with coherent or non-coherent backlight, or on an array of light-emitting diodes, or on reflecting array of e-paper elements, or a combination of a projection screen and a projector. The image source 4 may comprise a display screen or a projector based on one or more of the above technologies.

[0143] The source of the visual content for the image source 4 may be any external device capable of creating visual content. The source of the visual content may be for example PC, laptop, media player, etc., connected to the image source by a cable or by a wireless connection. The image source 4, meaning for example the display screen or the projector, is an integral part or component of the external device or alternatively a separate image source 4 arranged in data transfer communication with the external device. Accordingly, in some embodiments the image source 4 is a user device, such a PC, laptop, tablet computer, mobile phone, projector or the like, comprising the display screen or the projector.

[0144] The “image”, created by the image source 4, means the spatial distribution of local primary or secondary light sources with varying intensity and color, on a two-dimensional physical surface of image source 4. The image, formed by the image source 4, is then transformed by the optical system 3, 30 in such a way that the user of the display device observes a virtual flat or curved image virtual image 2, with the same visual content as the source image formed by theimage source 4.

[0145] To illustrate this, three arbitrary points A’, B’, C are chosen on the image source 4 surface, and the mapping of these points into the three points A, B, C of the virtual image is shown in Figure 11. According to the definition of the image source 4 presented above, each point of the image source 4 is considered as the light point source of color and intensity varying from one point to another. The real optical ray paths for these points are shown as thin solid lines, and the virtual paths as they are perceived by the user are shown as thin dashed lines. The virtual image 2 formed by the display device is located at a distance from the eyes of the viewer 1, which is greater than the physical distance between the eyes of the viewer and the actual display device, and may be less than or equal to infinity. The distance between the eyes of the viewer 1 and the virtual image 2 or the shape of the virtual image surface may be either fixed or varied to provide the best user experience for the viewer and to lower his / her eye strain. The distant virtual image 2 formed by the display device is magnified compared to the image of the image source 4. Therefore, for the viewer 1 the angular size of the virtual image 2 is comparable to the angular size of the image, formed by a conventional display device when observed from the normal distance. The viewer 1 can observe the virtual image 2 by both eyes simultaneously without accommodation-convergence conflict and without any additional device-specific wearable devices. However, if the user has myopia, he / she may have to use the same eyeglasses or contact lenses as he / she uses in everyday life. The volume with the cross-section, denoted with dashed lines and marked as 5 is called the eyebox of the system. For any position of the eyes of the viewer 1 inside this volume, the virtual image 2 is perceived correctly by both the eyes simultaneously. A larger volume of the eyebox 5 is usually desirable to improve the comfort of using the device, since it allows the head movements and head tilts of the viewer 1 without destroying the perception of the virtual image.

[0146] The exact surface of the mirror 3, as well as the surface (or surfaces) of lens 30 (or lenses) are described mathematically as parametrical analytic two-dimensional surfaces, where the displacement of the surface from its base plane is presented as a finite sum of some mathematical basis functions with corresponding weight coefficients.

[0147] Illustrative example of the mirror surface 7 as well as its base plane 8 are presented in Figure 7. The exact geometrical form of the curved surface 7 is fixed as the analytical function w(u,v) defined in the local coordinates (u,v) on the base plane 8, where w in each point (u,v) within some fixed region (1, which can berectangular or of more complex form, defines the distance between the base plane 8 and the curved surface 7, as illustrated in Figure 7. The set of the basis functions of the displacement decomposition can be chosen in any convenient way, for example, but not limiting to, as simple polynomials of the base plane local coordinates, Zernike polynomials, trigonometrical functions and others.

[0148] The same method of describing surface 7 is applied to the surfaces of lens 30 (or lenses). The set of basis functions can be the same for the mirror 3 and lens 30 (or lenses), or different. After the set of the basis functions is fixed, the exact shapes of the mirror 3 and lens 30 (or lenses) are completely determined by the corresponding sets of the weight coefficients. For instance, when the polynomials of order up to 3 are chosen as the basis functions, the displacement w of the mirror surface 7 in the point corresponding to the point on the base plane 8 with the local coordinates (u,v)

[0149]

[0150] In this example, the shape of the mirror surface 7 is completely determined by the 9 weight coefficients c_l...c_9. The weight coefficients of the mirror 3 and lens 30 (or lenses) are determined within the two-stage process of computer-aided numerical optimization. Main design objectives of the optical system, such as the desired angular size of the virtual image 2, desired eyebox 5 size, desired overall display device assembly volume and the actual size of the image source 4 are taken as the input data for the optimization. These design objectives are configured to satisfy the one or more characteristics A) - E), disclosed above. The whole design process has two stages: the initial stage and the main stage. Before the initial stage, the material of the lenses 30 is chosen. It must be transparent, and it is characterized by the refraction index. On the initial stage, the preliminary design of display device based on spherical mirror 3 and spherical lens 30 (or lenses) with the layout of the optical components presented in Figure 11, is obtained by using any of the known suitable optical design process. This optical system will have a folded optical path without axial symmetry due to the tilt of the mirror 3, lens 30 and image source 4, although the mirror 3 and lens 30 (or lenses) are axially symmetric. The optical system designed at this stage will have completely unsatisfactory performance, in terms of the optical quality of the virtual image 2. However, the spatial position of the base plane 8 for the spherical mirror 3 as well as its focal distance and the parameters of the lens 30 (or lenses)are then used as the starting point for the main stage of the optimization process. The shape of the spherical mirror 3 and lens 30 (or lenses) surfaces, obtained on the initial stage of the design process, are approximated in terms of the mathematical basis functions, selected for the analytical description of the surface of the curved mirror 3 and lens 30 (or lenses). The weight coefficients, obtained by these approximations, are used as the starting point for the main computer-based numerical optimization stage. During this process, the shape of the mirror 3 and the lens 30 (or lenses), as well as their position and tilt are changed. In each step of the optimization process simulation of backpropagation of the optical rays is performed. During this simulation, the spot sizes, formed by the rays, on the surface of the image source are calculated, when the rays are launched from the eyebox 5 of the display device in such a way that without the optical system these rays would converge to the points on the distant virtual image 2, or these rays form parallel ray bundles at different angles, if an infinite distance to the virtual image is chosen. The goal function of the optimization is chosen to be dependent on the spot sizes obtained by means of the simulation of the backpropagation. For example, this function may be chosen to be equal to the average spot size on the image plane. Additionally, geometric distortion of the image, obtained by means of backpropagation, may also be considered in the goal function. The optimization process is carried out with any known suitable numerical optimization algorithm, with the goal of minimizing the spot sizes on the image plane and, possibly, to minimize the geometrical distortion of the image. During the optimization, the weight coefficients of mirror 3 and lens 30 (or lenses), as well as position and tilt of their base planes and image source 4 are changed by the selected optimization algorithm to minimize the goal function. At some step the process stops, and the resulting values are taken for manufacturing the mirror 3 and the lens 30 (or lenses) as well as for building the mounting system for the optical components. The mirror 3 can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from metal or any suitable plastic with mirror coating. The lens 30 (or lenses) can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from any suitable transparent plastic or glass with chosen refraction index.

[0151] Alternatively, the surfaces of the curved mirror 3 and lens 30 (or lenses) can be described mathematically with the help of spline functions, for instance, with two-dimensional NURBS surface. In the case of the spline functions, all the surfaces are determined by the rectangular matrices of NxM control points, and,possibly, with the sets of knot vectors. The geometrical surface is fully controlled by this set of parameters. An illustration is presented in Figure 8, where the surface 10 is determined by the set of control points 11, which are defined in the local coordinates (u,v,w) around base plane 12, defined by an equation w=0. In Figure 8, a cross-section of the two-dimensional surface 10 is presented. The exact shape of the surface 10 in the local coordinates is described as the function of positions of the control points 11. For this mathematical description of the mirror surface 3 and the surfaces of the lens 30 (or lenses), a method of optimization, similar to the one described above is applied. At the first stage, a design based on the spherical mirror 3 and the spherical lens 30 (or lenses) is obtained. Then for the spherical mirror 3 and lenses 30 the positions of the control points are determined. On the second stage, these positions are modified by a computer-aided numerical optimization, carried out analogously to the one described above. Then the resulting surfaces are used for manufacturing of the mirror 3 and lens 30 (or lenses), as described above.

