Optical waveguide with curved grin element

Abstract

The invention relates to an optical waveguide (20) for arrangement in a beam path (5) of an optical arrangement having a device (11) for out-coupling and / or in-coupling imaging the beam path. The optical waveguide (20) comprises a GRIN element having at least one curved surface (12, 13), the GRIN element having a refractive index profile designed to reduce aberrations in the imaging path of a virtual image caused by the curvature of the GRIN element, the virtual image being generated by means of light waves guided by total internal reflection in the optical waveguide (20).

Description

Technical Field

[0001] The invention relates to an optical waveguide for arrangement in a beam path of an optical arrangement, such as a head mounted display (HMD), a head up display (HUD), a near eye display or an imaging arrangement or an imaging device, such as smart glasses with gesture recognition or eye tracking. Furthermore, the invention relates to an optical arrangement, such as for one of the aforementioned applications, an image capture device and an image reproduction device. Background Art

[0002] Head-mounted displays, for example in the form of smart glasses, or AR (augmented reality) head-mounted devices, or VR (virtual reality) head-mounted devices, or MR (mixed reality) head-mounted devices, or VR or MR glasses, or VR or MR helmets, are used in many contexts. In such contexts, after the light waves for generating the virtual image have been input coupled into the optical waveguide, they are usually guided by means of total internal reflection until they are output coupled. When the user looks through the "augmented reality glasses" (or simply "AR glasses"), they see the input coupled or superimposed "virtual image" superimposed on their physical world image ("real image"). This superposition is achieved by means of a beam combiner, which is transparent to ambient light on the one hand, but on the other hand also deflects the light beam generated by the external picture generator to the eye or into the eye box. The eye perceives this light beam as a virtual image. In the context of the present invention, the corresponding imaging path is defined for the purpose of describing the beam path of the physical surrounding environment image and the beam path of the input coupled virtual image. In the present context, the imaging path is understood to refer to the path of light from an object (e.g., an object in the physical surroundings) or from an image generator / projector that emits a virtual image to be input-coupled to the location where the image represented by the image is produced or perceived (e.g., the user's eye or eye movement range).

[0003] The most common waveguide technology in AR headsets is based on planar waveguides or plane-parallel waveguides. However, in order to support attractive product designs, curved waveguides would be desirable. Refractive error correction is usually achieved with the help of the so-called push-pull lens concept (i.e., a combination of lenses with different refractive powers upstream and downstream of the waveguide). However, together with planar waveguides, this leads to a large overall system thickness and, therefore, a high overall weight of the optical unit.

[0004] An optical waveguide (light guide) is understood to mean a waveguide designed to guide or transmit light waves through the waveguide within its interior by means of total internal reflection at the waveguide surface. Light waves are understood to mean electromagnetic waves with a wavelength in the range between 300 nm (ultraviolet light) and 2 μm (infrared light), in particular in the visible range and in the near infrared range and near ultraviolet range.

[0005] DE 10 2016 105 060 B3 describes, for example, a curved lens for an imaging optical unit and a pair of smart glasses.

[0006] In the case of a head-mounted display, for example, in the case of an AR head-mounted device, the image generated by the picture generation unit or the display is input-coupled into the optical waveguide, reflected once or multiple times in the optical waveguide by means of total internal reflection, and finally output-coupled so that the user of the head-mounted display can see the virtual image. The spatial area in which the user can visually perceive the virtual image is also called the eye range. The two outer surfaces of the optical waveguide are usually implemented as parallel plane surfaces, so that neither optical refractive power nor aberrations that impair image quality are generated in the optical waveguide. In addition, a head-mounted display (e.g., an AR head-mounted device) may include an optical waveguide and one or more additional lenses for each eye (push-pull lens principle). This lens or these multiple additional lenses are used to correct the refractive error (refractive error) or presbyopia of the eye (pull lens) and / or to make the virtual image appear focused at the desired distance (pull lens) without damaging the image of the physical surrounding environment (push lens).

[0007] Lenses for glasses usually have a meniscus shape. If an optical waveguide is integrated as a plane parallel sheet into the lens of a pair of glasses intended for use as a head mounted display, the combination of the optical waveguide with the push-pull lens necessarily results in a thick, bulky and heavy system. Obviously, the total thickness of the lens for a pair of glasses consisting of a push lens, a planar optical waveguide and a pull lens increases with the curvature of the meniscus. However, in progressive addition lenses, a relatively strong curvature is required to correct significant refractive errors (abnormal refraction, e.g., greater than + / - 3 diopters) or presbyopia.

[0008] In general, and especially in the case of a large field of view (FOV), the use of curved waveguides results in significant astigmatic imaging errors in the virtual image, which cannot be compensated within the waveguide. Correction outside the waveguide is also not possible, since the viewing of objects in the environment through the glasses (the imaging path of the real image representation of the surrounding environment) cannot be affected. Summary of the invention

[0009] Against this background, the problem underlying the present invention is to provide an advantageous optical waveguide for arrangement in a beam path of an optical arrangement, an optical arrangement, an image capture device and an image reproduction device. This problem is solved by an optical waveguide as claimed in claim 1, an optical arrangement as claimed in claim 18, an image capture device as claimed in claim 22 and an image reproduction device as claimed in claim 23. The dependent claims contain further advantageous configurations of the invention.

[0010] An optical waveguide according to the invention for arrangement in a beam path of an optical arrangement, such as an image reproduction device and / or an image capture device, comprises means for out-coupling and / or in-coupling an imaging beam path, ie a light wave.

[0011] For example, the waveguide according to the invention may be a waveguide of a head mounted display. Specifically, the waveguide may be designed to generate a virtual image representation and simultaneously provide a view of the surrounding environment (i.e., generate a real image representation of the surrounding environment). Furthermore, it may be designed to be arranged between a picture generation unit and an eye movement scope of a head mounted display.

[0012] The optical waveguide according to the invention comprises a GRIN element. A GRIN element or a GRIN material is understood to mean a gradient index element or a gradient index material (GRIN) having a gradient refractive index profile or refractive index distribution. The GRIN element is designed to guide light waves by means of total internal reflection and is not a component of the device for incoupling and / or outcoupling an imaging beam path (i.e., light waves). In other words, it can be arranged as an integral component of the optical waveguide in the beam path between the incoupling device and the outcoupling device.

[0013] The GRIN element of the optical waveguide according to the present invention comprises at least one curved surface. The surface may be concavely curved or convexly curved. For example, the GRIN element may comprise a first surface that is concavely curved or convexly curved (e.g., having a radius of curvature R 1 = r') and a concavely or convexly curved second surface (e.g., a front side with a radius of curvature R2 = r). These surfaces can also be configured as free-form surfaces or aspheric surfaces. Aspheric surfaces are understood to mean rotationally symmetric optical surfaces whose radius of curvature varies radially with the distance from the center.

