REFLECTIVE OPTICAL SYSTEM WITH ADJUSTABLE EFFECTIVE FOCAL LENGTH AND OPTICAL STRUCTURE

Description

[0001] The invention relates to a reflective optical system with adjustable effective focal length, the use of such a reflective optical system, and a method for calculating the mirror surfaces for such an optical system.

[0002] Optical systems with adjustable focal length can be used in both illumination and imaging systems. In illumination systems, the solution can be applied to beam shaping tasks, for example, for shaping laser beams in laser material processing. In imaging optical systems, optical systems with adjustable focal length can be used to image at least two different object fields in two states onto a common, fixed image plane.

[0003] Refractive optical systems with adjustable focal length are known in the prior art. For example, US 3,507,565 A and US 3,305,294 A describe lens systems with a variable focal length. In these solutions, consisting of a pair of lenses, a variation in focal length is achieved by an opposing, but equal, lateral movement.

[0004] However, refractive systems exhibit low transmission, high chromatic dependence of aberrations, and physical limitations in surface complexity, for example due to internal total reflections.

[0005] German patent application DE 10 201008 342 A1 describes an imaging system for imaging an object onto an image sensor. This system has a front face facing the object and a rear face facing away from the object, which, viewed from the object's perspective, is located behind the front face. Furthermore, the imaging system has a light entry device on the front face through which light from the object can enter the imaging system. The light then travels along the beam path between the object and the image sensor. A first and a second optical element are also described, which are arranged on the rear face in such a way that they can influence the beam path. The light entry device includes an electrically switchable liquid crystal element, which deflects the beam path, depending on the electrical switching state, by at least one first angle and a second angle different from the first.This electrically induced change in the beam path allows for a discretely switchable change in focal length.

[0006] Document US 2018 / 0164573 A1 discloses an anastigmat telescope with three aspherical mirrors, which has means for linearly moving the third mirror along the optical axis of the telescope in order to change the focal length of the telescope to a variety of focal lengths between at least a minimum focal length and a maximum focal length.

[0007] Furthermore, patent US 2015 / 0234153 A1 describes a reflective varifocal lens configured to change a focal length using an electrical signal, wherein the lens comprises a first conductive electrode layer, an electrically active polymer layer formed on the first electrode layer, a second conductive electrode layer formed on the electrically active polymer layer, and a reflective layer configured to reflect incident light toward the first electrode layer or the second electrode layer, wherein a shape of the electrically active polymer layer is changed by the electrical signal applied to the first electrode layer and the second electrode layer, and when the shape of the electrically active polymer layer changes, a shape of the reflective layer changes, thereby changing a focal length of reflected light.

[0008] Publication KR 2023 0003062 A discloses an optical system for laser processing that enables simpler and more reliable processing of multiple patterns simultaneously on the same part. The system comprises an ultrashort pulse laser source for generating a source laser beam; a device with separating means for separating a source laser beam into a plurality of separate laser beams, such that each of the separate laser beams is directed in a specific propagation direction; a spatial offset unit for obtaining a plurality of offset laser beams from the plurality of separate laser beams, such that each offset laser beam can propagate around a specific principal propagation axis and describe a movement around the principal propagation axis; and focusing means configured to focus each offset laser beam onto a workpiece in the direction of the specific propagation axis.

[0009] The object of the invention is therefore to provide an optical system that eliminates the disadvantages of such systems in the prior art and enables low chromatic aberrations.

[0010] This problem is solved by the reflective optical system with the features of claim 1 and an optical setup with the features of claim 13. The features of the dependent claims describe further developments of the invention.

[0011] The concept of adjustable effective focal lengths is transferred to a reflective application, which allows for both a continuous and a discretely adjustable focal length.

[0012] According to the invention, a reflective optical system with an adjustable effective focal length is proposed. The reflective optical system has at least two movable mirror surfaces arranged off-axis and sequentially along a beam path of the optical system. The movable mirror surfaces are each movable from a first displacement position, hereinafter also referred to simply as the first position, to at least a second displacement position, hereinafter also referred to as the second position.

[0013] In the first position, the first functional areas of the movable mirror surfaces are arranged in the beam path. According to the invention, the first functional areas are designed such that they together produce a first finite focal length.

[0014] In the second position, two additional functional areas of the movable mirror surfaces are arranged in the beam path. These second functional areas are designed such that together they produce a second, different, finite focal length. Therefore, the effective focal length of the optical system with the movable mirror surfaces in the first position differs from the effective focal length of the optical system with the movable mirror surfaces in the second position.