[0152] Alternatively, the curved mirror 3 can be replaced with a thin Fresnel reflector, and lens 30 (or lenses) can be replaced with thin Fresnel lens (or lenes), for example, to reduce the overall size and weight of the system. The exact shapes of the Fresnel reflector and Fresnel lenses can be obtained numerically by the two-step optimization method described below. Before the initial stage, a suitable transparent material with a known refraction index is chosen for the lenses. At the first stage, an initial design of the system with the spherical mirror 3 and planoconvex spherical lens 30 (or lenses) is obtained by any known suitable method of designing the optical systems with the principal layout of the optical elements as shown in Figure 11. Then, on the second stage, a flat Fresnel reflector and flat Fresnel lens (or lenses) are designed. To do this, the whole base plane of the mirror obtained on the previous stage, is divided into a two-dimensional array of small zones, for instance, of square or rectangular shape. The size of each zone has to be small, but much larger than the maximum wavelength of the visible light, for instance, 50 micrometers for the side of square-shaped zone, so the simple law of reflection of light from the geometrical optics can be applied instead of diffractionbased approach. For each zone, a certain geometrical normal direction is assigned. The geometrical normal for each zone is a direction, specified by pair of angles (cp,d). For the whole base plane, divided into NxM zones, where will be NxM pairs of geometrical normal angles. The initial direction of normal for each of NxM zones is determined by the spherical surface, obtained in the initial part of the optimization method. To do this, a geometrical center (u,v) of each zone iscalculated on the base plane, and the direction of the normal of the spherical surface is calculated for this point. Then this direction is used as the initial value for the corresponding zone of the Fresnel reflector. For the Fresnel lens (or lenses), the analogous procedure is applied. After all the initial values are fixed, a computer-aided numerical optimization of the direction of normal for each zone of each surface is performed. On each step of the optimization process the simulation of the backpropagation of the optical rays is performed. For each zone of the Fresnel reflector, all the light rays impinging on this zone are reflected in accordance with the normal direction, associated with this zone, by the law of reflection of geometrical optics, stating that the angle of reflection is equal to the angle of incidence, where these two angles are measured with respect to the direction of the normal.

[0153] To illustrate the above, a two-dimensional cross-section of the reflection is presented in Figure 9. In Figure 9, the base plane is denoted by 20, and the four zones are denoted as cl, c2, c3 and c4, with their borders displayed by the dotted lines. For each zone, a normal direction nl, n2, n3 and n4 are defined by the angles <p2, <P3> (p^, respectively. Incident parallel rays 22, impinging on each zone, are reflected 24 in different directions, depending on the zone and its normal direction. For the Fresnel lens (or lenses), the analogous procedure is applied, but instead of reflection, refraction of the light rays according to the normal direction of each zone and the refraction index of the selected material, as well as refraction of the rays on the back surface of the Fresnel lens are considered. During this simulation, the spot sizes, formed by the rays, on the surface of the image source 4 are calculated, when the rays are launched from the eyebox 5 of the system in such a way that without the optical system these rays would converge to the points on the distant virtual image 2, or these rays form parallel ray bundles at different angles, if an infinite distance to the virtual image is chosen. The goal function of the optimization is chosen to be dependent on the spot sizes obtained by means of the simulation of the backpropagation. For example, this function may be chosen to be equal to the average spot size on the image plane. Additionally, geometric distortion of the image, obtained by means of backpropagation, may also be considered in the goal function. The optimization process is carried out with any known suitable numerical optimization algorithm, with the goal of minimizing the spot sizes on the image plane and, possibly, to minimize the geometrical distortion of the image. On each step of this optimization process, the normal directions for each zone of each surface, as well as the positions of the base planes and theposition of the image source, are changed by the selected optimization algorithm to minimize the goal function. At some step the process of numerical optimization stops. The normal directions for each zone are then converted to the Fresnel reflector, as illustrated in Figure 10. For each zone on the base plane 20 of the reflector, a piece of three-dimensional plane is created. The projection of this piece on the base plane 20 coincides with the corresponding zone. The normal to the piece of plane coincides with the normal direction associated with the zone. The position of this piece of plane with respect to the base plane is chosen in such a way that the central point of the corresponding zone on the base plane 20 lies on the line of intersection of the piece of plane and the corresponding zone on the base plane 20. Then the edges of all the pieces of planes are connected to the edges of neighboring pieces of planes to form the continuous surface. This surface is considered as the working surface of the designed Fresnel reflector, as it is shown in Figure 10. The rays incident 22 on this surface are reflected in the same manner as the rays in the numerical model in the end of the main optimization process. For the Fresnel lens (or lenses), the analogous process of obtaining a continuous surface is applied. The designed Fresnel reflector can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from metal or any suitable plastic with mirror coating. The designed Fresnel lens (or lenses) can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from glass or any suitable plastic with chosen refractive index. Additionally, to simplify the manufacturing process, a threshold may be introduced, and if the maximal vertical distance between the edges of the two neighboring pieces of planes is below threshold, these pieces may be considered for the manufacturing purpose as the single piece of double size.

[0154] Another possible way to construct the Fresnel reflector and Fresnel lenses is based on dividing the base plane 20 of the mirror and lens (or lenses) to very small zones, with the number of zones greater than in the previous method. The two-stage optimization process is done in the same way as for the previous case. During the backpropagation simulation, all the rays are reflected and refracted according to the law of reflection and refraction, respectively, of the geometrical optics, regardless of the size of each zone in terms of the wavelength of the incident light. After the second stage of optimization stops, the small zones are merged into the larger groups of NxM zones, in such way that the size of each large zone is much greater than the wavelength of the field generated by the image source. For each larger zone, an analytical smooth curved surface piece w=w(u,v)is built in such a way that for each center of the small zone (u_nm,v_nm) the direction of the normal to the surface piece w coincides with the direction of the normal of the zone (n,m), which was previously obtained by the optimization process, and between these points the normal direction to the surface piece is interpolated. The edges of the neighboring surface pieces are then connected to each other to form the continuous surface. This surface is considered as the working surface of the designed Fresnel reflector. The same process is applied to the surfaces of Fresnel lens (or lenses). The designed Fresnel reflector can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from metal or any suitable plastic with mirror coating. The designed Fresnel lens (or lenses) can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from glass or any suitable plastic with chosen refractive index. The manufacturing of these optical elements is possibly more difficult compared to the previous surface, since it is necessary to manufacture curved surfaces instead of flat surfaces. However, better image quality can be obtained in this way.

[0155] Alternatively, the curved mirror 3 and lens 30 (or lenses) can be replaced with a diffractive reflector and diffractive lens (or lenses), with the microrelief numerically optimized to provide the desired ray reflections and refraction in the same way as described above. Since diffractive optical elements have optical properties highly dependent on the wavelength of the incident field, a three-band operation of the diffractive reflector and lens (or lenses) is required to provide user with the full-color virtual image. This means that the diffractive reflector and diffractive lens (or lenses) must provide the same behavior for three different wavelengths of incident light, corresponding to red, green and blue colors in human perception. Design of three-band diffractive reflector and diffractive lens (or lenses) can be done with any known suitable numerical algorithm of diffractive optical element design. The image source in this case has three wavelength monochromatic backlights for red, green and blue colors, where the wavelength of each component coincides with the wavelength of the corresponding band of the diffractive reflector. The monochromatic backlight is implemented with laser diodes. The three components may provide backlight for the image source simultaneously or in alternating order fast enough that the human eye can’t see the blinking of the image.

[0156] In the case when the level of the geometrical distortion of the virtual image provided with the disclosed display device, when comparing to the originalimage, after the optimization process is considered as not satisfactory, additional means of reducing it may be implemented. In the proposed system, due to its folded optical path and absence of rotational symmetry, geometrical distortion cannot be presented in terms of well-known distortion types of barrel, pincushion and mustache distortions. One of the ways to decrease the level of the geometrical distortion of the virtual image 2 is to introduce geometrical predistortion to the initial image data, in such a way that the predistortion, introduced by the numerical preprocessing into the image, after the image is displayed by the image source 4 will be compensated by the distortion introduced by the optical system itself, so the final virtual image will be free of any geometrical distortions. The predistortion, which is unique to each specific realization of the proposed display system, can be determined by numerical simulation of ray propagation for the final design of the display device optical system with the test image, comprised of a rectangular grid. Then for the simulated virtual image, the position of each grid knot of the image is compared to its ideal position, and the displacement for each knot is determined. The mathematical description of predistortion, which is necessary to compensate for the distortion introduced by the optical system can be calculated by any known suitable method of distortion correction. A special digital image processing unit is then introduced into the system. This unit takes the digital image from the external image data source, applies to this data the predistortion procedure with the parameters determined on the previous stage, and then transfers the data to the image source module to be used as the initial image of the system, so the viewer will see an undistorted virtual image 2. In the case, when the mobile phone is used as the physical image source 4, the predistortion can be introduced by a special software, installed to the mobile phone.

[0157] Another way to mitigate the geometrical distortion of the virtual image 2 is to introduce into the proposed display device a bent waveguide array slab, attached to the image source 4, which pixel-by-pixel transfers the initial image from a first plane to a second plane 2 and deliberately introduces the geometrical predistortion, which will be then compensated by the distortion, introduced by the optical system, and thus producing a final virtual image free of geometrical distortion. The first and second planes are curved surfaces or at least one of the is a curved surface. In addition, both methods of mitigating the geometrical distortion, described above, may be used in the disclosed display device simultaneously.

[0158] A variation of the distance from the eyes of the viewer to the virtualimage 2 can be introduced by a precise variation of the position of the image source 4 along the folded optical axis of the system. The variation of the position of the image source 4 may be done by numerically controlled motors, which mechanically move the image source 4 and thus the image source plane in the direction perpendicular to the optical axis of the system around its ideal position, obtained by the numerical optimization on the previous step. The movement may be user-controlled, to provide the best viewing experience, or automatic, to provide an additional stimulation of user’s accommodation system, or both.

[0159] Figure 12 shows schematically one embodiment of the desktop display device 100. The embodiment of figure 12 is a modification of the embodiment of figure 6 and the reference numerals of the figure 12 corresponds the features of figure 6.

