Waveguide and method for manufacturing the same - Patents.com

Abstract

The present invention relates to a waveguide (1) for transmitting electromagnetic waves, and in particular to a waveguide for transmitting image information from a proximal end (2) of the waveguide to a distal end (4) of the waveguide along a transmission direction (5) extending between the proximal and distal ends and across a cross section extending transversely to the transmission direction, wherein light may be transmitted through the waveguide (1) by Anderson localization, and the waveguide (1) has improved properties compared to conventional optical fiber bundles.

Description

[Technical field]

[0001] The present invention relates to a waveguide for transmitting electromagnetic waves, in particular a waveguide for transmitting image information, and to a method for manufacturing a waveguide, in particular an image guide. [Background technology]

[0002] An image guide generally includes a plurality of individual optical fibers, each including a core and a cladding surrounding the core, that are assembled into a bundle and arranged in a grid in cross section with a one-to-one relationship between the light input face and the light output face to form a plurality of pixels, each pixel essentially serving to transmit a brightness value or color information through the image guide.

[0003] In practice, it is often desirable for an image guide to have the highest possible resolution. In principle, this can be achieved by reducing the diameter of the individual optical waveguides. However, due to the laws of physics, the resolution cannot be increased arbitrarily, because as the diameter of the individual optical waveguides decreases, an increasing proportion of the field distribution of the transmitted modes exceeds the dimensions of the optical waveguides, especially the cladding, which leads to increased crosstalk between adjacent optical waveguides and thus increased blurring.

[0004] One approach to provide image guides with higher resolution is based on the wave phenomenon of transverse Anderson localization (TAL). It exploits the fact that a random distribution of refractive index across the cross-section of the image guide, simultaneously with a constancy of the refractive index along the length of the image guide, leads to a restriction of the coupled light in the cross-section due to destructive interference. In practice, for example, a number of individual optical fibers with different refractive indices can be combined to form a random fiber bundle. When a light beam is coupled into such a waveguide, it propagates along the length of the image guide with a limited lateral spread in the cross-section.

[0005] On the one hand, image guides based on the principle of lateral Anderson localization allow higher resolution, but on the other hand, the random distribution of refractive index gives rise to the drawback that the image quality of the transmitted image information, in particular the image sharpness, is subject to local variations or is difficult to control, e.g. the image sharpness in a certain area of ​​the cross-section may differ from the image sharpness in other areas of the cross-section.

[0006] Such non-uniformities make it difficult to actually produce image guides having certain quality standards. Depending on the quality standards applied in production, the reject rate can be high. The above-mentioned problems become even more severe when the cross-sectional area of ​​the image guide is made large. This is especially true for faceplates, where the edge length or cross-sectional diameter can be many times greater than the thickness of the faceplate.

[0007] A faceplate generally consists of a group or array of optical fibers, often relatively short (a few mm), whose axes are fused to the disk surface (a few mm 2 ~ A few centimeters 2) whose main property is to allow the transmission of images from one plate surface to the other in a strictly identical order, i.e. 1:1, or in a regular altered, e.g. rotated, manner. Summary of the Invention [Means for solving the problem]

[0008] It is therefore an object of the present invention to provide a waveguide, in particular an image guide, as well as a method for producing a waveguide, which ensures an increased uniformity, in particular of image sharpness, across the cross-section of the waveguide. One aspect of the object of the present invention is to make the uniformity across the cross-section more controllable and reproducible, for example in order to be able to avoid rejects during production and to reliably guarantee quality standards.

[0009] One aspect of the subject of the invention is the ability to provide a waveguide, in particular an image guide, having a large cross-sectional area, using Anderson localization which at the same time complies with the above mentioned conditions, in particular with a defined uniformity, this particularly relates to a waveguide formed as a faceplate.

[0010] Another aspect of the present invention is a filter with a cutoff frequency (f) greater than 170 line pairs per millimeter (lp / mm). cutAccording to another aspect of the present invention, a waveguide, particularly an image guide, can be provided using Anderson localization having a Michelson contrast of greater than 0.6. According to another aspect of the present invention, the waveguide has an area under the MTF calculated up to a cutoff frequency (f_cut) of greater than 80 lp / mm. According to another aspect of the present invention, the waveguide has a relative contrast P of greater than 0.40 (i.e., 40%) at 114 lp / mm. According to another aspect of the present invention, the waveguide has a relative contrast P of greater than 0.20 (i.e., 20%) at 144 lp / mm. According to another aspect of the present invention, the waveguide can have a relative contrast P of greater than 0.05 (i.e., 5%) up to 1,000 lp / mm. According to another aspect of the present invention, the waveguide has a relative contrast P of greater than 0.05 (i.e., 5%) from 114 to 287 lp / mm. According to another aspect of the present invention, a waveguide, particularly an image guide, can be provided having a Michelson contrast of greater than 0.6. In certain embodiments, for Group 6 and Group 7 images of positive or negative USAF51 targets described herein, the waveguide has a multi-scale structural similarity metric (MS-SSIM) of greater than 0.65 for waveguides having a transmission length of 20 mm or less, a multi-scale structural similarity metric (MS-SSIM) of greater than 0.60 for waveguides having a transmission length of 50 mm or less, a multi-scale structural similarity metric (MS-SSIM) of greater than 0.50 for waveguides having a transmission length of 100 mm or less, and / or a multi-scale structural similarity metric (MS-SSIM) of greater than 0.45 for waveguides having a transmission length of 1,000 mm or less.

[0011] In order to solve the above-mentioned problems, the present invention discloses a waveguide for transmitting electromagnetic waves using Anderson localization, in particular a waveguide for transmitting image information from a proximal end of the waveguide to a distal end of the waveguide along a transmission direction extending between the proximal and distal ends and across a cross section extending transversely to the transmission direction, the waveguide comprising a plurality of structural elements.

[0012] At least two different types of structural elements can be used, i.e. a first type having a first refractive index and a second type having a second refractive index different from the first refractive index. Thus, the plurality of structural elements can include at least one structural element of the first type and at least one structural element of the second type, or conversely, one or more structural elements of the first type and one structural element of the second type, or both multiple structural elements of the first type and multiple structural elements of the second type. Naturally, more than two different types, for example three different types of structural elements, can also be used.

[0013] These structural elements can extend proportionally along the transport direction and across the cross-section of the waveguide, respectively, such that a number of cross-sectional areas are defined in the cross-section of the waveguide, each of which corresponds to a cross-section of one structural element. Thus, these structural elements can extend side by side, in particular parallel to one another, along the transport direction of the waveguide, and the cross-sections of these structural elements can each occupy a planar portion of the cross-section of the waveguide and thus each define a cross-sectional area of ​​the cross-section of the waveguide. Thus, when looking at the cross-sectional surface of the waveguide, for example the light entrance surface or the light exit surface, the cross-sectional area can in particular correspond to the surface area formed by the structural elements.

[0014] According to some embodiments of the present invention, these structural elements, in particular the cross-sectional areas of these structural elements, are thereby formed non-uniformly, but are clearly defined by a predefined rule. These structural elements may therefore exhibit non-uniformity with respect to one another, i.e. may be formed non-uniformly with respect to one another, for example, may be arranged non-uniformly, may be shaped non-uniformly and / or may be configured non-uniformly. In particular, the non-uniformity does not have to be in the individual structural elements themselves, but may be in the structural elements as a whole, and thus, in particular, a physical disorder, i.e. a certain symmetry or a deviation from this symmetry, may be present. On the other hand, non-uniformly formed structural elements may be formed in a fixed manner by a predefined rule, i.e. they are not formed randomly. The feature that these structural elements may exhibit non-uniformity or disorder with respect to one another is therefore in opposition to regularity, in particular in the sense that the non-uniformity or disorder follows a defined rule and not randomness. Thus, in particular, the heterogeneity or disorder may be uniquely predetermined, or may be predetermined by a rule, or may be characterizable by a rule, or may be characterizable by a rule.

[0015] The non-uniformity of these structural elements, particularly the cross-sectional areas of these structural elements, can be manifested in a variety of ways.

[0016] For example, the cross-sectional areas of these structural elements may have a non-uniform, in particular non-periodic, arrangement that is determined uniquely by a predefined rule, for example, they may be arranged differently from a periodic grid, but they may also be distributed non-uniformly on the periodic grid, for example.

[0017] Alternatively or additionally, the cross-sectional areas of these structural elements may be non-uniform with respect to one another, in particular with geometries that are different from one another, for example with non-uniform diameters clearly defined by a predefined rule, but the geometries of the cross-sectional areas may also be of the same type but twisted (for example inverted) relative to one another, in particular in the case of cross-sectional areas having a non-circular shape, as disclosed, by way of non-limiting example, in US Pat. No. 11,079,538, the contents of which are incorporated herein by reference in their entirety.

[0018] In some embodiments, each fiber has a diameter, and at least one of the fiber diameter and the core-to-clad diameter ratio (if the fiber has a cladding) varies with radial displacement of the fiber from the central axis of the bundle, as disclosed, by way of non-limiting example, in U.S. Pat. No. 11,079,538, the entire contents of which are incorporated herein by reference.

[0019] Furthermore, alternatively or additionally, the structural elements may have unequal refractive indices, in particular different refractive indices, which are uniquely determined by a predetermined rule.

[0020] In particular, due to the physical effect of transverse Anderson localization, the limitation of the amplitude of the transmitted electromagnetic wave to a partial area of ​​the cross section of the waveguide can be obtained by the non-uniformity of the structural elements. These structural elements, in particular the cross-sectional area of ​​these structural elements, can therefore be made particularly non-uniform in such a way that the electromagnetic wave transmitted by the waveguide remains localized in a direction extending transversely to the transport direction, in particular so that the electromagnetic wave, or also a selected wavelength range, in particular visible light and / or infrared light and / or ultraviolet light, is transmitted in a directed or restricted manner, in particular image information. In this case, due to the restricted nature of the propagation of light in the waveguide according to the invention, the image information can be transmitted with high definition, which can be improved compared to conventional optical fiber image guides.

[0021] On the other hand, these structural elements, in particular the cross-sectional areas of these structural elements, can be formed in a fixed manner according to a predetermined rule, so that the waveguide has a reproducible structure, in particular so that other waveguides can be produced that have an identical structure to this waveguide. In other words, deviations from the inhomogeneity or symmetry inherent in the waveguide can be generated and reproduced for other waveguides solely on the basis of the predetermined rule. The predetermined rule may therefore contain, in particular, detailed information for describing and / or constructing the waveguide in its structure formed by a number of structural elements, in particular the cross-sectional areas.

[0022] The structure of the waveguide, defined by the cross-sectional area of ​​the structural elements in the cross section, may be invariant along the conveying direction or may be similar in a mathematical sense. In this case, the waveguide may have a region along the conveying direction, the cross-section of which varies, for example varying continuously in at least one region from the proximal end to the distal end or between the proximal and distal ends, or varying continuously in at least one section of length L. The length L may be at least as long as the maximum extension or difference of the cross-sectional changes, or at least corresponds to the maximum extension of the larger input cross-section.

[0023] In the case where the waveguide is mathematically similar along the conveying direction, this may or may not involve a change in cross-sectional shape. The corresponding positions of one or more structural elements at the proximal and distal ends may be changed so that they are twisted relative to each other, which can occur, for example, by twisting the waveguide during manufacture and / or by thermal post-treatment under the action of a rotational or correspondingly directed force. A combination of cross-sectional change and twisting is also conceivable.

[0024] In particular the rules for the unambiguous determination of the arrangement of the cross-sectional areas, the rules for the unambiguous determination of the geometry of the cross-sectional areas and / or the rules for the unambiguous determination of the refractive index of the structural elements can comprise the specification of characteristic quantities of each structural element in accordance with deterministic rules for determining in particular the position of the cross-sectional area, the area of ​​the cross-sectional area or the refractive index of each structural element.

[0025] In other words, the predefined rules may be deterministic rules that describe the structure of the waveguide with its structural elements, unambiguously and without relying on randomness, and that prescribe the characteristics of the structural elements.

[0026] The unambiguous designation rules, in particular deterministic rules for designating features, may include a sequence of fixed values, in particular a mathematical sequence of fixed values. The sequence of values ​​may be formed as a low-discrepancy sequence and / or as a deterministic sequence, for example as a Halton sequence, as a Sobol sequence, as a Niederreiter sequence, as a Hammersley sequence, as a Faure sequence, or as a combination of several sequences or sequences. For example, a part of a first sequence and a part of another sequence may be provided in a prescribed manner for designating a feature.

[0027] The unambiguous prescribing rules, in particular deterministic rules for assigning the features, may include using a particular value, in particular using a determinable, unambiguously specified value of a deterministic sequence for assigning the feature for a particular construction element, using another value of the deterministic sequence for assigning the feature for another construction element, checking whether the value or feature of the other construction element violates a prescribed condition, in particular taking into account the value or feature of the particular construction element, discarding the other value and using another value of the deterministic sequence for assigning the feature for another construction element if the prescribed condition is violated, or modifying the other value in a predefined manner such that the prescribed condition is fulfilled or is no longer violated. In this context, the prescribed condition may be in the form of a fixed minimum difference between these values ​​or features, in particular in the form of a fixed minimum distance between the positions of the cross-sectional areas of these construction elements. In this context, reference is made to the following exemplary description.

