Improved tomographic refractive index profile evaluation of non-symmetrical glass fiber preforms and fibers themselves

Abstract

To provide a method for determining a refractive index profile (RIP) of a preform when the RIP is substantially asymmetrical.SOLUTION: In the method: (i) the preform is scanned, starting with a first projection angle, and raw data are created representing an object through measured data; (ii) optionally, the object is rotated, and the step (i) is repeated iteratively until all projection angles have been scanned and all measured data have been created; (iii) the measured data are processed to form a sinogram and, if the optional step (ii) has been completed, the method proceeds to a step (v); (iv) the object is rotated, and the steps (i) and (iii) are repeated iteratively until all projection angles have been scanned; (v) a 2D RIP is calculated; (vi) a line section of interest is selected within the 2D RIP; (vii) a fitting procedure is applied to the line section of interest; and (viii) finally, refractive index steps / gradients and dimensions are determined.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present disclosure relates generally to refractive index measurements, and more particularly to a method for measuring the refractive index profile of a transparent cylindrical object, such as a fiber preform. [Background technology]

[0002] Transparent cylindrical objects such as fiber preforms, optical fibers, light pipes, and light tubes are used in a variety of optical applications. It is often desirable to know the refractive index profile (RIP) of such objects. For example, optical fibers are formed by heating a fiber preform and drawing the molten end into a thin glass thread. The RIP of the preform defines the RIP of the resulting optical fiber, which in turn determines the waveguiding properties of the optical fiber. It is therefore important to be able to accurately measure the RIP of a fiber preform.

[0003] There are various methods for determining the radial RIP of cylindrical optical objects, particularly optical fiber preforms. Cylindrical optical objects often have a cylindrical longitudinal axis about which the layer radius r is measured. k and layer refractive index n k At least one layer k having a refractive index distribution k extends radially, symmetrically and uniformly around the axis. Of course, many objects with non-radial, asymmetric, or gradient RIPs exist, and this disclosure focuses on objects with asymmetric RIPs. The deflection angle distribution ψ(ρ,θ) is measured, and the RIP is reconstructed from the deflection angle distribution (ρ is the scan position and θ is the measured projection angle). The RIP is also known as the refractive index distribution and is represented by the symbol n(x,y), where x and y are Cartesian coordinates.

[0004] The Cartesian coordinate system uniquely specifies each point within a three-dimensional space by means of three Cartesian numerical coordinates (x, y, z), where the three Cartesian numerical coordinates are the signed distances from the point to three fixed, mutually perpendicular, directed lines measured in the same unit of length. Each reference line is called a coordinate axis or simply an axis of the system, and the point at which they intersect is its origin, which is typically the ordered triplet (0, 0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the three axes, expressed as signed distances from the origin.

[0005] Unfortunately, the refractive index distribution cannot be measured directly. The refractive index distribution is usually determined indirectly as the deflection or interference of a light beam passing through a volume region of the optical element, and the stepwise transmission of the light beam through the optical element is called "scanning" and is performed in the direction of ρ. The spatial refractive index distribution within the optical element can be inferred from the interference or deflection of the outgoing light beam (output beam) based on the beam direction at the beam incidence point (incident beam). The group of deflection angles ψ measured during the scanning of the light beam for a single fixed projection angle θ in the direction (ρ direction) across the longitudinal axis forms a deflection angle distribution ψ(ρ, θ) (where θ is fixed).

[0006] For better visualization and illustration, the geometric relationships are schematically shown in FIG. 1. An object having a uniform refractive index n1 surrounded by a refractive index adjusting fluid having a refractive index n0 such that n0 < n1 is shown. The radius of the object is r1. The deflection angle ψ is defined as the angle between the output beam and the incident beam, and y is defined as the distance between the cylindrical longitudinal axis and the incidence point of the incident beam. When scanning the object, the beam refracts as soon as it contacts the object and is directed towards the center of the object. The shortest distance of the beam to the center of the object is given by the radius r * which appears in the formulation of subsequent numerical integrations (often called the inverse Abel transform in the literature).