[0014] Furthermore, the GRIN elements have a refractive index profile designed to reduce aberrations caused by the curvature of the GRIN elements in the imaging path of a virtual image representation generated by means of light waves guided by total internal reflection in the optical waveguide. Thus, the refractive index profile is designed to at least partially correct, preferably fully correct, the aforementioned aberrations.

[0015] The virtual image aberrations to be corrected arise due to the curvature of the waveguide, since the reflections at the curved surfaces (total internal reflections at the surfaces of the optical waveguide) have optical power. The curved surfaces change the convergence of the light beam. Therefore, in the case of multiple reflections, the convergence changes with each reflection, whereby aberrations, in particular strong astigmatism, occur. Now, the refractive index profile of the GRIN material allows to correct these typical aberrations of a simply curved optical waveguide. In addition, the GRIN material provides an additional degree of freedom in order to reduce (e.g. completely or at least partially correct) the aberrations caused by the GRIN element in the real image of the surrounding environment, optionally also by means of the refractive index profile and optionally by means of an adapted design of the curvature of at least one surface, preferably two surfaces. At least one surface (e.g. the first surface and / or the second surface) can be specifically configured in a spherical, cylindrical, toric or aspherical manner or as a freeform surface.

[0016] Preferably, the GRIN elements consist of isotropic materials without birefringence.

[0017] Advantageously, the GRIN elements have a refractive index profile that is additionally designed to reduce (in particular at least partially or completely correct) aberrations introduced or caused by the GRIN elements in an imaging path of a real image representation of the surroundings (i.e. the physical or actual surroundings), which imaging path passes through the GRIN elements.

[0018] In other words, the GRIN elements are designed to reduce or correct imaging errors in the in-coupled virtual image (these imaging errors are typically produced in a simple curved optical waveguide without a GRIN refractive index profile) and optionally additionally compensate for aberrations related to real imaging of the actual surroundings (looking through the waveguide in the direction of the surroundings). The aberrations introduced by the GRIN elements in the imaging path of the real image representation of the surroundings may be aberrations introduced by the curvature of the GRIN elements and / or by the refractive index profile designed to reduce aberrations induced in the imaging path of the virtual image representation.

[0019] The optical waveguide according to the invention is advantageous in that, due to its curved embodiment, it can be adapted to the meniscus shape of a lens of the spectacles, in particular to the meniscus shape of at least one of the lenses described in the opening paragraph. For example, significant astigmatic errors in the virtual image can be reduced or corrected by the GRIN element without affecting the view of objects in the environment through the optical waveguide. The invention enables a compact and lightweight arrangement with reduced system thickness (see Figure 1 ). This is advantageous, in particular from an aesthetic point of view. Compared to planar parallel light waveguides, significantly more attractive eyewear designs can be achieved. In addition, a large aberration-free field of view (FOV) can be achieved for the imaging path of the virtual image.

[0020] The concept underlying and part of the present invention consists of applying the basic principles of transformation optics to the present situation (see, for example [Pendry, Schurig, Smith, Science, Vol. 312, p. 1780 (2006)]). Transformation optics is distinguished by the ability to "bend" or steer light or electromagnetic waves in any desired way for a particular application. This is achieved by tailoring the medium in which the electromagnetic waves propagate. The desired properties of the medium are derived by mathematical transformations. What is unique here is that the form of Maxwell's equations remains unchanged even though there is a coordinate transformation. Instead, there is a "transformation" or change in the spatial distribution of the material parameters ε (permittivity, dielectric constant) and μ (magnetic permeability). The transformation properties have been described by different authors, inter alia, in [AJ Ward, JB Pendry, Journal of Modem Optics, 43 773-793 (1996)], [DM Hyroki http: / / arxiv.org / abs / physics / 0307029v1 (2003)], [Leonhardt Ulf; Philbin, Thomas G.: Transformation Optics and me Geometry of Light, Progress in Optics, Vol. 53, pp. 69-152].

[0021] The basic steps of the transformation are outlined below. In the first step a coordinate transformation is performed:

[0022] q 1 (x,y,z)q 2 (x,y,z)q 3 (x, y, z)

[0023] In a second step, Maxwell's equations are expressed in a new coordinate system, wherein the form of Maxwell's equations remains unchanged.

[0024]

[0025] In the third step, new values ​​of ε and μ are calculated

[0026]

[0027] In the formula

[0028]

[0029] Maxwell's equations can thus be transformed into new geometries or coordinate systems, which are particularly advantageous for the description of specific applications. ε and μ must be modified in the process.

[0030] If a planar optical waveguide is subjected to a suitable transformation, it can be converted into any desired shape, in particular into a spherically curved optical waveguide. Conversion into a waveguide that is, for example, cylindrical, toric, aspherical or designed as a free-form waveguide is also possible. These refractive index profiles or refractive index distributions (represented by ε and μ) should be adapted according to the transformation. As a result, the optical wavefield propagating through the transformed waveguide remains aberration-free, just as in the case of a planar optical waveguide. This derivation is described in detail within the scope of the first embodiment variant and the second embodiment variant. In an advantageous variant, in particular for an optical waveguide of cylindrical or spherical shape, the refractive index and therefore its profile depends on the ratio r′ / r, i.e. it can be expressed as, for example, a function n(r)=f(r′ / r), where r′ is a specified or defined radius of curvature of one of the at least one curved surfaces of the GRIN element.

[0031] The refractive index distribution of the GRIN element can have a radially symmetrical and / or cylindrical or cylindrically symmetrical and / or toric refractive index distribution, and / or a refractive index distribution with at least one constant refractive index area, wherein the at least one area is configured in a cylindrical or toric or spherical or aspherical manner or is configured as a freeform surface. The at least one constant refractive index area can coincide with or extend parallel to at least one curved surface of the GRIN element. From a manufacturing point of view, this variant has advantages. In order to affect the quality of viewing the physical surroundings through the optical waveguide as little as possible, the refractive index distribution of the GRIN element advantageously has a radially symmetrical configuration (n=n(r)) in the case of a curved waveguide. The origin of the coordinate system is at the center of rotation of the eye or at the center of the eye range, or on a straight line interconnecting the center of rotation of the eye with the center of the eye range.

[0032] If R 1 = r′ and R 2 = r are the inner and outer radii of the spherically curved waveguide respectively, then simply consider the concentric radius R 1 and R 2 The optical path length of a spherical surface (generally of radius r) must be constant, resulting in the following relationship for the refractive index profile: 2 =n 1 *R 1 / R 2 , or usually in optical waveguides, n(r) = n 1 *r′ / r. Let R 1 = r′, then this corresponds exactly to the extraordinary refractive index n of the planar optical waveguide transformed into polar coordinates ao (see the second exemplary embodiment below). Therefore, in an advantageous variant, n(r)=n 1*r′ / r applies to the refractive index profile n(r) of the GRIN element in the radial direction, where r′ is the radius of curvature of the first surface, r is the radius (i.e., the distance from the origin of the coordinate system defining the radius of curvature of the first surface r′), and n 1 is the refractive index of the GRIN element material at the first surface.

