Waveguide and method for manufacturing the same

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, assembled into a bundle and arranged in a grid in cross section with a one-to-one relationship between the light input and output faces to form a plurality of pixels, each pixel essentially responsible for transmitting 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, high resolution can be achieved by reducing the diameter of the individual optical waveguides. However, due to the laws of physics, resolution cannot be increased arbitrarily. This is because, as the diameter of the individual optical waveguides decreases, an increasing proportion of the field distribution of the transmitted mode exceeds the dimensions of the optical waveguide, especially the cladding, which leads to increased crosstalk between adjacent optical waveguides and therefore increased blurring.

[0004] One approach to providing image guides with higher resolution is based on the wave phenomenon of transverse Anderson localization (TAL). This exploits the fact that a random distribution of refractive index across the cross-section of an image guide, accompanied by a constancy of refractive index along the length of the image guide, results in a restriction of 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, the light beam propagates along the length of the image guide with a restricted lateral extent in the cross-section.

[0005] On the one hand, image guides based on the principle of lateral Anderson localization allow for 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, especially the image sharpness, is subject to local variations or is difficult to control, for example, the image sharpness in a particular 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 specific quality standards. Depending on the quality standards applied in production, there may be a high rate of rejects. The above-mentioned problems become even more severe when the cross-sectional area of ​​the image guide is made large. This is particularly true for faceplates, where the edge length or cross-sectional diameter may exceed the faceplate thickness by several times.

[0007] The faceplate generally consists of a group of often relatively short (a few mm) fused optical fibers or fibers whose axes lie just below the disk surface (a few mm). 2 ~A few centimeters 2) whose main property is to allow image transmission from one plate surface to the other in strictly the same order, i.e. 1:1, or in a regularly varied, 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 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 avoid rejects during production and to be able to reliably guarantee quality standards.

[0009] One aspect of the object of the present invention is to provide a waveguide, in particular an image guide, having a large cross-sectional area, using Anderson localization that simultaneously 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). cut) can be used to provide a waveguide, particularly an image guide. According to another aspect of the present invention, the waveguide has an area under the MTF calculated up to a cutoff frequency (f_cut) greater than 80 lp / mm. According to another aspect of the present invention, the waveguide has a relative contrast P 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 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 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 greater than 0.05 (i.e., 5%) from 114 to 287 lp / mm. Another aspect of the present invention is to provide a waveguide, particularly an image guide, having a Michelson contrast 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 Multiscale Structural Similarity Measure (MS-SSIM) greater than 0.65 for waveguides having a transmission length of 20 mm or less, a Multiscale Structural Similarity Measure (MS-SSIM) greater than 0.60 for waveguides having a transmission length of 50 mm or less, a Multiscale Structural Similarity Measure (MS-SSIM) greater than 0.50 for waveguides having a transmission length of 100 mm or less, and / or a Multiscale Structural Similarity Measure (MS-SSIM) greater than 0.45 for waveguides having a transmission length of 1,000 mm or less.

[0011] 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: 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. Of course, 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, so that a plurality of cross-sectional areas are defined in the cross-section of the waveguide, each corresponding to the 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 areas can in particular correspond to the surface areas formed by the structural elements.

[0014] According to some embodiments of the present invention, these structural elements, in particular their cross-sectional areas, are thereby non-uniformly formed but clearly defined by a predetermined rule. Thus, these structural elements may exhibit non-uniformity with respect to one another, i.e., may be non-uniformly formed with respect to one another, for example, may be non-uniformly arranged, non-uniformly shaped, and / or non-uniformly configured. In particular, the non-uniformity need not be present in the individual structural elements themselves, but may be present in the structural elements as a whole; thus, in particular, physical disorder, i.e., a certain symmetry or deviation from this symmetry, may be present. On the other hand, non-uniformly formed structural elements may be formed in a fixed manner according to a predetermined rule, i.e., they are not formed randomly. Therefore, the feature that these structural elements may exhibit non-uniformity or disorder with respect to one another is contrary 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 characterized by a rule, or may be characterizable by a rule.

[0015] The non-uniformity of these structural elements, particularly the cross-sectional area 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 predetermined 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 differ from one another, for example with non-uniform diameters clearly defined by a predetermined rule, but the geometries of the cross-sectional areas may also be of the same type but twisted (e.g., 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 U.S. 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 the 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 amplitude of the transmitted electromagnetic wave can be limited to a partial area of ​​the cross-section of the waveguide by the non-uniformity of the structural elements. These structural elements, in particular their cross-sectional area, can therefore be made particularly non-uniform so that the electromagnetic wave transmitted by the waveguide remains localized in a direction extending transversely to the propagation direction, in particular so that electromagnetic waves, or also selected wavelength ranges, in particular visible light and / or infrared light and / or ultraviolet light, are transmitted in a directed or restricted manner, in particular so that image information is transmitted. In this case, due to the restricted nature of the propagation of light in the waveguide according to the invention, 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 their cross-sectional areas, 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 having the same structure as this one can be produced. 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. Thus, the predetermined rule may include, in particular, detailed information for describing and / or constructing the waveguide in its structure formed by a plurality of structural elements, in particular their 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 mathematically similar. In this case, the waveguide may have a region along the conveying direction whose cross-section varies, for example continuously from the proximal end to the distal end or in at least one region between the proximal and distal ends, or continuously vary over at least one section of length L. The length L may be at least as long as the maximum extent or difference of the cross-sectional variation, or at least correspond to the maximum extent of the larger input cross-section.

[0023] In cases where the waveguide is mathematically similar along the transport direction, this waveguide may or may not have 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 manufacturing and / or by thermal post-treatment under the action of a rotational or correspondingly directed force. A combination of a change in cross-section and twisting is also conceivable.