[0007] In the case of an axially symmetric object having a refractive index distribution that is completely step-like, the deflection angle distribution ψ(y) can be mathematically described with reference to Equation (1) below.

[0008]

number

[0009] In equation (1), m is the number of layers of the object, n0 is the refractive index of the surrounding medium, and n k is the refractive index of the kth layer, r k is the radius of the kth layer. A known mathematical method for calculating the refractive index profile from the deflection angle distribution based on measured data according to equation (1) is based on the well-known numerical integration (called the "inverse Abel transform" in the literature) calculated from equation (2) below.

[0010]

number

[0011]

number

[0012] US Patent No. 4,227,806 describes a method for non-destructively determining the parameters of an optical fiber preform. The preform is scanned by a laser beam incident laterally on the core-cladding structure, and the deflection angle of the exiting beam is measured and then compared to theoretical or empirical deflection angle distributions of preforms with known refractive index distributions. During the measurement, the preform is placed in a bath containing a refractive index adjusting fluid to prevent the deflection angle from becoming too large.

[0013] US Patent No. 4,441,811 describes a method and apparatus for determining the refractive index profile of a cylindrical transparent optical preform. Again, the preform, inserted in an index-matching fluid, is scanned by a laterally incident light beam, extending perpendicular to the optical axis. The light beam is deflected by the glass of the preform and imaged by an optical device onto a positionable detector. The refractive index profile is calculated from the deflection angle distribution by means of numerical integration. Other preform parameters such as preform diameter, core diameter, eccentricity, and CCDR value (cladding-to-core diameter ratio) can also be determined from the reconstructed RIP.

[0014] Tomography is imaging by sectioning or slice- ing through the use of any type of transmitted wave (such as light wave).The use of computed tomography (CT) to determine the RIP of optical fiber preforms is well known. For example, see Y. Zhao et al., "Nondestructive Measurement for Arbitrary RIP Distribution of Optical Fiber Preforms," ​​Journal of Lightwave Technology, Vol. 22, No. 2, pp. 478-86 (2004); Y. Zhao et al., "Nondestructive Measurement of Refractive Index Profile for Holey Fiber Preforms," ​​Optics Express, Vol. 11, No. 20, pp. 2474-79 (2003); Y. Zhao et al., "Tomographic Reconstruction for Arbitrary Refractive Index Distribution of Optical Fiber Preforms," ​​Symposium on Optical Fiber Measurements, at 51-54 (2004); and A. Novozamsky, "Tomography Reconstruction of Geometry and Refractive Index Profile of Highly Asymmetric Optical Fiber Preforms," ​​Proc. SPIE, vol. 7746, pp. 77461O-1 to 77461O-6 (2010).

[0015] Methods for reconstructing the RIP from the deflection angle distribution measured laterally by using the inverse Abel transform can also be found in U.S. Patent Nos. 4,744,654, 5,078,488, and 4,515,475. The following technical papers describe methods using the inverse Radon transform: Michael R. Hutsel and Thomas K. Gaylord, "Concurrent three-dimensional characterization of the refractive-index and residual-stress distributions in optical fibers," Applied Optics, Vol. 51, No. 22, pp. 5442-52 (2012), and S. Fleming et al., "Nondestructive Measurement for Arbitrary RIP Distribution of Optical Fiber Preforms," ​​Journal of Lightwave Technology, Vol. 22, No. 2, pp. 478-86 (2004).

[0016] P. Chu et al., "Nondestructive Determination of Refractive Index Profile of an Optical Fiber: Fast Fourier Transform Method," Applied Optics, Vol. 182, No. 7, pp. 1117-22 (1979) (incorporated herein by reference), presents another method that utilizes fringe patterns. This method uses the Fast Fourier Transform (FFT) to solve the inverse Abel transform and convert the path length into a refractive index profile. The advantage of the FFT method is that it is computationally fast.