[0028] In an embodiment of the waveguide, the distribution of the area content of the Voronoi surfaces relative to the position of the cross-sectional surface of at least one type of structural element, in particular the midpoint, can satisfy at least one of the following conditions, which can be formed as a uniformity criterion for image sharpness in the image guide:

[0029] (i) Variance of the distribution V dis the variance V of the corresponding distribution for a random location of the cross-sectional area z Smaller and better, ratio V z / V d is between 1 and 10, in particular greater than 1, greater than 2, greater than 2.5, and / or less than 8, less than 7, or less than 6.5. z / V d may be in the range of 1 to 8, in the range of 2 to 7 or in the range of 2.5 to 6.5. Dispersion in the sense of the present application is in particular the function V=σ / A 2 should be understood to be the variance normalized to the cross-sectional area A of the waveguide, so that {overscore (σ)} applies, where σ represents the variance of the distribution of the area content of the Voronoi surface versus the position of the cross-sectional area of ​​the structuring element within the surface A.

[0030] (ii) Variance of the distribution V d is 0.38 / N 2,033 less than N, where N represents the number of structuring elements of at least one type, and the variance here is again in particular understood as the normalized variance.

[0031] (iii) Variance of the distribution V d may be greater than the variance of the corresponding distribution for the periodic positions of the cross-sectional area, and the variance V d / A 2 is greater than 0, especially 10 -10 Greater than 10 -9 Greater than or 10 -8 More generally, the variance is here again to be understood in particular as the normalized variance.

[0032] (iv) The amount of skewness of the distribution, S d is the amount of skewness of the corresponding distribution for random locations of the cross-sectional area, S z where the amount of skewness S d is in the range of 0 to 1.5, in particular greater than 0.01, greater than 0.05, greater than 0.1 and / or less than 1.4, less than 1.2 or less than 0.8. Alternatively or additionally, the quantity S z / Sd may be between 1 and 50, in particular greater than 1.1, greater than 1.3, greater than 1.9, and / or less than 25, less than 15, or less than 10.

[0033] (v) Kurtosis of distribution W d may be smaller than the kurtosis Wz of the corresponding distribution for a random location of the cross-sectional area, where the kurtosis W d is between 0 and 10, in particular greater than 0.5, greater than 1, greater than 2 and / or less than 10, less than 6, less than 5. Alternatively or additionally, the ratio W z / W d may be between 1 and 5, in particular greater than 1.1, greater than 1.5, greater than 2, and / or less than 4.5, less than 4, or less than 3.

[0034] The ratio of the total cross-sectional area of ​​the first type of construction element to the total cross-sectional area of ​​the second type of construction element may for example be in the range 1:9 to 9:1, in the range 3:7 to 7:3, in the range 4:6 to 6:4, in particular 5:5, which may also be understood as the degree of filling.

[0035] In particular, in the case where a plurality of structural elements are provided in the form of filamentary channels, the ratio of the total cross-sectional area of ​​the first type of structural elements to the total cross-sectional area of ​​the second type of structural elements may be in the range of 1:150-150:1, in the range of 1:100-100:1, or in the range of 1:50-50:1.

[0036] The total area of ​​the cross-sectional areas of the structural elements for each type may be, for example, at least 1 / (10*T), at least 1 / (5*T) or at least 1 / (3*T) of the cross-sectional area, where T represents the number of types of structural elements.

[0037] The first refractive index of the first type of structural element and the second refractive index of the second type of structural element are at least 10 -4 , e.g. at least 10 -3 , e.g. at least 10 -2 , e.g. at least 10 -1 , such as at least 1, such as at least 2, such as at least 3, such as at least 4.

[0038] With regard to the lateral extension of the structural elements, it can be provided that at least one cross-sectional area has a diameter of 100 nm to 50 μm, 400 nm to 20 μm or 1 μm to 16 μm.

[0039] Furthermore, it may be provided that at least one cross-sectional area has a diameter, in particular, preferably between 0.1 and 10 times the mean wavelength, between 0.2 and 5 times the mean wavelength or between 0.5 and 2 times the mean wavelength of the wavelength range of the electromagnetic waves to be transmitted.

[0040] With regard to the geometrical shape of these construction elements, it can be provided that the cross-sectional area has a non-circular or polygonal, for example pentagonal or hexagonal, geometry.

[0041] As mentioned above, the waveguide may include a plurality of structural elements, including at least two different types of structural elements. Here, it may be provided that in one embodiment of the waveguide, a first type of structural element and a plurality of second type of structural elements are included. Thus, the plurality of structural elements in particular includes exactly one first type of structural element.

[0042] The first type of structural element can be formed, in particular as a monolithic base body, with or from a first medium, which has a first refractive index, and the second type of structural element can be formed as a cavity in the base body, which preferably exhibits a second refractive index, for example due to the refractive index of air or a gas that may be present as medium in the cavity.

[0043] The cavities in the base body can be formed as filamentary channels, i.e. channels having a significantly smaller area compared to the cross-sectional area of ​​a waveguide that can be introduced into the base body by a laser beam, in particular of an ultrashort pulsed laser, for example. Furthermore, the filamentary channels in the base body can be reworked, in particular by chemical or physical etching processes, for example in order to smooth the contours of the filamentary channels.

[0044] In particular in the case where the waveguide is formed as a base body with a cavity, but is also independent of the base body, the waveguide may have a larger extension in the cross section than along the transport direction. In particular, the waveguide can be formed as a faceplate.

[0045] The waveguide is at least 4 mm 2 , at least 2,500 mm 2 , or at least 10,000 mm 2 It may be provided that the cross-sectional area of ​​the

[0046] The waveguide may have, in cross section, an extension that is for example at least twice as large as its extension along the transport direction, at least five times as large as its extension along the transport direction, or at least ten times as large as its extension along the transport direction.

[0047] The base body with the cavity can be produced or manufactured in various ways. On the one hand, the cavity in the base body can be formed by additive construction of the base body, for example by a 3D printing process. Alternatively or additionally, the cavity can be subtractively introduced into the base body, in particular as a hole introduced into the base body, in particular by an abrasive processing method, for example mechanical drilling. Depending on the method used, the hole is not limited to only a circular geometry.

[0048] The waveguide may be manufactured in a multi-train process, in particular such that the waveguide includes, in addition to the plurality of structural elements, at least a second plurality of structural elements, and the waveguide has, in a cross-section, at least two surface regions, each of which includes a cross-sectional area of ​​one of the two plurality of structural elements, which may have the same structure except for rotation and / or inversion.

[0049] Regarding the size of the waveguide along the transport direction, in particular when the waveguide is formed as a faceplate, it can be provided that the waveguide has an extension along the transport direction of less than 10 mm, less than 6 mm, or less than 5 mm.

[0050] In general, however, it may also be provided that the waveguide has an extension along the transport direction of at least 10 mm, at least 20 mm, at least 50 mm or at least 100 mm.

[0051] In the case where the waveguide is formed as a base body with a cavity, the cavity in the base body, in particular the filamentary channels and / or holes, may be filled with a second medium, which has a second refractive index.

[0052] With regard to the material, it may be provided that at least one structural element, in particular this or a structural element of a first type, in particular a structural element formed as a base body, comprises or consists of one or more of the following materials as a medium, namely glass, quartz glass, polymer, crystal, single crystal, polycrystalline material and / or glass ceramic.

[0053] Furthermore, at least one structural element, in particular this or a structural element of the first type, in particular a structural element formed as a base body, may comprise or consist of a material which is a medium, which in the wavelength range to be transmitted, in particular from 2 μm to 20 μm, has an attenuation of less than 100 dB / m, in particular less than 50 dB / m, in particular less than 10 dB / m, in particular less than 1 dB / m, in particular an infrared-transparent material, in particular a chalcogenide which contains at least one element from the group including, in particular, oxygen, sulfur, selenium and tellurium and at least one element from the group including, in particular, arsenic, germanium, phosphorus, antimony, lead, boron, aluminum, gallium, indium, titanium, sodium.

[0054] Furthermore, optically active materials can be provided, for example, as part of the medium or filling and / or also as layers or coatings or other modifications on the surface of an assembly of structural elements formed as rods or tubes, thus enabling, for example, modification of the guided electromagnetic waves, for example in the sense of amplification or conversion, to be achieved.

[0055] Another structural element, in particular this or a structural element of the second type, may comprise or consist of another of the above-mentioned materials, in other words, a structural element, in particular this or a structural element of the second type, and therefore in particular a cavity in the base body filled with a second medium, may also comprise or consist of one or more of the above-mentioned materials, which are media, in particular such materials that the above-mentioned structural element, in particular the first type of structural element, does not comprise.

[0056] As mentioned above, the waveguide may include a plurality of structural elements that are at least two different types of structural elements, for example, one structural element of a first type and multiple structural elements of a second type as mentioned above can be used.

[0057] In another embodiment, it is now provided that a plurality of first type construction elements and a plurality of second type construction elements can be used.

[0058] The first type of structural element may in particular be formed as a rod-like or tubular body having or consisting of a first medium, the first medium having a first refractive index.

[0059] The second type of structural element may in particular be formed as a rod-like or tubular body comprising or consisting of a second medium, the second medium having a second refractive index, and / or may be formed as a cavity in the first type of structural element, the cavity being filled with the second medium which constitutes or has the second refractive index.

[0060] In particular, in cases where a second type of structural element may exist as a filled cavity within a first type of structural element, the structural elements may be formed as a core-shell system, such that the core corresponds to the filled cavity.

[0061] In this context, a rod-like or tubular body should not be understood as only having a circular cross-sectional geometry.

[0062] The present invention further relates to a waveguide for transmitting electromagnetic waves, in particular having one or more of the features described herein, and in particular to a waveguide for transmitting image information from a proximal end of the waveguide to a distal end of the waveguide along a transport direction extending between the proximal and distal ends and across a cross-section extending transversely to the transport direction, the waveguide comprising a plurality of structural elements, at least two different types, namely a first type of structural elements having a first refractive index and a second type of structural elements having a second refractive index, the structural elements respectively extending proportionately along the transport direction and across the cross-section of the waveguide such that a plurality of cross-sectional areas, each corresponding to the cross-section of one of the structural elements, are defined in the cross-section of the waveguide, the waveguide having a greater extension in the cross-section than along the transport direction.

[0063] The invention further relates to a waveguide for transmitting electromagnetic waves, in particular having one or more of the characteristics described herein, in particular a waveguide for transmitting image information from a proximal end of the waveguide to a distal end of the waveguide along a transport direction extending between the proximal and distal ends and across a cross-section extending transversely to the transport direction, the waveguide comprising a plurality of structural elements, at least two different types, namely a first type having a first refractive index and a second type having a second refractive index, each extending proportionally along the transport direction and across the cross-section of the waveguide, such that a plurality of cross-sectional areas, each corresponding to the cross-section of one of the structural elements, are defined in the cross-section of the waveguide, at least one of the structural elements having an attenuation of less than 100 dB / m, in particular less than 50 dB / m, in particular less than 10 dB / m, in particular less than 1 dB / m, in the wavelength range from 2 μm to 20 μm, in particular comprising or consisting of an infrared-transparent material.

[0064] Depending on the extension of the waveguide in the conveying direction, the following attenuation may also be provided: for a waveguide with an extension in the conveying direction of at least 5 mm, an attenuation of less than 100 dB / m may be provided; for a waveguide with an extension in the conveying direction of at least 10 cm, an attenuation of less than 50 dB / m may be provided; for a waveguide with an extension in the conveying direction of at least 1 m, an attenuation of less than 30 dB / m may be provided.

[0065] The invention further relates to a method for producing a waveguide, in particular one having one or more of the characteristics described herein, which method comprises providing a structural element, in particular in the form of a monolithic base body, of a first type, with or consisting of a first medium having a first refractive index, and introducing a plurality of structural elements of a second type, with a second refractive index, cavities being introduced for this purpose in the base body, which cavities are filled with the second medium.

[0066] The second type of structural elements can be introduced such that a plurality of cross-sectional areas, each corresponding to the cross-section of one of the second type of structural elements, can each extend proportionately across the cross-section of the waveguide as defined in the cross-section of the waveguide.

[0067] According to the invention, the second type of structural element can furthermore be introduced in such a way that the cross-sectional area of ​​the second type of structural element has a non-uniform, in particular aperiodic, arrangement but clearly defined by a predetermined rule and / or has a non-uniform, but clearly defined geometry, e.g. diameter, by a predetermined rule.