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

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

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

[0027] The unambiguous definition rules, in particular deterministic rules for specifying features, may involve using a specific value, in particular using a determinable, unambiguously specified value of a deterministic sequence for specifying a feature for a specific structural element, using another value of the deterministic sequence for specifying a feature for another structural element, checking whether the value or feature of the other structural element violates a specified condition, in particular taking into account the value or feature of the specific structural element, and, if so, discarding the other value and using another value of the deterministic sequence to specify a feature for another structural element, or modifying the other value in a defined manner so that the specified condition is met or no longer violates it. In this context, the specified 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 structural elements. In this context, reference is made to the exemplary description below.

[0028] In embodiments of the waveguide, the position of the cross-sectional surface of at least one type of structural element, in particular the distribution of the area content of the Voronoi surfaces relative to 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 in the cross-sectional area z Smaller is 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 V=σ / A 2 should be understood to be the variance normalized to the cross-sectional area A of the waveguide, so that applies, where σ represents the variance of the distribution of the area content of the Voronoi surface with respect to the position of the cross-sectional area of ​​the structural element within surface A.

[0030] (ii) Variance of the distribution V d is 0.38 / N 2,033 may be less than N, where N represents the number of structural elements of at least one type, and the variance here is again understood in particular 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 equal to 10 -8 More particularly, the variance here should also be understood 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 in 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 The ratio may be between 1 and 50, and in particular may be 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 W of the distribution d may be smaller than the kurtosis Wz of the corresponding distribution for random locations in the cross-sectional area, where 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 1 to 5, and in particular may be 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 structural elements to the total cross-sectional area of ​​the second type of structural elements may be, for example, 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 that is preferably 0.1 to 10 times the mean wavelength of the wavelength range of the electromagnetic waves to be transmitted, 0.2 to 5 times the mean wavelength, or 0.5 to 2 times the mean wavelength.

[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, a waveguide can include a plurality of structural elements, including at least two different types of structural elements. Here, it may be provided that an embodiment of the waveguide includes one structural element of a first type and a plurality of structural elements of a second type. Thus, the plurality of structural elements in particular includes exactly one structural element of the first type.

[0042] The first type of structural element can be formed, in particular as a monolithic base body, using 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 has a second refractive index, for example due to the refractive index of air or a gas that may be present as a 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 than the cross-sectional area of ​​a waveguide that can be introduced into the base body by a laser beam, in particular of an ultrashort pulse laser. Furthermore, the filamentary channels in the base body can be reworked, in particular by chemical or physical etching processes, for example, 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 the extension along the transport direction, at least five times as large as the extension along the transport direction, or at least ten times as large as the 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 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 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] With regard to the size of the waveguide along the transport direction, it may 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, in particular if the waveguide is formed as a faceplate.

[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: glass, quartz glass, polymer, crystalline, monocrystalline, polycrystalline material and / or glass ceramic.

[0053] Furthermore, at least one structural element, in particular this structural element of the first type or a structural element, in particular a structural element formed as a base body, may comprise or consist of a material that is a medium, which in the wavelength range to be transmitted, in particular 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 containing at least one element from the group including oxygen, sulfur, selenium and tellurium and at least one element from the group including 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 filler 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 achieving, for example, a modification of the guided electromagnetic waves, for example in the sense of amplification or conversion.

[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 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, and as mentioned above, for example, one structural element of a first type and a number of structural elements of a second type can be used.

[0057] In another embodiment, it is now provided that a plurality of first type structural elements and a plurality of second type structural 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 having or having the second refractive index.

[0060] In particular, in cases where a second type of structural element can exist as a filled cavity within a first type of structural element, the structural element can be formed as a core-shell system, with the core corresponding 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, particularly 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 conveying direction extending between the proximal and distal ends and across a cross-section extending transversely to the conveying direction, the waveguide comprising a plurality of structural elements of 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 proportionally along the conveying 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 conveying direction.

[0063] The present invention further relates to a waveguide for transmitting electromagnetic waves, in particular having one or more of the features 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 of at least two different types, namely a first type having a first refractive index and a second type having a second refractive index, the structural elements extending proportionally along the transport direction and across the cross-section of the waveguide such that a plurality of cross-sectional areas are defined in the cross-section of the waveguide, each cross-sectional area corresponding to the cross-section of one of the structural elements, 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 the wavelength range from 2 μm to 20 μm, and 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 be provided: for a waveguide having 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 having 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 having 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 a waveguide 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, comprising or consisting of a first medium, having a first refractive index, and introducing a plurality of structural elements of a second type, having a second refractive index, cavities being introduced in the base body for this purpose, which cavities are filled with a second medium.

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

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

[0068] It may be provided that the method for manufacturing a waveguide comprises specifying characteristics for each structural element of the second type according to deterministic rules, in particular for defining 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 shown 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 of the cross-sectional surfaces of at least one type of structuring element, in particular the centers, can satisfy at least one of the above conditions, in particular (i), (ii), (iii), (iv), (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 an ultrashort pulse 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 for 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, with draw factors of at least 1:2, at least 1:10 or at least 1:100 being particularly contemplated.

[0078] These longitudinally assembled waveguides may then be disassembled into sections transverse to the transport direction, and these 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 with a draw factor of at least 1:2, at least 1:10, or at least 1:100 being taken into account.

[0080] These waveguides and / or sections may each be assembled to form a preform, in particular according to the details above, such that the arrangement of the assembly is uniquely determined by predetermined 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 lengthwise, thereby creating a mirror image of the cross-section.

[0082] In this context, sections formed from at least one separate 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. Furthermore, the elongated assembled waveguides and / or the elongated assembled sections may be fused by applying 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 the 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 plurality of identical waveguides, which may be produced independently of one another, so that in particular different waveguides having the same structure can be produced only according to predetermined rules.