[0017] However, the difference from the actual RIP due to the simple reconstruction of the RIP or the refractive index profile n(r) (in the symmetric case) or n(x,y) (in the asymmetric case) from the laterally measured deflection angle distribution using either the inverse Abel transform or the inverse Radon transform is not negligible. The reason for this error is a known measurement artifact that occurs at the refractive index discontinuity at the boundary between the transparent object and the environment or at the boundary between radial refractive index steps. Measurements made at the boundary where the refractive index jumps from a low refractive index to a high refractive index in the volume region near the boundary of the optical object (when viewed from the outside to the inside) result in regions that cannot be illuminated or characterized in principle. The occurrence of non-measurable regions caused by the measurement method in the case of an upward refractive index jump is typical for optical fibers where the refractive index of the core is relatively higher than that of the inner cladding layer.

[0018] The error source is illustrated in the schematic of FIG. 2 by referring to a simple case, i.e., a rod having a uniform refractive index distribution n1, which is inserted into a refractive index adjusting fluid (also called a refractive index matching fluid or immersion fluid) having a refractive index n0, where n0 is less than n1. During the scanning of the rod, a beam that collides tangentially at the incident point is refracted towards the center of the rod and exits the rod as an outgoing beam having different propagation directions, resulting in a beam path as shown in FIG. 2. Thus, there exists an area or region within the object where the light beam cannot pass tangentially (i.e., is never illuminated by the beam during measurement). This area is shown hatched in FIG. 2 and is indicated by the radius r * and the angle β (beta), where the angle β is 90 degrees - ψ / 2. As a result, it is impossible to measure the deflection angle in the region r * < r < r1, and this measurement error reveals that the reconstructed refractive index value is lower than the actual refractive index.

[0019] For example, typical differences and errors in the reconstruction RIP of step refractive index profiles are profile roundness and too small step height. The publication by Werner J. Glantschnig, "Index profile reconstruction of fiber preforms form data containing a surface refraction component," Applied Optics, Vol. 29, No. 19, pp. 2899-2907 (1990) ("Glantschnig publication" incorporated herein by reference), is one of the publications that addresses the problem posed by non-measurable regions. Glantschnig suggests that the actual missing deflection angle in the non-measurable region can be inferred by interpolation based on three measurement points inside the deflection angle distribution just before the discontinuity.

[0020] Interpolation based on three measurement points does not always give good results. Thus, some methods for measuring RIP cannot provide an accurate measurement of the RIP of a simple homogeneous rod. One reason for this shortcoming is the presence of refractive index discontinuities at the boundaries or edges of the rod. The Glantschnig publication explains why refractive index discontinuities are not accurately reconstructed from deflection function data. The Glantschnig publication proposes a method for measuring RIP, but it requires precise measurement of the deflection angle at the edges of the object, which is difficult to the point of being impractical.

[0021] To solve these problems, U.S. Patent No. 8,013,985 issued to Corning Incorporated (hereby incorporated by reference) proposes a modification of this reconstruction method. To measure the RIP of a transparent cylindrical object such as a fiber preform, the beam deflection angle function is measured. An estimated RIP, which represents the actual RIP, is fitted to the measured deflection angle distribution by a numerical model. In the measurement, the fiber preform to be measured is placed between a laser and a transform lens. The preform has a central axis and a cylindrical surface that defines the preform radius R. An incident beam that strikes the cylindrical surface at a height x is deflected within the preform and emerges again at another angle as an exit beam, which is detected by a photodetector and processed by a controller. The deflection angle, defined as the angle between the exit beam and the incident beam, is altered by changing the height x of the laser beam, and the deflection angle distribution is measured.

[0022] For this purpose, a symmetric correlation is completed on the measured deflection function to define a central coordinate. The measured deflection function is then bisected about the central coordinate, and a refractive index half-profile is obtained for each of the halves, resulting in an estimated refractive index profile for each half. The relevant parameters for the RIP calculation are the radius r of the preform, k and the refractive index of the layer, n k The target angle distribution ψ t is iteratively fitted to the measured deflection function, and measurement points close to boundaries (index discontinuities) are omitted in or on the edge of the preform. This arithmetically iterative method of fitting a mathematical function can be called "fitting".