[0160] The embodiment of figure 12 comprises further one or more premodifying lenses 30. The pre-modifying lenses 30 are supported connected to the image source connection arrangement or the image source support element 52 and the image source connector 54. The pre-modifying lenses 30 are fixedly or detachably connected to the image source connector 54 with a lens connector 55. The pre-modifying lenses 30 are arranged to face the image source 4 and receive the image light emitted by the image source 4 and pass the image light in the emit direction B.

[0161] The first adjustment arrangement of the image source connection arrangement is arranged to adjust the position or the orientation of the premodifying lenses 30 together with the image source 4 or the image source connector 54.

[0162] Figure 13 shows schematically another embodiment of the display device. The display device comprises the optical system with folded optical path without axial symmetry. The optical system comprises two optical curved mirrors 3, 32. The image source 4 comprises a light-emitting or light-reflecting flat or curved image-forming system. The image source 4 is based on any available conventional technology, for instance, but not limited to, the one based on liquid crystal matrix with coherent or non-coherent backlight, or on an array of lightemitting diodes, or on reflecting array of e-paper elements, or a combination of a projection screen and a projector.

[0163] The source of the visual content for the image source 4 may be any external device capable of creating visual content. The source of the visual content may be PC, laptop, media player, etc., connected to the image source by a cable orby a wireless connection. The image source 4 may comprise a display screen or a projector based on one or more of the above technologies.

[0164] The image source 4, meaning for example the display screen or the projector, is an integral part or component of the external device or alternatively a separate image source 4 arranged in data transfer communication with the external device. Accordingly, in some embodiments the image source 4 is a user device, such a PC, laptop, tablet computer, mobile phone, projector or the like, comprising the display screen or the projector.

[0165] Here the “image”, created by the image source 4, means the spatial distribution of local primary or secondary light sources with varying intensity and color, on a two-dimensional physical surface of image source 4.

[0166] The image, formed by the image source 4, is then transformed by the optical system in such a way that the viewer 1 of the display device observes a virtual flat or curved image 2, with the same visual content as the source image formed by the image source 4.

[0167] To illustrate the above, three arbitrary points A’, B’, C are chosen on the image source 4 surface, and the mapping of these points into the three points A, B, C of the virtual image 2 is shown in Figure 13. According to the definition of the image source 4 presented above, each point of the image source is considered as the light point source of color and intensity varying from one point to another. The real optical ray paths for these points are shown as thin solid lines, and the virtual paths as they are perceived by the user are shown as thin dashed lines. The virtual image 2 formed by display device is located at a distance from the eyes of the viewer 1, which is greater than the physical distance between the eyes of the viewer 1 and the actual display device, and may be less than or equal to infinity. The distance between the eyes of the viewer 1 and the virtual image 2 or the shape of the virtual image surface may be either fixed or varied to provide the best user experience for the viewer 1 of the display device and to lower his / her eye strain. The distant virtual image 2 formed by the display device is magnified compared to the original source image of the image source 4, so for the viewer 1 of the display device the angular size of the virtual image 2 is comparable to the angular size of the image, formed by a conventional display device when observed from the normal distance. The viewer 1 can observe the virtual image 2 by both eyes simultaneously without accommodation-convergence conflict and without any additional device-specific wearable devices. However, if the user has myopia, he / she may have to use the same eyeglasses or contact lenses as he / she uses ineveryday life. The volume with the cross-section, denoted with dashed lines and marked as 5 is usually called the eyebox of the system. For any position of the eyes of the viewer 1 inside this volume, the virtual image 2 is perceived correctly by both the eyes simultaneously. A larger volume of the eyebox 5 is usually desirable to improve the comfort of using the device, since it allows the movements and tilts of the head of the viewer 1 without destroying the perception of the virtual image.

[0168] The exact surfaces of the mirrors 3, 32 are described mathematically as parametrical analytic two-dimensional surfaces, where the displacement of the surface from its base plane is presented as a finite sum of some mathematical basis functions with corresponding weight coefficients.

[0169] In Figure 7, an illustrative example of mirror surface 7 as well as its base plane 8 is presented. This model is applicable to both the mirrors 3, 32 of the system. The exact geometrical form of the curved surface 7 is fixed as the analytical function w(u,v] defined in the local coordinates (u,vj on the base plane 8, where w in each point (u,vj within some fixed region (1, which can be rectangular or of more complex form, defines the distance between the base plane 8 and the curved surface 7, as illustrated in Figure 7. The set of the basis functions of the displacement decomposition can be chosen in any convenient way, for example, but not limiting to, as simple polynomials of the base plane local coordinates, Zernike polynomials, trigonometrical functions and others. The set of the basis functions can be either the same for both mirrors 3, 32, or different for each mirror 3, 32. After the set of the basis functions is fixed, the exact shapes of the mirrors 3, 32 are completely determined by the two sets of the weight coefficients. For instance, when the polynomials of order up to 3 are chosen as the basis functions, the displacement w of the mirror surface in the point corresponding to the point on the base plane with the local coordinates (u,vj

[0170]

[0171] In this example, the shape of the one of the mirror surfaces is completely determined by the 9 weight coefficients c_l...c_9. The weight coefficients of the mirrors are determined within the two-stage process of the computer-aided numerical optimization. Main design objectives of the optical system, such as the desired angular size of the virtual image 2, desired eyebox 5 size, desired overall display device assembly volume and the actual size of the image source 4 are taken as the input data for the optimization. These design objectives are configured to satisfy the one or more characteristics A) - E), disclosed above. The whole designprocess has two stages: the initial stage and the main stage. On the initial stage, the preliminary design of display device based on two spherical mirrors 3, 32 with the layout of the optical components presented in Figure 11, is obtained by using any of the known suitable optical design process. This optical system will have a folded optical path and no axial symmetry due to the tilts of the mirrors 3, 32 and image source 4, although the mirrors 3, 32 are axially symmetric. The optical system designed at this stage will have completely unsatisfactory performance, in terms of the optical quality of the virtual image 2. However, the spatial position of the base planes for the spherical mirrors as well as their focal distance are then used as the starting point for the main stage of the computer-based numerical optimization process. The shapes of the spherical mirrors, obtained on the initial stage of the design process, are approximated in terms of the mathematical basis functions, selected for the analytical description of the surfaces of the curved mirrors. Two sets of the weight coefficients, obtained by this approximation, are used as the starting point for the main optimization stage. During this process, the shapes of the mirrors 3, 32, as well as their positions and tilts are changed. In each step of the optimization process simulation of backpropagation of the optical rays is performed. During this simulation, the spot sizes, formed by the rays on the surface of the image source are calculated, when the rays are launched from the eyebox 5 of the system in such a way that without the optical system these rays would converge to the points on the distant virtual image 2, or these rays form parallel ray bundles at different angles, in an infinite virtual image is chosen. The goal function of the optimization is chosen to be dependent on the spot sizes obtained by means of the simulation of the backpropagation. For example, this function may be chosen to be equal to the average spot size on the image plane. Additionally, geometric distortion of the image, obtained by means of backpropagation, may also be considered in the goal function. The optimization process is carried out with any known suitable numerical optimization algorithm, with the goal of minimizing the spot sizes on the image plane and, possibly, to minimize the geometrical distortion of the image. During the optimization, the weight coefficients of the mirrors, as well as positions and tilts of their base planes and image source are changed by the selected optimization algorithm to minimize the goal function. At some step the process stops, and the resulting values are taken for manufacturing the mirrors as well as for building the mounting system for the optical components. The mirrors 3, 32 can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from metal or any suitable plastic withmirror coating.

[0172] Alternatively, the surfaces of the curved mirrors 3, 32 can be described mathematically with the help of spline functions, for instance, with two-dimensional NURBS surface. In the case of the spline functions, all the surfaces are determined by the rectangular matrices of NxM control points, and, possibly, with the sets of knot vectors. The geometrical surface is fully controlled by this set of parameters. An illustration is presented in Figure 8, where the surface 10 is determined by the set of control points 11, which are defined in the local coordinates (u,v,wj around base plane 12, defined by an equation w=0. In Figure 8, a cross-section of the two-dimensional surface 10 is presented. The exact shape of the surface 10 in the local coordinates is described as the function of positions of the control points 11. For this mathematical description of the mirror surfaces, a method of optimization, similar to the one described above is applied. At the first stage, a design based on spherical mirrors is obtained. Then for the spherical mirrors the positions of the control points are determined. On the second stage, these positions are modified by a computer-aided numerical optimization, carried out analogously to the one described above. Then the resulting surfaces are used for manufacturing of the mirrors 3, 32, as described above.