[0086] Apart from the fact that this method can be used to produce a plurality of identical waveguides, it is also suitable for producing a plurality of waveguides that are identical with respect to at least certain properties, for example, the plurality of waveguides can meet the uniformity criteria defined for image sharpness and / or can meet one or more of the conditions mentioned above regarding 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 relative to the center.

[0087] The invention further relates to a waveguide having one or more of the characteristics described above for the waveguide, in particular, the waveguide being manufactured or manufacturable 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 plurality of structural elements, the cross-sectional areas of which are non-uniformly formed but uniquely formed according to a predetermined rule, and the two or more waveguides being identically formed such that the cross-sectional areas of which are non-uniformly formed in the same way.

[0089] Hereinafter, embodiments of the present invention will be described with reference to the figures illustrated. [Brief explanation 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)] 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)] 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). [Figure 3] 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] 1 is a schematic cross-sectional view of a waveguide with two types of structural elements, the types / refractive indices of which are / are determined according to a deterministic rule; [Figure 5] 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 of 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 structural element located within a first type of structural element, plotted in logarithmic representation against the number of second type of structural elements. [Figure 6(b)] 1 is a plot in double logarithmic representation 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 structural element located within a first type of structural element versus the number of second type of structural elements. [Figure 7(a)] FIG. 10 shows 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. 10 is a diagram showing an example of positioning by a Sobol sequence. [Figure 7(c)] FIG. 10 is a diagram illustrating an example of random positioning. [Figure 7(d)] FIG. 10 is a diagram showing an example of periodic positioning as another comparative example. [Figure 8(a)] 10A and 10B show examples of Voronoi surfaces for the position of the cross-sectional surface of a second type of construction element disposed within a first type of construction element having a square cross-section; [Figure 8(b)] FIG. 10 is a diagram showing an example of positioning according to a Sobol sequence. [Figure 8(c)] FIG. 10 is a diagram illustrating an example of random positioning. [Figure 8(d)] FIG. 10 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, 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. 10 is a schematic perspective view of the reassembled waveguide. [Figure 9(e)] FIG. 1 is a schematic perspective view of a waveguide fused under pressure. [Figure 10(a)] 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)]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 twisted relative to each other in a predetermined manner. [Figure 10(c)] 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)] 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 twisted relative to each other in a predetermined manner. [Figure 11] Schematic representation of various possibilities for waveguides in which the structural elements or cross-sectional areas of the structural elements are formed non-uniformly but are clearly defined by predetermined rules. [Figure 12] Schematic representation of various aspects for variations between structural elements or cross-sectional areas of structural elements and possible combinations of these aspects. [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 includes a first type of structural element and a plurality 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 non-uniformly formed but that are uniquely determined by a predetermined rule, each of which includes 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 another type. [Figure 15] FIG. 10 is a photograph of the face of a fabricated waveguide having a first type of structural element formed therein and a plurality of second type structural elements formed as filamentary channels within the first type of structural element. [Figure 16] FIG. 1 shows a photograph (and various enlarged sections) of a fabricated waveguide having a plurality of first type structural elements and a plurality of second type structural elements. [Figure 17] FIG. 17 shows a photograph of the waveguide of FIG. 16 applied as an image guide. [Figure 18] FIG. 10 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. [Figure 23] FIG. 1 illustrates the curve progression of an error function. [Figure 24] 10 is a graph showing discrete Fourier transform data of Example 8. [Figure 25] 10 is a graph showing the MTF of Example 1. [Figure 26] 10 is a graph showing MTF data for Example 2. [Figure 27] 10 is a graph showing MS-SSIM data for Example 3. [Figure 28] 10 is a graph showing MS-SSIM data for Example 4. [Figure 29A] 10 is a graph showing MS-SSIM data for Example 5. [Figure 29B] 10 is a graph showing MS-SSIM data for Example 5. [Figure 29C] 10 is a graph showing MS-SSIM data for Example 5. [Figure 30] 10 is a graph showing MS-SSIM data for Example 6. [Figure 31] 10 is a graph showing MS-SSIM data for Example 7. [Figure 32] 10 is a graph showing MS-SSIM data for Example 10. [Figure 33] 10 is a graph showing the Fourier coefficients and relative contrast P of Example 9. [Figure 34] FIG. 10 shows MTF values ​​calculated at different magnifications. [Figure 35] 10 is a graph showing the determination of the cutoff frequency from the MTF data of GALOF. [Figure 36] 1 is a graph showing determination of fcut from MTF data for FOP. [Figure 37A] Figure 1 shows images of Group 6 and Group 7 of the USAF51 target through different products. [Figure 37B] Figure 1 shows images of Group 6 and Group 7 of the USAF51 target through different products. [Figure 38] FIG. 10 illustrates sub-image partitions for MS-SSIM calculations for small diameter image guides. DETAILED DESCRIPTION OF THE INVENTION

[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 plurality of structural elements 10, each extending along the waveguide's 1 transport direction, perpendicular to the drawing, and each extending proportionally across the waveguide's 1 cross section. Each structural element 10 thus defines a cross-sectional area 20, i.e., a percentage of the area of ​​the waveguide's 1 cross section. The illustrated examples of waveguides 1 each have at least two different types of structural elements, each with a different refractive index. These principle embodiments serve to illustrate several variations in the inhomogeneity, which may differ in detail 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 structural element 10a formed as a base body, which houses a plurality of second-type structural elements 10b. The second-type structural elements 10b can thus be formed, for example, as cavities or hollow channels extending along the transport direction within the first-type structural element 10a. In this case, the first-type structural element 10a formed as a base body contains a first material having a first refractive index, while the second-type structural element 10b formed as a cavity, for example, exhibits a second refractive index due to the presence of air or another gas therein. In this case, the cross-sectional area 20 of the first-type 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 each of the second-type structural elements 10b corresponds to the cross-sectional area of ​​the cavity. However, cavities within the main body may be filled with a second material, whereby second-type structural elements 10b correspond to the filled cavities. As shown schematically in the figure, the cross-sectional areas 20 of the second-type structural elements 10b are non-uniform in that their positions are unevenly distributed across the cross-section and are not located on a periodic grid. At the same time, however, the positions of these structural elements are uniquely determined by predetermined 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 unevenly arranged, but also have a non-uniform geometry, in this case a non-uniform diameter, with 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 predetermined rule.

