Optical system with an adhesive layer having a stiffness gradient

Abstract

The invention relates to an optical system which has a first optical element, a second optical element and a first adhesive layer. The first adhesive layer is arranged between the first optical element and the second optical element and is configured to connect the first optical element and the second optical element. The first adhesive layer also has a first stiffness gradient which points from an edge of the optical system to a thermal expansion centre of the optical system.

Description

Description Optical system with an adhesive layer with a stiffness gradient TECHNICAL FIELD The application relates to optical systems with multiple optical elements and more specifically to the connection of the multiple optical elements by means of adhesive layers. BACKGROUND Adhesive layers that bond optical elements together in optical systems can have low stiffness, particularly in optical systems that have a high diameter-to-thickness ratio. If the optical systems are exposed to thermal fluctuations, such as when the optical systems are used in head-mounted displays (HMDs) for virtual reality (VR) systems, the thermal fluctuations combined with the low stiffness can lead to changes in the position and shape of the optical elements. In addition, the low stiffness of the adhesive layers can allow the optical elements to vibrate relative to one another, which can lead to undesirable optical effects. However, increasing the stiffness of the adhesive layers to avoid these problems can impair the optical performance of the optical system. Against this background, it is an object of the present disclosure to reduce position and shape changes as well as vibrations of optical elements in an optical system without impairing the optical performance of the optical system. SUMMARY OF THE INVENTION To achieve this goal, the present invention provides an optical system. The optical system comprises a first optical element and a second optical element, and a first adhesive layer. The first adhesive layer is disposed between the first optical element and the second optical element and is configured to bond the first optical element and the second optical element. The first adhesive layer further has a first stiffness gradient extending from an edge of the optical system to a thermal expansion center of the optical system. SHORT DESCRIPTION OF THE CHARACTERS Examples of the present disclosure are described below with reference to the attached figures, in which like reference numerals refer to like elements. Figs. 1A and 1B illustrate the general concept of the present disclosure according to examples of the present disclosure. Figs. 2A and 2B illustrate exemplary optical systems according to examples of the present disclosure. Fig. 3 shows a plan view of an adhesive layer of the optical system of Figs. 2A and 2B according to examples of the present disclosure. Figs. 4A to 4C show exemplary stiffness profiles within adhesive layers of an optical system according to examples of the present disclosure. Figs. 5A and 5B show further exemplary stiffness profiles within adhesive layers of an optical system according to examples of the present disclosure. It should be understood that the provision of these figures is not intended to limit the present disclosure to the aspects shown in the figures. Rather, these figures are provided to aid in understanding the present invention. Those skilled in the art will readily understand that aspects of the present invention shown in one figure may be combined with aspects from another figure, or that aspects shown in a figure may be omitted without departing from the scope of the present disclosure. DETAILED DESCRIPTION The following describes an optical system comprising at least a first optical element and a second optical element, as well as an adhesive layer arranged therebetween. The adhesive layer has a stiffness gradient from the edge of the optical system. system to a thermal expansion center. In other words, the stiffness within the first adhesive layer increases from the edge to the thermal expansion center. The increase in stiffness results in the adhesive layer having low stiffness at the edge and high stiffness in the thermal expansion center. The high stiffness in the thermal expansion center means that there are no changes in the position and / or shape of the optical elements when the temperature increases. The stiffness gradient from the edge of the optical system to the thermal expansion center and the decrease in stiffness from the thermal expansion center to the edge of the optical system simultaneously ensure that the high stiffness in the thermal expansion center does not impair the optical performance of the optical system. Fig. 1B illustrates the effect of the stiffness gradient compared to Fig. 1A. In Fig. 1A, the optical system deforms with increasing temperature due to the low stiffness k of the adhesive layers, which is indicated by the low linear curve in the graph of Fig. 1A. In Fig. 1B, the optical system essentially does not deform with increasing temperature. In other words, the stiffness gradient results in the optical system deforming only very slightly or not