[0033] The radius of curvature R of the first surface 1 =r′ and / or the radius of curvature R2=r of the second surface can be at least 50 mm, for example, between 50 mm and 1000 mm, in particular between 70 mm and 130 mm. If the first surface and / or the second surface is configured as a free-form surface or an aspherical surface, the radius of curvature should be understood as a best fit radius. One of these surfaces can also have a planar configuration. In the direction of the optical axis of the imaging path represented by the real image of the surrounding environment or in the direction of the main light ray or in the radial direction, the maximum thickness of the GRIN element can be at least 0.1 mm and / or at most 10 mm, in particular between 0.1 mm and 10 mm, preferably between 0.5 mm and 3 mm, for example, between 1 mm and 2 mm. In the context of head-mounted displays, the aforementioned dimensions are particularly advantageous in the context of applications in combination with lenses for correcting refractive errors, because these dimensions enable a compact optical arrangement.

[0034] In another variant, the refractive index variation Δn in the GRIN element is between 0.005 and 0.20. In particular, the refractive index variation Δn in the GRIN element may be between 0.01 and 0.15, especially in the radial direction (radial refractive index difference). In the direction x, the gradient δn / dx of the refractive index n may be, for example, between 0 mm -1 With 0.02mm -1 Preferably, in the direction x perpendicular to the principal ray direction of the imaging path represented by the real image of the surrounding environment, or in the direction x parallel to the principal ray direction of the imaging path represented by the real image of the surrounding environment, or in the radial direction x, or in the direction x perpendicular to the optical axis, or in the direction x parallel to the optical axis, the gradient δn / dx of the refractive index n is between 0 mm and 1 mm. -1 With 0.02mm -1 For a typical radius of the order of 100 mm for an eyeglass lens and a thickness of about 1 mm, this results in a radial refractive index difference in the lens of the order of Δn ˜0.01 and δn / dx ˜0.01 mm. -1 These are refractive index gradients that can be easily manufactured using current technology.

[0035] The first surface and / or the second surface can be implemented as a complex surface or a spherical surface or an aspherical surface or a cylindrical surface or a cylindrical symmetric manner or as a free-form surface. Thereby, the quality of the optical waveguide for projection imaging of the virtual image and the perspective application (real image representation of the surrounding environment) can be optimized simultaneously. If at least one push lens and / or pull lens is used, it is included in the optimization of the perspective imaging (real image representation of the surrounding environment) and / or the virtual image representation. The push lens and the pull lens can be configured as separate elements attached or otherwise connected to the optical waveguide, in particular the GRIN element, via an air gap or via an aerogel or liquid (embedded GRIN waveguide), and they themselves can have an uneven refractive index distribution (refractive index profile) and / or a free-form surface. The connection between the push lens and / or the pull lens and the optical waveguide can be achieved by molding, adhesive bonding or bonding. In an alternative, the lens can also be printed on the optical waveguide by means of 3D printing. The lens and the optical waveguide can also be manufactured in one piece, for example, by means of 3D printing.

[0036] In another advantageous variant, the GRIN element is designed to introduce a refractive power that is not equal to zero (e.g. a positive refractive power and / or a negative refractive power) into the imaging path of the real image and / or the virtual image. In other words, it is designed to manipulate the beam path or the wavefront like a refractive lens or in a manner similar to a refractive lens. Thus, the GRIN element can act like a pull lens and / or a push lens. Thus, it can be designed to correct refractive errors, in particular spherical and / or astigmatism, and / or to focus the virtual image representation. This is advantageous in that it can be managed without at least one of the aforementioned lenses for correcting refractive errors and / or for focusing the virtual image representation, and the system thickness can therefore be reduced. In this variant, the effect of the push lens and / or the pull lens is taken over by the GRIN element.

[0037] According to the present invention, a curved waveguide, in particular a waveguide that matches the meniscus shape of a lens for glasses, can be designed so that it acts like an optically flat waveguide by means of using a suitably designed gradient refractive index (GRIN) material instead of a homogeneous material. Due to the GRIN material, a suitable design allows aberrations (e.g., astigmatism) due to the curved surfaces in the waveguide to be partially or completely compensated, and thus the quality of the virtual image is acceptable to the user of a head-mounted display (e.g., an AR headset). Aberrations due to the GRIN elements of the optical waveguide in the imaging path of the real image representation of the surrounding environment (i.e., in the perspective case) can be compensated by at least one additional curved GRIN element or by pushing and pulling the lens. In another embodiment, the GRIN elements in the curved optical waveguide are designed so that the aberrations that appear in the imaging path of the real image representation of the surrounding environment are small (astigmatism < 0.15 dpt) and do not need to be compensated.

[0038] In general, it may be advantageous to allow for arbitrary refractive index profiles n=n(x, y, z) in the GRIN elements of the optical waveguide, e.g. in case of non-concentric radii of curvature of the surfaces, in order to minimize as many or all aberrations as possible of the outcoupled virtual image representation due to deviations from an ideal, generally anisotropic refractive index profile, except for astigmatism. In principle, the refractive index within the GRIN element may thus vary in three dimensions defining a coordinate system or a reference system, i.e. have a gradient in all three dimensions. In a preferred variant, the refractive index within the GRIN element varies in at least a first and a second dimension defining a coordinate system or a reference system, i.e. have a gradient in these dimensions. The refractive index may be constant (i.e. have no gradient) along a third dimension defining a coordinate system, wherein the third dimension forms an inclination angle with the direction of the main ray of the imaging path of the real image representation of the surroundings or the direction of the optical axis. Preferably, the absolute value of the inclination angle is greater than 2 degrees. For example, the absolute value of the inclination angle may be between 5 and 20 degrees. This configuration enables the production of the optical waveguide to be simplified, wherein its cost is reduced.

[0039] The optical arrangement according to the invention comprises at least one optical element having at least one curved surface. The at least one optical element can be implemented as a lens, for example, a meniscus shape or a plano-concave or plano-convex lens. For example, the lens can be implemented as a lens for glasses in order to correct refractive errors (especially refractive errors and / or presbyopia) and / or focus a virtual image representation. The at least one optical element can also be implemented as a different optical element, for example, a Fresnel lens, a diffractive or holographic optical element, or a GRIN lens, etc. The optical arrangement according to the invention comprises at least one optical waveguide according to the invention as described above.