[0094] The waveguide shown in cross section in Fig. 1(c) again comprises two types of structural elements 10a, 10b, the cross-sectional area of ​​which is arranged within each of the first type structural elements 10a, in particular as a core-sheath system. Thus, in this case, a plurality of first type structural elements 10a and a plurality of second type structural elements 10b are provided. These structural elements or their cross-sectional areas are non-uniformly shaped so that the first type structural elements 10a (which house the second type structural elements 10b) are arranged non-uniformly, in particular aperiodically, across the cross-section of the waveguide, this arrangement being determined by a predetermined 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, and 10c with different refractive indices. In particular, the cavities in structural element 10a, formed as a base body, may be filled with different media. Thus, structural elements 10b and 10c have non-uniformity, in particular in that their refractive indices differ from one another, and the determination of which structural elements formed as cavities receive which refractive indices may follow a predetermined rule.

[0096] 2 shows two further examples of waveguides 1 that can be used specifically as image guides. Here again, the waveguide 1 includes a plurality 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 Figure 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 therefore the refractive indexes thereof, 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 includes a plurality of structural elements 10 arranged on a periodic lattice, in this example with non-uniform cross-sectional areas. 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 predetermined rule. Furthermore, the structural elements 10 may exhibit non-uniformity, in particular a predetermined non-uniformity, in that the refractive indices of these structural elements differ from one another. In this regard, a discrete number of different refractive indices 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-shaped, 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 periodic lattice in the cross-section, which corresponds to a hexagonal lattice in this example. It is therefore assumed 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 their cross-sectional areas 20.

[0100] 4 and 5, an example of how these structural elements can be formed non-uniformly, but uniquely defined by a predetermined rule, is provided 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, and this rule can include a deterministic sequence (e.g., a Halton sequence). This sequence forms a component of the deterministic rule described in more detail herein for specifying the feature number of the structural element. For better understanding, this rule is described in individual steps, whereby, in particular, the overall structure of the waveguide defined by these steps is important, and the determination of the overall structure can precede the fabrication 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 predetermined 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, and 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 the 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., including 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 circle of the waveguide 1. The values ​​of the sequence lie in the range [0,1) x [0,1) and can be scaled according to the dimensions of a given area of ​​the waveguide.

[0104] Halton sequences are multidimensional extensions of one-dimensional van der Corput sequences to different bases. A van der Corput sequence x with base b 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 structural elements 10 are in place, and the sequence covers the entire range [0,1) x [0,1), so further assignments are made. The sequence elements are passed through the sequence. The assignment to structural elements, in particular to structural elements of the second type 10b, is made by the minimum Euclidean distance. Column elements that are assigned to a structural element already selected or that are out of alignment are ignored, and the process continues with the next column element. This continues until a number of structural elements, in particular of the second type 10b, corresponding to the desired filling rate has been selected.

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

[0107] The first embodiment shows a circular waveguide or a preform for a waveguide 1 (Fig. 4), which is formed from 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, whereby certain occupied structural elements receive one refractive index and other structural elements receive the other refractive index, until a predetermined degree of filling is reached.

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

[0110] Now, if another column point 102 lies outside the circle or is overlapping, then these column points 102 are discarded and the next column point 102 is added, continuing until a predetermined 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) illustrates the occupancy of a given surface. The objective here is to position structural elements, such as holes with a diameter, on a square plate 110 with an edge length D according to a Halton sequence, for example, for laser filamentation or drilling processes. Here, the sequence points 112 are scaled from a value range [0, 1) to a specified area dimension range [-D / 2, D / 2). This is done until a predetermined fill level is reached. The fill factor is the ratio of the total area of ​​these holes to the substrate area. The holes can be positioned according to the sequence points (FIG. 5a). Alternatively, the sequence points can be rounded to the hole diameter (FIG. 5b). If overlapping holes are undesirable (overlapping pairs of holes 114), such sequence points should be discarded. Accordingly, the overlapping arrangement (FIG. 5b) is discarded and moved forward further in the sequence. Similarly, other specifications may be present, for example, specifying a minimum spacing between structural elements.

[0113] It will be understood that the method described in more detail above and illustrated in more detail by two examples is applicable, without limitation, to other possible variations of structural elements, having three or more refractive indices and / or varying or variable geometries, dimensions, e.g., 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 conditions of the available surface are then adapted or expanded accordingly on a case-by-case basis to achieve the desired and required occupancy.

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

[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) of the distribution of areal inclusions of Voronoi areas relative to the square of the total area of ​​the occupied cross sections, A, for the positions of the cross-sectional areas of at least one type of structural element is: 2 ) is shown, and this variance is plotted over the number N of structural elements of this at least one type, shown in logarithmic (Fig. 6a) and double logarithmic (Fig. 6b) representations.

[0116] A waveguide according to the present 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 (dispersion = 0.38 A) corresponding to dispersion curve 204 are shown. 2 / N 2,033 ) is shown. It is clear that the dispersion (per N) of the distribution of the waveguide according to the invention is smaller than that of the waveguide with random disorder.