[0068] In the method for manufacturing a waveguide, it may be provided that the rules for the unambiguous definition of the arrangement and / or geometry of the cross-sectional area comprise, in particular, assigning characteristic quantities for each structural element of the second type according to deterministic rules, in order to define the position and / or area of ​​the cross-sectional area of ​​each structural element.

[0069] The unambiguous specification rules, in particular deterministic rules for defining the features, may in particular involve the use of sequences of fixed values, in particular mathematical sequences. Reference is further made to the sequences given above. Reference is further made to the steps of using, checking and, if necessary, discarding / changing the values, as detailed above.

[0070] The distribution of the surface areas of the Voronoi surfaces relative to the positions, in particular the centers, of the cross-sectional surfaces of at least one type of structuring element may satisfy at least one of the above mentioned conditions, in particular (i), (ii), (iii), (iv) and (v).

[0071] In the process of producing the waveguide, the cavities can be introduced into the base body as filamentary channels, in particular with a laser beam, for example with an ultrashort pulsed laser. Furthermore, the filamentary channels in the base body can be post-treated, in particular by chemical and / or physical etching processes, for example to smooth the contours of the filamentary channels, in particular before they are filled with the second medium.

[0072] The cavities may be introduced into the base body at a mutual distance that is greater than the diameter of the cavities, for example twice the diameter of the cavities or three times the diameter of the cavities.

[0073] The cavities may be created by additive construction of the base body and / or may be introduced into the base body subtractively, in particular by abrasive machining methods, for example mechanical drilling.

[0074] With regard to materials, it may be provided that the main body comprises or consists, as a medium, of one or more of the materials listed above. Furthermore, at least one second type of structural element may comprise or consist, as a medium, of one or more of the materials mentioned with regard to the first type of main body, in particular of materials that the main body does not comprise.

[0075] The present invention further relates to a method of manufacturing a waveguide, which may be specifically referred to as a tension method or a multi-tension method, comprising one or more of the method steps described herein.

[0076] In these methods, a waveguide having one or more of the above characteristics can be assembled with one or more other waveguides, each also having one or more of the above characteristics, such that the waveguides have parallel transport directions to form a preform.

[0077] These assembled waveguides can then be drawn together lengthwise along the transport direction, in particular with draw factors of at least 1:2, at least 1:10 or at least 1:100 being considered.

[0078] These longitudinally assembled waveguides may then be decomposed into sections transverse to the transport direction, which sections may then be assembled again with transport directions parallel to each other to form a preform.

[0079] The assembled sections can then be drawn together lengthwise along the conveying direction, again taking into account draw factors of at least 1:2, at least 1:10, or at least 1:100.

[0080] These waveguides and / or sections, respectively, may be assembled to form a preform, in particular according to the details given above, such that the arrangement of the assembly is uniquely determined by predefined rules.

[0081] These waveguides and / or sections may further be assembled to form a preform such that the structures formed by the cross-sectional areas of the second structural elements, respectively, are rotated relative to one another in the cross-section, in particular in a predetermined manner, and in particular are not rotated relative to one another. Furthermore, during assembly, these waveguides and / or sections may be folded back in the length direction, thereby creating a mirror image of the cross-section.

[0082] In this context, sections formed from at least one other preform may be assembled, which may be assembled according to a common decision rule or may be substantially identical but according to different decision rules.

[0083] Furthermore, the waveguides and / or sections, respectively, may be assembled in an automated manner, in particular by a robot, and the elongated assembled waveguides and / or the elongated assembled sections may be fused by application of heat and / or pressure, in particular under vacuum.

[0084] The invention further relates to a method for manufacturing a waveguide, in which two or more waveguides are manufactured, which are formed in the same manner such that the cross-sectional areas of the structural elements of a second type each have the same, non-uniform, but uniquely defined by a predetermined rule, arrangement and / or the same, non-uniform, but uniquely defined by a predetermined rule, geometry, e.g. diameter.

[0085] In particular, the method may be designed as a method for producing a number of identical waveguides, which may be produced independently of one another, so that in particular different waveguides having the same structure can be manufactured only according to predefined rules.

[0086] Apart from the fact that the method can be used to produce a number of identical waveguides, the method is also suitable for producing a number of waveguides that are identical at least with respect to certain properties, for example, they can meet the uniformity criteria defined for image sharpness and / or they can meet one or more of the conditions mentioned above with respect to the location of the cross-sectional area of ​​at least one type of structural element, in particular the distribution of the areal content of the Voronoi surfaces with respect to the center.

[0087] The invention further relates in particular to a waveguide having one or more of the characteristics described above for the waveguide, and which has been or can be produced by a process including one or more of the process steps described above.

[0088] Finally, the invention also relates to a set comprising two or more waveguides, each of which has in particular one or more of the characteristics described above for the waveguides and which has been or can be produced by a method comprising in particular one or more of the method steps described above, the waveguides each comprising a number of structural elements, which structural elements, in particular the cross-sectional areas of these structural elements, are formed non-uniformly but uniquely according to a predetermined rule, and the two or more waveguides are formed identically such that the structural elements, in particular the cross-sectional areas of these structural elements, are formed non-uniformly in the same manner.

[0089] Hereinafter, embodiments of the present invention will be described with reference to the figures illustrated. [Brief description of the drawings]

[0090] [Figure 1(a)] 1 is a schematic diagram of a cross-section of a waveguide having two types of structural elements, the cross-sectional areas of which are non-uniformly arranged. [Figure 1(b)] 1 is a schematic diagram of a cross-section of a waveguide having two types of structural elements, the cross-sectional areas of which are non-uniformly arranged. [Figure 1(c)]1 is a schematic diagram of a cross-section of a waveguide having two types of structural elements, the cross-sectional areas of which are non-uniformly arranged. [Figure 1(d)] 1 is a schematic diagram of a cross-section of a waveguide having three types of structural elements, the cross-sectional areas of which are non-uniformly arranged. [Figure 1(e)] 1 is a schematic diagram of a cross-section of a waveguide having three types of structural elements, the cross-sectional areas of which are non-uniformly arranged. [Figure 2(a)] FIG. 1 is a schematic perspective view of two waveguides having two types of structural elements whose cross-sectional areas are non-uniformly distributed on a grating. [Figure 2(b)] FIG. 1 is a schematic perspective view of two waveguides having multiple structural elements with non-uniform refractive index (multiple types) and / or non-uniform geometry (diameter). [Diagram 3] FIG. 1 is a schematic cross-sectional view of a waveguide with two types of structural elements whose cross-sectional areas are non-uniformly distributed on a hexagonal lattice. [Figure 4] FIG. 2 is a schematic cross-sectional view of a waveguide with two types of structural elements, the types / refractive indices of these structural elements being / are determined according to a deterministic rule. [Diagram 5] FIG. 1 is a schematic cross-sectional view of a waveguide, e.g. in the form of a faceplate, having a first type of structural element as a base body and a plurality of second type structural elements as cavities in the base body, the positions of the second type of structural elements in the base body being fixed according to a deterministic rule. [Figure 6(a)] 1 is a plot of the variance of the distribution of area inclusions of Voronoi surfaces versus the position of the cross-sectional area of ​​a second type of structuring element located within a first type of structuring element, plotted in logarithmic representation versus the number of second type of structuring elements. [Figure 6(b)] 1 is a plot in double logarithmic representation of the variance of the distribution of the area content of Voronoi surfaces versus the position of the cross-sectional area of ​​a second type of structuring element located within a first type of structuring element versus the number of second type of structuring elements. [Figure 7(a)] FIG. 13 is a diagram showing an example of a Voronoi surface for the position of the cross-sectional surface of a second type of structuring element according to a Halton sequence disposed within a first type of structuring element having a circular cross-section. [Figure 7(b)] FIG. 13 is a diagram showing an example of positioning by a Sobol sequence. [Figure 7(c)] FIG. 13 is a diagram showing an example of random positioning. [Figure 7(d)] FIG. 13 is a diagram showing an example of periodic positioning as another comparative example. [Figure 8(a)] FIG. 2 shows examples of Voronoi surfaces for the position of the cross-sectional surface of a second type of structuring element disposed within a first type of structuring element having a square cross-section. [Figure 8(b)] FIG. 13 is a diagram showing an example of positioning according to a Sobol sequence. [Figure 8(c)] FIG. 13 is a diagram showing an example of random positioning. [Figure 8(d)] FIG. 13 is a diagram showing an example of periodic positioning as another comparative example. [Figure 9(a)] FIG. 1 is a schematic perspective view of a waveguide assembled in a preform, the waveguide being drawn lengthwise. [Figure 9(b)] FIG. 1 is a schematic perspective view of a waveguide that has been drawn lengthwise and from which it is reassembled into a preform. [Figure 9(c)] FIG. 1 is a schematic perspective view of a waveguide that has been drawn lengthwise and from which it is reassembled into a preform. [Figure 9(d)] FIG. 2 is a schematic perspective view of the reassembled waveguide. [Figure 9(e)] FIG. 2 is a schematic perspective view of a waveguide fused under pressure. [Figure 10(a)] FIG. 10 is a schematic cross-sectional view of the waveguides assembled in FIG. 9 to form a preform, again as a section of one waveguide drawn lengthwise, the waveguides not twisted relative to each other. [Figure 10(b)]FIG. 10 is a schematic cross-sectional view of the assembled waveguides in FIG. 9, again as a section of one waveguide drawn lengthwise, the waveguides twisted relative to each other in a predetermined manner to form a preform. [Figure 10(c)] FIG. 10 is a schematic cross-sectional view of the waveguides assembled in FIG. 9 to form a preform, again as sections of two waveguides drawn lengthwise, the waveguides not twisted relative to each other. [Figure 10(d)] FIG. 10 is a schematic cross-sectional view of the assembled waveguides in FIG. 9, again to form a preform, as sections of two waveguides drawn lengthwise, the waveguides twisted relative to each other in a predetermined manner. [Figure 11] Schematic diagrams of various possibilities for waveguides in which the structural elements or the cross-sectional area of ​​the structural elements are formed non-uniformly, but are clearly defined by predetermined rules. [Figure 12] Schematic diagram of various embodiments for the variation between structural elements or cross-sectional areas of structural elements and possible combinations of these embodiments. [Figure 13] Schematic diagrams of various alternative possibilities for waveguides having structural elements or cross-sectional areas of structural elements that are formed non-uniformly but uniquely according to a predetermined rule, each of which comprises a first type of structural element and a number of second type of structural elements. [Figure 14] Schematic diagrams of various alternative possibilities for waveguides having structural elements or cross-sectional areas of structural elements that are formed non-uniformly but that are uniquely determined by a predetermined rule, each of which comprises a plurality of structural elements of a first type and a plurality of structural elements of a second type and, if appropriate, a plurality of structural elements of a further type. [Figure 15] FIG. 13 is a photograph of the face of a fabricated waveguide having a first type structural element formed therein and a plurality of second type structural elements formed as filamentary channels within the first type structural element. [Figure 16] FIG. 2 shows a photograph (and various enlarged sections) of a fabricated waveguide having a plurality of a first type of structural elements and a plurality of a second type of structural elements. [Figure 17] FIG. 17 shows a photograph of the waveguide of FIG. 16 applied as an image guide. [Figure 18] FIG. 13 is a diagram showing the MTF of a sample. [Figure 19] FIG. 1 is a diagram showing diffraction-limited MTF. [Figure 20] FIG. 1 shows the derivative of the measured edge spread function (ESF), which is the line spread function (LSF), which needs to be Fourier transformed to obtain the MTF. [Figure 21] 1 is a graph showing that as the cutoff frequency shifts to higher values, the magnification increases and therefore the effective pixel size decreases. [Figure 22] 1 is a graph of spatial frequency versus intensity. [Diagram 23] FIG. 2 illustrates the curve progression of an error function. [Figure 24] 13 is a graph showing discrete Fourier transform data of Example 8. [Diagram 25] 1 is a graph showing the MTF of Example 1. [Figure 26] 13 is a graph showing MTF data for Example 2. [Figure 27] 1 is a graph showing MS-SSIM data of Example 3. [Figure 28] 1 is a graph showing MS-SSIM data of Example 4. [Figure 29A] 1 is a graph showing MS-SSIM data of Example 5. [Figure 29B] 1 is a graph showing MS-SSIM data of Example 5. [Figure 29C] 1 is a graph showing MS-SSIM data of Example 5. [Diagram 30] 1 is a graph showing MS-SSIM data of Example 6. [Diagram 31] 13 is a graph showing MS-SSIM data of Example 7. [Diagram 32] 1 is a graph showing MS-SSIM data for Example 10. [Diagram 33] 13 is a graph showing the Fourier coefficients and relative contrast P of Example 9. [Diagram 34] FIG. 1 shows the values ​​of MTF calculated at different magnifications. [Diagram 35] 1 is a graph showing the determination of the cutoff frequency from the MTF data of GALOF. [Diagram 36] 1 is a graph showing the determination of fcut from MTF data for FOP. [Figure 37A] FIG. 1 shows images of Group 6 and Group 7 of USAF51 targets through different products. [Figure 37B] FIG. 1 shows images of Group 6 and Group 7 of USAF51 targets through different products. [Figure 38] FIG. 13 shows sub-image partitions for MS-SSIM calculations of small diameter image guides. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0091] FIG. 1 shows various main examples of waveguides 1 that can be used in particular as image guides. The waveguides 1 shown in cross section each include a number of structural elements 10, each extending along the transport direction of the waveguide 1 perpendicular to the drawing of the present specification, each structural element 10 extending proportionately across the cross section of the waveguide 1. Each structural element 10 therefore defines a cross-sectional area 20, i.e. a proportion of the area of ​​the cross section of the waveguide 1. The examples of waveguides 1 shown each have at least two different types of structural elements, each with a different refractive index. These principle embodiments serve to illustrate some variants of inhomogeneity, which may differ in details from the deterministic positioning of the structural elements determined according to the present invention.