[0023] According to U.S. Pat. No. 8,013,985, the fitting is performed by inserting the unknown parameters of the RIP, i.e., the value of the radius R of the preform (or the value of the radius of the refractive index discontinuity), as well as the unknown refractive index value, into the equation (1) above (but without considering the arccosine part shown in the second line of the equation), and the unknown parameters are the target angular distribution ψ t is the measured deflection angle distribution ψm Thus, the target angle distribution is fitted to the measured deflection angle distribution with the unknown parameters.

[0024] Based on the thus fitted and simulated target angular distribution, a reconstructed refractive index profile is derived, which has a reconstructed preform radius R that is larger than the radius of the inner object region. * When the RIP is a cylindrical object having at least one discontinuity, the method is applied to various object regions each defined by a discontinuity.

[0025] In this method, the simulated target angular distribution ψ t is the deflection angle distribution ψ measured by fitting unknown parameters. m A radial refractive index distribution that may be fitted to the refractive index profile and extend to the boundaries of discontinuities located further outward is derived from the simulated target angular distribution.

[0026] Thus, the detection of the complete RIP of an optical object having several layers radially separated by refractive index discontinuities requires successive measurements, calculations and estimations of the layers defined by each discontinuity from the outside to the inside. Systematic and numerical errors may result in the fitting of the simulated target angle distribution. Furthermore, it has been found that the comparison of the deflection angle distributions, i.e., the simulated and the measured, is not very illustrative and requires a high level of expertise to determine whether and optionally how the fitting is optimal or whether and optionally which values ​​require post-correction or further modification.

[0027] Similar to the '985 patent, U.S. Patent No. 10,508,973, issued to the assignee of the present application (Heraeus Quarzglas GmbH & Co. KG of Hanau, Germany) and incorporated herein by reference, discloses a fitting procedure for axisymmetric preforms. The '973 patent teaches a method for determining the refractive index profile of cylindrical optical objects, particularly preforms for optical fibers. The method involves the steps of (a) adjusting the measured deflection angle distribution, including determining the extreme values ​​of the deflection angle distribution, to obtain an adjusted deflection angle distribution, (b) converting the adjusted deflection angle distribution into an adjusted refractive index profile, (c) evaluating the adjusted refractive index profile for fixing orientation values ​​for the layer radius and layer refractive index of the virtual refractive index profile, (d) generating a simulated deflection angle distribution based on the virtual refractive index profile with orientation values ​​and converting the deflection angle distribution into a simulated refractive index profile, (e) fitting the simulated refractive index profile to the adjusted refractive index profile by iterative fitting of parameters to obtain a fitted simulated refractive index profile defined by the fitted parameters, and (f) obtaining the refractive index profile as a virtual refractive index profile with the fitted parameters. The method represents the state of the art for determining the RIP when the RIP is substantially or completely step-index.

[0028] State-of-the-art methods suffer from at least one of two errors. The first type of error is RIP measurement artifacts. All reconstructed profiles (including tomographically reconstructed 2D or 2D RIP) have typical profiling measurement artifacts (underestimated refractive index steps, distorted profiles, rounded edges, etc.), so an accurate evaluation is not possible. The second type of error is systematic errors due to asymmetry. Ignoring the asymmetry of nearly symmetric preforms by simply fitting a symmetric distribution (which usually allows to handle measurement artifacts in the symmetric case) leads to large systematic errors.

[0029] Thus, there remains a need for a method to determine the RIP of cylindrical transparent objects that do not have an axisymmetric or nearly axisymmetric refractive index distribution. The RIP may or may not be substantially or completely step-index. There is also a need for a method that minimizes measurement artifact errors. Of course, the method must also be improved in terms of validity, accuracy, reliability and reproducibility. A related need is a method to improve preform assembly and meet preform customer requirements, especially for preforms of increasingly complex design. Summary of the Invention