[0015] According to the invention, the mirror surfaces are arranged in any position such that the object-side and image-side sections of the optical axis of the optical system remain fixed regardless of their position. This means that the beam position at the input and output of the optical system is constant, independent of the mirror positions. In other words, the optical system has exactly one input / output channel through which the light rays to be imaged can enter and exit. The position of the object-side and image-side sections of the optical axis of the optical system is not changed by moving the movable mirror surfaces from the first position to the second position.

[0016] This can be achieved, for example, by compensating for a change in the beam position within the optical system caused by a displacement and / or tilt of one of the movable mirror surfaces by a suitable displacement and / or tilt of the other movable mirror surface. It is also possible to shift each of the movable mirrors in such a way that the beam position remains unchanged within the optical system.

[0017] The optical system according to the invention can be designed, in particular, to have a plurality of positions. The mirror surfaces can be designed, in particular, to allow discrete or continuous adjustment of the effective focal lengths.

[0018] The application is not limited to specific wavelength ranges and conceptually allows for use from the UV to the IR wavelength range. It can be used for both terrestrial and extraterrestrial applications. According to the invention, it can also be used in simple microscope optics for imaging with different focal lengths as a continuous or discrete system. Compared to the prior art, the presented solution does not represent a complete telescope but can be coupled with various types of telescopes. In general, an independent application of the beam-shaping assembly without additional telescopes is also conceivable. The arrangement can be configured as a relay system or downstream of the telescope.

[0019] In an advantageous embodiment of the optical system, movable mirror surfaces, whose functional areas together produce a focal length, are preferably arranged together on a single substrate, wherein the substrate is movable relative to the beam path.

[0020] In a further advantageous embodiment of the optical system, the mirror surfaces are shaped and arranged such that two light rays passing through an object point in an object plane, spaced apart from the object-side section of the optical axis, and immediately afterwards passing through the optical system with mirror surfaces in the first position, intersect at a first image point in an image plane; and two light rays passing through the same object point in the object plane, spaced apart from the object-side section of the optical axis, and immediately afterwards passing through the optical system with mirror surfaces in the second position, intersect at a second image point in the image plane.In other words, the movable mirror surfaces and their functional areas are designed and arranged in such a way that an object located in an object plane is imaged onto a single image plane. The magnification factor of an image produced by the optical system with mirror surfaces in the first position differs from the magnification factor of the image produced by the optical system with mirror surfaces in the second position.

[0021] In a particularly advantageous embodiment of the optical system, the system comprises four or more, preferably an even number, movable mirror surfaces. The larger number of movable mirror surfaces, each with at least two functional areas, allows for the targeted coordination of several finite focal lengths, which are achieved by the functional areas arranged in the beam path. In particular, the focal lengths achieved in the different positions can be coordinated such that the object and image planes remain fixed at different magnifications. Such a setup can therefore, for example, simplify the realization of the fixed object and image planes described above at different magnifications. The first and fourth movable mirror surfaces can be arranged together on a first substrate.Regardless, the second and third movable mirror surfaces can be arranged together on a second substrate. Furthermore, such a setup can include a beam deflection unit. A beam deflection unit can be any element that deflects a light beam by a specific angle. Beam deflection units designed as retroreflectors, capable of deflecting the light beam by 180°, are particularly advantageous.

[0022] Preferably, the first movable mirror surface, the second movable mirror surface, the beam deflection unit, the third movable mirror surface, and the fourth movable mirror surface are arranged sequentially in the beam path. The mirror surfaces are designed such that the first and fourth movable mirror surfaces have functional areas that together produce specific focal lengths, and the second and third movable mirror surfaces have functional areas that together produce specific focal lengths.

[0023] In particularly advantageous embodiments of the invention, at least one, preferably two, and most preferably each of the movable mirror surfaces forms an angle of 45° with the optical axis. This can particularly mean that the vertices of the movable mirror surfaces form an angle of 45° with the optical axis. It is especially advantageous if the beam path is deflected by 45° by reflection at the mirror surfaces.

[0024] In further advantageous embodiments of the invention, the optical system has a displacement path along which a movable mirror surface can be moved from the first to the second position. The displacement path is advantageously linear and preferably runs along a direction that lies within the movable mirror surface that is displaceable along the displacement path and / or is orthogonal to the optical axis. This makes it particularly easy to ensure that the beam position is not changed by moving the mirror surfaces along the displacement path.