[0092] The waveguide shown in cross section in FIG. 1(a) has a first type of structural element 10a formed as a base body, which contains a number of second type of structural elements 10b. The second type of structural elements 10b can thus be formed, for example, as cavities or hollow channels extending along the transport direction in the first type of structural element 10a. In this case, the first type of structural element 10a formed as a base body contains a first material having a first refractive index, and the second type of structural element 10b formed, for example, as a cavity, exhibits a second refractive index, for example due to air or another gas contained therein. In this case, the cross-sectional area 20 of the first type of structural element 10a corresponds to the cross-sectional area of ​​the waveguide minus the holes in this area defined by the cavities, and the cross-sectional area 20 of the second type of structural element 10b corresponds, respectively, to the cross-sectional area of ​​the cavities. However, cavities in the main body may also be filled with a second material, whereby the second type of structural elements 10b correspond to the filled cavities. As shown diagrammatically in the figure, the cross-sectional areas 20 of the second type of structural elements 10b are non-uniform in that their positions are distributed non-uniformly over the entire cross-section, in particular not located on a periodic grid. At the same time, however, the positions of these structural elements are unambiguously determined by predefined rules, as will be explained in more detail herein.

[0093] The waveguide shown in cross section in Fig. 1(b) has two types of structural elements 10a, 10b, namely one structural element 10a, again formed as a base body, having a first refractive index, and several structural elements 10b having a second refractive index different from the first refractive index. In the example shown here, the cross-sectional areas 20 of the second type of structural elements 10b are not only non-uniformly arranged, but also have a non-uniform geometry, in this case a non-uniform diameter, in which there is a limited number, i.e. two different diameters. In this case, the non-uniformity of the arrangement and / or the non-uniformity of the geometry are clearly determined by a predefined rule.

[0094] The waveguide shown in cross section in Fig. 1(c) again has two types of structural elements 10a, 10b, the cross-sectional area of ​​the second type of structural elements 10b being arranged in the first type of structural elements 10a, in particular as a core-sheath system. Thus, in this case, a plurality of first type of structural elements 10a and a plurality of second type of structural elements 10b are provided. These structural elements or the cross-sectional areas of these structural elements are formed non-uniformly, such that the first type of structural elements 10a (which accommodate the second type of structural elements 10b) are arranged non-uniformly, in particular aperiodically, over the cross-section of the waveguide, this arrangement being determined by a predefined rule.

[0095] The waveguides shown in cross-section in Figures 1(d) and 1(e) correspond in some embodiments to the waveguides shown in Figures 1(a) and 1(b), respectively, but have three types of structural elements 10a, 10b, 10c with different refractive indices. In particular, the cavities in the structural element 10a formed as a base body may be filled with different media. The structural elements 10b, 10c therefore have inhomogeneity, in particular in that their refractive indices are different from one another, and the determination of which of the structural elements formed as cavities receive which refractive index may follow a predefined rule.

[0096] 2 shows two further examples of a waveguide 1 that can be used in particular as an image guide. Here again, the waveguide 1 includes a number of structural elements 10, each of which extends from a proximal end 2 to a distal end 4 of the waveguide 1 along a transport direction 5 and is, for example, rod-shaped.

[0097] The waveguide shown in Fig. 2(a) has a plurality of first type structural elements 10a and a plurality of second type structural elements 10b. In this example, the cross-sectional areas of these structural elements are arranged on a periodic lattice. However, these structural elements have a non-uniform arrangement in that the first type structural elements 10a and the second type structural elements 10b, and thus the refractive index, are non-uniformly arranged and / or distributed, and this arrangement and / or distribution is uniquely determined by a predetermined rule.

[0098] The waveguide shown in FIG. 2(b) again comprises a number of structural elements 10 arranged on a periodic grating, in this example the cross-sectional areas of the structural elements having non-uniform geometries. In particular, these geometries may differ in that the diameters of these structural elements or the cross-sectional areas of these structural elements differ from one another. The form of this non-uniformity may be clearly defined by a predefined rule. Furthermore, the structural elements 10 may exhibit a non-uniformity in that the refractive indexes of these structural elements differ from one another, in particular a predefined non-uniformity. In this regard, a discrete number of different refractive indexes may be provided, for example 2, 3, 4 etc., but in principle a continuous variation of the refractive index may also be provided.

[0099] Figure 3 shows another cross-section of a waveguide, which in some embodiments corresponds to the waveguide shown in Figure 2(a). The waveguide shown in Figure 3 has a plurality of, in particular rod-like, structural elements 10, i.e. a plurality of first type structural elements 10a and a plurality of second type structural elements 10b, which are arranged in a cross-section on a periodic lattice, which corresponds in this example to a hexagonal lattice. It is therefore envisaged that at least one of these structural elements 10, or its cross-sectional area 20, is equidistant from, and preferably adjacent to, six directly adjacent structural elements 10, or its cross-sectional area 20.

[0100] With reference to Figures 4 and 5, an example of how these structural elements can be formed non-uniformly, but uniquely defined by a predefined rule is given below. For this purpose, a rule for uniquely defining the feature number, e.g. the position, type, refractive index or even the geometry, can be provided, which rule can include a deterministic sequence (e.g. a Halton sequence). This sequence forms a component of the deterministic rules described in more detail in this specification for specifying the feature numbers of the structural elements. For better understanding, the rules are described in individual steps, whereby, in particular, the overall structure of the waveguide defined by these steps is important, the determination of the overall structure can precede the manufacture of the waveguide, so that the overall structure of the waveguide is uniquely predetermined.

[0101] In a waveguide according to the invention, for example the available area, e.g. cross-sectional area, of the waveguide is filled with structural elements in positions that can be determined in this way according to predefined parameters and according to deterministic rules, these parameters generally including the dimensions, in particular the shape and size, of the structural elements as well as information about, for example, the position and spacing of the structural elements, as well as a filling factor indicating the proportion of the surface that should be filled with one or more types of structural elements.

[0102] For example, for a round shape of the waveguide 1 (see FIG. 3), for example, also for a preform of the waveguide 1 (see FIG. 10) with a predetermined arrangement and number of structural elements (here in this example same diameter, hexagonal close-packed), for example, structural elements 10b occupied by a medium having a second refractive index can be selected for a predetermined filling rate according to a deterministic algorithm (e.g. involving a Halton sequence).

[0103] For this purpose, points 102 can be generated, for example, according to a 2D halftone sequence within a square 100 surrounding the circular shape of the waveguide 1. The values ​​of the sequence are in the range [0,1)×[0,1) and can be scaled according to the dimensions of a given area of ​​the waveguide.

[0104] The Halton sequence is a multidimensional extension of the one-dimensional van der Corput sequence to different bases. n =φ b (n) is defined as the reciprocal of the base b representation of the number n. For example, any positive integer n>=0 can be expressed as a sum in base b>=2.

number

number

number

[0105] These structuring elements 10 are in place and the column covers the entire range [0,1)×[0,1), so further allocation is made. The column elements are passed through the column. The allocation to structuring elements, in particular to structuring elements 10b of the second type, is made by the minimum Euclidean distance. Column elements that are thus assigned to an already selected structuring element or that are out of alignment are ignored and the process continues with the next column element. This continues until a number of structuring elements 10b of the second type, in particular, corresponding to the desired filling factor, has been selected.

[0106] This is illustrated by two embodiments for clarity.

[0107] A first embodiment shows a circular waveguide or a preform for a waveguide 1 (Figure 4), which is made of at least two types of i.e. circular structural elements having two different refractive indices predetermined in a hexagonal packing or arrangement.

[0108] Here, the placement is determined according to a deterministic sequence specification with two occupied refractive indices until a predefined degree of filling is reached, whereby certain occupied structural elements receive one refractive index and other structural elements receive the other refractive index.

[0109] This can be done under the following conditions: the structuring element closest to the column point 102 is occupied (e.g. assigned to type 10b), provided that the column point is within the circle and the position or structuring element concerned is not already occupied (e.g. assigned to type 10b). In these cases, this column point is discarded and the next column point in the sequence is used. Thus, a first point is determined by a deterministic sequence, scaled to a shape (black point), the above conditions are checked and in this first case, the grey structuring element is occupied. Subsequent points are treated accordingly.

[0110] Now, if another column point 102 lies outside the circle or overlaps, then these column points 102 are discarded and the next column point 102 is added, continuing until a predefined fill level is reached.

[0111] This shows the result of discarding points 102v outside the circle (which are now kept) or overlapping points, and a fill level of 50%.

[0112] Another example of an embodiment (FIG. 5) shows the occupation of a given surface. The objective here is to position structural elements, for example holes with a diameter, on a square plate 110 of edge length D according to the Halton sequence, for example for a laser filamentation or drilling process. Here, the sequence points 112 are scaled from a range of values ​​[0,1) to a dimensional range of the area specified here [-D / 2,D / 2). This is done until a predefined filling level is reached. The filling factor is the ratio of the total area of ​​these holes to the substrate area. The holes can be arranged according to the sequence points (FIG. 5a). Alternatively, the sequence points can be rounded to the diameter of the holes (FIG. 5b). If it is not desired for holes to overlap (overlapping pairs of holes 114), such sequence points should be discarded. The overlapping arrangement (FIG. 5b) is accordingly discarded and carried forward further in the sequence. Similarly, here further, there may be another specification, which for example prescribes a minimum spacing of the structural elements.

[0113] It is understood that the method described in more detail above and illustrated in more detail by two examples can also be applied, without limitation, to other possible variations of structural elements, which have three or more refractive indices and / or varying or variable geometries, dimensions, such as two or more diameters and / or shapes, or combinations thereof, at any, possibly predetermined, surface, or the method can more specifically predetermine the structure. The occupancy or occupancy possibilities of the available surface are then adapted or expanded accordingly on a case-by-case basis to achieve the desired required occupancy.

[0114] With reference to FIG. 6, the waveguide according to the present invention meets certain uniformity criteria, in particular with regard to the non-uniformity of the structural elements and, preferably, in the case of a waveguide designed as an image guide, with regard to image sharpness.

[0115] For example, the distribution of areal inclusions corresponding to or uniquely assignable to the cross-sectional areas of the structural elements may satisfy certain conditions. An exemplary variance (normalized variance V = σ / A 2 ) is shown, and this variance is plotted over the number N of structuring elements of this at least one type, shown in logarithmic (FIG. 6a) and double logarithmic (FIG. 6b) representations.

[0116] A waveguide according to the invention can be characterized by a deterministic sequence as described above. Thus, dispersion curve 200 is based on the location of the cross-sectional area determined by a Halton sequence, and dispersion curve 202 is based on the location of the cross-sectional area determined by a Sobol sequence. For comparison, dispersion curve 204 based on a randomly determined location of the cross-sectional area and a fitted curve 206 (variance=0.38A) corresponding to dispersion curve 204 are also shown. 2 / N 2,033 ) is shown. It is clear that the variance (per N) of the distribution of the waveguide according to the invention is smaller than the variance of the waveguide with random disorder.

[0117] Note that the curves shown are based on a distribution over the range of values ​​from [0,1).

[0118] 7 and 8 show exemplary Voronoi surfaces 210 for the position 212 of the cross-sectional area of ​​the structural elements in the case of a waveguide having a circular cross-section (FIG. 7) and a square cross-section (FIG. 8, which is the basis of FIG. 6). FIGS. 7a, 8a show the position 212 and the Voronoi surface 210 based on the Halton sequence, and FIGS. 7b, 8b on the Sobol sequence, respectively, corresponding to the non-uniformity of the waveguide according to the invention. For comparison, FIGS. 7c, 8c show the position 212 and the Voronoi surface 210 based on a random arrangement, and FIGS. 7d, 8d on a periodic arrangement. It is clear that the waveguide according to the invention is characterized by the fact that the structural elements, and in particular the cross-sectional area of ​​these structural elements, are formed non-uniformly, but with a higher uniformity than in the case of a random arrangement.