[0173] Alternatively, the curved mirrors 3, 32 can be replaced with a thin Fresnel reflectors, for example, to reduce the overall size and weight of the system. The exact shapes of the Fresnel reflectors can be obtained numerically by the two-step optimization method described below. At the first stage, an initial design of the system with the spherical mirrors is obtained by any known suitable method of designing of the optical systems with the principal layout of the optical elements as shown in Figure 13. Then, on the second stage, flat Fresnel reflectors are designed. To do this, the whole base plane of each mirror, obtained on the previous stage, is divided into a two-dimensional array of small zones, for instance, of square or rectangular shape. The size of each zone has to be small, but much larger than the maximum wavelength of the visible light, for instance, 50 micrometers for the side of square-shaped zone, so the simple law of reflection of light from the geometrical optics can be applied instead of diffraction-based approach. For each zone, a certain geometrical normal direction is assigned. The geometrical normal for each zone is a direction, specified by pair of angles (cp,d). For the whole base plane, divided into NxM zones, where will be NxM pairs of geometrical normal angles. The initial direction of normal for each of NxM zones is determined by the spherical surface, obtained in the initial part of the optimization method. To do this,a geometrical center (u,vj of each zone is calculated on the base plane, and the direction of the normal of the spherical surface is calculated for this point. Then this direction is used as the initial value for the corresponding zone of the Fresnel reflector. This procedure is applied to both mirrors. After all the initial values are fixed, a computer-aided numerical optimization of the direction of normal for each zone is performed. On each step of the optimization process the simulation of the backpropagation of the optical rays is performed. For each zone of the Fresnel reflectors, all the light rays impinging on this zone are reflected in accordance with the normal direction, associated with this zone, by the law of reflection of geometrical optics, stating that the angle of reflection is equal to the angle of incidence, where these two angles are measured with respect to the direction of the normal.

[0174] To illustrate this, a two-dimensional cross-section of the reflection is presented in Figure 9. In the figure 9, the base plane is denoted by 20, and the four zones are denoted as cl, c2, c3 and c4, with their borders displayed by the dotted lines. For each zone, a normal direction nl, n2, n3 and n4 are defined by the angles <Pi, <p2, <P3> <p4, respectively. Incident parallel rays 22, impinging on each zone, are reflected 24 in different directions, depending on the zone and its normal direction. During this simulation, the spot sizes, formed by the rays, on the surface of the image source are calculated, when the rays are launched from the eyebox 5 of the system in such a way that without the optical system these rays would converge to the points on the distant virtual image 2, or these rays form parallel ray bundles at different angles, if an infinite distance to the virtual image is chosen. The goal function of the optimization is chosen to be dependent on the spot sizes obtained by means of the simulation of the backpropagation. For example, this function may be chosen to be equal to the average spot size on the image plane. Additionally, geometric distortion of the image, obtained by means of backpropagation, may also be considered in the goal function. The optimization process is carried out with any known suitable numerical optimization algorithm, with the goal of minimizing the spot sizes on the image plane and, possibly, to minimize the geometrical distortion of the image. On each step of this optimization process, the normal directions for each zone, as well as the position of the base planes and the position of the image source, are changed by the selected optimization algorithm to minimize the goal function. At some step the process of numerical optimization stops. The normal directions for each zone are then converted to the Fresnel reflector, as illustrated in Figure 10. This procedure is applied to both mirrors 3, 32. For each zone on thebase plane of the reflector, a piece of three-dimensional plane is created. The projection of this piece on the base plane coincides with the corresponding zone. The normal to the piece of plane coincides with the normal direction associated with the zone. The position of this piece of plane with respect to the base plane is chosen in such a way that the central point of the corresponding zone on the base plane lies on the line of intersection of the piece of plane and the corresponding zone on the base plane. Then the edges of all the pieces of planes are connected to the edges of neighboring pieces of planes to form the continuous surface. This surface 20 is considered as the working surface of the designed Fresnel reflector, as it is shown in Figure 10. The rays 22 incident on this surface are reflected 24 in the same manner as the rays in the numerical model in the end of the main optimization process. The designed Fresnel reflectors can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from metal or any suitable plastic with mirror coating. Additionally, to simplify the manufacturing process, a threshold may be introduced, and if the maximal vertical distance between the edges of the two neighboring pieces of planes is below threshold, these pieces may be considered for the manufacturing purpose as the single piece of double size.

[0175] Another possible way to construct the Fresnel reflectors is based on dividing the base planes of the mirrors into very small zones, with the number of zones greater than in the previous method. The two-stage optimization process is done in the same way as for the previous case. During the backpropagation simulation, all the rays are reflected according to the law of reflection of the geometrical optics, regardless of the size of each zone in terms of the wavelength of the incident light. After the second stage of optimization stops, the small zones are merged into the larger groups of NxM zones, in such way that the size of each large zone is much greater than the wavelength of the field generated by the image source. For each larger zone, an analytical smooth curved surface piece w=w(u,v] is built in such a way that for each center of the small zone (u_nm,v_nmj the direction of the normal to the surface piece w coincides with the direction of the normal of the zone (n,m), which was previously obtained by the optimization process, and between these points the normal direction to the surface piece is interpolated. The edges of the neighboring surface pieces are then connected to each other to form the continuous surface. This surface is considered as the working surface of the designed Fresnel reflector. This procedure is applied to both mirrors. The designed Fresnel reflectors can be manufactured by any conventionalmethod, for example, but not limited to, by CNC milling or by casting from metal or any suitable plastic with mirror coating. The manufacturing of these reflectors is possibly more difficult compared to the previous surfaces, since it is necessary to manufacture curved surfaces instead of flat surfaces. However, better image quality can be obtained in this way.

[0176] Alternatively, the curved mirrors 3, 32 can be replaced with diffractive reflectors, which have the microrelief numerically optimized to provide the desired ray reflections in the same way as described above. Since diffractive optical elements have optical properties highly dependent on the wavelength of the incident field, a three-band operation of the diffractive reflectors is required to provide user with the full-color virtual image. This means that the diffractive reflectors must provide the same behavior for three different wavelengths of incident light, corresponding to red, green and blue colors in human perception. Design of three-band diffractive reflectors can be done with any known suitable numerical algorithm of diffractive optical element design. The image source in this case has three wavelength monochromatic backlights for red, green and blue colors, where the wavelength of each component coincides with the wavelength of the corresponding band of the diffractive reflector. The monochromatic backlight is implemented with laser diodes. The three components may provide backlight for the image source simultaneously or in alternating order fast enough that the human eye can’t see the blinking of the image.

[0177] In the case when the level of the geometrical distortion of the virtual image 2 provided with the disclosed display device, when comparing to the original image, after the optimization process is considered as not satisfactory, additional means of reducing it may be implemented. In the proposed system, due to its folded optical path and absence of rotational symmetry, geometrical distortion cannot be presented in terms of well-known distortion types of barrel, pincushion and mustache distortions. One of the ways to decrease the level of the geometrical distortion of the virtual image 2 is to introduce geometrical predistortion to the initial image data, in such a way that the predistortion, introduced by the numerical preprocessing into the image, after the image is displayed by the image source will be compensated by the distortion introduced by the optical system itself, so the final virtual image 2 will be free of any geometrical distortions. The predistortion, which is unique to each specific realization of the proposed display system, can be determined by numerical simulation of ray propagation for the final design of the display device optical system with the test image, comprised of a rectangular grid.Then for the simulated virtual image, the position of each grid knot of the image is compared to its ideal position, and the displacement for each knot is determined. The mathematical description of predistortion, which is necessary to compensate for the distortion introduced by the optical system can be calculated by any known suitable method of distortion correction. A special digital image processing unit is then introduced into the system. This unit takes the digital image from the external image data source, applies to this data the predistortion procedure with the parameters determined on the previous stage, and then transfers the data to the image source module to be used as the initial image of the system, so the user will see an undistorted virtual image. In the case, when the mobile phone is used as the physical image source 4, the predistortion can be introduced by a special software, installed to the mobile phone.

[0178] Another way to mitigate the geometrical distortion of the virtual image 2 is to introduce into the proposed display device a bent waveguide array slab, attached to the image source, which pixel-by-pixel transfers the initial image from a first plane to a second plane and deliberately introduces the geometrical predistortion, which will be then compensated by the distortion, introduced by the optical system, and thus producing a final virtual image free of geometrical distortion. The first plane and the second plane are both curved surfaces, or one of the first and second planes is a curved surface. In addition, both methods of mitigating the geometrical distortion, described above, may be used in the disclosed display device simultaneously.

[0179] A variation of the distance from the eyes of the viewer 1 to the virtual image 2 can be introduced by a precise variation of the position of the image source 4 along the folded optical axis of the system. The variation of the position of the image source 4 may be done by numerically controlled motors, which mechanically move the image source 4 and thus the image source plane in the direction perpendicular to the optical axis of the system around its ideal position, obtained by the numerical optimization on the previous step. The movement may be user-controlled, to provide the best viewing experience, or automatic, to provide an additional stimulation of user’s accommodation system, or both.

[0180] Figure 13a shows one of the possible practical embodiments of the desktop display device, build according to the procedure disclosed above and configured to meet one or more of the characteristics A) - B). A cross-section of the optical elements of the two-mirror display device is plot in scale. A global right-handed Cartesian coordinate system having mutually orthogonal X, Y, and Z axes isset so the plane XZ is a symmetry plane of the display device optical system. The first mirror 3 is characterized by the position of its base plane 8 having a normal vector lying in the XZ plane and forming an angle al=34.8494 degrees with the X axis, the plane passing through the point Ml with the global coordinates x=0.458m, y=0, z=0. The plane 8 has its local right-handed Cartesian coordinate system having mutually orthogonal U, V, and W axes with the local coordinate origin u=0, v=0, w=0 at the point Ml and the unit vectors U and V lying in the base plane 8. The directions of the unit vectors U and W are shown in Figure 13a. The mirror 3 is characterized in the local coordinates by the equation

[0181] — p4 • v3— p5 • v • u2— p6

[0182]

[0183] plO • u2• v3— pll • u4• v,

[0184] where the parameters are R=2.594, pl=-0.000508724, p2=-0.0082019, p3=0.123697, p4=-0.0584982, p5=0.0226189, p6=-0.344234, p7=0.292703, p8=0.10017, p9=-l.49912, pl0=0.675599, pll=0.32148. The size of the projection of the mirror 3 on its base plane 8 is 0.35m * 0.28m in U and V directions, respectively.