[0025] It can be particularly advantageous if the displacement paths along which two displaceable mirror surfaces, whose functional surface together effect a focal length, can be displaced from the first to the second position are in the same direction and / or of the same magnitude.

[0026] In particularly advantageous embodiments of the invention, at least one of the mirror surfaces is configured as a freeform shape that can be described by a basic description with higher-order terms. The basic description can be, in particular, spherical, elliptical, aspherical, parabolic, or hyperbolic. The higher-order terms can advantageously be Zernike polynomials. The freeform shape is configured, in particular, to form the functional domains of the mirror surfaces described above.

[0027] The production of free-form mirrors also enables precise referencing through optical sub-apertures and mechanical support structures on the monolithic optics, which can be manufactured in one step with the optical mirror surface, thus simplifying adjustment and enabling it with high accuracy.

[0028] In further advantageous embodiments, at least one of the mirror surfaces has an aperture that can be used as a reference for checking the position and orientation of the mirror surfaces relative to each other. The aperture can be formed as a region within the freeform shape of the mirror surface. Advantageously, an additional reflective surface can be integrated on one of the mirror surfaces, with the additional reflective surface taking over the task of checking the position and orientation. This additional reflective surface can also be integrated into the freeform shape.

[0029] Furthermore, embodiments of the invention are possible in which at least one optical reference is arranged on the optical components, such as the mirror surfaces or the substrates of the mirror surfaces. In addition, in advantageous embodiments of the invention, mechanical references and / or mechanical support structures can be arranged on at least one of the optical components in a pre-assembled or machined manner.

[0030] In a further embodiment of the invention, at least one refractive element is arranged in the beam path of the optical system. This can be particularly useful for applications with a narrowly limited wavelength range in which chromatic aberrations do not play a significant role.

[0031] In particularly advantageous embodiments, the reflectivity of the mirror surfaces is greater than 90%, preferably greater than 95%, at wavelengths greater than or equal to 900 nm, and / or at wavelengths between 300 nm and 900 nm, and / or at wavelengths less than or equal to 300 nm. Particularly advantageous are embodiments in which the mirror surfaces reflect light in the visible range, i.e., at wavelengths between 400 nm and 800 nm. Advantageously, the reflectivity of the mirror surfaces for light with a wavelength in the wavelength range between 400 nm and 800 nm is greater than 50%, particularly advantageously greater than 75%, and most advantageously greater than 90%.The reflectivity can be greater than 50%, particularly advantageously greater than 75%, and most advantageously greater than 90% in the entire range between 400 nm and 800 nm, or only in a 5 nm, advantageously 50 nm, and particularly advantageously 100 nm wide sub-range between 400 nm and 800 nm.

[0032] According to the invention, an optical setup is proposed comprising a previously described optical system and at least one imaging optical system, in particular a telescope optic or a microscope optic, wherein the optical system is integrated into the imaging optical system or is positioned upstream or downstream of the imaging optical system. By shifting the mirror surfaces to different displacement positions, the magnification factor of the overall system can be changed.

[0033] According to the invention, a method for calculating surface shapes of the movable mirror surfaces for the optical system described above, comprising two effective focal lengths, is also provided, comprising the steps: Defining an optimization parameter / goal (e.g., wavefront criterion, RMS spot radius, MTF) for the system. Defining the geometric boundary conditions: ∘ Defining distances and angles between the mirror surfaces, where the distances are defined in the direction of the beam path as well as laterally to the beam path, ∘ Defining the displacement path of the movable mirror surfaces, Defining the diameter of the mirror surfaces. Defining the optical boundary conditions: ∘ Defining application wavelength(s), ∘ Defining the effective focal length and / or achievable magnification factors of the optical system and the resulting definition of object and image field(s) as well as the numerical apertures for both configurations, Defining the pupil position and size, Defining the basic description and the associated core properties (e.g.,Surface curvature, conic constant, aspheric coefficients), ∘ Defining the mathematical description to be used for the freeform surfaces, ∘ Defining the power distribution for the mirror surfaces (converging, diverging), ∘ If necessary, a more precise definition of the relative surface position of the freeforms (e.g., the surface vertices).

[0034] Such a procedure can be carried out using available optical design and / or optimization tools. Naturally, the procedure described above can be extended to any number of effective focal lengths or achievable magnifications while maintaining a fixed object and image plane.

[0035] The following figures and examples are intended to explain the subject matter of the invention in more detail without limiting it to the embodiments shown herein.