[0040] At least one optical element and an optical waveguide are arranged continuously in the beam path of the imaging path of the real image representation and / or the virtual image representation. In the beam path of the imaging path of the real image representation and / or the virtual image representation, at least one optical element can be arranged upstream or downstream of the optical waveguide, in particular upstream or downstream of the GRIN element. Specifically, at least one optical element and an optical waveguide can be arranged continuously in the direction of the defined main light direction or optical axis of the imaging path of the real image representation of the surrounding environment through the at least one optical element and through the optical waveguide. Therefore, the optical waveguide, in particular the GRIN element, can be arranged upstream or downstream of at least one optical element in the beam path of the imaging path of the real image representation and / or the virtual image representation. For example, the GRIN element of the optical waveguide can be geometrically arranged between the eye range or the eye of the observer and the virtual image plane. Geometrically, at least one optical element can be arranged between the GRIN element of the optical waveguide and the eye range or the eye of the observer.

[0041] The optical arrangement may be designed for a head-mounted display (HMD) (which may be, for example, an AR headset or a VR headset, or a MR headset, or a pair of AR or VR or MR glasses, or an AR or VR or MR helmet, or a pair of smart glasses), or for a heads-up display (HUD), for a near-eye display, or for an imaging arrangement or imaging device (e.g., smart glasses with gesture recognition or eye tracking).

[0042] The optical arrangement according to the invention has the features and advantages already mentioned above in connection with the optical waveguide according to the invention. The optical element may be configured as a refractive lens (e.g., a lens for spectacles) and / or designed to correct ametropia (e.g., myopia and / or hyperopia and / or astigmatism and / or presbyopia, etc.) and / or to focus a virtual image representation. In this case, the optical element may be designed to correct ametropia in the imaging path of a real image representation of the surroundings and / or to correct ametropia in the imaging path of a virtual image representation and / or to focus a virtual image representation in the imaging path of a virtual image representation. In particular, the optical element may have a spherical or aspherical embodiment or an embodiment as a free-form lens. For example, the optical arrangement according to the invention may comprise at least one push lens and / or at least one pull lens. The pull lens causes the virtual image to appear at a desired distance in front of the eye of the observer and optionally corrects the wearer's ametropia for the virtual image. Depending on the refractive error, it may be convergent or divergent. The push lens ensures that the image of the physical surroundings is corrected for the observer (e.g., the wearer of spectacles). Since the observer or wearer always perceives the surroundings through the system consisting of the optical waveguide, the push lens and the pull lens, the combination of these elements must be adapted to the respective observer or wearer.

[0043] The optical waveguide is preferably configured such that the curvature of at least one of the surfaces of the GRIN element (e.g., the curvature of the first surface and / or the curvature of the second surface) matches the curvature of at least one curved surface of the at least one optical element. For example, the curvature of the GRIN element may match the meniscus shape of a lens for glasses. The GRIN element may be placed directly against the optical element by the curvature of the GRIN element. In particular, the GRIN element and the optical element may have the same curvature over more than at least 50%, such as more than at least 80%, preferably 100%, of the surfaces facing each other when in contact.

[0044] At least one optical element can be configured as a separate element or as an element connected to the optical waveguide in a fixed or detachable manner or by means of a fixed spacer. The optical element can then have an inhomogeneous refractive index distribution and / or a free-form surface. In another variant, the optical arrangement according to the invention can include at least one additional GRIN element for reducing (e.g., compensating for) the aberrations introduced by the GRIN element along the imaging path represented by the real image of the surrounding environment. The additional GRIN element can be a separate component or element. However, it can also be a component of at least one optical element having at least one curved surface.

[0045] An image reproduction device according to the invention comprises at least one optical waveguide according to the invention or an optical arrangement according to the invention as described above. An image capture device according to the invention comprises at least one optical waveguide according to the invention. The image capture device may be an imaging arrangement or an imaging device (e.g. smart glasses with gesture recognition or eye tracking). An image reproduction device according to the invention and an image capture device according to the invention have the aforementioned features and advantages. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The present invention is explained in more detail below with reference to the accompanying drawings based on exemplary embodiments. Although the present invention has been more specifically described and illustrated with the aid of preferred exemplary embodiments, the present invention is not limited to the disclosed examples, and other variants can be derived from the present invention by those skilled in the art without departing from the scope of protection of the present invention.

[0047] These figures are not necessarily accurate and drawn to scale in every detail, and may be presented in an exaggerated or reduced form for the sake of clarity. Therefore, the functional details disclosed herein should not be understood as limiting, but merely as an illustrative basis to provide guidance for those skilled in the art to use the present invention in various ways.

[0048] When used in a series of two or more elements, the expression "and / or" as used herein means that any of the listed elements may be used alone, or any combination of two or more of the listed elements may be used. For example, if a composition is described as comprising components A, B, and / or C, the composition may comprise: A alone; B alone; C alone; A and B together; A and C together; B and C together; or A, B, and C together.

[0049] Figure 1 Variants of lens arrangements for AR headsets are schematically shown.

[0050] Figure 2 The beam path through the plane-parallel waveguide is schematically shown.

[0051] Figure 3 The path of a beam through a curved waveguide is schematically shown.

[0052] Figure 4 The schematic diagram shows the different viewing angles. Figure 3 Lateral deviations occurring in the waveguide are shown.

[0053] Figure 5 An optical waveguide according to the invention is schematically shown in cross section according to a first embodiment variant and a second embodiment variant.

[0054] Figure 6 According to a third embodiment variant, a beam path through an optical waveguide according to the invention and a refractive index distribution in a GRIN element of the optical waveguide are shown.

[0055] Figure 7 The lateral deviations are shown for different viewing angles for a third embodiment variant.

[0056] Figure 8 According to a fourth embodiment variant, a beam path through an optical waveguide according to the invention and a refractive index distribution in a GRIN element of the optical waveguide are shown.

[0057] Fig. 9 The lateral deviations are shown for different viewing angles for a fourth embodiment variant.

[0058] Fig.10 According to a fifth embodiment variant, a beam path through an optical waveguide according to the invention and a refractive index distribution in a GRIN element of the optical waveguide are shown.

[0059] Fig.11 The lateral deviations are shown for different viewing angles for a fifth embodiment variant.

[0060] Fig.12 According to a sixth embodiment variant, a beam path through an optical waveguide according to the invention and a refractive index distribution in a GRIN element of the optical waveguide are shown.

[0061] Fig.13 The lateral deviations for different viewing angles are shown for a sixth embodiment variant.

[0062] Fig.14 According to a seventh embodiment variant, a beam path through an optical waveguide according to the invention and a refractive index distribution in a GRIN element of the optical waveguide are shown.

[0063] Fig.15 The lateral deviations are shown for different viewing angles for a seventh embodiment variant.

[0064] Fig.16The spherical refractive power of the optical waveguide of the seventh embodiment variant in the imaging path of a real image representation of the surroundings is shown.

[0065] Fig.17 The astigmatism of the optical waveguide of the seventh embodiment variant in the imaging path of the real image representation of the surroundings is shown.

[0066] Fig.18 According to an eighth embodiment variant, a beam path through an optical waveguide according to the invention and a refractive index distribution in a GRIN element of the optical waveguide are shown.