[0030] To meet these and other needs, and with that objective in mind, the present disclosure provides a method for determining the refractive index profile of an object, such as a preform, particularly when the RIP is not substantially symmetric. The method includes the following steps: 1. A method comprising: (a) preparing an object comprising an optical object having a longitudinal axis, the object having at least one layer extending outwardly about the longitudinal axis, the at least one layer lacking perfect rotational symmetry in cross section; (b) scanning the object with a light beam starting from a first projection angle and creating raw data representing the object through measurement data; (c) optionally rotating the object and iteratively repeating step (b) until all projection angles have been scanned and all measurement data have been created; (d) processing the measurement data to form a sinogram, and upon completion of optional step (c), proceeding to step (f); (e) rotating the object and iteratively repeating steps (b) and (d) until all projection angles have been scanned; (f) calculating a 2D RIP; (g) selecting a line section of interest within the 2D RIP; (h) applying a fitting procedure to the line section of interest; and (i) determining a refractive index step / gradient and dimensions.

[0031] It is to be understood that both the foregoing general description and the following detailed description are exemplary of the present disclosure and are not restrictive. [Brief description of the drawings]

[0032] The present disclosure is best understood from the following detailed description when read in connection with the accompanying drawings. It is emphasized that, according to common practice, the various features of the drawings are not to scale. Conversely, dimensions of the various features have been arbitrarily increased or decreased for clarity. The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawings contained therein will be provided by the Office upon request and payment of the necessary fee. The drawings include the following figures: [Figure 1] FIG. 1 shows a radiation path through an object having a uniform refractive index distribution, illustrating generally the various geometric relationships. [Diagram 2] FIG. 2 shows a radiation path through an object with a uniform refractive index distribution illustrating a measurement artifact in refractive index profiling due to the hatched non-measurable area where tangential radiation cannot be detected. [Diagram 3] FIG. 3 shows the variables applicable to determining the refractive index profile using computed tomography. [Figure 4] FIG. 4 is a schematic diagram of a deflection function measurement system. [Figure 5A] FIG. 5A is a graph of an example of a deflection angle distribution ψ(ρ) (in degrees) plotted against position (in millimeters) along the ρ axis after measuring deflection functions in various directions at a given projection angle (e.g., θ=8°) during a first stage of an improved method for evaluating an asymmetric glass fiber preform. [Figure 5B] FIG. 5B is a graph that emphasizes the central portion of the graph of FIG. 5A using a reduced scale along both the abscissa and ordinate. [Figure 6] FIG. 6 illustrates a Radon transform that can be used to calculate data during the first stage of an improved method for evaluating an asymmetric glass fiber preform. [Figure 7] FIG. 7 is the resulting sinogram by calculating the phase shift and stacking the measurement data shown in FIG. [Figure 8] FIG. 8 shows a plot of the relative refractive index in the xy plane (ie, for a line section of the preform) after applying the inverse Radon transform to the sinogram of FIG. [Figure 9] FIG. 9 is a flow diagram illustrating the steps of a particular embodiment of an improved method for evaluating an asymmetric glass fiber preform. [Figure 10] FIG. 10 is a flow diagram summarizing the steps of a particular embodiment of a fitting procedure applied to one step of the improved method shown in FIG. [Figure 11] FIG. 11 shows a graph of the relative refractive index n(r)-1.4587 plotted against radius r (in millimeters) with a tailored refractive index profile n′(r) and a hypothetical refractive index profile n*(r) modeled by evaluation of the profile of a preform having a step profile. [Figure 12] FIG. 12 is a graph of the relative refractive index n(r)-1.4587 plotted against radius r (in millimeters) illustrating the generalized fitting procedure. [Figure 13] FIG. 13 illustrates an embodiment of the method of the present disclosure applied to a preform having a single elliptical core, specifically, a sinogram produced by the method. [Figure 14] FIG. 14 illustrates an application of one embodiment of the disclosed method to a preform having a single elliptical core, specifically, a plot of the relative refractive index n(x,y)-1.446 in the xy plane showing the reconstructed 2D RIP of a preform having a single elliptical core. [Figure 15]FIG. 15 illustrates an example of an embodiment of the method of the present disclosure applied to a preform having a single elliptical core, specifically, a graph illustrating a line section fitting procedure for data taken along a line section drawn through the core of the diagram in FIG. [Figure 16] FIG. 16 illustrates an application of one embodiment of the disclosed