[0119] Figure 9 shows steps of a method for manufacturing a waveguide by a multi-draw method. In this process, a number of waveguides 1 are assembled and drawn lengthwise to form a preform 30 (Figure 9a). These waveguides 1 may for example be an arrangement of structural elements 10, 20 or 10a, 10b, for example according to Figure 3 or an alternative arrangement, for example according to those shown in Figures 1(a) to 1(e), which may already be drawn in a known manner.

[0120] The assembled, elongated waveguide ("multi-fiber") is then disassembled into sections and reassembled to form the preform 40 (Figure 9b, "multi-multi assembly"). The preform 40 may then be drawn lengthwise again (Figure 9c) and, if necessary, disassembled into sections again and assembled (Figure 9d). Finally, the assembly thus obtained may be melted by application of heat and / or pressure, in particular under vacuum (Figure 9e).

[0121] With reference to FIG. 10, the assembled waveguides drawn in the length direction ("multi-fiber", here "M1") may be assembled without twisting relative to each other during assembly into another preform (FIG. 10a) or may be rotated relative to each other in a particular predetermined manner (FIG. 10b). Furthermore, during assembly, sections from at least two different assembled waveguides drawn in the length direction ("M1", "M2") may be assembled without twisting (FIG. 10c) or may be rotated relative to each other in a particular predetermined manner (FIG. 10d). When the first preform is assembled, these waveguides may be arranged without twisting or may be arranged without twisting, or may be rotated relative to each other in a particular predetermined manner, similar to the arrangement shown in FIG. 10a, FIG. 10b. In the case where the preform is assembled from parts of at least two different waveguides ("M1", "M2"), the arrangement of these different waveguides may follow the above-mentioned arrangement of different types of structural elements (e.g., FIG. 3) and may therefore also be uniquely determined by a predetermined rule.

[0122] Various embodiments of the non-uniformity of the structural elements according to the invention are again explained below by way of example with reference to figures 11 to 14. As mentioned above, the structural elements, in particular their cross-sectional areas, are characterized on the one hand by a non-uniformity relative to one another and on the other hand by a regularity, which has the effect that the non-uniformity of the structural elements is clearly predetermined, in particular deterministic and / or reproducible and not subject to chance.

[0123] For example, the structural elements or cross-sectional areas of the structural elements may have a non-uniform arrangement that is uniquely determined by a predetermined rule, may have mutually non-uniform geometries that are uniquely determined by a predetermined rule, and / or may have mutually non-uniform refractive indices that are uniquely determined by a predetermined rule.

[0124] Fig. 11 shows by means of a tree diagram various possibilities for realizing a non-uniform arrangement that is clearly determined by a predefined rule. Fig. 11a shows as a starting point a structural element 10a, which can be formed, for example, as a matrix material (it is also possible that the structural element 10a is formed as air or is not present). Fig. 11b shows another starting point derived therefrom, with a structural element 10a and a number of periodic positions P for the occupation of the structural element, in this case with a periodic positioning. Fig. 11d shows another starting point derived from Fig. 11a, with a structural element 10a and a number of non-periodic positions P for the occupation of the structural element to obtain a non-periodic positioning. Starting from the starting points shown in Figs. 11b and 11d, as will be explained in more detail below, a waveguide according to the invention is obtained by occupying the positions P with a structural element.

[0125] Starting from Fig. 11b, Fig. 11c shows a waveguide 1 having structural elements 10b, 10c whose cross-sectional area has a periodic positioning and / or is periodically located. The waveguide shown in Fig. 11c has three types of structural elements 10a, 10b, 10c, each of which may have a different refractive index. For example, the structural element 10a may be formed as a matrix material, and the structural elements 10b and 10c may be voids in the matrix material filled with materials of different refractive index.

[0126] However, it is also possible that one of the materials of the structural elements 10b and 10c here corresponds to the matrix material of the structural element 10a, or that no matrix material is present in the (filled) cavities corresponding to these structural elements (see further below in FIG. 13a). It is also possible that the structural element 10a is formed as air, or that it is absent and that the structural elements 10b and 10c adjoin each other (see further below in FIG. 14a).

[0127] The waveguide 1 shown in FIG. 11c has structural elements 10b, 10c with periodic positioning. However, the types of structural elements 10b, 10c are different and the occupation of these different types on the regular lattice is non-uniform but determined by a predetermined rule. In particular, therefore, the mutual variation between the structural elements 10b, 10c is non-uniform but determined by a predetermined rule. In particular, the structural elements 10b, 10c can be described as deterministically disordered. Thus, FIG. 11c shows the case of a waveguide 1, in which these structural elements or the cross-sectional area of ​​these structural elements have a non-uniform arrangement that is uniquely determined by a predetermined rule. The term "arrangement" should be understood here to mean that the selection or occupation of the various types of structural elements 10b, 10c at each periodic position is non-uniform but determined by a predetermined rule, i.e. not random.

[0128] Furthermore, it is possible that the structural elements 10b, 10c do not differ with respect to their refractive index, e.g. have the same refractive index, or are made of the same material, but differ with respect to other aspects (see FIG. 12 below). It is also possible that the structural elements 10b, 10c differ with respect to their refractive index as well as with respect to other aspects.

[0129] Starting from FIG. 11d, FIG. 11e shows a waveguide 1 having two types of structural elements, namely a structural element 10a, which may be formed, for example, as a matrix material, and a number of structural elements 10b, which may be formed, for example, in particular, as filled cavities in a matrix material. In this case, the cross-sectional areas of the structural elements 10b are non-periodically positioned. Here, the positioning of the structural elements 10b can represent a non-uniformity, which in this case is determined by a predefined rule. In particular, the second type of structural elements 10b may have a position that is non-uniform but is determined by a predefined rule. Thus, FIG. 11e shows the case of a waveguide 1, in which these structural elements or the cross-sectional areas of these structural elements have a non-uniform arrangement, which is clearly determined by a predefined rule. The term "arrangement" should be understood here to mean that these structural elements or some structural elements or the cross-sectional areas of the structural elements are arranged non-periodically, the position being determined by a predefined rule, i.e. not random. In the case of Fig. 11e, it is provided in particular that the second type of structural elements 10b have a uniform refractive index, have a uniform geometry and / or are uniformly formed with respect to other aspects, in particular identically formed, in which case one can speak of a uniform occupation of the non-periodic positions.

[0130] In contrast, Fig. 11f shows, starting from Fig. 11d, a waveguide 1 in which a non-periodic positioning of structural elements is provided with structural elements 10b, 10c of different types at the same time. In this case, the non-uniformity, which is clearly determined by a predefined rule, may be present in the non-periodic positioning of the structural elements 10b, 10c, or in the occupancy, i.e. in the mutual variation between the structural elements 10b, 10c, or in both the positioning and the occupancy.

[0131] FIG. 12 shows various possibilities of variation that structural elements can have with respect to one another (middle row) alongside possible combinations of these variations (bottom target), which should not be understood as definitive, by way of example. The variations shown can be used in particular for the occupation of positions in structural elements that are formed inhomogeneously, but are clearly determined by a predefined rule. Structural elements whose cross-sectional areas are arranged in periodic or aperiodic positions, for example in a matrix material, can differ between themselves, for example, with respect to their shape, with respect to their type or refractive index, with respect to their substructures and / or with respect to their rotation (and / or local position).

[0132] For example, variations in the geometry of the structural element, in particular in the cross-sectional area of ​​the structural element, can be formed as variations in shape (number of corners, diameter). Variations in geometry can also be formed as variations in substructures. A substructure can in particular be that the structural element, in particular the cross-sectional area of ​​the structural element, has at least two different regions of different refractive index, in particular a core and a surrounding cladding (core-cladding system).

[0133] In combination, for example, a first type of structural element may have a polygonal shell and / or a polygonal core, and a second type of structural element may have a circular shell and a polygonal core (bottom row, first column). These two types of structural elements can then be used to occupy, for example, periodic or aperiodic positions.

[0134] Further, for example, a first type of structural element may have a first refractive index and a first diameter and a second type of structural element may have a second refractive index and a second diameter (bottom row, second column), or a first type of structural element may have a core-clad system having a core with a first diameter and a second type of structural element may have a core-clad system having a core with a second diameter (bottom row, third column), or a first type of structural element may have a core-clad system having a core with a first refractive index and a second type of structural element may have a core-clad system having a core with a second diameter (bottom row, third column). The structural element of the first type may have a core-clad system having a core with a centered core and the structural element of the second type may have a core with a rotation about a pivot point outside the core (row below, fourth column), or the structural element of the first type may have a core-clad system having a core with a rotation about a pivot point outside the core (row below, fifth column), or the structural element of the first type may have a core-clad system having a centered core and the structural element of the second type may have a core with a rotation about a pivot point outside the core (row below, sixth column), etc.

[0135] FIG. 13a shows a waveguide 1, each of which is similar in some aspects to the waveguide of FIG. 11c. The waveguide has a first structural element 10a, which may be formed, for example, as a matrix material. Furthermore, the waveguide comprises a plurality of structural elements 10b, which may be formed, for example, as filamentary cavities in the matrix material. The structural elements 10b are arranged in periodic positions, but not all periodic positions are occupied by structural elements. Thus, FIG. 13a shows the case of a waveguide 1, in which the structural elements or the cross-sectional areas of the structural elements have a non-uniform arrangement, which is clearly determined by a predefined rule. The term "arrangement" should be understood here to mean that these structural elements or some structural elements or the cross-sectional areas of the structural elements are arranged in periodic locations, some periodic locations are occupied and some periodic locations are not occupied, and the occupation is unambiguously determined and formed by a predefined rule, i.e. not random.

[0136] Figure 13b shows a waveguide 1, which in each case is similar in some aspects to the waveguide of Figure 11f. The waveguide has a first structural element 10a, which may be formed, for example, as a matrix material. Furthermore, the waveguide comprises a number of structural elements 10b having a first diameter and a number of structural elements 10c having a second diameter. In this example, these structural elements are non-periodically positioned, the non-periodic positioning being non-uniform but clearly defined by a predefined rule. Thus, Figure 13b shows the case of a waveguide 1, where these structural elements or the cross-sectional area of ​​these structural elements have a non-uniform arrangement that is uniquely determined by a predefined rule. In this case, the term "arrangement" should be understood to mean that these structural elements or several structural elements or cross-sectional areas of the structural elements are arranged non-periodically and the non-periodic position is determined by a predetermined rule, i.e. is not random, and / or these structural elements are formed non-uniformly but have a variation between them which is uniquely determined by a predetermined rule, the variation being formed, for example, as two types of structural elements having different diameters.

[0137] FIG. 14 shows several waveguides 1, each of which has a plurality of structural elements of a first type and a plurality of structural elements of a second type (possibly of other types in FIG. 14d). In particular, the waveguides 1 shown here do not have a matrix material (and therefore, in particular, they are not formed as faceplates either), but rather the structural elements are adjacent to each other. The waveguides 1 shown in FIG. 14 have in common that the different types of these structural elements, in particular the cross-sectional areas of these structural elements, are periodically arranged, but the occupation of the periodic positions by the types of structural elements is formed non-uniformly, but is clearly determined by a predetermined rule. The waveguides 1 shown in FIG. 14 are therefore characterized in that the structural elements or the cross-sectional areas of the structural elements have a non-uniform arrangement that is uniquely determined by a predetermined rule, where the term "arrangement" is understood to mean that the selection or occupation of the various types of structural elements at the periodic positions is non-uniform, but is determined by a predetermined rule, i.e. is not random.

[0138] FIG. 14a shows diagrammatically a waveguide 1 having a number of structural elements 10a and a number of structural elements 10b having different refractive indices.

[0139] Figure 14b shows a waveguide 1 having a number of structural elements 10d and a number of structural elements 10e with different refractive indices and different substructures, defined by the substructures 10a and 10b (having refractive indices a and b) and 10a and 10c (having refractive indices a and c), respectively, such that the structural elements 10d and 10e are formed as a core-shell system with different cores.

[0140] 14c similarly shows a waveguide 1 with a number of structural elements 10d and a number of structural elements 10e having different refractive indices and different substructures, the substructures being defined by the substructures 10a and 10b (having refractive indices a and b) and 10c and 10b (having refractive indices c and b), respectively, such that the structural elements 10d and 10e are formed as a core-clad system with different claddings.

[0141] Figure 14d similarly shows a waveguide 1 having a number of structural elements 10e, a number of structural elements 10f, a number of structural elements 10g and a number of structural elements 10h, which have different refractive indices and different substructures, represented by the substructures 10a and 10b (having refractive indices a and b), 10a and 10c (having refractive indices a and c), 10b and 10d (having refractive indices b and d) and 10c and 10d (having refractive indices c and d), respectively, such that the structural elements 10e, 10f, 10g and 10h are formed as a core-shell system, where both the shell and the core are different.