[0036] It shows: Figure 1 shows a schematic representation of an embodiment of an optical system according to the invention in two positions. Figure 2 shows a substrate with two mirror surfaces of an optical system according to the invention. Figure 3 shows a perspective view of another embodiment of the optical system according to the invention. Figure 4 shows the embodiment of the optical system according to the invention. Figure 3 in two positions. Figure 5 shows the embodiment of the optical system according to the invention. Figure 3 In side view. Figure 6 shows a schematic representation of another embodiment of an optical system according to the invention in two positions.

[0037] Figure 1Figure 1 shows a schematic representation of a first embodiment of an optical system 1 according to the invention. The optical system 1 has a first movable mirror surface 2 and a second movable mirror surface 8. Both mirror surfaces 2, 8 each form an angle with the beam path 15 and are arranged sequentially along the beam path 15. Figure 1 The optical system 1 according to the invention is shown in two different states: In Figure 1a ) both movable mirror surfaces 2, 8 are each in a first position. In Figure 1b ) both movable mirror surfaces 2, 8 are each arranged in a second position.

[0038] Each of the movable mirror surfaces 2, 8 has two functional areas: The first movable mirror surface 2 has a first functional area 3 and a second functional area 4. The second movable mirror surface 8 has a first functional area 9 and a second functional area 10.

[0039] When the first mirror surface 2 is in the first position, the first functional area 3 is arranged in the beam path 15 of the optical system. When the first mirror surface 2 is in the second position, the second functional area 4 of the first movable mirror is arranged in the beam path 15 of the optical system. When the second mirror surface 8 is in the first position, the first functional area 9 of the second mirror surface is arranged in the beam path 15 of the optical system. In the second position of the second mirror surface 8, the second functional area 10 is arranged in the beam path 15 of the optical system.

[0040] The functional areas of the movable mirror surfaces are each designed such that together they produce a finite focal length. In other words, light rays incident parallel to the optical axis, subsequently reflected by the first functional area 3 of the first movable mirror surface 2, and then reflected by the first functional area 9 of the second movable mirror surface 8, are focused onto a first focus located on the image-side portion of the optical axis. Light rays incident parallel to the optical axis, subsequently reflected by the second functional area 4 of the first movable mirror surface 2, and then reflected by the second functional area 10 of the second movable mirror surface 8, are focused onto a second focus located on the image-side portion of the optical axis.In principle, more than two functional areas per mirror surface are possible, so that more than two finite focal lengths can be achieved.

[0041] According to the invention, the movable mirror surfaces 2, 8 are movable from their respective first positions to their respective second positions. A displacement path, i.e., the path along which one of the movable mirror surfaces can be moved from its first position to its second position, can, for example, be straight. It is also possible to incorporate embodiments in which the movable mirror surfaces 2, 8 can be moved to more than two positions or continuously. Such additional positions can, for example, be arranged at various points along the displacement path between the first and second positions. At least one or all of the movable mirror surfaces 2, 8 can, for example, be guided on a linear guide or a hinge / solid-state mechanism.

[0042] According to the invention, the mirror surfaces are arranged in every position such that the beam position at the input and output of the optical system remains unchanged. This means that the mirror surfaces in the first and second positions are arranged such that object-side sections of the optical axis 16 and image-side sections of the optical axis 17 are fixed.

[0043] In the embodiment of the Figure 1This is achieved, for example, by arranging the mirror surfaces such that both the point in the beam path where the beam path intersects a movable mirror surface or a functional area of ​​the mirror surface, and the angle between the incident and outgoing beam paths, are the same in every position. Embodiments are also conceivable in which deviations from the rules described above are possible. Since two movable mirror surfaces are provided according to the invention, a positional deviation caused by a displacement or tilting of one mirror can be compensated for by a corresponding displacement or tilting of the other mirror.

[0044] For example, embodiments are possible in which the position in the beam path where a movable mirror surface is arranged differs between the first and second positions. Such an embodiment is found, for example, in Figure 6 shown. In this embodiment, however, the resulting offset of the beam path can be compensated for by the second movable mirror surface.

[0045] Figure 1b Figure 25a shows an example of a first displacement direction, indicating the direction in which both movable mirror surfaces 2, 8 can be moved from their respective first to their respective second positions. Alternatively or additionally, the movable mirror surfaces can also be moved in the direction of a second displacement direction 25b. The second displacement direction is shown in Figure 25a. Figure 1bperpendicular to the drawing plane. The direction of translation can be, for example, within the mirror plane, or perpendicular to the perpendicular of the mirror surface.