method to a single elliptical core preform, specifically, a plot of the relative refractive index n(x,y)-1.446 versus position r in millimeters for a single elliptical core preform, comparing two different line sections and single measurements versus tomographic measurements. [Figure 17] FIG. 17 illustrates an example of the application of one embodiment of the method of the present disclosure to a preform having a single core with an octagonal cladding, specifically, the sinogram produced by the method. [Figure 18] FIG. 18 illustrates an example of the application of one embodiment of the disclosed method to a preform having a single core with an octagonal cladding, specifically, a plot of the relative refractive index n(x,y)-1.446 in the xy plane showing the reconstructed 2D RIP of a preform having a single core with an octagonal cladding. [Figure 19] FIG. 19 illustrates an example of the application of one embodiment of the method of the present disclosure to a preform having a single core with an octagonal cladding, specifically, a graph illustrating the line section fitting procedure for data taken along a first line section drawn through the core in the diagram of FIG. [Figure 20] FIG. 20 illustrates an example of the application of one embodiment of the method of the present disclosure to a preform having a single core with an octagonal cladding, specifically, a graph illustrating the line section fitting procedure for data taken along the second line section drawn through the core in the view of FIG. [Figure 21] FIG. 21 illustrates an example of an embodiment of the method of the present disclosure applied to a preform having seven cores, specifically, the sinogram produced by the method. [Figure 22]FIG. 22 illustrates an example of an embodiment of the disclosed method applied to a seven-core preform, specifically, a plot of the relative refractive index n(x,y)-1.4587 in the xy plane showing a reconstructed 2D RIP of a seven-core preform. [Diagram 23] FIG. 23 illustrates an example of the application of one embodiment of the disclosed method to a preform having seven cores, specifically a graph illustrating the line section fitting procedure for data taken along a first line section drawn through the central cores of the diagram in FIG. [Figure 24] FIG. 24 illustrates an example of the application of one embodiment of the disclosed method to a preform having seven cores, specifically a graph illustrating the line section fitting procedure for data taken along the second line section drawn through the central cores of the view in FIG. [Diagram 25] FIG. 25 illustrates an example of the application of one embodiment of the method of the present disclosure to a preform having six cores, specifically the sinogram produced by the method. [Figure 26] FIG. 26 illustrates an example of the application of an embodiment of the disclosed method to a six-core preform, specifically, a plot of the relative refractive index n(x,y)-1.4587 in the xy plane showing a reconstructed 2D RIP of a six-core preform. [Figure 27] FIG. 27 illustrates an example of the application of one embodiment of the disclosed method to a preform having six cores, specifically a graph showing the line section fitting procedure for data taken along a line section drawn through the first core of the diagram in FIG. [Figure 28] FIG. 28 illustrates an example of the application of one embodiment of the disclosed method to a preform having six cores, specifically a graph showing the line section fitting procedure for data taken along a line section drawn through the different cores of the diagram in FIG. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0033] In this specification and in the claims that follow, reference will be made to a number of terms, which shall be defined to have the following meanings ascribed to them: Terms such as "include," "includes," "including," "have," "has," "having," "comprise," "comprises," "comprising," and the like, mean inclusive but not limited, i.e., inclusive and not exclusive. The term "substantially," as used herein, is a descriptive term indicating approximation, meaning "to a great extent" or "to the majority, but not all, of what is specified," and is intended to avoid precise numerical boundaries for specified parameters.

[0034] The term "about" (or "approximately") means that amounts, sizes, formulations, parameters, and other quantities and characteristics are not and need not be exact, but may be approximate and / or larger or smaller, as desired, to reflect tolerances, conversion factors, rounding, measurement errors, and the like, and other factors known to those of skill in the art. When a value is described as being about or approximately equal to a particular number, the value is within ±10% of that number. For example, a value that is about 10 refers to a value between 9 and 11, inclusive. When the term "about" is used in describing a value or an endpoint of a range, the disclosure should be understood to include the particular value or endpoint. Regardless of whether or not a numerical value or an endpoint of a range herein is described as being "about," the endpoint of the numerical value or range is intended to include two embodiments: those modified by "about" and those not modified by "about." It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint.