[0067] Fig.19 The lateral deviations for different viewing angles are shown for an eighth embodiment variant.

[0068] Fig. 20 The spherical refractive power of the optical waveguide of the eighth embodiment variant in the imaging path of a real image representation of the surroundings is shown.

[0069] Fig.21 The astigmatism of the optical waveguide of the eighth embodiment variant in the imaging path of the real image representation of the surroundings is shown.

[0070] Fig. 22 An image reproduction device according to the invention is schematically shown.

[0071] Fig.23 An image capturing device according to the invention is schematically shown. DETAILED DESCRIPTION

[0072] First, based on Figures 1 to 4 The starting point of the present invention is explained.

[0073] Figure 1 Variants of the lens arrangement 1 of an AR head-mounted device are schematically shown. Here, (a) and (b) show exemplary embodiments of a positive meniscus lens 3 for glasses for correcting hyperopia and a negative meniscus lens 4 for glasses for correcting myopia, and (c) and (d) show two exemplary embodiments of a push-pull lens combination 3, 4, which includes a planar light waveguide 2 for a wearer of a hyperopic head-mounted device. Variant (c) fully corrects the refractive error (spherical and cylindrical) in the viewing direction by means of the two meniscus lenses 3, 4, but has a very large system volume. In contrast, variant (d) implements the push lens 3 and the pull lens 4 as plano-convex lenses and plano-concave lenses, respectively, which makes the system volume more compact, but cannot correct the refractive error well enough. Embodiment variant (e) shows a curved light waveguide 20 according to the present invention, which has a first radius R 1= r' and the second radius R2 = r. The inner faces of the push lens 3 and the pull lens 4 have the same radius as the adjacent light waveguide face. This design enables the most compact system volume and complete refractive error correction. To illustrate the system volume, the system thickness is marked with an arrow in the reference numeral 9 and the system volume is marked with an arrow in the reference numeral 19.

[0074] The aperture or eye relief, i.e. the location from which the virtual image representation generated by means of the waveguide 2, 20 is visually perceptible, is marked with reference numeral 6. An optical axis 7 of the imaging path of the real image representation of the surroundings is defined starting from the eye relief 6; this optical axis simultaneously defines the viewing direction through the lens arrangement 1. The central axis of the lens arrangement 1 is marked with reference numeral 8 and coincides with the optical axis 7 in the example shown.

[0075] Figure 2 Schematically shown is a beam path 5 through a plane-parallel optical waveguide 2 having a planar face 14. The optical waveguide 2 comprises an input coupling means 10 in the form of an input coupling face. Furthermore, the optical waveguide comprises an output coupling means 11 which outcouples light waves from the optical waveguide 2 in the direction of the eye field.

[0076] Figure 3 The beam path 5 through the bent optical waveguide 2 is schematically shown. The collimated light is coupled into Figure 2 and Figure 3 The light is reflected at the plane 14 and then passes through the optical waveguide 2. Figure 2 In contrast, in Figure 3 In the case of the bent optical waveguide 2, the outcoupled light is no longer collimated and has strong astigmatism. Figure 4 The schematic diagram shows the different viewing angles. Figure 3 The lateral deviations shown occur in the optical waveguide 2. The reference circle shown has a diameter of 60 arc minutes.

[0077] Various embodiment variants of the optical waveguide according to the invention are explained below.

[0078] Figure 5 A portion or a partial region of an optical waveguide 20 according to the invention is schematically shown in cross section according to a first embodiment variant and a second embodiment variant. The optical waveguide 20 comprises a first surface 12 with a radius of curvature r and a second surface 13 with a radius of curvature r'. The first surface 12 and the second surface 13 are designed concentrically.

[0079] Within the scope of the first embodiment variant, the optical waveguide 20 is shaped as a cylinder and the first surface 12 and the second surface 13 form concentric partial cylindrical barrel surfaces.

[0080] To transform the Cartesian coordinates (x', y', z') into cylindrical coordinates, the radius r' based on the Cartesian coordinates is

[0081]

[0082] Transformed into the radius r in cylindrical coordinates, r = r (r'), where the angle Φ and the coordinate z (z = z') remain unchanged (see formula (5.5) in [Leonhardt Ulf; Philbin, Thomas G.: Transformation Optics and the Geometry of Light, Progress in Optics, Vol. 53, pp. 69-152]).

[0083] If a transformation from Cartesian coordinates to cylindrical coordinates is applied, the following formula results for the dielectric tensor ε in Cartesian coordinates [Leonhardt Ulf; Philbin, Thomas G.: Transformation Optics and the Geometry of Light, Progress in Optics, Vol. 53, pp. 69-152]:

[0084]

[0085] The eigenvalues ​​of the tensor are

[0086]

[0087] And therefore, the dielectric tensor in diagonal form is:

[0088]

[0089] in

[0090]

[0091] A corresponding derivation can also be performed for the magnetic permeability tensor μ.

[0092] Within the scope of the second embodiment variant, the optical waveguide 20 is shaped as a sphere, and the first surface 12 and the second surface 13 form concentric spherical partial surfaces.

[0093] In a manner similar to the first embodiment variant, the dielectric tensor in diagonal form yields the following formula for the transformation from Cartesian coordinates to polar coordinates:

[0094]

[0095] in

[0096] R = dr / dr′.

[0097] Typically, ε and μ are 2nd order tensors, and thus transformed materials typically behave like optical uniaxial or biaxial crystals. That is, they exhibit anisotropic properties even in the case of isotropic initial materials. If the anisotropic refractive index profile follows the specifications given by transformation optics, the optical wavefield remains aberration-free during propagation through the waveguide. If there is no wavefield compression along the radial direction, e.g. as in the case of cloaking applications, then R = dr / dr' = 1. In the case of further consideration of the transformation to polar coordinates, in this case the dielectric tensor reduces to

[0098] εΓ=diag(r' 2 / r 2 , 1, 1)

[0099] If the initial material is assumed to have a dielectric constant ε and a magnetic permeability μ, and if μ=1 is also chosen, then the planar waveguide transformed into a sphere behaves like an optical uniaxial crystal with an ordinary refractive index given by:

[0100]

[0101] And the extraordinary refractive index is given by:

[0102]

[0103] It has been found that |n o -n ao |<<1 is suitable for typical applications and an anisotropic material without birefringence can therefore be assumed to be a good approximation. In practical applications, it is advantageous to use isotropic materials for manufacturing reasons.

[0104] In a similar manner to polar coordinates, the ordinary refractive index can be derived:

[0105]

[0106] And the extraordinary refractive index:

[0107]

[0108] For cylindrical coordinates with R=1.

[0109] In all embodiment variants, the GRIN elements can in principle be produced by arranging films with a suitable refractive index on one another.In embodiment variants, the GRIN elements have a toric or spherical geometry.