at all with increasing temperature. This is due to the stiffness gradient running towards the thermal expansion center, which is indicated by the increase in stiffness k towards the thermal expansion center in the graph of Fig. 1B. In the examples in Figs. 1A and 1B, the thermal expansion center is located at the center of the optical system. This is merely an example.The thermal expansion center can be located at any other point within the optical system. The general concept of the present disclosure presented at the outset will be illustrated below using the exemplary optical systems of Figs. 2A to 3 and the exemplary stiffness curves of Figs. 4A to 5B. Fig. 2A shows an optical system 100. The optical system 100 includes a first optical element 110, a first adhesive layer 120, a second optical element 130, a second adhesive layer 140, and a third optical element 150. The first optical element 110, the second optical element 130 and the third optical element 150 are configured to provide a respective optical function. The optical function function can, for example, be an enlargement or a reduction of a field of view by the respective optical element. In the context of an HMD, the optical function can, for example, be an enlargement of the field of view relative to a display arranged a short distance in front of the user's eyes. The optical function can also be a transmission of light, for example in a waveguide. Depending on their respective optical function, the first optical element 110, the second optical element 130 and the third optical element 150 each have a first, a second and a third refractive index, respectively. Consequently, the first optical element 110, the second optical element 130 and the third optical element 150 can each be, for example, a lens, a Fresnel lens or a waveguide. To illustrate this, in Fig. 2A the first optical element 110 is shown as a convex lens and the third optical element as a concave lens.It should be understood that these examples are not exhaustive. The first optical element 110, the second optical element 130, and the third optical element 150 can be any type of optical element configured to provide an optical function. Furthermore, the first optical element 110, the second optical element 130, and the third optical element 150 can be single-piece optical elements, as shown in Fig. 2A, or multi-piece optical elements, i.e., optical elements composed of individual segments. Since each of the first optical element 110, the second optical element 130, and the third optical element 150 can provide a different optical function, the optical system 100 can provide an optical function resulting from the combination of these optical functions. It should be understood that the optical system 100 may include more or fewer optical elements than shown in Figure 2A. Since the optical system 100 is a multi-optical element optical system, the optical system 100 includes at least two optical elements. However, the present disclosure allows for any greater number of optical elements, such as the optical system 100 including three optical elements. When temperatures fluctuate, the first optical element 110, the second optical element 130, and the third optical element 150 may deform, for example, by changing their length or deforming in some other way. For example, the first optical element 110, the second optical element 130, and the third optical element 150 have respective first, second, and third coefficients of thermal expansion that differ from one another. The different coefficients of thermal expansion of the respective optical elements can cause changes in position and deformations of the optical elements relative to one another and thus of the optical system 100. This can impair the structural integrity and, in particular, the optical function of the optical system 100. As described below, the first adhesive layer 120 and the second adhesive layer 140 are configured to substantially prevent or compensate for these deformations. The first adhesive layer 120 is arranged between the first optical element 110 and the second optical element 130 and is configured to connect the first optical element 110 and the second optical element 130. Similarly, the second adhesive layer 140 is arranged between the second optical element 130 and the third optical element 150 and is configured to connect the second optical element 130 and the third optical element 150. As already explained, the optical system 100 has at least two optical elements and can have any number of optical elements, each of which is incorporated into the optical system 100 with a further adhesive layer. Thus, the optical system has at least one adhesive layer and can include more than one adhesive layer depending on the number of optical elements. The first adhesive layer 120 has a first stiffness gradient extending from an edge of the optical system 100 to a thermal expansion center of the optical system 100. The first adhesive layer 120 or the entire optical system 100 can also be a disk with a radius R, as shown, for example, in Fig. 3. Stiffness k in the context of this disclosure refers to the resistance of the adhesive layer 120 with respect to deformation of the first optical element 