[0117] Note that the curves shown are based on a distribution over a 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 for waveguides having a circular cross-section (FIG. 7) and a square cross-section (FIG. 8, which is the basis for FIG. 6). FIGS. 7a and 8a show the position 212 and Voronoi surface 210 based on the Halton sequence, while FIGS. 7b and 8b show the positions 212 and Voronoi surface 210 based on the Sobol sequence, respectively, corresponding to the non-uniformity of the waveguide according to the present invention. For comparison, FIGS. 7c and 8c show the position 212 and Voronoi surface 210 based on a random arrangement, while FIGS. 7d ​​and 8d show the positions 212 and Voronoi surface 210 based on a periodic arrangement. It is clear that the waveguide according to the present invention is characterized by the non-uniformity of the structural elements, and in particular the cross-sectional areas of the structural elements, but with a higher uniformity than in the case of a random arrangement.

[0119] Figure 9 shows steps in a method for manufacturing a waveguide by a multi-draw method. In this process, a plurality 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 preform 40 (FIG. 9b, "multi-multi assembly"). Preform 40 may then be drawn lengthwise again (FIG. 9c) and, if desired, disassembled into sections and reassembled (FIG. 9d). Finally, the assembly thus obtained may be fused by applying heat and / or pressure, particularly under vacuum (FIG. 9e).

[0121] Referring to FIG. 10, lengthwise drawn assembled waveguides ("multi-fibers," here "M1") may be assembled without twisting relative to one another during assembly into another preform (FIG. 10a) or may be rotated relative to one another in a particular predetermined manner (FIG. 10b). Furthermore, during assembly, sections from at least two different lengthwise drawn assembled waveguides ("M1," "M2") may be assembled without twisting (FIG. 10c) or may be rotated relative to one another 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 one another in a particular predetermined manner, similar to the arrangement shown in FIGS. 10a and 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., Figure 3) and may therefore also be uniquely determined by predetermined rules.

[0122] Various embodiments of the non-uniformity of the structural elements according to the invention will again be described 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 predetermined 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 for the structural element 10a to be formed as air or not present at all). FIG. 11b shows another starting point derived therefrom, which includes a structural element 10a and a plurality of periodic positions P for the structural element to occupy, in this case with periodic positioning. FIG. 11d shows another starting point derived from FIG. 11a, which includes a structural element 10a and a plurality of non-periodic positions P for the structural element to occupy, in order to obtain a non-periodic positioning. Starting from the starting points shown in FIGS. 11b and 11d, a waveguide according to the present invention is obtained by occupying the positions P with a structural element, as will be explained in more detail below.

[0125] Starting from Fig. 11b, Fig. 11c shows a waveguide 1 having structural elements 10b, 10c whose cross-sectional areas have periodic positioning and / or are periodically positioned. 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, structural element 10a may be formed as a matrix material, and structural elements 10b and 10c may be voids in the matrix material filled with materials of different refractive indexes.

[0126] However, it is also possible that one of the materials of structural elements 10b and 10c corresponds here to the matrix material of 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 structural element 10a is formed as air, or is absent, and structural elements 10b and 10c are adjacent to 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 distribution of these different types on the regular lattice is non-uniform but determined by a predetermined rule. Therefore, in particular, 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 illustrates the case of a waveguide 1 in which these structural elements or their cross-sectional areas have a non-uniform distribution that is uniquely determined by a predetermined rule. The term "distribution" here should be understood to mean that the selection or distribution 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 for the structural elements 10b, 10c to not differ in terms of their refractive index, e.g., have the same refractive index, or be made of the same material, but differ in other respects (see FIG. 12 below).It is also possible for the structural elements 10b, 10c to differ in terms of their refractive index as well as in other respects.

[0129] Starting from FIG. 11d, FIG. 11e shows a waveguide 1 having two types of structural elements: a structural element 10a, which may be formed, for example, as a matrix material, and a plurality of structural elements 10b, which may be formed, for example, as filled cavities in a matrix material. In this case, the cross-sectional areas of the structural elements 10b are positioned aperiodically. Here, the positioning of the structural elements 10b can represent a non-uniformity determined by a predetermined rule. In particular, the second type of structural elements 10b may have a non-uniform, but determined by a predetermined 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 that is clearly determined by a predetermined rule. The term "arrangement" here should be understood to mean that these structural elements or some structural elements or the cross-sectional areas of the structural elements are arranged aperiodically, and the positions are determined by a predetermined 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, a uniform geometry and / or are uniformly formed with respect to other aspects, in particular identically formed, which in this case can be said to be a uniform occupation of the aperiodic 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 predetermined rule, can 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] 12 shows various possibilities for variations that structural elements can have relative to one another (center 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 non-uniformly formed but clearly determined by a predetermined rule. Structural elements whose cross-sectional areas are arranged in periodic or aperiodic positions, for example in a matrix material, can differ among themselves, for example, in terms of their shape, their type or refractive index, their substructure, and / or 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 realized as variations in shape (number of corners, diameter). Variations in geometry can also be realized as variations in the substructure. The substructure can in particular be such that the structural element, in particular the cross-sectional area of ​​the structural element, has at least two different regions with different refractive indices, 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 with a core having a first diameter, and a second type of structural element may have a core-clad system with a core having a second diameter (bottom row, third column), or a first type of structural element may have a core-clad system with a core having a first refractive index, and a second type of structural element may have a core-clad system with a core having a second diameter. The structural elements may have a core-clad system having a core with a centered core and a second type of structural element having a core with a rotation about a pivot point outside the core (row below, fourth column), or a first type of structural element may have a first diameter and a rotation about a pivot point outside the structural element and a second type of structural element has a second diameter and a rotation about a pivot point outside the structural element (row below, fifth column), or a first type of structural element may have a core-clad system having a centered core and a second type of structural element has a core with a rotation about a pivot point outside the core (row below, sixth column), etc.