[0142] Figure 14e shows a waveguide 1 having multiple structural elements 10c and multiple structural elements 10d having different geometries and different substructures, where the substructure of structural element 10c is defined by substructure elements 10a and 10b (having refractive indices a and b and a first core diameter) and the substructure of structural element 10d is defined by substructure elements 10a and 10b (having refractive indices a and b and a second core diameter).

[0143] FIG. 14f shows a waveguide 1 having multiple structural elements 10c and multiple structural elements 10d with different geometries and different substructures, where the substructure of structural element 10c is defined by substructure elements 10a and 10b (having refractive indices a and b and a centrally located core) and the substructure of structural element 10d is defined by substructure elements 10a and 10b (having refractive indices a and b and an eccentrically located core).

[0144] 15a and 15b show an example of a photo of a practically manufactured waveguide 1 having a monolithic base body, which is a first type of structural element 10a, into which a number of filamentary channels, which are second type of structural elements 10b, are introduced by laser filamentation, these channels having aperiodic positioning, which is non-uniform but clearly defined by a predefined rule. However, in the case of laser filamentation, it can also be provided, for example, that the laser scans the substrate line by line, resulting in a periodicity or grid. In particular, in such a case, the second type of structural elements 10b formed as filamentary channels can also be arranged in periodic positions, in which some periodic positions are occupied and some periodic positions are not occupied, the occupation being determined unambiguously by a predefined rule.

[0145] FIG. 16a shows a photograph as an example of an actually manufactured waveguide 1, which has a number of fibers having a first refractive index, which are structural elements of a first type 10a, and a number of fibers having a second refractive index, which are structural elements of a second type 10b, and FIG. 16b shows an enlarged view and a sketch thereof. In this case, the fibers of the structural elements 10a, 10b are adjacent to each other and are positioned according to a periodic lattice, the occupation of the positions by the types 10a, 10b being formed non-uniformly, but clearly determined by a predefined rule. The first type 10a and the second type 10b of the structural elements may be surrounded by a third type 10c of the structural elements formed as a cladding tube. The cladding tube may have a lower refractive index than both the first type 10a of the structural elements and the second type 10b of the structural elements.

[0146] Figure 17 shows a photograph of the waveguide 1 of Figure 16a applied as an image guide, transmitting an image showing the number 5. Due to the non-uniformity in the arrangement of the structural elements, a high resolution image transmission based on the phenomenon of lateral Anderson localization is achieved here. At the same time, the arrangement according to a predefined rule allows locally controllable image sharpness and uniformity.

[0147] In summary, a waveguide 1 may be provided, for example, in which the structural elements, in particular the cross-sectional areas of the structural elements, have a non-uniform arrangement that is uniquely determined by a predetermined rule, and the non-uniform arrangement that is uniquely determined by a predetermined rule is (a) the structural elements, in particular those which are formed as a periodic positioning of the cross-sectional areas of the structural elements and which are periodically arranged, have a mutual variation which is non-uniform but which is uniquely determined by a predetermined rule; the variation of the periodically arranged structural elements with respect to one another may be realized as a variation of the type of structural elements, the refractive index of the structural elements and / or the geometry of the structural elements (e.g. shape, diameter and / or substructures); (b) formed as a non-periodic positioning of structural elements, in particular cross-sectional areas of structural elements, the non-periodic positioning of the structural elements being formed non-uniformly but unambiguously according to a predetermined rule; Optionally, the structural elements are non-uniform but also have variations with respect to one another that are uniquely defined by a predefined rule, and / or (c) is formed as a positioning of structural elements at periodic locations, in particular cross-sectional areas of the structural elements, some periodic locations being occupied and some periodic locations being unoccupied, the occupation being determined univocally by predetermined rules; Optionally, the structural elements are further non-uniform, but have variations therebetween that are clearly defined by predefined rules.

[0148] As mentioned above, these structural elements may differ from each other in their shape or geometry. In particular, in the case where the waveguide is formed as a fiber rod by a preform fiber drawing process that may be repeated several times, the initial shape or geometry may be retained, but may also appear deformed in the waveguide due to thermal and mechanical effects that may occur in the process. In particular, at least some structural elements may have a hexagonal shape and / or a hyperbolic polygonal shape, in particular a triangular shape or a hexagonal shape. The introduction of structural elements by a laser process may also include such geometric variations, for example by correspondingly guiding the laser beam or a laser beam or laser radiation and / or optically adjusting the beam profile.

[0149] In some embodiments, the waveguide has a cutoff frequency (f_cut) that is greater than 170 line pairs per millimeter (lp / mm), greater than 180 lp / mm, greater than 190 lp / mm, greater than 200 lp / mm, greater than 210 lp / mm, greater than 220 lp / mm, greater than 230 lp / mm, greater than 240 lp / mm, greater than 250 lp / mm, greater than 275 lp / mm, greater than 300 lp / mm, greater than 400 lp / mm, greater than 500 lp / mm, greater than 600 lp / mm, greater than 700 lp / mm, greater than 800 lp / mm, greater than 900 lp / mm, and / or less than 1,000 lp / mm.

[0150] According to another aspect of the invention, the waveguide has an area under the MTF calculated up to a cutoff frequency (f_cut) that is greater than 80 lp / mm, greater than 90 lp / mm, greater than 100 lp / mm, greater than 125 lp / mm, greater than 150 lp / mm, greater than 175 lp / mm, greater than 200 lp / mm, greater than 225 lp / mm, greater than 250 lp / mm, greater than 275 lp / mm, greater than 300 lp / mm, greater than 325 lp / mm, greater than 350 lp / mm, greater than 375 lp / mm, greater than 400 lp / mm, greater than 425 lp / mm, greater than 450 lp / mm, greater than 475 lp / mm, and / or less than 500 lp / mm.

[0151] MTF is a method to compare the performance of different optical systems and can be understood as the performance of a waveguide represented by a periodic sinusoidal pattern at different spatial frequencies, for example as shown in Figure 18, taken from imatest.com. At lower frequencies (compare the top and bottom halves of the sinusoidal pattern chart in Figure 18), the image and object contrast is the same, but the limited resolution of the optical system causes blurring of the image at higher spatial frequencies, which causes a loss of contrast. The modulation of the visibility of the amplitude decreases from 1 to 0 (as shown in the middle graph).

[0152] The MTF at a spatial frequency f is defined as the ratio of image contrast to object contrast at a given frequency.

number

[0153] In principle, the performance may depend on different orientations. The aperture stop in an optical system also constitutes a limit for the transmission of higher spatial frequency components, so this resulting MTF can be considered as an upper limit (diffraction limit) for any imaging system. It can be calculated from the absolute value of the optical transfer function (OTF), which is the normalized autocorrelation of the exit pupil. For rectangular and circular apertures, the diffraction-limited MTF is shown in Figure 19, taken from https: / / spie.org / publications / tt52_151_diffraction_mtf?SSO=1.

[0154] These apertures have the same cutoff frequency ξ cutoff which depends on the wavelength and f-number of the system and indicates the maximum spatial frequency that can be resolved. The aperture shapes are slightly different due to different aperture geometries. All of the lesser performing real optical systems fall below each line.

[0155] MTF is not only applicable to lens systems, but is also suitable for evaluating the performance of any optical transmission, such as image transmission through a coherent fiber bundle.

[0156] It should be noted that in addition to the MTF of the fiber bundle, the MTF of the imaging system itself (e.g., microscope) contributes to the overall transmission performance, so the evaluation should always be done considering the MTF of a blank target (without waveguides).

[0157] How to measure the MTF of a real optical system is described in ISO 12233:2017 (Photography-Electronic still picture imaging-Resolution and spatial frequency response). The so-called oblique edge method is used, where the one-dimensional MTF is estimated from the knife-edge image, since the complete Heaviside function consists of all frequency components. Aberrations from optical imaging systems cause edge blurring due to suppression of the transmission of higher frequency components.

[0158] The derivative of the measured edge spread function (ESF) is the line spread function (LSF) which must be Fourier transformed to obtain the MTF (see Figure 20 taken from Hang Li, Changxiang Yan, and Jianbing Shao, “Measurement of the Modulation Transfer Function of Infrared Imaging System by Modified Slant Edge Method,” J. Opt. Soc. Korea 20, 381-388 (2016)).

[0159] The edge should be tilted slightly (5°-10°) with respect to the pixel orientation of the camera system when integrating the pixel intensity on a line perpendicular to the edge orientation in order to achieve sub-pixel resolution. The pixel size of the detector, or the effective pixel size after optical magnification, constitutes the upper limit (Nyquist limit) for the smallest spatial frequency that can be resolved. Therefore, when measuring and evaluating the MTF of the image guide, it must be ensured that the optical inspection system does not limit the resolution capabilities. This can be done by comparison with a blank target as a reference. The above mentioned effect can be seen in Figure 21, where the cut-off frequency shifts to higher values ​​as the magnification increases, and therefore the effective pixel size decreases.

[0160] As mentioned above, the pixel size of the image constitutes an upper limit for the MTF. To ensure that the observed loss in transmission quality is due to the performance of the optical system and not the sampling of the image, a series of images are taken for the MTF calculation, with increasing resolution, as shown in Figure 26. The change in magnification between successive images should be 1.5x to 2x. The lighting conditions (Lambertian white light source in transmitted light configuration) are determined by checking the histogram of the image and determining whether this is a maximum value (e.g. 2x for an 8-bit image). 8 The image guide is butt-coupled (physically contacted) to the white / black transition of the target without the use of an immersion fluid.

[0161] The calculated MFT is shown in Figure 34. It is clear that the high resolution image suffers from strong noise in the high frequency range, while the low resolution image has an artificially low cutoff frequency due to the Nyquist limit. Therefore, the data used for the MTF calculation is determined as follows:

[0162] For a set of MTF curves from images with increasing resolution, the formula

number

[0163] To determine the cutoff frequency of the image guide from the MTF and hence the resolution, first, multiply the frequency by 1.5 on the frequency axis by f cut_lin We restrict the entire data set to , because noise increases in the high frequency range where the amplitude is small. For this subset of data, the formula

number

[0164] Since the determination of the MTF is based on Fourier analysis, the investigation of fiber bundles with a visible periodic arrangement suffers from significant fixed pattern noise, especially when incorporating EMA. Prominent frequency components corresponding to the fiber pitch cause resonances in the MTF whose amplitudes can even exceed unity. To avoid these artifacts, a standard peak detection algorithm with a Gaussian filter width of 10 lp / mm is applied to this data to identify local maxima. Data within a symmetrical region of three times the full width at half maximum of the peaks are discarded. The procedure described above to determine the characteristics of the MTF is then applied. The results for the analyzed fiber bundle with a fiber pitch of 3 μm and EMA are shown in Figure 36. Here, the blue data points are ignored. The corresponding values ​​are f cut_lin =135.3lp / mm, f cut = 165.0 lp / mm, and Area = 75.8 lp / mm. Again, the determined cutoff frequency corresponds well to a discernible line pair for G7E3 (161.3 lp / mm) in FIG. 37A.

[0165] To determine the Fourier coefficients of relative contrast P, the negative United States Air Force (USAF51) resolution test target was used because it produces images with a low degree of noise. Elements of groups 6-9 of the USAF51 target were used in tests to probe values ​​at higher resolution. Normalization was performed by comparing the results obtained for an image of a target not viewed through the waveguide ("blank target image") with an image of a target viewed through the waveguide ("sample target image").

[0166] To calculate the relative contrast P, the coefficients of the Fourier series are obtained for a given spatial frequency for both the blank target image and the sample target image, as shown, for example, in FIG. 22, and the ratio between the results obtained over one period is the value of P that is added to the final plot.

[0167] The imaging procedure was: 1) taking pictures of the blank target image and the sample target image with the same acquisition parameters (e.g., camera contrast, lighting conditions, and exposure); 2) for each element size, acquiring a grayscale profile in Image J; 3) calculating the values ​​of the Fourier series elements corresponding to the frequencies under investigation in grayscale values; 4) plotting the ratio between the values ​​obtained for the blank target image and the sample target image.

[0168] In some embodiments of the invention, the waveguide has a relative contrast P at 114 lp / mm that is greater than 0.40 (i.e., 40%), greater than 0.45, greater than 0.50, greater than 0.55, greater than 0.60, greater than 0.65, greater than 0.70, greater than 0.75, greater than 0.80, greater than 0.85, and / or less than 0.90. The waveguide may have a relative contrast P at 144 lp / mm that is greater than 0.20 (i.e., 20%), greater than 0.25, greater than 0.30, greater than 0.35, greater than 0.40, greater than 0.45, greater than 0.50, greater than 0.55, greater than 0.60, greater than 0.65, and / or less than 0.70. The waveguide may have a relative contrast P of greater than 0.05 (i.e., 5%), greater than 0.10, greater than 0.15, greater than 0.20, greater than 0.25, greater than 0.30, greater than 0.35, greater than 0.40, greater than 0.45, greater than 0.50, greater than 0.55, greater than 0.60, greater than 0.65, and / or less than 0.70 at or below 1,000 lp / mm. The waveguide may have a relative contrast P of greater than 0.05, greater than 0.10, greater than 0.20, greater than 0.30, greater than 0.40, greater than 0.50, greater than 0.60, greater than 0.70, greater than 0.80, and / or less than 0.90 at 114-287 lp / mm.