[0185] The second mirror 32 is characterized by the position of its base plane 8’ having a normal vector lying in the XZ plane and forming an angle al= -79.5809 degrees with the X axis, the plane passing through the point M2 with the global coordinates x=0.408297m, y=0, z=0.155029. The plane 8’ has its local right-handed Cartesian coordinate system having mutually orthogonal U’, V’, and W’ axes with the local coordinate origin u’=0, v'=0, w’=0 at the point M2 and the unit vectors U’ and V’ lying in the base plane 8’. The directions of the unit vectors U’ and W’ are shown in Figure 13a. The mirror 32 is characterized in the local coordinates by the equation

[0186]

[0187] where the parameters are R’=1.164, pl=-0.00109678, p2=-0.0450355, p3=0.0346113, p4=0.172346, p5=0.358539, p6=0.740405, p7=0.0466106, p8=0.0500081, p9=-l.24484, pl0=1.43302, pll=0.806611. The size of the projection of the mirror 32 on the base plane 8’ is 0.35m * 0.3m in U and V directions, respectively.

[0188] The flat rectangular image source 4 is characterized by the position ofits central point M3 with the global coordinates x=0.195665m, y=0, z=-0.125066, and its normal vector lying in the XZ plane and forming an angle al=127.774 degrees with the X axis. The size of the image source is 0.25m * 0.2m, where its longest side is aligned with the Y axis.

[0189] The optical system of this embodiment of the display device is designed to meet the following objectives: the distance between the user and the virtual image is infinity, the angular size of the virtual image is 24 degrees * 13.5 degrees, the maximal eyebox cross-section size in the YZ plane is 0.12m * 0.1m, respectively. The XZ cross-section of the eyebox 5 is shown in Figure 13a. The simulated resolving power of the display device for a rectangular aperture of a size 0.12m * 0.1m in the YZ plane, averaged across the whole image source, is approximately 8.3 cycles / mm, the worst resolving power is 4.6 cycles / mm. These values ensure the required resolving power for an aperture ofY size of 65 mm, since in an aberrationlimited optical system, reducing the effective aperture increases resolving power by reducing aberration-induced image blur.

[0190] The simulated geometrical distortion of the rectangular grid introduced by the optical system of the display device of figure 13a is presented in Figure 13b. The level of geometrical distortions can be characterized as moderate and in general acceptable. The level of geometrical distortions can be additionally reduced by any of the methods disclosed in this document.

[0191] Figure 14 shows schematically one embodiment of the desktop display device 100. The embodiment of figure 14 is a modification of the embodiment of figure 6, and the reference numerals of the figure 14 corresponds the same features of figure 6.

[0192] Figure 14 shows schematically one embodiment of the desktop display device 100. The desktop display device 100 comprises a body 50 comprising a support element 59, or stand, arranged to support the desktop display device 100 on a planar surface such as a table top.

[0193] The body 50 further comprises a second reflector connection arrangement 58 arranged to support the second reflector 32 having a second reflective surface 33. The second reflector connection arrangement comprises a second reflector support element 58. The second reflector 32 is fixedly or detachably connected to the second reflector support element 58. The second reflector 32 connected to the second reflector support element 58 is configured reflect the image light incident from the image source 4 towards the first reflector 3 in a reflection direction C.The second reflector connection arrangement is provided with a third adjustment arrangement arranged to adjust position of the second reflector 32 for adjusting the position of the second reflector 32. The third adjustment arrangement is arranged to adjust the orientation of the second reflector 32 for adjusting the reflection direction C.

[0194] The first, second and third adjustment arrangements are arranged to form the adjustment system. The first, second and third adjustment arrangements are interconnected in the adjustment system such that the position or orientation of the image source 4, the first reflector 3 and the second reflector 32 are adjusted together maintaining the relative orientation of the image source 4, the first reflector 3 and the second reflector 32 fixed.

[0195] Figure 15 shows schematically a further embodiment of the display device. The display device comprises the image source 4 and the optical system arranged to provide a folded optical path without axial symmetry. The optical system comprises two optical curved mirrors 3, 32 and a freeform lens 30, or system of one or more lenses. The image source 4 is a light-emitting or lightreflecting flat or curved image-forming system, based on any available conventional technology, for instance, but not limited to, the one based on liquid crystal matrix with coherent or non-coherent backlight, or on an array of lightemitting diodes, or on reflecting array of e-paper elements, or a combination of a projection screen and a projector. The source of the visual content for the image source 4 may be any external device capable of creating visual content. The source of the visual content may be for example PC, laptop, media player, etc., connected to the image source by a cable or by a wireless connection. The image source 4 may comprise a display screen or a projector based on one or more of the above technologies.

[0196] The source of the visual content for the image source 4 may be any external device capable of creating visual content. The source of the visual content may be PC, laptop, media player, etc., connected to the image source by a cable or by a wireless connection. The image source 4, meaning for example the display screen or the projector, is an integral part or component of the external device or alternatively a separate image source 4 arranged in data transfer communication with the external device. Accordingly, in some embodiments the image source 4 is a user device, such a PC, laptop, tablet computer, mobile phone, projector or the like, comprising the display screen or the projector.

[0197] Here the “image”, created by the image source 4, means the spatialdistribution of local primary or secondary light sources with varying intensity and color, on a two-dimensional physical surface of image source 4. The image, formed by the image source 4, is then transformed by the optical system 3, 30, 32 in such a way that the viewer 1 of this display device observes a virtual flat or curved image 2, with the same visual content as the source image formed by the image source 4. To illustrate this, three arbitrary points A’, B’, C are chosen on the image source 4 surface, and the mapping of these points into the three points A, B, C of the virtual image 2 is shown in Figure 15. According to the definition of the image source 4 presented above, each point of the image source 4 is considered as the light point source of color and intensity varying from one point to another. The real optical ray paths for these points are shown as thin solid lines, and the virtual paths as they are perceived by the user are shown as thin dashed lines. The virtual image 2 formed by display device is located at a distance from the eyes of the viewer 1, which is greater than the physical distance between the eyes of the viewer 1 and the actual display device, and may be less than or equal to infinity. The distance between the eyes of the viewer 1 and the virtual image 2 or the shape of the virtual image surface may be either fixed or varied to provide the best user experience for the display device viewer 1 and to lower his / her eye strain. The distant virtual mage 2 formed by the display device is magnified compared to the original source image of the image source 4, so for the display device viewer 1 the angular size of the virtual image 2 is comparable to the angular size of the image, formed by a conventional display device when observed from the normal distance. The viewer 1 can observe the virtual image 2 by both eyes simultaneously without accommodation-convergence conflict and without any additional device-specific wearable devices. However, if the user has myopia, he / she may have to use the same eyeglasses or contact lenses as he / she uses in everyday life. The volume with the cross-section, denoted with dashed lines and marked as 5 is usually called an eyebox of the system. For any position of the eyes of the viewer 1 inside this volume, the virtual image 2 is perceived correctly by both the eyes simultaneously. A larger volume of the eyebox 5 is usually desirable to improve the comfort of using the device, since it allows the movements and tilts of the head of the viewer 1 without destroying the perception of the virtual image 2.

[0198] The exact surfaces of the mirrors 3, 32, as well as the surface (or surfaces) of lens 30 (or lenses) are described mathematically as parametrical analytic two-dimensional surfaces, where the displacement of the surface from its base plane is presented as a finite sum of some mathematical basis functions withcorresponding weight coefficients. In Figure 7, an illustrative example of mirror surface 7 as well as its base plane 8 is presented. This model is applicable to both the mirrors 3, 32 of the system. The exact geometrical form of the curved surface 7 is fixed as the analytical function w(u,v) defined in the local coordinates (u,v) on the base plane 8, where w in each point (u,v) within some fixed region (1, which can be rectangular or of more complex form, defines the distance between the base plane 8 and the curved surface 7, as illustrated in Figure 7. The set of the basis functions of the displacement decomposition can be chosen in any convenient way, for example, but not limiting to, as simple polynomials of the base plane local coordinates, Zernike polynomials, trigonometrical functions and other. The same method of describing surface is applied to the surfaces of lens 30 (or lenses). The set of the basis functions can be either the same for both mirrors 3, 32 and lens 30 (or lenses), or different for each surface. After the set of the basis functions is fixed, the exact shapes of the mirrors 3, 32 and lens 30 (or lenses) are completely determined by the two sets of the weight coefficients. For instance, when the polynomials of order up to 3 are chosen as the basis functions, the displacement w of the mirror surface in the point corresponding to the point on the basis plane 8 with the local coordinates (u,v)