[0046] An optical system according to the invention can, in addition to the at least two movable mirror surfaces 2, 8, also include further mirror surfaces or other optical elements. Each of the further mirror surfaces or each of the other optical elements can be movable or fixed. In the embodiment of the Figure 1 The optical system includes a deflecting mirror 36. The deflecting mirror 36 is fixed in place. The deflecting mirror 36 is located in the beam path between the first movable mirror surface 2 and the second movable mirror surface 8.

[0047] Furthermore, it is possible to combine several of the arrangements described above, each featuring two movable mirror surfaces. An example of a combination of two arrangements, each with two movable mirror surfaces, is shown below. It is also possible to combine the arrangement described above with any number of movable mirror surfaces.

[0048] Figure 2Figure 1 shows a perspective view of a single substrate 20 on which two movable mirror surfaces 2, 8 are arranged. The functional areas of these mirror surfaces together produce a finite focal length. This means that the movements of the two movable mirror surfaces 2, 8 are necessarily mechanically coupled. In particular, the functional areas can be arranged within the movable mirror surfaces 2, 8 such that the first and second functional areas of the mirror surfaces 2, 8 are spaced apart from each other with the same direction and magnitude. This ensures, for example, that when the substrate is moved, the first functional areas are always located in the beam path, or the second functional areas are always located in the beam path. This can make the optical arrangement more robust against external disturbances. Likewise, the overall system design can be simplified.

[0049] Figure 3Figure 1 shows a perspective view of an optical system with four movable mirror surfaces 2, 5, 7, 8 and a deflecting unit 6. The deflecting unit 6 has two mirror surfaces. The four movable mirror surfaces and the beam deflecting unit 6 are arranged in the beam path 15 such that a first movable mirror surface 2, a second movable mirror surface 5, the beam deflecting unit 6, a third movable mirror surface 7, and a fourth movable mirror surface 8 are arranged successively in the beam path.

[0050] Each of the four movable mirror surfaces 2, 5, 7, 8 has at least two functional areas. For example, the first mirror surface 2 has a first functional area 3 and a second functional area 4. The fourth movable mirror surface, for example, has a first functional area 9 and a second functional area 10. The functional areas 3, 4, 9, 10 of the first 2 and fourth movable mirror surfaces 8 are configured such that they together produce a specific finite focal length. The functional areas of the second 5 and third movable mirror surfaces 7 are configured such that they together produce a specific finite focal length.

[0051] The functional areas can be designed in such a way that an image plane and an object plane are constant regardless of whether the first or second functional areas are arranged in the beam path.

[0052] It is also possible to realize the optical setup with the properties described above without a deflection unit 6 or with a differently designed deflection unit.

[0053] Figure 4 shows the structure of Figure 3 in a frontal view. The object-side sections 16 and image-side sections 17 of the optical axis are perpendicular to the viewing plane. In Figure 4a The structure with the four movable mirror surfaces 2, 5, 7, 8 is shown in their respective first positions, in which the respective first functional areas 3, 9 are arranged in the beam path 15. Figure 4bFigure 1 shows the setup with the four movable mirror surfaces 2, 5, 7, 8 in their respective second positions, in which the respective second functional areas 4, 10 are arranged in the beam path 15. The displacement from the first to the second displacement position is of the same magnitude for the first and fourth movable mirror surfaces 2, 8 along a first direction 25. The displacement from the first to the second position is of the same magnitude for the second and third movable mirror surfaces 5, 7 along a second direction 26. Figure 4The first direction 25 and the second direction 26 are opposite. Furthermore, the position of the object-side segment of the optical axis 16, i.e., the distance 32 to an origin 33 of a global coordinate system, remains constant regardless of the position. Additionally, the position of the image-side segment of the optical axis 17, i.e., the distance 31 to the origin 33 of a global coordinate system, remains constant regardless of the position.

[0054] Figure 5 shows the structure of Figure 3 and 4 in a side view. Reference symbol list:

[0055] 1 Optical system 2 First movable mirror surface 3 First functional area of ​​the first movable mirror surface 4 Second functional area of ​​the first movable mirror surface 5 Second movable mirror surface 6 Beam deflection unit 7 Third movable mirror surface 8 Fourth movable mirror surface 9 First functional area of ​​the fourth movable mirror surface 10 Second functional area of ​​the fourth movable mirror surface 11 Object plane 12 Image plane 15 Beam path 16 Object-side section of the optical axis 17 Image-side section of the optical axis 20 (First) substrate 21 Second substrate 25 Displacement path 25 First displacement direction 25 Second displacement direction 25 Third displacement direction 26 Displacement path 31 Position of image-side optical axis 32 Position of object-side optical axis 33 Origin of a coordinate system 35 Angle between optical axis and mirror surface 36 Deflection mirror