110 and the second optical element 130. In simplified terms, the stiffness k can be approximated as a location-dependent stiffness k(r) based on a location-dependent elastic modulus E(r) and a location-dependent geometry function Fc(r) of the adhesive layer 120, as shown in equation (1): / c(r) = E(r) * F c (r) (1) The location-dependent geometry function Fc(r) describes the geometry of the adhesive layer 120 in equation (1). The location dependence of the stiffness k(r), the elastic modulus E(r) and the geometry function Fc(r) results from the dependence of these values ​​or this function on the radial position within the optical system, as shown, for example, at the bottom in Figs. 2A and 2B or in the middle of Fig. 3. It should be understood that equation (1) represents a simplified approximation of the location-dependent stiffness k(r). The location-dependent stiffness k(r) can also be specified in other ways, each as a function of a location-dependent elastic modulus E(r) and a location-dependent geometric function Fc(r) of the adhesive layer 120, depending on which form of stiffness, for example tensile stiffness or flexural stiffness, or combination of forms of stiffness is considered. Based on equation (1), the stiffness gradient can be approximated as shown in equation (2): dfc(r) dE(r) dF G (r) - dr = - dr * - dr (2) Consequently, the stiffness gradient depends on the derivative of the location-dependent elastic modulus E(r) and the corresponding derivative of the geometric function Fc(r) of the adhesive layer 120. Analogous to equation (1), equation (2) is also intended to represent only a simplified approximation in order to define the core of the term stiffness gradient as the derivative of a stiffness based on a location-dependent elastic modulus. Depending on the specifically considered form of stiffness or combination of forms of stiffness, the actual calculation of the stiffness gradient can take additional or different terms into account. Examples of additional terms that can be taken into account in equation (1) and thus in equation (2) are a relative extensibility and a compressibility orTransverse contraction of the adhesive layer 120 and the formation of polymer zones in the adhesive layer 120, such as an adhesion zone at the edge or a cohesion zone in the middle. Example elastic values ​​for the position-dependent elastic modulus E(r) at the edge of the optical system range from 10 kPa to 10 MPa. Example elastic values ​​for the position-dependent elastic modulus E(r) in the thermal expansion center of the optical system range from 1 MPa to 5 GPa. The thermal expansion center in the context of this application refers to the region of the optical system 100 in which the optical system 100 has its minimum due to the previously discussed thermally induced deformation of the optical elements of the optical system 100. In other words, the thermal expansion center refers to the region of the optical system from which a radial thermal deformation of the optical system 100 emanates without substantially deform. This region may, as shown in Figs. 4A to 4C, coincide with an axis of symmetry of the optical system 100, for example, if all elements of the optical system 100 are axially symmetric. However, this region may also be located at a location other than the geometric center of the optical system 100. As previously stated, the stiffness gradient extends from an edge of the optical system 100 to a thermal expansion center of the optical system 100. The stiffness gradient caused by this stiffness gradient substantially prevents deformation of the optical system without impairing the optical function of the optical system 100. The stiffness gradient substantially reduces or prevents impairment of the optical function by minimizing the deformation of the optical element 110 and the optical element 130. The stiffness decreasing toward the edge of the optical system 100 prevents impairment of the optical function that would otherwise result from high stiffness.It should be understood that, although the optical function could deteriorate partially due to the stiffness profile in a region of the optical system 100 in some examples of the present disclosure, this deterioration in one region could be minimal relative to the entire optical system 100. At the same time, the stiffness profile can compensate for or prevent deformation of the optical system 100 and a positional shift of the first optical element 110 relative to the second optical element 130 due to temperature fluctuations. In summary, the stiffness gradient of the adhesive layer 120 ensures that temperature fluctuations do not lead to deformation of the optical system 100. At the same time, due to the stiffness gradient, the adhesive layer 120 essentially does not impair the optical function. More specifically, in some examples of the present disclosure, the first adhesive layer 120 may have a stiffness maximum in the thermal expansion center. The stiffness maximum may be configured to secure the connection between the first optical element 110 and the second optical element 130. Furthermore, the first stiffness gradient may ensure an optical function of the optical system 100, ie, ensure that the optical