[0199]

[0200] In this example, the shape of the one of the mirror surfaces are completely determined by the 9 weight coefficients c_l...c_9. The weight coefficients of the mirrors 3, 32 and lens 30 (or lenses) are determined within the two-stage process of the computer-aided numerical optimization. Main design objectives of the optical system, such as the desired angular size of the virtual image 2, desired eyebox 5 size, desired overall display device assembly volume and the actual size of the image source 4 are taken as the input data for the optimization. These design objectives are configured to satisfy the one or more characteristics A) - E), disclosed above. The whole design process has two stages: the initial stage and the main stage. Before the initial stage, the material of the lenses is chosen. It must be transparent, and it is characterized by the refraction index. On the initial stage, the preliminary design of display device based on two spherical mirrors 3, 32 and spherical lens 30 (or lenses) with the layout of the optical components presented in Figure 15, is obtained by using any of the known suitable optical design process. This optical system will have the folded optical path and no axial symmetry due to the tilts of the mirrors 3, 32, lenses 30 and imagesource 4, although the mirrors 3, 32 and lens 30 (or lenses) are axially symmetric. The optical system designed at this stage will have completely unsatisfactory performance, in terms of the optical quality of the virtual image 2. However, the spatial position of the base planes for the spherical mirrors 3, 32 as well as their focal distance and the parameters of the lens 30 (or lenses) are then used as the starting point for the main stage of the computer-based numerical optimization process. The shapes of the spherical mirrors 3, 32 and lens 30 (or lenses) surfaces, obtained on the initial stage of the design process, are approximated in terms of the mathematical basis functions, selected for the analytical description of the surfaces of the curved mirrors 3, 32 and lens 30 (or lenses). The sets of the weight coefficients, obtained by this approximation, are used as the starting point for the main optimization stage. During this process, the shapes of the mirrors 3, 32 the lens 30 (or lenses), as well as their positions and tilts are changed. In each step of the optimization process simulation of backpropagation of the optical rays is performed. During this simulation, the spot sizes, formed by the rays on the surface of the image source 4 are calculated, when the rays are launched from the eyebox 5 of the system in such a way that without the optical system these rays would converge to the points on the distant virtual image 2, or these rays form parallel ray bundles at different angles, if an infinite distance to the virtual image is chosen. The goal function of the optimization is chosen to be dependent on the spot sizes obtained by means of the simulation of the backpropagation. For example, this function may be chosen to be equal to the average spot size on the image plane. Additionally, geometric distortion of the image, obtained by means of backpropagation, may also be considered in the goal function. The optimization process is carried out with any known suitable numerical optimization algorithm, with the goal of minimizing the spot sizes on the image plane and, possibly, to minimize the geometrical distortion of the image. During the optimization, the weight coefficients of the mirrors and lens (or lenses), as well as positions and tilts of their base planes and image source are changed by the selected optimization algorithm to minimize the goal function. At some step the process stops, and the resulting values are taken for manufacturing the mirrors and the lens (or lenses), as well as for building the mounting system for the optical components. The mirrors can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from metal or any suitable plastic with mirror coating. The lens (or lenses) can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from anysuitable transparent plastic or glass with chosen refraction index.

[0201] Alternatively, the surfaces of the curved mirrors 3, 32 and lens 30 (or lenses) can be described mathematically with the help of spline functions, for instance, with two-dimensional NURBS surface. In the case of the spline functions, all the surfaces are determined by the rectangular matrices of NxM control points, and, possibly, with the sets of knot vectors. The geometrical surface is fully controlled by this set of parameters. An illustration is presented in Figure 8, where the surface 10 is determined by the set of control points 11, which are defined in the local coordinates (u,v,w) around base plane 12, defined by an equation w=0. In Figure 8, a cross-section of the two-dimensional surface 10 is presented. The exact shape of the surface 10 in the local coordinates is described as the function of positions of the control points 11. For this mathematical description of the mirror surfaces and the surfaces of the lens (or lenses), a method of optimization, similar to the one described above is applied. At the first stage, a design based on the spherical mirrors and the spherical lens (or lenses) is obtained. Then for the spherical mirrors 3, 32 and lenses 30 the positions of the control points are determined. On the second stage, these positions are modified by a computer-aided numerical optimization, carried out analogously to the one described above. Then the resulting surfaces are used for manufacturing of the mirrors and lens (or lenses), as described above.

[0202] Alternatively, the curved mirrors 3, 32 can be replaced with thin Fresnel reflectors, and lens 30 (or lenses) can be replaced with thin Fresnel lens (or lenes), for example, to reduce the overall size and weight of the system. The exact shapes of the Fresnel reflectors and Fresnel lenses can be obtained numerically by the two-step optimization method described below. Before the initial stage, a suitable transparent material with a known refraction index is chosen for the lenses. At the first stage, an initial design of the system with the spherical mirrors and planoconvex spherical lens (or lenses) is obtained by any known suitable method of designing of the optical systems with the principal layout of the optical elements as shown in Figure 15. Then, on the second stage, flat Fresnel reflectors and flat Fresnel lens (or lenses) are designed. To do this, the whole base plane of each mirror, obtained on the previous stage, is divided into a two-dimensional array of small zones, for instance, of square or rectangular shape. The size of each zone has to be small, but much larger than the maximum wavelength of the visible light, for instance, 50 micrometers for the side of square-shaped zone, so the simple law of reflection of light from the geometrical optics can be applied instead of diffraction-based approach. For each zone, a certain geometrical normal direction is assigned. The geometrical normal for each zone is a direction, specified by pair of angles (cp,d). For the whole base plane, divided into NxM zones, where will be NxM pairs of geometrical normal angles. The initial direction of normal for each of NxM zones is determined by the spherical surface, obtained in the initial part of the optimization method. To do this, a geometrical center (u,v) of each zone is calculated on the base plane, and the direction of the normal of the spherical surface is calculated for this point. Then this direction is used as the initial value for the corresponding zone of the Fresnel reflector. This procedure is applied to both mirrors. For the Fresnel lens (or lenses), the analogous procedure is applied. After all the initial values are fixed, a computer-aided numerical optimization of the direction of normal for each zone is performed. On each step of the optimization process the simulation of the backpropagation of the optical rays is performed. For each zone of the Fresnel reflectors, all the light rays impinging on this zone are reflected in accordance with the normal direction, associated with this zone, by the law of reflection of geometrical optics, stating that the angle of reflection is equal to the angle of incidence, where these two angles are measured with respect to the direction of the normal.

[0203] To illustrate the above, a two-dimensional cross-section of the reflection is presented in Figure 9. In the figure 9, the base plane is denoted by 20, and the four zones are denoted as cl, c2, c3 and c4, with their borders displayed by the dotted lines. For each zone, a normal direction nl, n2, n3 and n4 are defined by the angles

[0204]

[0205] <p2, <P3> <p4, respectively. Incident parallel rays 22, impinging on each zone, are reflected 24 in different directions, depending on the zone and its normal direction. For the Fresnel lens (or lenses), the analogous procedure is applied, but instead of reflection, refraction of the light rays according to the normal direction of each zone and the refraction index of the selected material, as well as refraction of the rays on the back surface of the Fresnel lens are considered. During this simulation, the spot sizes, formed by the rays, on the surface of the image source 4 are calculated, when the rays are launched from the eyebox 5 of the system in such a way that without the optical system these rays would converge to the points on the distant virtual image, or these rays form parallel ray bundles at different angles, in an infinite virtual image is chosen. The goal function of the optimization is chosen to be dependent on the spot sizes obtained by means of the simulation of the backpropagation. For example, this function may be chosen to be equal to the average spot size on the image plane. Additionally, geometric distortion of theimage, obtained by means of backpropagation, may also be considered in the goal function. The optimization process is carried out with any known suitable numerical optimization algorithm, with the goal of minimizing the spot sizes on the image plane and, possibly, to minimize the geometrical distortion of the image. On each step of this optimization process, the normal directions for each zone, as well as the position of the base planes and the position of the image source, are changed by the selected optimization algorithm to minimize the goal function. At some step the process of numerical optimization stops. The normal directions for each zone are then converted to the Fresnel reflector, as illustrated in Figure 10. This procedure is applied to both mirrors 3, 32. For each zone on the base plane of the reflector, a piece of three-dimensional plane is created. The projection of this piece on the base plane coincides with the corresponding zone. The normal to the piece of plane coincides with the normal direction associated with the zone. The position of this piece of plane with respect to the base plane is chosen in such a way that the central point of the corresponding zone on the base plane lies on the line of intersection of the piece of plane and the corresponding zone on the base plane. Then the edges of all the pieces of planes are connected to the edges of neighboring pieces of planes to form the continuous surface. This surface is considered as the working surface 20 of the designed Fresnel reflector, as it is shown in Figure 10. The rays 22 incident on this surface are reflected 24 in the same manner as the rays in the numerical model in the end of the main optimization process. For the Fresnel lens (or lenses), the analogous process of obtaining a continuous surface is applied. The designed Fresnel reflectors can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from metal or any suitable plastic with mirror coating. The designed Fresnel lens (or lenses) can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from glass or any suitable plastic with chosen refractive index. Additionally, to simplify the manufacturing process, a threshold may be introduced, and if the maximal vertical distance between the edges of the two neighboring pieces of planes is below threshold, these pieces may be considered for the manufacturing purpose as the single piece of double size.