[0110] based on Figure 6 and Figure 7 A third variation is described. Figure 6 The top of the figure defines two Cartesian coordinate systems (x, y, z) and (x′, y′, z′), which are arranged to be inclined to each other by an angle α around the x-axis or the x′ axis corresponding to the x-axis. In this case, the z-direction defines the direction of the main ray of the imaging path of the real image representation of the surrounding environment or the direction of the optical axis (perspective direction). In the following figures (especially in Figure 6 , Figure 8 and Fig.10 The specifications in the embodiment variants also correspond to these coordinate systems.

[0111] also, Figure 6 The beam path through the optical waveguide 20 according to the invention is shown in cross section in the yz plane, as well as the refractive index profile in the GRIN element of the optical waveguide in the x'y' plane. The optical waveguide 20 shown has a thickness 22 of 2 mm in the z direction and a length 23 of 22 mm in the y direction. The optical waveguide 20 is configured in a meniscus-shaped manner, wherein the radius of curvature R of the meniscus is 1 = r′ and R 2 = r is 125 mm. The centers of curvature are located on the z-axis and are offset by 2 mm relative to each other. Therefore, in this exemplary embodiment, the outer faces of the GRIN elements are not concentric. The considered field angle range is 10°×10°. In the example shown, the optical waveguide 20 includes a GRIN element composed of a GRIN material.

[0112] The refractive index distribution along the x′y′ plane in the GRIN element is shown in Figure 6 In this case, the refractive index preferably varies continuously, but it can also be reproduced by individual layers or regions with a constant refractive index, as in Figure 6 The bottom of the embodiment of the invention is shown in the corresponding figures of the further embodiment variants. In the figures, the refractive index of the individual regions is indicated between brackets by way of example.

[0113] The maximum refractive index difference within the GRIN element is 0.10 (Δn=0.10). The refractive index profile is configured so that it varies in the x′y′ plane (e.g. Figure 6 ) and is constant in the third dimension (along the z' axis) at an inclination angle of α = -5 degrees with the z axis at the top of the figure. The GRIN element causes the light waves outcoupled from the waveguide 20 to form a collimated beam path. Therefore, the astigmatism in the virtual image originally caused by the curvature of the optical waveguide 20 is compensated by the gradient refractive index profile within the GRIN element.

[0114] Figure 6The waveguide in the image plane images an object in the object plane (infinity) onto the image plane (infinity). The rays emitted from a single object point form parallel beams, i.e., when all rays are coupled in at the coupling-in plane, they are parallel. Therefore, Figure 6 Each beam in the image appears at a different object point in the object plane. The angle between the incident beam and the optical axis is called the field angle.

[0115] After total internal reflection at the outer face of the waveguide, the light beams are coupled out at different angles (viewing angles) at the output coupling face. In the case of aberration-free imaging, all light rays in the individual output coupled light beams are again exactly parallel to each other. However, since the refractive index profile in this embodiment variant does not exactly satisfy the equations of transformation optics, aberrations, in particular astigmatism, occur. As a result, the light rays in the light beam are no longer parallel, but exhibit various directional deviations (lateral deviations). The amplitude of these lateral deviations is therefore a measure of the size of the aberrations in the imaging path represented by the virtual image.

[0116] For this embodiment variant, Figure 7 The pupil plane (x F y F The lateral deviation in the y plane for different field angles. The diameter of the reference circle shown is 2 arc minutes. XAN marks the y plane around the pupil plane. F The YAN represents the field angle in the case of rotation around the pupil plane. F Field angle in the case of axis rotation, in each case in degrees.

[0117] Thus, the lateral deviation shown in the center of the lower row relates to a field angle XAN of 0° and a field angle YAN of 0°, and the lateral deviation shown on the left thereof occurs in the case of a field angle YAN of -5° and a field angle XAN of 0°. The lateral deviation for a field angle YAN of 5° and a field angle XAN of 0° is shown on the right side at the bottom. Since the gradient refractive index profile in the GRIN element is formed in a mirror-symmetrical manner with respect to the y′z′ plane, as shown in FIG. Figure 6 As shown, for a field angle of -5° the lateral deviation of XAN corresponds to Figure 7 The lateral deviation of the XAN at a field angle of 5° is shown at the top. Figure 4 Thus, in this embodiment variant, the refractive index profile of the GRIN elements results in aberrations in the imaging path represented by the virtual image due to the reduced curvature of the GRIN elements.

[0118] Figure 8 A fourth embodiment variant is shown. Fig. 9 The associated lateral deviation is shown in FIG. The fourth embodiment variant differs from the third embodiment variant in that the radius of curvature R of the meniscus is 1= r′ and R 2 =r is 200 mm, and the tilt of the GRIN medium (i.e. the tilt of the 3rd dimension (z′ axis) in which the refractive index is constant) α=-15.6°. Therefore, the 3rd dimension forms an angle of -15.6° with the z-axis or the main ray direction or the optical axis direction (perspective direction) of the imaging path represented by the real image of the surrounding environment. The field angle range, the thickness 22 in the z-direction and the width 23 in the y-direction of the GRIN element correspond to those of the first embodiment variant. The refractive index distribution with the minimum aberration in the calculated virtual image again has the maximum refractive index difference Δn within the GRIN material: Δn=0.10. When compared with the third embodiment variant, Figure 8 The refractive index profile at the bottom has a significantly stronger variation in the x′ direction. Fig. 9 As is evident in , a stronger tilt in the 3rd dimension leads to a significant reduction of lateral aberrations. Thus, in this embodiment variant, the refractive index profile of the GRIN elements leads to aberrations in the imaging path represented by the virtual image due to an even further reduction of the curvature of the GRIN elements.

[0119] Based on the following Fig.10 and Fig.11 In the third embodiment variant, the optical waveguide 20 has a meniscus with a curvature radius R 1 =R 2 The field angle range considered is 22.5°×10°. The GRIN element has a thickness 22 of 1.2 mm and a width 23 of 10 mm. The maximum refractive index difference of the GRIN material is 0.12 (Δn=0.12). The third dimension (z′ axis) with a constant refractive index forms an angle α=14° with the z axis when rotated about the x axis. The refractive index distribution in the x′y′ plane is shown in Fig.10 bottom. Fig.11 The lateral deviations that occur in this embodiment variant for a field angle YAN of -5° to 5° and for a field angle XAN of 0° to 11.25° are shown. The diameter of the reference circle shown is 2 arc minutes. Compared to the previous embodiment variants, the lateral deviations of this embodiment variant are sufficiently small even at a field angle XAN of more than 5°.

[0120] Based on the following Fig.12 and Fig.13 The sixth embodiment variant is explained in detail. In this embodiment variant, the radius of curvature of the meniscus of the GRIN element is 150 mm. The field angle range is 5°×5°. The GRIN element shown has a thickness of 1.0 mm and a width of 15 mm.