function of the optical system 100 is not impaired by the stiffness of the first adhesive layer 120. Exemplary stiffness curves caused by the stiffness gradient are discussed below with reference to Figs. 4A to 5B. Figs. 4A to 4C show stiffness curves of the stiffness k of the first adhesive layer 120, which exhibit the stiffness gradient. In the exemplary stiffness curves, the thermal expansion center is located in the geometric center of the optical system 100. It should be noted that the representation of the thermal expansion center in the geometric center of the optical system is merely exemplary. The thermal expansion center can also be located in other regions of the optical system. Fig. 4A shows an example of a discrete stiffness profile. Accordingly, in the example of Fig. 4A, the stiffness gradient is also discrete. In the example of Fig. 4A, the stiffness is constant in some sections and thus the stiffness gradient is zero in some sections and only non-zero at certain transitions. These transitions represent transitions between adhesive zones, which are shown in Fig. 2A as well as in Fig. 3. In other words, the adhesive layer 120 can comprise a plurality of adhesive zones, such as three adhesive zones 120i, 1202, and 1203, which are arranged laterally adjacent to one another. It should be understood that the number of adhesive zones can be varied and the three adhesive zones 120i, 1202, and 1203 serve only as an example.The plurality of adhesive zones may include any number of adhesive zones required to create a stiffness gradient within the meaning of this disclosure based on a plurality of adhesives having different stiffnesses. In addition to creating a discrete stiffness profile, adhesive zones, each arranged adjacent to further adhesive zones on both sides, can be configured to convert internal stress in the first adhesive layer 120 into compression. By converting the internal stress into compression, the first adhesive layer 120 itself can be prevented from contributing significantly to a deformation of the optical system 100. For this purpose, the first adhesive layer can have a Poisson's ratio of less than 0.45. Fig. 4B shows an example of a sectionally continuous stiffness curve. In the example of Fig. 4B, the stiffness increases in sections with varying degrees and constantly from the edge of the optical system 100 to the thermal expansion center. Thus, the stiffness gradient is constant in sections and not zero in each case, jumping at each transition to the stiffness gradient value of the next section. As in the example of Fig. 4A, such a discrete stiffness curve can be generated with the plurality of adhesive zones, such as the three adhesive zones 120i, 1202, and 1203. In this case, the adhesives of the respective adhesive zones each have a stiffness that constantly increases toward the thermal expansion center. Fig. 4C shows an example of a continuous stiffness gradient. Consequently, in the example of Fig. 4C, the stiffness gradient is continuous. In other words, the stiffness increases from the edge of the optical element 100 toward the thermal expansion center without significant discontinuities. The stiffness gradient is accordingly also continuous. In this example, the adhesive layer 120 may not include the plurality of adhesive zones, as illustrated, for example, in Fig. 2B. It should be noted that, with the exception of the plurality of adhesive zones, the optical system 100 of Fig. 2B corresponds to the optical system 100 of Fig. 2A. A continuous stiffness profile and thus a continuous stiffness gradient can be created, for example, by adding glass particles to the adhesive of the adhesive layer 120 in the liquid state. The glass particles can, for example, be a glass particle powder with an average sphere size in the range of a few nanometers to a few micrometers. The addition is carried out in such a way that an inhomogeneous glass particle density is achieved in the adhesive layer 120 during curing. As a result, the adhesive layer 120 in the cured state has a continuous stiffness profile or a continuous stiffness gradient as shown in Fig. 4C. The glass particles or the glass particle powder have a refractive index that approximately corresponds to the refractive index of the first adhesive layer 120. The same approach can, for example, also be used for the example in Fig.4B can be used to achieve a continuous increase in stiffness in each adhesive zone. Figs. 5A and 5B show two further exemplary discrete stiffness curves. In both examples, the thermal expansion center is located at the geometric center of the optical system 100. In Fig. 5A, the stiffness increases from the edge in sections, e.g., per adhesive zone, before decreasing again and reaching a maximum at the thermal expansion center. The example in Fig. 5A shows that stiffness gradients from the edge to the thermal expansion center do not have to increase continuously, but can rise and fall until they reach a global stiffness maximum. In other words, the stiffness gradient of the first adhesive layer 120 can point from the edge of the optical system 100 to the global stiffness maximum. In Fig. 5B, the optical system 100 has a radial stiffness maximum in the region of the second adhesive