[0169] In certain embodiments, the waveguide has a Michelson contrast that is greater than 0.6, greater than 0.7, greater than 0.8, greater than 0.9, and / or less than 1.0.

[0170] Michelson contrast is the difference in luminance between dark and light areas of an image.

number

number

[0171] In certain embodiments, for waveguides having a transmission length up to 20 mm, the waveguides have a multi-scale structural similarity metric index (MS-SSIM) that is greater than 0.65, greater than 0.70, greater than 0.75, greater than 0.80, greater than 0.85, greater than 0.90, greater than 0.95, and / or less than 1.00 for Group 6 and Group 7 images of positive or negative USAF51 targets described herein. In some embodiments, for waveguides having a transmission length up to 50 mm, the waveguides have a MS-SSIM that is greater than 0.60, greater than 0.65, greater than 0.70, greater than 0.75, greater than 0.80, greater than 0.85, greater than 0.90, greater than 0.95, and / or less than 1.00. In some embodiments, for waveguides having transmission lengths up to 100 mm, the waveguides have an MS-SSIM that is greater than 0.50, greater than 0.55, greater than 0.60, greater than 0.65, greater than 0.70, greater than 0.75, greater than 0.80, greater than 0.85, greater than 0.90, greater than 0.95, and / or less than 1.00. In some embodiments, for waveguides having transmission lengths up to 1,000 mm, the waveguides have an MS-SSIM that is greater than 0.45, greater than 0.50, greater than 0.55, greater than 0.60, greater than 0.65, greater than 0.70, greater than 0.75, greater than 0.80, greater than 0.85, greater than 0.90, greater than 0.95, and / or less than 1.00.

[0172] The measurement conditions for calculating the MS-SSIM here are magnifications of 300 to 1,000 times.

[0173] When two images, e.g., a blank target image and a sample target image, are compared by an imaging system, there are different methods described in the literature to compare the two images and evaluate the quality of the sample target image. The most widely used statistical measures are the peak signal-to-noise ratio (PSNR) or the mean square error (MSE), but they do not correlate well with the perception of the human visual system. The assumption that human vision is adapted to extract structural information from images leads to the development of the structural similarity metric (SSIM), a pixel-based comparison used to measure the similarity between two images [Zhou Wang, AC Bovik, HR Sheikh and EP Simoncelli, “Image quality assessment: from error visibility to structural similarity,” in IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600-612, April 2004, doi:10.1109 / TIP.2003.819861.].

[0174] For two aligned images with pixel vectors x = {xi|I = 1,2,…,N} and y = {yi|I = 1,2,…,N}, SSIM calculates

number

number

number

[0175] The maximum value of SSIM(x,y)=1 is achieved only for identical images.

[0176] As a single-scale method, SSIM lacks the variation of human image perception for different sampling densities or viewing distances. Therefore, a multiscale extension of SSIM that considers image details at different resolution levels considers multiscale structural similarity metric (MS-SSIM) [Z. Wang, EP Simoncelli and AC Bovik, “Multiscale structural similarity for image quality assessment,” The Thrity-Seventh Asilomar Conference on Signals, Systems & Computers, 2003, 2003, pp. 1398-1402 Vol.2, doi: 10.1109 / ACSSC.2003.1292216.]:

number

[0177] Here, during M-1 iterations of the low-pass filtered and downsampled image by 2, the luminance l of the image at scale M is M (x,y) and contrast c j(x,y) and structural comparison s j (x,y) is calculated. Weighting parameter α Μ , β j , γ j was calibrated to human image perception by Wang et al. for M=5, yielding β1=γ1=0.0448, β2=γ2=0.2856, β3=γ3=0.3001, β4=γ4=0.2363 and α5=β5=γ5=0.1333.

[0178] To make the comparison, images of Groups 6 and 7 of the positive and negative USAF51 resolution target groups were taken at different magnifications, where the blank target image served as the reference image and the image taken through the image guide was the sample target image. The targets were illuminated from below by a Lambertian white light source. The magnification and illumination were not changed between images, and the histograms of the images were checked to see if this was the maximum value (e.g. 2 for an 8-bit image). 8 Saturation was avoided by making sure that the images were not clipped with a sigma −1 = 255). Before applying the MS-SSIM calculation, the images were aligned and cropped to the same size using a template matching algorithm.

[0179] In cases where the image guide dimensions are too small to fully visualize all elements of Groups 6 and 7, the image must be divided into a series of non-overlapping sub-images (see Figure 38). The size of the sub-images is dictated by the maximum rectangular area that can be transmitted through the waveguide. For each pair of corresponding reference and target sub-images (which can also be aligned by a template matching algorithm), the MS-SSIM of the composite image and its area fraction are calculated. The area-weighted sum constitutes the MS-SSIM of the entire image.

[0180] Conventional fiber bundles, consisting of a (fairly) regular arrangement of core-clad monofibers that transport light by total internal reflection, tend to imprint the underlying structure in the transmitted image, resulting in a pixelated appearance. This is especially evident when extra-mural absorbers (EMA) are incorporated into the fiber bundle. This artifact, known as honeycomb effect, is due to the non-transparent cladding material around the individual cores, so that only their individual locations in the observed field of view are transported. Apart from the reduction of information, this can cause image processing problems related to computer-aided diagnosis if such a transmitted image is sampled in a rectangular pattern on the sensor chip (Rongguang Liang, “Optical Design for Biomedical Imaging”, Chapter 8 ‐ Endoscope Optics, SPIE, (2011)). Therefore, numerous approaches exist to mitigate this effect, including bandpass filtering in the Fourier domain, interpolation, superposition of images with small displacements, compressive sensing and Bayesian approximation, or fiber-core-targeted scanning (see Antonios Perperidis et al., Image computing for fiber-bundle endomicroscopy: A review, Medical Image Analysis, 62, p. 101620, (2020); Qian Li et al., Depixelation of coherent fiber bundle imaging by fiber-core-targeted scanning, Applied Optics, 60 (26), p. 7955 (2021); and references therein). These methods are typically time-consuming and computationally expensive, resulting in reduced SNR or not applicable for real-time analysis.

[0181] Image guides whose transmission is mediated by the multi-beam interference localization phenomenon generally have aperiodic assemblies because they do not have the fixed pattern noise mentioned above, and therefore have superior optical image appearance. This distinction becomes very noticeable when analyzing the discrete Fourier transform of the image shown in Figure 24.

[0182] In such a conventional fiber optic plate (FOP, center row in FIG. 24), the visible periodic structure results in a pronounced multi-peak structure in the discrete Fourier transform.

[0183] As shown in the bottom graph in FIG. 24 of Example 8, the integrated line scan (from top to bottom) of the FFT of the FOP features at least two sharper peaks apart from the central peak, which have an amplitude of at least 25% of the central peak and are at a distance of at least 10 times the width of the central peak from said peak. These can be identified by a common peak detection algorithm with appropriate parameter settings that take into account the noise level of the graph (blur, sharpness, distance, amplitude, as known to experts). In contrast, the waveguide of the present disclosure may have an integrated line scan with a zero peak having an amplitude of at least 25% of the central peak.

[0184] Here, these measurements were made under Lambertian illumination using either a Zeiss SmartZoom 5 microscope with the "PlanApp D 10x / 0.6FWD 10mm" objective (Figure 26 (blank and FOP), Figures 30-31, Figure 34 and Figure 37A) or a Keyence VHX 6000 with the "VH-ZST" dual zoom objective (Figure 26 (TALOF), Figures 27-29, Figures 32-33, Figures 35-36, Figure 37B and Figure 39).

[0185] A first embodiment of the present invention relates to a waveguide (1) for transmitting electromagnetic waves, in particular a waveguide (1) for transmitting image information from a proximal end (2) of the waveguide to a distal end (4) of the waveguide along a conveying direction (5) extending between the proximal and distal ends and across a cross section extending transversely to the conveying direction, the waveguide (1) having a cutoff frequency (f) greater than 170 lp / mm. cut )

[0186] In a second embodiment of the present invention, the waveguide (1) has a cutoff frequency (f cut ) in the first embodiment.

[0187] A third embodiment of the present invention relates to a waveguide (1) for transmitting electromagnetic waves, and in particular to a waveguide (1) for transmitting image information from a proximal end (2) of the waveguide to a distal end (4) of the waveguide along a transport direction (5) extending between the proximal and distal ends and across a cross-section extending transversely to the transport direction, the waveguide (1) having a relative contrast P of greater than 0.40 at 114 lp / mm.

[0188] A fourth embodiment of the invention relates to the waveguide (1) of the third embodiment, wherein the waveguide (1) has a relative contrast P greater than 0.40 and less than 0.90 at 114 lp / mm.

[0189] A fifth embodiment of the present invention relates to a waveguide (1) for transmitting electromagnetic waves, in particular a waveguide (1) for transmitting image information from a proximal end (2) of the waveguide to a distal end (4) of the waveguide along a transport direction (5) extending between the proximal and distal ends and across a cross-section extending transversely to the transport direction, the waveguide (1) having a relative contrast P of greater than 0.20 at 114 lp / mm.

[0190] A sixth embodiment of the present invention relates to the waveguide (1) of the fifth embodiment, wherein the waveguide (1) has a relative contrast P greater than 0.20 and less than 0.70 at 144 lp / mm.

[0191] A seventh embodiment of the present invention relates to a waveguide (1) for transmitting electromagnetic waves, in particular a waveguide (1) for transmitting image information from a proximal end (2) of the waveguide to a distal end (4) of the waveguide along a transport direction (5) extending between the proximal and distal ends and across a cross-section extending transversely to the transport direction, the waveguide (1) having a relative contrast P of greater than 0.05 at up to 1,000 lp / mm.

[0192] An eighth embodiment of the present invention relates to the waveguide (1) of the seventh embodiment, wherein the waveguide (1) has a relative contrast P of greater than 0.05 and less than 0.70 at up to 1,000 lp / mm.

[0193] A ninth embodiment of the present invention relates to a waveguide (1) for transmitting electromagnetic waves, in particular for transmitting image information from a proximal end (2) of the waveguide to a distal end (4) of the waveguide along a transport direction (5) extending between the proximal and distal ends and across a cross-section extending transversely to the transport direction, the waveguide (1) having a relative contrast P of greater than 0.05 at 114-287 lp / mm.

[0194] A tenth embodiment of the present invention relates to the waveguide (1) of the ninth embodiment, wherein the waveguide (1) has a relative contrast P of more than 0.05 and less than 0.90 at 114 to 287 lp / mm.

[0195] An eleventh embodiment of the present invention relates to a waveguide (1) for transmitting electromagnetic waves, in particular a waveguide (1) for transmitting image information from a proximal end (2) of the waveguide to a distal end (4) of the waveguide along a conveying direction (5) extending between the proximal and distal ends and across a cross-section extending transversely to the conveying direction, the waveguide (1) having an area under the MTF calculated up to a cutoff frequency (f_cut) greater than 80 lp / mm.

[0196] A twelfth embodiment of the present invention relates to the waveguide (1) of the eleventh embodiment, wherein the waveguide (1) has an area under the MTF calculated up to a cutoff frequency (f_cut) that is greater than 80 lp / mm and less than 500 lp / mm.

[0197] A thirteenth embodiment of the present invention relates to a waveguide (1) for transmitting electromagnetic waves, in particular a waveguide (1) for transmitting image information from a proximal end (2) of the waveguide to a distal end (4) of the waveguide along a transport direction (5) extending between the proximal and distal ends and across a cross-section extending transversely to the transport direction, the waveguide (1) having a Michelson contrast greater than 0.6.

[0198] A fourteenth embodiment of the present invention relates to the waveguide (1) of the thirteenth embodiment, in which the Michelson contrast is greater than 0.6 and less than 1.0.

[0199] A fifteenth embodiment of the present invention relates to a waveguide (1) for transmitting electromagnetic waves, in particular a waveguide (1) for transmitting image information from a proximal end (2) of the waveguide to a distal end (4) of the waveguide along a transport direction (5) extending between the proximal and distal ends and across a cross-section extending transversely to the transport direction, the waveguide (1) having an MS-SSIM greater than 0.65 mm for a transmission length of up to 20 mm, an MS-SSIM greater than 0.60 mm for a transmission length of up to 50 mm, an MS-SSIM greater than 0.50 for a transmission length of up to 100 mm, and / or an MS-SSIM greater than 0.45 for a transmission length of up to 1,000 mm.

[0200] A sixteenth embodiment of the present invention relates to the waveguide (1) of the fifteenth embodiment, wherein the waveguide (1) has an MS-SSIM greater than 0.65 and less than 1.00 for a transmission length up to 20 mm.