[0121] Fig.12The bottom left shows the refractive index profile in the xz plane in cross-section. Here, the refractive index in the y direction is constant. This means that the refractive index profile is not aligned with the outer faces (ie, the first and second surfaces). Fig.12 The bottom right diagram of shows the position of the second surface (ie, Fig.12 1 . The refractive index profile on the front side 13 of the optical waveguide 20 shown. The position along the surface is plotted on the x-axis of the diagram. The corresponding refractive index is plotted on the y-axis of the diagram. The refractive index decreases with increasing y-values, i.e., starting from the incoupling face 10 along the surface 13.

[0122] Fig.13 The lateral deviation of a sixth embodiment variant is schematically shown in . As in the previous embodiment variants, the diameter of the reference circle shown is 2 arc minutes.

[0123] Based on the following Figures 14 to 17 To explain the seventh embodiment variant. In this variant, the astigmatism in the virtual image is corrected for a field angle of 5°×5°. In the area of ​​the GRIN element, the waveguide 20 has a thickness of 1 mm and a length of 18 mm. In this embodiment variant, the radius of curvature of the concave surface 12 of the meniscus of the GRIN element of the optical waveguide 20 is 150 mm. The second surface (i.e., the convex surface 13 of the meniscus) is designed as a toroidal surface. The radius of curvature Rz of the second surface 13 in the image plane (the radius in the case of rotation around the x-axis) is 150.0 mm. The radius of curvature Rx perpendicular to the image plane (the radius in the case of rotation around the y-axis) is 134.5 mm.

[0124] In this embodiment variant, the astigmatism is corrected not only for the virtual image but also for the imaging path of the image representation of the physical surroundings (as seen through the waveguide). In this case, a toric design of the second surface is necessary in order to compensate for the astigmatism that occurs in the perspective direction due to the design of the waveguide as a GRIN element.

[0125] The maximum refractive index difference in the GRIN material is 0.02 (Δn=0.02), where the refractive index takes values ​​of 1.50 to 1.52. In this example, the refractive index profile is aligned with the convex outer face (i.e., the second surface 13). That is, the refractive index is constant on the convex outer face, but the refractive index increases in the interior of the optical waveguide as the distance from the convex outer face increases. From a manufacturing point of view, this is advantageous because films with corresponding refractive indices can be arranged on each other. Fig.14The bottom shows the refractive index distribution for various cross-sectional planes. In this case, the simplified diagram shown on the middle left shows the distribution in a cross section in the xz plane, the diagram shown on the middle right shows a cross section in the yz plane, and the diagram shown on the bottom shows a cross section in the xy plane. Fig.15 The lateral deviation is shown for this embodiment variant.

[0126] Fig.16 The optical waveguide 20 for the seventh embodiment variant shows the spherical refractive power (in diopters) in the imaging path of a real image representation of the surroundings (perspective direction) in xy representation. The scale on the right marks the refractive power in diopters. The dimensions in mm are plotted on the x-axis and y-axis. In this case, the refractive power has a value of 0.385 diopters + / - 0.015 diopters. The optical waveguide according to the invention thus influences the spherical refractive power with a constant absolute value, which can be obtained by a push-pull concept. Fig.17 2 shows the perspective astigmatism in diopters in a simplified diagram. The scale on the right marks the astigmatism in diopters. The perspective astigmatism through the optical waveguide 20 of the seventh embodiment variant is less than 0.05 diopters (dpt) in the marking area 24. Therefore, no compensation is required.

[0127] exist Fig.16 and Fig.17 In FIG. 2 , the marking area 24 has a size of approximately 40 mm×20 mm. The refractive index profile of the optical waveguide and the convex outer face are matched to each other so that when looking through the optical waveguide, the astigmatism is less than 0.05 dpt and thus objects in the environment are images with almost no aberration. The spherical refractive power of the optical waveguide is almost constant over the entire area and can therefore be obtained (i.e. utilized), for example, in the case of a push-pull concept.

[0128] Based on the following Figures 18 to 21 To explain the eighth embodiment variant. In this variant, the first surface and the second surface each have a meniscus shape with a different radius of curvature. The first surface (i.e., the concave surface facing the eye) has a spherical design with a radius of curvature of 200 mm. The second surface (i.e., the convex surface of the meniscus) has a toroidal design with a radius of curvature Rz of 140 mm and a radius of curvature Rx of 133.6 mm. In this variant, the field angle range is 40°×10°. The maximum refractive index difference in the GRIN material is 0.01 (Δn=0.01), where the refractive index takes a value of 1.51 to 1.52. The refractive index distribution is aligned with at least one of these external surfaces (i.e., with the first surface and / or the second surface). The GRIN element has a thickness 22 of 1.2 mm and a width 23 of 12 mm. Fig.18In FIG. 1 , the refractive index distribution is shown in a cross section in the xz plane, a cross section in the yz plane and a cross section in the xy plane. The shown area has an extent of 10 mm in the x direction.

[0129] For this variant, Fig.19 The lateral deviation is shown for different viewing angles. The diameter of the reference circle is 2 arc minutes. Fig. 20 shows the spherical optical power in diopters, and Fig.21 The perspective astigmatism in diopters through the optical waveguide is shown. In both figures, the dashed area 25 marks the extent of the optical waveguide in the x-direction and the y-direction in each case with a field of view of 40°×10°. Fig.19 In the example, the spherical refractive power of the light guide is 1.3 diopters + / - 0.04 diopters, which can be used when integrated into a push / pull lens. Even without a push / pull lens, the refractive power of the light guide can be used to correct refractive errors (specifically up to 1.3 diopters). Fig. 20 It is evident in the figure that the perspective astigmatism through the optical waveguide is less than 0.05 diopters, ie no further compensation is required.

[0130] Fig. 22 Schematically shown is an image reproduction device 30 according to the invention (e.g. a head mounted display), which comprises an optical arrangement 31 according to the invention. The optical arrangement 31 according to the invention comprises an optical waveguide 20 according to the invention, in particular an optical waveguide according to one of the above-described embodiment variants. Furthermore, the optical arrangement 31 comprises at least one optical element 3, 4, such as a lens. The optical element 3, 4 may be configured as a push lens and / or a pull lens. The optical element 3, 4 may be designed to correct ametropia and / or to focus a virtual image representation, etc. In Fig. 22 In an alternative to the variant shown, the image reproduction device 30 according to the invention may comprise only the optical waveguide 20 according to the invention instead of the optical arrangement 31 .

[0131] Fig.23 Schematically an image capturing device 32 according to the invention is shown, which comprises at least one optical waveguide 20 according to the invention. In this case, the output coupling means 11 are designed as input coupling means and the input coupling means or input coupling surface 10 are designed as output coupling means or output coupling surface.