[0206] Another possible way to construct the Fresnel reflectors and Fresnel lenses is based on dividing the base planes of the mirrors 3, 32, and lens 30 (or lenses) to very small zones, with the number of zones greater than in the previous method. The two-stage optimization process is done in the same way as for the previous case. During the backpropagation simulation, all the rays are reflectedaccording to the law of reflection of the geometrical optics, regardless of the size of each zone in terms of the wavelength of the incident light. After the second stage of optimization stops, the small zones are merged into the larger groups of NxM zones, in such way that the size of each large zone is much greater than the wavelength of the field generated by the image source. For each larger zone, an analytical smooth curved surface piece w=w(u,v) is built in such a way that for each center of the small zone (u_nm,v_nm) the direction of the normal to the surface piece w coincides with the direction of the normal of the zone (n,m), which was previously obtained by the optimization process, and between these points the normal direction to the surface piece is interpolated. The edges of the neighboring surface pieces are then connected to each other to form the continuous surface. This surface is considered as the working surface of the designed Fresnel reflector. This procedure is applied to both mirrors. The same process is applied to the surfaces of Fresnel lens (or lenses). The designed Fresnel reflectors can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from metal or any suitable plastic with mirror coating. The designed Fresnel lens (or lenses) can be manufactured by any conventional method, for example, but not limited to, by CNC milling or by casting from glass or any suitable plastic with chosen refractive index. The manufacturing of these optical elements is possibly more difficult compared to the previous surfaces, since it is necessary to manufacture curved surfaces instead of flat surfaces. However, better image quality can be obtained in this way.

[0207] Alternatively, the curved mirrors 3, 32 and lens 30 (or lenses) can be replaced with diffractive reflectors and diffractive lens (or lenses), which have the microrelief numerically optimized to provide the desired ray reflections and refraction in the same way as described above. Since diffractive optical elements have optical properties highly dependent on the wavelength of the incident field, a three-band operation of the diffractive reflectors and lens (or lenses) is required to provide user with the full-color virtual image. This means that the diffractive reflectors and diffractive lens (or lenses) must provide the same behaviour for three different wavelengths of incident light, corresponding to red, green and blue colors in human perception. Design of three-band diffractive reflectors and diffractive lens (or lenses) can be done with any known suitable numerical algorithm of diffractive optical element design. The image source in this case has three wavelength monochromatic backlights for red, green and blue colors, where the wavelength of each component coincides with the wavelength of thecorresponding band of the diffractive reflector. The monochromatic backlight is implemented with laser diodes. The three components may provide backlight for the image source simultaneously or in alternating order fast enough that the human eye can’t see the blinking of the image.

[0208] In the case when the level of the geometrical distortion of the virtual image 2 provided with the disclosed display device, when comparing to the original image, after the optimization process is considered as not satisfactory, additional means of reducing it may be implemented. In the proposed system, due to its folded optical path and absence of rotational symmetry, geometrical distortion cannot be presented in terms of well-known distortion types of barrel, pincushion and mustache distortions. One of the ways to decrease the level of the geometrical distortion of the virtual image 2 is to introduce geometrical predistortion to the initial image data, in such a way that the predistortion, introduced by the numerical preprocessing into the image, after the image is displayed by the image source will be compensated by the distortion introduced by the optical system itself, so the final virtual image 2 will be free of any geometrical distortions. The predistortion, which is unique to each specific realization of the proposed display system, can be determined by numerical simulation of ray propagation for the final design of the display device optical system with the test image, comprised of a rectangular grid. Then for the simulated virtual image, the position of each grid knot of the image is compared to its ideal position, and the displacement for each knot is determined. The mathematical description of predistortion, which is necessary to compensate for the distortion introduced by the optical system can be calculated by any known suitable method of distortion correction. A special digital image processing unit is then introduced into the system. This unit takes the digital image from the external image data source, applies to this data the predistortion procedure with the parameters determined on the previous stage, and then transfers the data to the image source module to be used as the initial image of the system, so the user will see an undistorted virtual image. In the case, when the user’s mobile phone is used as the physical image source, the predistortion can be introduced by a special software, installed to the user’s phone.

[0209] Another way to mitigate the geometrical distortion of the virtual image is to introduce into the proposed display device a bent waveguide array slab, attached to the image source 4, which pixel-by-pixel transfers the initial image from a first plane to a second plane and deliberately introduces the geometrical predistortion, which will be then compensated by the distortion, introduced by theoptical system, and thus producing a final virtual image free of geometrical distortion. The first plane and the second plane are curved surfaces, or alternatively the first or the second plane is curved surface. In addition, both methods of mitigating the geometrical distortion, described above, may be used in the disclosed display device simultaneously.

[0210] A variation of the distance from the eyes of the viewer 1 to the virtual image 2 can be introduced by a precise variation of the position of the image source 4 along the (folded) optical axis of the system. The variation of the position of the image source may be done by numerically controlled motors, which mechanically move the image source unit and thus the image source plane in the direction perpendicular to the optical axis of the system around its ideal position, obtained by the numerical optimization on the previous step. The movement may be user-controlled, to provide the best viewing experience, or automatic, to provide an additional stimulation of user’s accommodation system, or both.

[0211] Figure 16 shows schematically one embodiment of the desktop display device 100. The embodiment of figure 16 is a modification of the embodiment of figure 14 and the reference numerals of the figure 16 corresponds the features of figure 14.

[0212] The embodiment of figure 16 comprises further one or more premodifying lenses 30. The pre-modifying lenses 30 are supported connected to the image source connection arrangement or the image source support element 52 and the image source connector 54. The pre-modifying lenses 30 are fixedly or detachably connected to the image source connector 54 with a lens connector 55. The pre-modifying lenses 30 are arranged to face the image source 4 and receive the image light emitted by the image source 4 and pass the image light in the emit direction B.

[0213] The first adjustment arrangement of the image source connection arrangement is arranged to adjust the position or the orientation of the premodifying lenses 30 together with the image source 4 or the image source connector 54.

[0214] In some embodiments the image source has curved form, as shown in figure 17. A flexible display unit of any available technology (for instance, flexible OLED or any other) is used as the physical image source. The exact geometrical form of the curved image source is optimized to achieve even better virtual image quality. In the case when the flexible display allows bending, but not stretching, its exact geometrical form is defined analytically as a parametric representation of adevelopable surface (a sub-class of ruled surfaces). First, a base plane for the surface is selected.

[0215] To define a curved image source, a pair of analytical curves of lengths equal to the corresponding lengths of the opposite edges of the physical flexible display unit is considered. These curves will be further referred to as generating curves. Each generating curve lies in a plane orthogonal to the base plane. The generating curves are defined as polynomials of order greater than one, or as any other analytic curves or splines, parametrized by the two sets of coefficients, respectively. The generating curves are considered as the opposite edges of the flexible display unit surface. The distance between the corresponding ends of the two generating curves must be equal to the length of the other two sides of the flexible display unit. Then the developable surface, based on generating curves, is built by using any available algorithm, which builds a developable surface from two curves. If the obtained developable surface has self-intersections or bends with a radius too small for the physical flexible display unit, the generating curves must be redefined. The obtained developable surface is then analytically presented in the parametric form as the function w(u,v) of the point (u,v) on the base plane, where each point (u,v) lies within some fixed region (1.

[0216] In Figure 17, an illustrative example of a flexible display unit surface 35 as well as its base plane 8 and two generating curves 33 and 34 are presented. Each of the generating curves 33, 34 lies in the planes parallel to the UW plane and orthogonal to the base plane UV 8. A region (1 of the points (u,v), for which the parametric surface w(u,v) is defined, is depicted in dashed lines and marked as 36. The exact form of the flexible image source is then obtained by the two-step optimization process like the one described above. On the initial stage of the optimization, the image source is set to be flat. On the second stage of the optimization, the exact surface of the flexible image source is optimized at the same time as the surface of mirror(s) and, possibly, lenses by modifying the set of coefficients which define the two generating curves, and then rebuilding the exact form of the flexible image source as the developable surface. In the case when the flexible display unit allows stretching as well as bending, its exact surface is optimized in the same way as the surfaces of the mirrors and lenses.

[0217] In some embodiments, the display device includes a positioning system, which allows adjusting of the spatial position and tilt of the display device to provide the best user experience by aligning the eyebox position with the user’s eyes. An illustration of such an adjustment is presented schematically in Figure 18(not to scale). When the user’s head 1 is, for example, moved in the vertical direction and tilted to a position marked as 37, the user’s eyes leave the eyebox 5, so the user will not be able to observe the full virtual image 2. To avoid this problem, the display device 3 must be also moved and rotated to a new position, marked as 39, so the new position of the eyebox 38 will be aligned with the new location of the user’s head 37, and the user will be able to see the new virtual image 40.

[0218] This positioning system may include, but is not limited to, 1) A base, which is placed on the table or any other horizontal surface. 2) A vertical column, which provides support to the display device. The column is connected to the base by a rotating joint, which allows rotation around a vertical axis. The column also has a sliding mechanism to adjust the position of the display device in a vertical direction. 3) A pivot mechanism, which provides connection between the vertical column and the display device and allows adjustment of the tilt of the display device by rotating it around the horizontal axis.