[0201] A seventeenth embodiment of the present invention relates to a waveguide (1) for transmitting electromagnetic waves, in particular a waveguide (1) for transmitting image information from a proximal end (2) of the waveguide to a distal end (4) of the waveguide along a transport direction (5) extending between the proximal and distal ends and across a cross-section extending transversely to the transport direction, the waveguide (1) having a transmission length greater than 100 mm, and the waveguide (1) having an MS-SSIM greater than 0.50.

[0202] An eighteenth embodiment of the present invention relates to a waveguide (1) according to the seventeenth embodiment, wherein for the waveguide (1) having a transmission length greater than 100 mm, the waveguide (1) has an MS-SSIM greater than 0.50 and less than 1.00.

[0203] A nineteenth embodiment of the present invention relates to a waveguide (1) for transmitting electromagnetic waves, in particular a waveguide (1) for transmitting image information from a proximal end (2) of the waveguide to a distal end (4) of the waveguide along a transport direction (5) extending between the proximal and distal ends and across a cross-section extending transversely to the transport direction, the waveguide (1) having an integrated line scan with zero peaks at an amplitude of at least 25% of a central peak.

[0204] A twentieth embodiment of the present invention relates to a waveguide (1) according to any one of the preceding embodiments, wherein the waveguide (1) comprises a plurality of structural elements (10), including at least two different types of structural elements, namely a first type of structural elements (10a) having a first refractive index and a second type of structural elements (10b) having a second refractive index.

[0205] A 21st embodiment of the present invention relates to a waveguide (1) according to any one of the preceding embodiments, in which each structural element (10) extends along the transport direction (5) and proportionally across a cross-section of the waveguide (1), whereby in the cross-section of the waveguide (1) a plurality of cross-sectional areas (20) are defined, each corresponding to a cross-section of one structural element (10), each structural element (10), in particular the cross-sectional area (20) of each structural element being formed non-uniformly but uniquely defined by a predetermined rule.

[0206] A 22nd embodiment of the present invention relates to a waveguide according to any one of the preceding embodiments, wherein the structural elements, in particular the cross-sectional areas of the structural elements, have a non-uniform, in particular non-periodic, predetermined arrangement which is uniquely defined by a predetermined rule, and / or the structural elements, in particular the cross-sectional areas of the structural elements, have a non-uniform, in particular mutually different geometry, e.g. a non-uniform diameter, which is uniquely determined by a predetermined rule, and / or the structural elements have a non-uniform, in particular mutually different refractive index which is uniquely determined by a predetermined rule.

[0207] A 23rd embodiment of the present invention relates to a waveguide according to any one of the preceding embodiments, in which the structural elements, in particular the cross-sectional areas of the structural elements, are formed non-uniformly so that the electromagnetic waves transmitted by the waveguide remain localized in a direction transverse to the transport direction, in particular for transmitting image information.

[0208] A 24th embodiment of the present invention relates to a waveguide according to any one of the preceding embodiments, wherein the proximal end is twisted relative to the distal end.

[0209] A 25th embodiment of the present invention relates to a waveguide as in any one of the preceding embodiments, wherein each fiber has a diameter, a core and optionally a cladding, and at least one of the fiber diameter and the core-to-clad diameter ratio varies with radial displacement of the fiber from a central axis of the bundle.

[0210] A twenty-sixth embodiment of the present invention relates to the use of a waveguide (1) according to any one of the preceding embodiments, wherein the waveguide (1) is a rigid or at least partially flexible image guide used as a component in medical devices for endoscopy, or as an X-ray imaging faceplate, as an image correcting optical component, or as a fiber optic component such as a (resizing) taper, or as an image inverter, e.g. used in night vision devices, as a component for spatial multiplexing for data communication, as a component in remote optical sensing, as a component in lighting applications and as an energy relay for light field energy systems.

[0211] A 27th embodiment of the present invention relates to a combination of one or more of the above-mentioned embodiments.

[0212] example The following waveguides were prepared and analyzed.

[0213] Example 1 An 18 mm thick glass optical fiber bundle (GALOF (Glass Anderson Localization Optical Fiber bundle) or TALOF (Transverse Anderson Localization Optical Fiber bundle)) in which the majority of the light is transmitted via Anderson localization instead of conventional total internal reflection was prepared as follows. Two types of glass rods (mono) of the same diameter but with a refractive index difference of 0.33 were arranged in a predetermined manner as disclosed herein with a mixture of about 50:50 in a hexagonal multi-structure and drawn into a fiber bundle. In a second drawing step, a number of these multi-fibers were assembled in a multi-multi arrangement, where the multi-fibers are randomly oriented. Additional drawing steps were used in the same manner until the diameter of the mono-fibers was reduced to a size of 700-800 nm and GALOFs were produced.

[0214] For a blank target, SCHOTT North America Fiber Optic Plate (FOP) Product No. 24A, as well as GALOF, the slanted sharp edge of the monochromatic image was used to determine the MTF as described herein, and the results are shown in FIG.

[0215] As shown in Figure 25, the GALOF image guide did not reach the resolution limit of the optical detection system (blank). However, the GALOF outperformed the FOP, even though it was imaged at a lower magnification. Furthermore, the MTF of the FOP shows artifacts (peaks / singularities) due to the visible periodic structure of the waveguide, which causes a high contribution in the corresponding Fourier component.

[0216] Example 2 The slanted sharp edges of a monochrome image were observed through the GALOF of Example 1 at magnifications of 200x, 300x, 500x, 1,000x and 1,500x. The MTFs for the blank and the GALOF were determined as described herein. The results are shown in FIG.

[0217] As shown in Figure 26, the expansion of the resolvable spatial frequency range with increasing magnification is noticeable for the blank image due to the Nyquist limit related to the effective pixel size. Only at the highest resolution is saturation of the blank image visible due to the marginal performance of the imaging system. A similar behavior is observed for the TALOF MTF, and in this case the saturation (which occurs around 500x magnification) is limited by the optical transmission performance of the waveguide. The image below the graph shows the transmitted slanted edge picture of the TALOF used for the analysis.

[0218] Example 3 Images of the negative USAF51 target described herein were viewed through GALOF of Example 1 at 300x, 500x and 1,000x magnification. MS-SSIM was determined as described herein. The results are shown in Figure 27.

[0219] Example 4 Images of positive USAF51 targets described herein were viewed through GALOF of Example 1 at magnifications of 300x, 500x and 1,000x. MS-SSIM was determined as described herein. The results are shown in FIG.

[0220] Example 5 Images of the negative USAF51 target described herein were observed at 1,000x magnification through 10mm and 20mm samples of GALOF of Example 1. MS-SSIM was determined as described herein and compared to images taken under the same conditions using a SCHOTT FOP product RFG 88 with a fiber diameter of 3μm. The results are shown in FIG. 29A. FIG. 29B shows images and MS-SSIM of another measurement of 10mm, 20mm, 50mm and 100mm samples of GALOF of Example 1 at 1,000x magnification. FIG. 29C is a plot of the data of FIG. 29A and FIG. 29B.

[0221] Example 6 An image of the negative USAF51 target described herein was viewed at 1,000x through a 5 cm sample of the GALOF of Example 1. MS-SSIM was determined as described herein. The results are shown in FIG.

[0222] Example 7 An image of the negative USAF51 target described herein was viewed at 1,000x magnification through GALOF of Example 1. MS-SSIM was determined as described herein. The results are shown in Figure 31.

[0223] Example 8 A uniformly illuminated image of a square of Group 1 of the negative USAF51 target was viewed through the GALOF of Example 1 at 200x magnification and compared to a blank image and a fiber bundle (center, Honsun with 6μm fiber diameter). The discrete Fourier transform was determined in comparison as described herein. The results are shown in Figure 33.

[0224] The top row in Fig. 33 shows a uniformly back-illuminated (Lambertian) area without (left, blank) and with (middle, 5 mm thick FOP with 6 μm fiber diameter, hexagonal packaging; right, GALOF) image guide transmission. The middle row shows the discrete Fourier transform (FFT) of the corresponding images, with a typical high DC peak in the center. For the FOP, a prominent off-center peak is visible, reflecting the 6-fold symmetry of the fiber arrangement. The TALOF FFT shows an increase at some frequencies, but no clear peaks. The bottom row shows the integrated line scan (along the symmetry axis from top to bottom). The blank and TALOF curves can be described as monotonically decreasing functions (ignoring noise). The FOP curve shows a prominent narrow peak structure, symmetric about the central position with an amplitude significantly larger than the noise level (25% of the central peak), which gives rise to local maxima.

[0225] Example 9 A glass optical fiber bundle was prepared in the same manner as in Example 1, except that the thickness was 10 mm.

[0226] An image of the negative USAF51 target described herein was viewed through GALOF. The Fourier coefficients and relative contrast P were determined for GALOF and SCHOTT's 3 μm FOP product RFG 88, as described herein. The results are shown in FIG.

[0227] FIG. 33 shows the values ​​of the Fourier coefficients for the blank and sample images (top) and the resulting relative contrast P, the ratio between the corresponding values ​​(FOP and GALOF) and the reference (blank).

[0228] Example 10 Images of all elements of Group 7 of the positive USAF51 targets described herein were viewed through GALOF at 300x magnification. MS-SSIM was determined for samples of 50mm and 1,000mm length, respectively, as described herein above. The results are shown in FIG.

Claims

1. A waveguide (1) for transmitting electromagnetic waves, in particular for transmitting image information from a proximal end (2) of said waveguide to a distal end (4) of said waveguide along a transport direction (5) extending between said proximal and distal ends and across a cross section extending transversely to said transport direction, For Group 6 and Group 7 images of positive USAF51 targets or negative USAF51 targets, the waveguide (1) has an MS-SSIM greater than 0.65 for a transmission length of 20 mm or less, an MS-SSIM greater than 0.60 for a transmission length of 50 mm or less, an MS-SSIM greater than 0.50 for a transmission length of 100 mm or less, and an MS-SSIM greater than 0.45 for a transmission length of 1,000 mm or less. Waveguide (1).

2. A waveguide (1) for transmitting electromagnetic waves, in particular for transmitting image information from a proximal end (2) of said waveguide to a distal end (4) of said waveguide along a transport direction (5) extending between said proximal and distal ends and across a cross section extending transversely to said transport direction, The waveguide (1) has a cutoff frequency (f ｃｕｔ ) Waveguide (1).

3. The waveguide (1) has a cutoff frequency (f ｃｕｔ ) A waveguide (1) according to claim 2.

4. The waveguide (1) has an area under the MTF calculated up to a cutoff frequency (f_cut) of greater than 80 lp / mm. A waveguide (1) according to claim 2.

5. The waveguide (1) has an area under the MTF calculated up to a cutoff frequency (f_cut) that is greater than 80 lp / mm and less than 500 lp / mm. A waveguide (1) according to claim 4.

6. A waveguide (1) for transmitting electromagnetic waves, in particular for transmitting image information from a proximal end (2) of said waveguide to a distal end (4) of said waveguide along a transport direction (5) extending between said proximal and distal ends and across a cross section extending transversely to said transport direction, The waveguide (1) has a relative contrast P of greater than 0.40 at 114 lp / mm, a relative contrast P of greater than 0.20 at 144 lp / mm, and a relative contrast P of greater than 0.05 from 114 to 287 lp / mm. Waveguide (1).

7. The waveguide (1) has a relative contrast P of greater than 0.40 and less than 0.90 at 114 lp / mm, a relative contrast P of greater than 0.20 and less than 0.70 at 144 lp / mm, and a relative contrast P of greater than 0.05 and less than 0.90 at 114 to 287 lp / mm. A waveguide (1) according to claim 6.

8. The waveguide (1) has a relative contrast P of greater than 0.05 and less than 0.70 at 1,000 lp / mm or less; A waveguide (1) according to claim 6.

9. The waveguide (1) has a Michelson contrast greater than 0.

6. A waveguide (1) according to any one or more of the preceding claims.

10. the Michelson contrast is greater than 0.6 and less than 1.0; A waveguide (1) according to claim 9.

11. The waveguide (1) comprises a plurality of structural elements (10), at least two different types, namely a first type of structural elements (10a) having a first refractive index and a second type of structural elements (10b) having a second refractive index. A waveguide (1) according to any one or more of the preceding claims.

12. the structural elements, in particular their cross-sectional areas, are formed non-uniformly so that the electromagnetic waves transmitted by the waveguide remain localized in a direction transverse to the transport direction, in particular for transmitting image information, A waveguide (1) according to any one of the preceding claims.

13. said waveguide (1) being a rigid or at least partially flexible image guide used as a component in medical devices for endoscopy or as an X-ray imaging faceplate, as an image correcting optical component or as a fiber optic component such as a (resizing) taper or as an image inverter, e.g. used in night vision devices, as a component for spatial multiplexing for data communication, as a component in remote optical sensing, as a component in lighting applications and as an energy relay for light field energy systems, A waveguide (1) according to any one of the preceding claims.

Images