[0132] Reference numerals list:

[0133] 1 Lens arrangement

[0134] 2 Waveguide

[0135] 3. First lens

[0136] 4 Second lens

[0137] 5 Beam path

[0138] 6 Eye Movement Range

[0139] 7 Optical Axis

[0140] 8 Center axis

[0141] 9 System thickness

[0142] 10 Input coupling device / input coupling surface

[0143] 11 Output coupling device

[0144] 12 Concave curved first surface

[0145] 13 Convexly curved second surface

[0146] 14 Planar surface

[0147] 19 System diameter

[0148] 20 Optical waveguide

[0149] 21 xy plane

[0150] 22 Thickness

[0151] 23 Length

[0152] 24 Marking Area

[0153] 25 Marking Area

[0154] 30 Image reproduction equipment

[0155] 31 Optical Arrangement

[0156] 32 Image Capture Devices

[0157] XAN field angle

[0158] YAN field angle

[0159] x-coordinate

[0160] y coordinate

[0161] z-coordinate

[0162] x′ coordinate

[0163] y′ coordinate

[0164] z′ coordinate

Claims

1. An optical waveguide (20) for arrangement in a beam path (5) of an optical arrangement having a device (11) for out-coupling and / or in-coupling an imaging beam path, It is characterized in that The optical waveguide (20) comprises a GRIN element having at least one curved surface (12, 13), wherein the GRIN element has a refractive index profile designed to reduce aberrations caused by the curvature of the GRIN element in an imaging path of a virtual image representation, the virtual image representation being generated by means of light waves guided in the optical waveguide (20) by total internal reflection.

2. The optical waveguide (20) as claimed in claim 1, It is characterized in that The GRIN element has a refractive index profile designed to reduce aberrations introduced by the GRIN element in an imaging path extending through the GRIN element, the imaging path being an imaging path of a true image representation of a surrounding environment.

3. The optical waveguide (20) as claimed in claim 2, It is characterized in that The aberrations introduced by the GRIN element in the imaging path of the real image representation of the surrounding environment are aberrations introduced by the curvature of the GRIN element and / or by a refractive index profile designed to reduce the aberrations induced in the imaging path of the virtual image representation.

4. The optical waveguide (20) according to any one of claims 1 to 3, It is characterized in that The refractive index profile of the GRIN element has a radially symmetric and / or a cylindrical and / or a toric refractive index profile and / or a refractive index profile having at least one constant refractive index region.

5. The optical waveguide (20) as claimed in claim 4, It is characterized in that The at least one constant refractive index region is configured in the manner of a cylindrical surface and / or a toric surface and / or a spherical surface and / or an aspherical surface or is configured as a free-form surface.

6. The optical waveguide (20) according to claim 4 or 5, It is characterized in that The at least one constant refractive index region coincides with or extends parallel to at least one curved surface of the GRIN element.

7. The optical waveguide (20) according to any one of claims 1 to 6, It is characterized in that n(r)=f(r' / r) applies to the refractive index profile of the GRIN element in the radial direction, wherein r' is a given radius of curvature of one of the at least one curved surface (12, 13) of the GRIN element.

8. The optical waveguide (20) according to any one of claims 1 to 7, It is characterized in that The radius of curvature R1=r′ of the first surface (12) of the GRIN element and / or the radius of curvature R2=r of the second surface (13) of the GRIN element is at least 50 mm, and / or the thickness (22) of the GRIN element in the main ray direction (9) of the imaging path of the real image representation of the surrounding environment or in the radial direction is at least 0.1 mm and / or at most 10 mm.

9. The optical waveguide (20) according to any one of claims 1 to 8, It is characterized in that The refractive index change Δn in the GRIN element is between 0.005 and 0.

20.

10. The optical waveguide (20) according to any one of claims 1 to 9, It is characterized in that In the radial direction, the refractive index variation Δn of the GRIN element is between 0.01 and 0.

15.

11. The optical waveguide (20) according to any one of claims 1 to 10, It is characterized in that In the direction x, the gradient of the refractive index n δn / dx is at 0 mm -1 With 0.02mm -1 between.

12. The optical waveguide (20) according to claim 11, It is characterized in that In a direction x perpendicular to the main ray direction (9) of the imaging path represented by the real image of the surrounding environment, or in a direction x parallel to the main ray direction (9) of the imaging path represented by the real image of the surrounding environment, or in a radial direction x, or in a direction x perpendicular to the optical axis (7), or in a direction x parallel to the optical axis (7), the gradient δn / dx of the refractive index n is between 0 mm and 1 With 0.02mm- 1 between.

13. The optical waveguide (20) according to any one of claims 1 to 12, It is characterized in that The first surface (12) and / or the second surface (13) are implemented in the form of a toric surface, a spherical surface, an aspherical surface, a cylindrical surface, or as a free-form surface.

14. The optical waveguide (20) according to any one of claims 1 to 13, It is characterized in that The refractive index within the GRIN element varies in at least a first dimension and a second dimension defining a coordinate system.

15. The optical waveguide (20) as claimed in claim 14, It is characterized in that The refractive index is constant along a third dimension of the defined coordinate system, wherein the third dimension forms an oblique angle with the main ray direction (9) of the imaging path of the real image representation of the surroundings.

16. The optical waveguide (20) as claimed in claim 15, It is characterized in that The absolute value of the inclination angle is greater than 2 degrees.

17. The optical waveguide (20) according to any one of claims 1 to 16, It is characterized in that The GRIN element is designed to introduce a refractive power different from zero into the imaging path of the real image and / or the virtual image.

18. An optical arrangement (31) comprising at least one optical element (3, 4) having at least one curved surface, It is characterized in that The optical arrangement (31) comprises at least one optical waveguide (20) as claimed in any one of claims 1 to 17, wherein the at least one optical element (3, 4) and the optical waveguide (20) are arranged continuously in a beam path of an imaging path of the real image representation and / or the virtual image representation.

19. The optical arrangement (31) as claimed in claim 18, It is characterized in that The optical element (3, 4) is configured as a lens and / or is designed to correct refractive errors in an imaging path of a real image representation of the surrounding environment and / or to correct refractive errors in an imaging path of the virtual image representation and / or to focus the virtual image representation in the imaging path of the virtual image representation.

20. An optical arrangement (31) as claimed in claim 18 or 19, It is characterized in that The optical waveguide (20) is designed such that the curvature of at least one of the surfaces (12, 13) of the GRIN element matches the curvature of at least one curved surface of the at least one optical element (3, 4).

21. The optical arrangement (31) as claimed in any one of claims 18 to 20, It is characterized in that At least one further GRIN element is present in order to reduce aberrations introduced by the GRIN element along the imaging path of the real image representation of the surroundings.

22. An image capture device comprising at least one optical waveguide (20) according to any one of claims 1 to 17.

23. An image reproduction device comprising at least one optical waveguide (20) as claimed in any one of claims 1 to 17 or comprising an optical arrangement (31) as claimed in any one of claims 18 to 21.

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