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

[0136] FIG. 13b illustrates a waveguide 1, which in some respects resembles the waveguide of FIG. 11f. The waveguide has a first structural element 10a, which may be formed, for example, as a matrix material. Furthermore, the waveguide includes a plurality of structural elements 10b having a first diameter and a plurality of structural elements 10c having a second diameter. In this example, the structural elements are non-periodically positioned, and the non-periodic positioning may be non-uniform but clearly defined by a predetermined rule. Thus, FIG. 13b illustrates the case of a waveguide 1, where 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. 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, the non-periodic position being determined by a predetermined rule, i.e. not random, and / or that these structural elements are formed non-uniformly but have variations between them that are uniquely determined by a predetermined rule, the variations being formed, for example, as two types of structural elements having different diameters.

[0137] FIG. 14 shows several waveguides 1, each having a plurality of structural elements of a first type and a plurality of structural elements of a second type (and possibly 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); rather, the structural elements are adjacent to one another. The waveguides 1 shown in FIG. 14 share in common that the different types of 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 non-uniform but clearly determined by a predetermined rule. Thus, the waveguides 1 shown in FIG. 14 are characterized by a non-uniform arrangement of the structural elements or the cross-sectional areas of the structural elements, which is unambiguously 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 determined by a predetermined rule, i.e., not random.

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

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

[0140] 14c similarly shows a waveguide 1 having multiple structural elements 10d and multiple structural elements 10e with different refractive indices and different substructures, where the substructures are defined by substructure elements 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 core-clad systems with different claddings.

[0141] 14d similarly shows a waveguide 1 having multiple structural elements 10e, 10f, 10g, and 10h, each having different refractive indices and different substructures, represented by 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, where the substructures are such that structural elements 10e, 10f, 10g, and 10h are formed as a core-shell system in which 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 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 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] Figure 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 exemplary photographs of an actually fabricated waveguide 1 having a monolithic base body, i.e., a first-type structural element 10a, into which a plurality of filamentary channels, i.e., second-type structural elements 10b, have been introduced by laser filamentation. These channels have aperiodic positioning, which is non-uniform but clearly defined by a predetermined rule. However, in the case of laser filamentation, it is also possible, for example, for the laser to scan the substrate line by line, resulting in a periodicity or grid. In particular, in such a case, the second-type structural elements 10b formed as filamentary channels can also be arranged at periodic positions, where some periodic positions are occupied and some periodic positions are unoccupied, and the occupation is unambiguously determined by a predetermined rule.

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

[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 placement of the structural elements, high-resolution image transmission based on the phenomenon of lateral Anderson localization is achieved here. At the same time, the placement according to a predetermined 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 (a) The structural elements, in particular those formed as a periodic positioning of the cross-sectional areas of the structural elements and arranged periodically, have a mutual variation that is non-uniform but is uniquely determined by a predetermined rule; The variations of the periodically arranged structural elements relative to one another may be formed as variations in 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 substructure), (b) formed as aperiodic positioning of structural elements, in particular cross-sectional areas of structural elements, the aperiodic positioning of the structural elements being formed unevenly 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 unambiguously defined by predetermined rules, and / or (c) 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 unambiguously by predetermined rules; Optionally, the structural elements are further non-uniform, but have variations therebetween that are clearly defined by predetermined rules.

[0148] As mentioned above, these structural elements may differ from one another 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 multiple times, the initial shape or geometry may be retained, but may appear deformed in the waveguide due to thermal and mechanical effects that may occur in the process. In particular, at least some of the structural elements may have a hexagonal and / or hyperbolic polygonal shape, in particular a triangular or 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 its 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 for comparing 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, as shown, for example, 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 are the same, but the limited resolution of the optical system results in blurring of the image at higher spatial frequencies, which causes a loss of contrast. The visibility of the modulation 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, this performance can depend on different orientations. Since the aperture stop in an optical system also constitutes a limit to the transmission of higher spatial frequency components, the resulting MTF can be considered as the upper limit (diffraction limit) of 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 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 is composed of all frequency components. Aberrations from optical imaging systems cause edge blurring due to the suppression of 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] To achieve subpixel resolution, the edge should be tilted slightly (5°-10°) relative to the camera system's pixel orientation when integrating pixel intensities along a line perpendicular to the edge orientation. The detector pixel size, or effective pixel size after optical magnification, constitutes the upper limit (Nyquist limit) for the minimum resolvable spatial frequency. Therefore, when measuring and evaluating the MTF of an image guide, it must be ensured that the optical inspection system does not limit its resolution capabilities. This can be done by comparison with a blank target as a reference. The above effect can be seen in Figure 21, where the cutoff frequency shifts to higher values ​​as magnification increases, thus decreasing the effective pixel size.

[0160] As mentioned above, the pixel size of the image constitutes an upper limit for the MTF. To ensure that any observed loss in transmission quality is due to the performance of the optical system and not the image sampling, 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 if this is a maximum value (e.g., 2x for an 8-bit image). 8 It is adjusted to avoid pixel saturation in the lowest magnification images by making sure it is not clipped at -1=255) and is kept constant throughout the series. The image guide is butt-coupled (physically contacted) to the white / black transition of the target without the use of immersion fluid.