zone 1202. Due to the circular shape of the optical system 100 and the centering of the curve on the geometric center, the stiffness maximum in the region of the second adhesive zone 1202 appears twice in the stiffness curve of Fig. 5B. In other words, the optical system 100 of the example of Fig. 5B has an annular stiffness maximum region around the thermal expansion center. This stiffness maximum region can be used to compensate for temperature-dependent deformation of the first optical element 110 and the second optical element 130. Due to the first radial stiffness gradient, in some examples of the present disclosure, the first adhesive layer 120 can be further configured to compensate for a deformation of the first optical element 110 and the second optical element 130, so that the deformation occurs quasi-isotropically or along a preferred direction. In other words, due to the first stiffness gradient, the first adhesive layer 120 can be configured to compensate for a bending deformation by substantially preventing or counteracting the deformation of the first optical element 110 and the second optical element 130 through a targeted differential radial stiffness and thermal expansion. Due to the first stiffness gradient, in some examples of the present disclosure, the first adhesive layer 120 may be further configured to generate a bending moment that is configured to counteract a bending moment generated by the thermal expansion of the first optical element 110 and the second optical element 130. Due to the stiffness maximum, the first adhesive layer 120 may be configured to ensure the strength of the adhesive bond. The bending moment generated by the adhesive The radially varying bending moment generated by the layer 120, in combination with the bending moment of the first optical element 110 and that of the second optical element 130, leads to an effectively bending deformation-free state of the optical system 100. The first adhesive layer 120 can thus compensate for or specifically adjust a deformation of the optical system 100. The first adhesive layer 120 can further have a first refractive index. The first refractive index can be configured to correspond to a refractive index of at least one of the first optical element 110 and the second optical element 130. This can ensure the optical function of the first optical element 110 and the second optical element 130, respectively, since a correspondence of the refractive indices can prevent, for example, total internal reflection at the interface between the first adhesive layer 120 and the first optical element 110 and the second optical element 130, respectively. Correspondence of the refractive indices in the context of this application is understood to mean a deviation of up to 2.5%. The first refractive index can also be lower than a refractive index of the second optical element 130 if the second optical element 130 is a waveguide. In this way, total reflection can be ensured, for example that the critical angle of total reflection in the first adhesive layer 120 is below 60°, for example below 55° or below 50°. The first adhesive layer 120 can have a transmittance configured to substantially not absorb light in the visible spectral range. This transmittance can ensure that the first adhesive layer 120 does not act as an optically dampening or color-filtering element. The first adhesive layer 120 can also be specifically adjusted for color or spectral filtering, for example, for color-neutral or color-weighted filtering for sunglasses or to increase image contrast in AR systems, to act as a color filter, for example, with regard to yellow, green, or red, or to act as a spectral filter for absorbing UV and / or IR radiation. In some examples of the optical system 100 according to the present disclosure, in which the first optical element 110 is a lens and the second optical element 130 is a waveguide, the first adhesive layer 120 may be configured to provide total reflection corresponding to total reflection of the waveguide. In other words, the first adhesive layer 120 may be configured to provide total reflection for the waveguide guide, so that light coupled out of the waveguide is not absorbed or reflected by the first adhesive layer 120. Furthermore, if the first optical element 110 is a lens and the second optical element 130 is a waveguide, the adhesive layer can have a first region and a second region. The first region can have a first refractive index that provides total reflection in the first region of the optical system. The second region can have a second refractive index that is greater than or equal to the first refractive index. With these refractive indices in the first adhesive layer 120, total reflection for the light guided in the waveguide can be provided on the one hand. On the other hand, unwanted total reflections at other interfaces can be avoided. The second adhesive layer 140 is arranged between the second optical element 130 and the third optical element 150 and is configured to connect the second optical element 130 and the third optical element 150. Furthermore, the second adhesive layer has a second stiffness gradient extending from an edge of the optical system 100 to a thermal