Claims

1. A reflective optical system (1) with an adjustable effective focal length, comprising at least two displaceable mirror surfaces (2, 8) which are arranged off-axis and successively along a beam path (15) of the optical system (1) and can each be displaced from a first displacement position to a second displacement position, wherein, - first functional areas (3, 9) in the first displacement position of the displaceable mirror surfaces (2, 8) is arranged in the beam path (15), and the first functional areas (3, 9) are configured such that they together effectuate a first finite focal length; and - second functional areas (4, 10) in the second displacement position of the displaceable mirror surfaces (2, 8) are arranged in the beam path (15), and the second functional areas (4, 10) are configured such that they together effectuate a second finite focal length; wherein the mirror surfaces (2, 8) are arranged in each displacement position such that the object- and image-side sections (16, 17) of the optical system's optical axis are fixed independently of the displacement position.

2. The optical system (1) according to the preceding claim, wherein displaceable mirror surfaces (2, 8), whose functional areas (3, 4, 9, 10) together produce a focal length, are arranged together on a single substrate (20), the substrate (20) being displaceable relative to the beam path.

3. The optical system (1) according to any one of the preceding claims, wherein the mirror surfaces (2, 5, 7, 8) are shaped and arranged such that two light beams, which pass through an object point in an object plane (11) spaced apart from the object-side section of the optical axis (16) and immediately afterwards pass through the optical system (1) with mirror surfaces in the first displacement position, having an intersection point in a first image point in an image plane (12); and two light beams, which pass through the same object point in the object plane (11) spaced apart from the object-side section of the optical axis (16) and immediately afterwards pass through the optical system (1) with mirror surfaces in the second displacement position, having an intersection point in a second image point in the image plane (12).

4. The optical system (1) according to any one of the preceding claims, comprising four displaceable mirror surfaces (2, 5, 7, 8) and a beam deflection unit (6), wherein the first (2) and fourth displaceable mirror surfaces (8) are arranged together on a first substrate (20), and the second (5) and third displaceable mirror surfaces (7) are arranged together on a second substrate (21), wherein the first displaceable mirror surface (2), the second displaceable mirror surface (5), the beam deflection unit (6), the third displaceable mirror surface (7) and the fourth displaceable mirror surface (9) are arranged successively in the beam path (15), wherein the first (2) and the fourth displaceable mirror surfaces (8) have functional areas (3, 4, 9, 10) which each together produce specific focal lengths, and the second (5) and the third displaceable mirror surfaces (7) have functional areas which each jointly produce specific focal lengths.

5. The optical system (1) according to any one of the preceding claims, wherein each mirror surface forms an angle of 45° with the optical axis.

6. The optical system according to any one of the preceding claims, wherein a displacement path, along which a displaceable mirror surface can be displaced from the first to the second displacement position, passes linearly and preferably along a direction lying within that displaceable mirror surface and / or is orthogonal to the optical axis.

7. The optical system according to any one of the preceding claims, wherein displacement paths along which two displaceable mirror surfaces, which together produce a focal length, can be displaced from the first to the second displacement position are aligned and / or equal in length.

8. The optical system according to any one of the preceding claims, wherein at least one of the mirror surfaces is designed as a free form which is writable by a basic specification, in particular spherical, elliptical, aspherical, parabolic or hyperbolic, with higher-order terms, in particular Zernike polynomials.

9. The optical system according to any one of the preceding claims, wherein at least one of the mirror surfaces has an aperture that can be used as a reference to control the mirror surfaces' position and orientation relative to each other.

10. The optical system according to any one of the preceding claims, wherein at least one optical reference is arranged on at least one of the displaceable mirror surfaces or at least one substrate.

11. The optical system according to any one of the preceding claims, wherein a mechanical reference and / or support structure is mounted or machined on at least one of the displaceable mirror surfaces or at least one substrate.

12. The optical system according to any one of the preceding claims, wherein the mirror surfaces' reflectivity of light with a wavelength between 400 nm and 800 nm is greater than 50%, particularly advantageously greater than 75%, and most particularly advantageously greater than 90%.

13. The optical structure comprising an optical system according to the preceding claims and at least one imaging optical system, particularly a telescope or a microscope, wherein the optical system is integrated into the imaging optical system or is connected upstream or downstream of the imaging optical system.