[0161] The calculated MTF is shown in Figure 34. It is clear that the high-resolution image is affected by 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 and hence the resolution from the MTF, first multiply the frequency by 1.5 times f cut_lin This is because noise increases in the high frequency range where the amplitude is small. For this subset of data, the formula

number

[0164] Because the determination of the MTF is based on Fourier analysis, the investigation of fiber bundles with visible periodic arrangements 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 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 symmetric region of three times the full width at half maximum of the peak is discarded. The procedure described above to characterize 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 =135.3 lp / mm, f cut = 165.0 lp / mm, and Area = 75.8 lp / mm. Again, the determined cutoff frequency corresponds well to a distinguishable line pair for G7E3 (161.3 lp / mm) in Figure 37A.

[0165] To determine the Fourier coefficients of relative contrast P, a 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 resolutions. Normalization was performed by comparing results obtained for an image of the target not viewed through the waveguide ("blank target image") with an image of the 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 added to the final plot.

[0167] The imaging procedure is as follows: 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, obtaining a grayscale profile in Image J; 3) calculating the value of the Fourier series element corresponding to the frequency of interest in the grayscale values; and 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 1,000 lp / mm or less. 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 of 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 of 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 comparing two images, e.g., a blank target image and a sample target image, using an imaging system, there are various methods described in the literature for comparing the two images and assessing the quality of the sample target image. The most widely used statistical measures, such as peak signal-to-noise ratio (PSNR) or mean square error (MSE), 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 led 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 is

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 variability of human image perception for different sampling densities or viewing distances. Therefore, a multiscale extension of SSIM that takes into account image details at various resolution levels, known as multiscale structural similarity metric (MS-SSIM), is considered [Z. Wang, EP Simoncelli and AC Bovik, “Multiscale structural similarity for image quality assessment,” The Thirty-Seventh Asilomar Conference on Signals, Systems & Computers, 2003, pp. 1398-1402 Vol. 2, doi: 10.1109 / ACSSC.2003.1292216.]:

number

[0177] Here, for M-1 iterations of low-pass filtered and downsampled images by two, the intensity l of the image at scale M is M (x,y) and contrast c j(x,y) and structural comparison s j (x, y) and the 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 a blank target image served as the reference image and an 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 kept constant 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 ensuring that images were not clipped at −1 = 255. Images were aligned and cropped to the same size using a template matching algorithm before applying the MS-SSIM calculation.

[0179] In cases where the dimensions of the image guide 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 a sub-image is determined 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, composed of a (fairly) regular arrangement of core-clad monofibers that transmit light by total internal reflection, tend to imprint underlying structures in the transmitted image, resulting in a pixelated appearance. This is particularly evident when extra-mural absorbers (EMA) are incorporated into the fiber bundle. This artifact, known as honeycombing, results from the non-transparent cladding material around each individual core, resulting in only distinct locations within the observed field of view being transmitted. Aside from the reduction in information, this can cause image processing problems relevant to computer-aided diagnosis if such transmitted images are 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, image superposition with small displacements, compressed 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 to real-time analysis.

[0181] Image guides whose transmission is mediated by multi-beam interference localization phenomena 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 apparent when analyzing the discrete Fourier transform of the image shown in Figure 24.

[0182] In such conventional fiber optic plates (FOPs, middle row in Figure 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 (top to bottom) of the FFT of the FOP features at least two sharper peaks apart from the central peak, with amplitudes at least 25% of the central peak and separated from said peak by a distance at least 10 times the width of the central 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, a waveguide of the present disclosure may have an integrated line scan with a zero peak with an amplitude at least 25% of the central peak.

[0184] Here, these measurements were made under Lambertian illumination using either a Zeiss SmartZoom 5 microscope with a "PlanApp D 10x / 0.6FWD 10mm" objective (Figure 26 (blank and FOP), Figures 30-31, Figures 34 and 37A) or a Keyence VHX 6000 with a "VH-ZST" dual zoom objective (Figure 26 (TALOF), Figures 27-29, Figures 32-33, Figures 35-36, Figures 37B and 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 transmission direction (5) extending between the proximal and distal ends and across a cross section extending transversely to the transmission direction, the waveguide (1) having a cutoff frequency (f) greater than 170 lp / mm. cut )

[0186] A second embodiment of the present invention is a waveguide (1) having a cutoff frequency (f) greater than 170 lp / mm and less than 1,000 lp / mm. 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 conveying direction (5) extending between the proximal and distal ends and across a cross-section extending transversely to the conveying direction, wherein the waveguide (1) has a relative contrast P of greater than 0.40 at 114 lp / mm.

[0188] A fourth embodiment of the present 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 conveying direction (5) extending between the proximal and distal ends and across a cross-section extending transversely to the conveying direction, wherein the waveguide (1) has 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, 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 conveying direction (5) extending between the proximal and distal ends and across a cross-section extending transversely to the conveying direction, wherein the waveguide (1) has a relative contrast P of greater than 0.05 at 1,000 lp / mm or less.

[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 1,000 lp / mm or less.

[0193] A ninth 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, wherein the waveguide (1) has a relative contrast P of greater than 0.05 at 114 to 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, wherein the waveguide (1) has 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 conveying direction (5) extending between the proximal and distal ends and across a cross-section extending transversely to the conveying direction, wherein the waveguide (1) has 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 transmission lengths up to 20 mm.

[0201] A seventeenth embodiment of the present invention relates to a waveguide (1) for transmitting electromagnetic waves, 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 conveying direction (5) extending between the proximal and distal ends and across a cross-section extending transversely to the conveying direction, wherein the waveguide (1) has a transmission length greater than 100 mm, and the waveguide (1) has an MS-SSIM greater than 0.50.