[0219] In some embodiments, an auxiliary system for tracking the position of the user’s head and automatic adjustment of the display device position and / or tilt is included. The purpose of this system is to provide the best user experience by automatically aligning the eyebox position with the actual position of the user’s eyes. This practically extends the viewing range for the display device, enabling user to, for example, lean back in the chair without losing the perception of the virtual image due to eyebox position mismatch. The system consists of 1) one or more video cameras, mounted on the display device and providing continuous monitoring of the position and tilt of the user’s head; 2) a processing unit, which acquires the image from the camera(s) in real time, and calculates the user’s head position and tilt by using any available suitable image recognition algorithm; 3) a mechanism which provides the necessary movement of the display device, as described above, and which is powered by one or more electrical motors, controlled by the processing unit. The processing unit continuously monitors the position of the user’s head according to the images captured by the camera (or cameras) and sends commands to the mechanism to change the position and the tilt of the display device, if it appears that the user has permanently changed his or her posture, moving the head to a different position in space.

[0220] In some embodiments, the display device is foldable. The foldable means that the display device is foldable such that the volume occupied by the display device may be decreased for transportation. Accordingly, the display devicecomprises a use position in which the display device is used and a transport position for transporting the display device. The display device may be arranged to between the use position and the transport position by folding the display device. The volume occupied by the display device in the transport position is smaller than the volume occupied by the display device in the use position. The reflectors 3, 32 and the image source 4 or support thereof are connected with joints having two fixed positions - the use position and the transport position.

[0221] The invention has been described above with reference to the examples shown in the figures. However, the invention is in no way restricted to the above examples but may vary within the scope of the claims.

Claims

CLAIMS1. A desktop display device (100) arranged to generate a virtual image, cha ra cte r i z e d in that the display device (100) comprises:- a body (50) arranged to support the desktop display device on a support surface,- an image source (4) provided to the body (50) and configured to emit image light forming a visual image,- an optical system (3, 30, 32) provided to the body (50) and comprising a first reflector (3) having a first concavely structured reflective surface (7) configured reflect the image light emitted from the image source (4) in a viewing direction (A), the first concavely structured reflective surface (7) is configured as a first non-rotationally symmetric freeform reflective surface (7),- the first reflector (3) being configured to generate a magnified virtual image from the image light emitted from the image source (4) in the viewing direction (A),- the optical system (3, 30, 43) being configured to generate a folded optical path without axial symmetry from the image source (4) to the viewing direction (A), and- the optical system (3, 30, 43) is configured generate an eyebox (5) for observation of the virtual image by a user.

2. A desktop display device (100) according to claim 1, cha ra cte r i z e d in that the image source (4) comprises a planar or curved surface configured to emit image light.

3. A desktop display device (100) according to claim 2, cha ra cte r i z e d in that the image source is a display screen.

4. A desktop display device (100) according to any one of claims 1 to 3, cha ra cte r i z e d in that:- the first reflector (3) comprises a concave mirror surface (7) configured to provide the first concavely structured reflective surface (7); or - the first reflector (3) comprises a Fresnel reflector surface (7), which is a reflective surface comprising a plurality of reflective zones configured such that a local reflection angle varies as a function of lateral position across the surface (7) or- the first reflector (3) comprises a diffractive reflector surface (7) configured such that a local reflection angle varies as a function of lateral position across the surface (7).

5. A desktop display device (100) according to any one of claims 1 to 4, c h a r a c t e r i z e d in that the optical system (3, 30, 32) comprises one or more pre-modifying lenses (30) arranged to face the image source (4), the image light from the image source (4) is incident on the one or more pre-modifying lenses (30).

6. A desktop display device (100) according to claim 5, c h a r a c t e r i z e d in that the one or more pre-modifying lenses (30) comprise a Fresnel lens and / or diffractive lens.

7. A desktop display device (100) according to claim 5, c h a r a c t e r i z e d in that the one or more pre-modifying lenses (30) comprise a plane-convex lens.

8. A desktop display device (100) according to any one of claims 1 to 7, c h a r a c t e r i z e d in that the optical system comprises a second reflector (32) having a second concavely structured reflective surface (33) configured reflect the image light emitted from the image source (4) or from the one or more premodifying lenses (30) to the first reflector (3).

9. A desktop display device (100) according to claim 8, c h a r a c t e r i z e d in that:- the second reflector (32) comprises a concave mirror surface (33) configured to provide the second concavely structured reflective surface (33); or - the second reflector (32) comprises a Fresnel reflector surface (33) configured such that a local reflection angle varies as a function of lateral position across the surface (33); or- the second reflector (32) comprises a diffractive reflector surface (33) configured such that a local reflection angle varies as a function of lateral position across the surface (33).

10. A desktop display device (100) according to claim 8 or 9, c h a r a c t e r i z e d in that the second concavely structured reflective surface(33) is configured as a second non-rotationally symmetric freeform reflective surface (33).

11. A desktop display device (100) according to any one of claims 1 to 10, cha ra cte r i z e d in that the image source (4) is arranged as an integral image source to the body (50) or the image source (4) is provided as a detachable image source to the body (50).

12. A desktop display device (100) according to any one of claims 1 to 11, cha ra cte r i z ed in that- the image source (4) is fixedly arranged to the body (50); or - the image source (4) is arranged adjustably to the body (50).

13. A desktop display device (100) according to any one of claims 1 to 12, cha ra cte r i z ed in that- the first reflector (3) is fixedly arranged to the body (50); or - the first reflector (3) is adjustably arranged to the body (50) - the first reflector (3) and the second reflector (32) are fixedly arranged to the body (50); or- the first reflector (3) and the second reflector (32) are arranged adjustably arranged to the body (50).

14. A desktop display device (100) according to claim 12 or 13, cha ra cte r i z e d in that the desktop display device (100) comprises adjustment system configured to adjust position of one or more of the following:- the image source (4),-the first reflector (3),- the second reflector (32), and- the one or more pre-modifying lenses (30).

15. A desktop display device (100) according to claim 12 or 13, cha ra cte r i z e d in that the adjustment system is arranged to adjust position such that the relative position of at least two of the following is not changed:- the image source (4),-the first reflector (3),- the second reflector (32), and- the one or more pre-modifying lenses (30).

16. A desktop display device (100) according to any one of claims 1 to 15, cha ra cte r i z e d in that the body (50) comprises a support element (59) arranged to support the display device (100) on a planar surface.

17. A desktop display device (100) according to any one of claims 1 to 16, cha ra cte r i z e d in that the first non-rotationally symmetric freeform reflective surface (7), or the second non-rotationally symmetric freeform reflective surface (33), or the first and second non-rotationally symmetric freeform reflective surfaces (7, 33) are configured comprise:- locally varying principal curvatures in two orthogonal directions; or - locally varying principal curvatures in two orthogonal directions and characterized by an offset (w) from a base plane with local coordinates (u, v) defined by a polynomial function of order N > 2, w = 2i,fcCtifeulvfe, 1 < i + k < N, where at least one coefficient c_(i, k), is non-zero.

18. A desktop display device (100) according to claim 17, cha ra cte r i z e d in that the first reflector (3) , or the second reflector (32), or the first and second reflectors (3, 32) are configured based on computer-based numerical optimization comprising ray-tracing method of the polynomial coefficients c_(i, k) to form the magnified virtual image.

19. A desktop display device (100) according to any one of claims 1 to 18, cha ra cte r i z ed in that the eyebox (5) is configured to have:- an eyebox dimension of at least 45 mm in at least one direction transversal to the viewing direction (A) of the folded optical path; or- an eyebox dimension of at least 65 mm in at least one direction transversal to the viewing direction (A) of the folded optical path.

20. A desktop display device (100) according to any one of claims 1 to 19, cha ra cte r i z ed in that:- the optical system (3, 30, 43) is configured generate the magnified virtual image at an optical infinity distance from the eyebox (5), the optical infinity distance being at least 5 m;- the optical system (3, 30, 43) is configured generate the magnified virtual image at an optical infinity distance from the eyebox (5), the optical infinitydistance being at least 6 m; or- the optical system (3, 30, 43) is configured generate the magnified virtual image at an optical infinity distance from the eyebox (5), the optical infinity distance being at least 10 m.

21. A desktop display device (100) according to any one of claims 1 to 20, cha ra cte r i z ed in that:- the magnified virtual image generated by the optical system (3, 30, 43) has angular size of at least 20 degrees; or- the magnified virtual image generated by the optical system (3, 30, 43) has angular size of at least 25 degrees.

22. A desktop display device (100) according to any one of claims 1 to 21, cha ra cte r i z ed in that:- the optical system (3, 30, 43) is configured provide resolving power of the image source (4) in the eyebox (5) at least 5 cycles / mm; or- the optical system (3, 30, 43) is configured provide resolving power of the image source (4) in the eyebox (5) at least 10 cycles / mm.

23. A desktop display device (100) according to any one of claims 1 to 21, cha ra cte r i z e d in that display device (100) comprises an auxiliary system configured to track the position of the user’s head and automatically adjust position or tilt of the of the display device position.

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