expansion center of the optical system 100. In other words, the definition of the second adhesive layer 140 corresponds to the definition of the first adhesive layer. The preceding statements regarding the first adhesive layer 120 thus also apply to the second adhesive layer 140 or each further adhesive layer of the optical system 100. Accordingly, the second adhesive layer 140 can be configured to generate a second bending moment analogous to the first adhesive layer 120. By means of the first bending moment and the second bending moment, the first adhesive layer 120 and the second adhesive layer 140 can be configured to provide a combined bending moment that counteracts a bending moment generated by thermal expansion of the first optical element 110, the second optical element 130, and the third optical element 150. Furthermore, the second adhesive layer 140 can have a second refractive index. The first refractive index of the first adhesive layer and the second refractive index of the second adhesive layer 140 can therefore have a refractive index difference that is inversely proportional to the aperture angle of a transmitting light cone. Otherwise, the refractive index difference can impair the optical function of the optical system 100. In some examples of the present invention, the optical system may further include an anti-reflective coating. The anti-reflective coating may be disposed between the first adhesive layer 120 and the first optical element 110, between the first adhesive layer 120 and the second optical element 130, or between both the adhesive layer 120 and the first optical element 110 and between the first adhesive layer 120 and the second optical element 130. Similarly, an anti-reflective coating may be disposed with respect to the second adhesive layer 140, as well as the second optical element 130 and the third optical element 150, or with respect to any additional adhesive layer. The optical system 100 can have a thickness of less than 250 pm, for example, a thickness of 100 pm or 50 pm. The individual adhesive layers and optical elements can have a thickness between 10 pm and 100 pm. The invention is further illustrated by the following examples. In one example, an optical system comprises a first optical element and a second optical element and a first adhesive layer, wherein the first adhesive layer is arranged between the first optical element and the second optical element and is configured to connect the first optical element and the second optical element, and the first adhesive layer has a first stiffness gradient pointing from an edge of the optical system to a thermal expansion center of the optical system. In one example, the first adhesive layer may have a stiffness maximum in the thermal expansion center, wherein the stiffness maximum may be configured to secure the connection between the first optical element and the second optical element, and wherein the first stiffness gradient may ensure an optical function of the optical system. In one example, the first stiffness gradient may be continuous. In one example, the first stiffness gradient may be discrete. In one example, the first adhesive layer may comprise a plurality of adhesive zones arranged laterally adjacent to one another. In one example, the adhesive zones of the plurality of adhesive zones arranged on both sides laterally adjacent to further adhesive zones of the plurality of adhesive zones may be configured to convert internal stress into compression. In one example, the first adhesive layer may have a Poisson's ratio of less than 0.45. In one example, the first adhesive layer may have a first refractive index configured to match a refractive index of at least one of the first optical element and the second optical element or to be lower than a refractive index of the second optical element, wherein the second optical element is a waveguide. In one example, the first adhesive layer may have a transmittance configured to substantially not absorb light in the visible spectral range. In one example, the adhesive layer may be configured to deform, wherein the deformation of the first adhesive layer may be configured to compensate for a deformation of the first optical element and the second optical element. In one example, the first adhesive layer may be configured to generate a bending moment configured to counteract a bending moment generated by thermal expansion of the first optical element and the second optical element. In one example, the optical system may further comprise a third optical element and a second adhesive layer, wherein the second adhesive layer may be arranged between the second optical element and the third optical element and may be configured to connect the second optical element and the third optical element, wherein the second adhesive layer may have a second stiffness gradient pointing from an edge of the optical system to a thermal expansion center of the optical system, and wherein the first adhesive layer and the second adhesive layer may be configured to generate a combined bending moment configured to counteract a bending moment generated by thermal expansion of the first optical element, the second optical element, and the third optical element.