[0202] An 18th embodiment of the present invention relates to a waveguide (1) according to the 17th 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 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 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 proportionally along the transport direction (5) and across the cross-section of the waveguide (1), so that in the cross-section of the waveguide (1) a plurality of cross-sectional areas (20) are defined, each corresponding to the cross-section of one structural element (10), and each structural element (10), in particular the cross-sectional area (20) of each structural element, is formed non-uniformly but is uniquely defined by a predetermined rule.

[0206] A 22 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 aperiodic, predetermined arrangement which is univocally 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 univocally determined by a predetermined rule, and / or the structural elements have a non-uniform, in particular mutually different refractive index which is univocally 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, wherein the structural elements, in particular the cross-sectional area 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 according to 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-cladding diameter ratio varies with radial displacement of the fiber from the central axis of the bundle.

[0210] A 26th 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 used for example 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 light is transmitted via Anderson localization instead of conventional total internal reflection was prepared as follows: Two types of glass rods (mono) with the same diameter but a refractive index difference of 0.33 were arranged in a predetermined manner as disclosed herein in an approximately 50:50 mixture in a hexagonal multi-fiber structure and drawn into a fiber bundle. In a second drawing step, a number of these multi-fibers were assembled in a multi-multi configuration, where the multi-fibers are randomly oriented. Additional drawing steps were used in the same manner until the diameter of the mono fiber was reduced to a size of 700-800 nm, producing a GALOF.

[0214] For a blank target, SCHOTT North America Fiber Optic Plate (FOP) Product No. 24A, as well as GALOF, the beveled sharp edge of the monochrome image was used to determine the MTF as described herein, and the results are shown in Figure 25.

[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 low magnification. Furthermore, the MTF of the FOP exhibits 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 beveled sharp edges of a monochrome image were viewed through the GALOF of Example 1 at magnifications of 200x, 300x, 500x, 1,000x, and 1,500x. The MTFs for the blank and GALOF were determined as described herein. The results are shown in Figure 26.

[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 limited performance of the imaging system. 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 analysis.

[0218] Example 3 Images of the negative USAF51 target described herein were viewed through the 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 the positive USAF51 target described herein were viewed through the GALOF of Example 1 at 300x, 500x, and 1,000x magnification. MS-SSIM was determined as described herein. The results are shown in Figure 28.

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

[0221] Example 6 An image of the negative USAF51 target described herein was viewed at 1,000x magnification through a 5 cm sample of the GALOF of Example 1. MS-SSIM was determined as described herein. The results are shown in Figure 30.

[0222] Example 7 Images of the negative USAF51 target described herein were viewed at 1,000x magnification through the 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 at 200x magnification through the GALOF of Example 1 and compared to a blank image and a fiber bundle (center, Honsun, with a 6 μm fiber diameter). The discrete Fourier transform was determined by comparison as described herein. The results are shown in Figure 33.

[0224] The top row in Figure 33 shows a uniformly back-illuminated (Lambertian) area without image-guided transmission (left, blank) and with image-guided transmission (center, 5 mm thick FOP with 6 μm fiber diameter, hexagonal packaging; right, GALOF). The middle row shows the discrete Fourier transform (FFT) of the corresponding image, with a typical high DC peak in the center. The FOP exhibits a pronounced off-center peak, reflecting the six-fold symmetry of the fiber arrangement. The TALOF FFT shows rises at several frequencies but no distinct 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 exhibits a pronounced narrow peak structure, symmetric about the center with an amplitude significantly greater than the noise level (25% of the central peak), resulting in a local maximum.

[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 Figure 33.

[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 50 mm and 1,000 mm long samples, respectively, as described herein above. The results are shown in Figure 32.

Claims

1. A waveguide (1) for transmitting electromagnetic waves from a proximal end (2) of said waveguide (1) to a distal end (4) of said waveguide (1) along a conveying direction (5) extending between said proximal end and said distal end and across a cross section extending transversely to said conveying direction, The waveguide (1) comprises a plurality of structural elements (10), the structural elements have a non-uniform arrangement that is uniquely determined by a predetermined rule; For Group 6 and Group 7 images of a positive USAF51 target, the waveguide (1) has an MS-SSIM greater than 0.65 for transmission lengths of 20 mm or less, an MS-SSIM greater than 0.60 for transmission lengths of 50 mm or less, an MS-SSIM greater than 0.50 for transmission lengths of 100 mm or less, and an MS-SSIM greater than 0.45 for transmission lengths of 1,000 mm or less. Waveguide (1).

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

3. The waveguide (1) has a cutoff frequency (f) greater than 170 lp / mm and less than 1,000 lp / mm. ｃｕｔ ) A waveguide (1) according to claim 1.

4. The waveguide (1) has a cutoff frequency (f ｃｕｔ ) the area under the MTF calculated up to A waveguide (1) according to claim 1.

5. The waveguide (1) has a cutoff frequency (f ｃｕｔ ) the area under the MTF calculated up to A waveguide (1) according to claim 1.

6. 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. A waveguide (1) according to claim 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 1.

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 1.

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

6. A waveguide (1) according to claim 1.

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

11. The optical element includes at least two different types of structural elements, namely, a first type (10a) having a first refractive index and a second type (10b) having a second refractive index. A waveguide (1) according to claim 1.

12. the cross-sectional area of ​​the structural element is non-uniform so that the electromagnetic waves transmitted by the waveguide (1) remain localized in a direction transverse to the transport direction in order to transmit image information; A waveguide (1) according to claim 1.

13. The waveguide (1) is a rigid or at least partially flexible image guide used as: (1) a component in an endoscopic medical device; (2) as an X-ray imaging faceplate; (3) as an image correction optical component; (4) as a fiber optic component; (5) as a component for spatial multiplexing for data communication; (6) as a component in remote optical sensing; (7) as a component in lighting applications; or (8) as an energy relay for a light field energy system. A waveguide (1) according to claim 1.

Images