[0001] In one example, the first adhesive layer and the second adhesive layer may have a refractive index difference from each other that is inversely proportional to an aperture angle of a transmitting light cone. In one example, the first optical element may have a first coefficient of thermal expansion, the second optical element may have a second coefficient of thermal expansion, and the first coefficient of thermal expansion and the second coefficient of thermal expansion may be different from each other. In one example, the first optical element and the second optical element may be one of a single-piece optical element and a multi-piece optical element. In one example, the first optical element may be a lens, the second optical element may be a waveguide, and the first adhesive layer may be configured to provide total internal reflection corresponding to total internal reflection of the waveguide. In one example, the first adhesive layer may have a first region and a second region and may be further configured to have a first refractive index in the first region that provides total reflection in the first region of the optical system, and to have a second refractive index in the second region that is greater than or equal to the first refractive index. The foregoing description has been provided to describe an optical system having an adhesive layer with a stiffness gradient. It should be understood that the description is in no way intended to limit the scope of the invention to the precise embodiments discussed in this description. Rather, those skilled in the art will recognize that embodiments may be combined, modified, or simplified without departing from the scope of the invention as defined by the following claims.

Claims

Patent claims 1. An optical system comprising: a first optical element and a second optical element; and a first adhesive layer, wherein the first adhesive layer: is disposed between the first optical element and the second optical element and is configured to bond the first optical element and the second optical element, and the first adhesive layer has a first stiffness gradient pointing from an edge of the optical system to a thermal expansion center of the optical system.

2. The optical system of claim 1, wherein: the first adhesive layer has a stiffness maximum in the thermal expansion center, the stiffness maximum being configured to secure the connection between the first optical element and the second optical element, and the first stiffness gradient ensuring an optical function of the optical system.

3. An optical system according to any one of the preceding claims, wherein the first stiffness gradient is continuous.

4. An optical system according to any one of claims 1 to 2, wherein the first stiffness gradient is discrete.

5. An optical system according to any one of the preceding claims, wherein the first adhesive layer comprises a plurality of adhesive zones arranged laterally adjacent to one another.

6. The optical system of claim 5, wherein adhesive zones of the plurality of adhesive zones arranged on both sides laterally adjacent to further adhesive zones of the plurality of adhesive zones are configured to convert internal stress into compression.

7. The optical system of claim 6, wherein the first adhesive layer has a Poisson's ratio of less than 0.

45.

8. The optical system of any one of the preceding claims, wherein the first adhesive layer has a first refractive index configured to: match a refractive index of at least one of the first optical element and the second optical element; or be lower than a refractive index of the second optical element, wherein the second optical element is a waveguide.

9. An optical system according to any one of the preceding claims, wherein the first adhesive layer has a transmittance configured to substantially not absorb light in the visible spectral range.

10. Optical system according to any one of the preceding claims, wherein the adhesive layer is adapted to deformation, wherein the deformation of the first adhesive layer is adapted to compensate for a deformation of the first optical element and the second optical element.

11. An optical system according to any one of the preceding claims, wherein the first adhesive layer is configured to generate a bending moment configured to counteract a bending moment generated by thermal expansion of the first optical element and the second optical element.

12. The optical system of any one of the preceding claims, further comprising a third optical element and a second adhesive layer, wherein: the second adhesive layer is disposed between the second optical element and the third optical element and is configured to bond the second optical element and the third optical element, the second adhesive layer has a second stiffness gradient pointing from an edge of the optical system to a thermal expansion center of the optical system, and the first adhesive layer and the second adhesive layer are configured to generate a combined bending moment configured to counteract a bending moment generated by thermal expansion of the first optical element, the second optical element, and the third optical element.

13. Optical system according to any one of the preceding claims, wherein the first adhesive layer and the second adhesive layer have a refractive index difference which is inversely proportional to an opening angle of a transmitting light cone.

14. An optical system according to any one of the preceding claims, wherein: the first optical element has a first coefficient of thermal expansion, the second optical element has a second coefficient of thermal expansion, and the first coefficient of thermal expansion and the second coefficient of thermal expansion are different from each other.

15. An optical system according to any one of the preceding claims, wherein the first optical element and the second optical element are one of a single-piece optical element and a multi-piece optical element.

16. An optical system according to any one of the preceding claims, wherein: the first optical element is a lens, the second optical element is a waveguide, and the first adhesive layer is configured to provide total internal reflection corresponding to total internal reflection of the waveguide.

17. The optical system of claim 16, wherein the first adhesive layer has a first region and a second region and is further configured to: have a first range refractive index in the first region that provides total internal reflection in the first region of the optical system, and have a second range refractive index in the second region that is greater than or equal to the first range refractive index.

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