[0035] The term "about" or "substantially" refers to all terms within the range, unless otherwise specified. For example, about 1, 2, or 3 is equivalent to about 1, about 2, or about 3, and further includes about 1 - 3, about 1 - 2, and about 2 - 3. The disclosed specific values and preferred values for compositions, components, ingredients, additives, and the like, and their ranges, are for illustrative purposes only and do not exclude other defined values or other values within the defined range. The compositions and methods of the present disclosure include any value or any combination of values, those having specific values, more specific values, and the described preferred values.

[0036] As used in this disclosure, the indefinite article "a" or "an" and its corresponding definite article "the" mean at least one, or one or more, unless otherwise specified. The terms indicating directions used in this disclosure (e.g., up, down, right, left, front, back, top, bottom) are used only with respect to the drawn figures and the coordinate axes given in those figures and are not intended to imply an absolute orientation.

[0037] It is well known to use computed tomography (CT) to determine the refractive index profile (RIP) of an optical fiber preform. The variables applicable to determining the RIP using CT are defined by the figures provided in FIG. 3. An object having a refractive index distribution n(x,y) surrounded by a refractive index adjustment fluid having a refractive index n0 such that n0 < n(x,y) is shown. The Cartesian coordinates x and y belong to the physical object (e.g., a glass body). When scanning the object, the beam refracts as soon as it contacts the object and is directed towards the center of the object along the path indicated by the arrow. The deflection angle ψ is defined as the angle between the outgoing beam and the incoming beam.

[0038] During CT, the object is rotated. The mechanism for holding and rotating the sample (typically a rotary stage) is not shown in FIG. 4 for simplicity. However, tomography requires an accurate method for rotating the sample. Manual rotation is possible but not practical. An electric rotary stage with an encoder is more suitable.

[0039] Rotation of the object by an angle θ, called the projection angle, results in Cartesian coordinates x' and y'. The scanning procedure is performed in the direction y' along the scan position ρ. For a given fixed projection angle, such a scan results in a measured deflection angle ψ(ρ,θ=fixed). It is necessary to measure the deflection angle distribution ψ(ρ,θ) for a large set of projection angles θ to determine the exact RIP. Thus, the deflection angle distribution ψ(ρ,θ) is measured and the RIP is reconstructed from the deflection angle distribution (ρ is the scan position and θ is the measured projection angle).

[0040] The method is described below with reference to a transparent cylindrical object in the form of a fiber preform. However, those skilled in the art will appreciate that the described method can be generally applied to any cylindrical object having a refractive index at a given wavelength of radiation, and that the corresponding deflection angle distribution can be measured via lateral transmission of a wavelength of radiation, and that there exists a target deflection angle distribution function that can be expressed as a function that can be fitted to the measured data. Referring now to the drawings, in which like reference numbers refer to like elements throughout the various figures that make up the drawings, FIG. 4 is a schematic diagram illustrating an exemplary embodiment of a basic deflection angle distribution measurement system 100 that can be used to establish a measured deflection angle distribution function. The deflection angle is calculated by the formula: ψ=arctan(projection on camera / distance to camera).

[0041] The system 100 has a pair of optical axes 15 and a third optical axis (not shown) between a pair of off-axis mirrors 4. One or more laser sources (such as laser diodes 1a, 1b, and 1c) each generate a laser beam (or "light beam") and provide the one or more laser beams to one or more beam combiner fibers 2, which deliver the one or more laser beams to a beam conditioner 3. (In optical fiber communications, a single-mode optical fiber is an optical fiber designed to carry only a single mode of light, i.e., a transverse mode. Standard G.652 defines the most widely used form of single-mode optical fiber). The one or more beam combiner fibers 2 are either Y-shaped fibers with two inputs and one output, or X-shaped fibers with crosstalk at the splice region. The beam conditioner 3 is aligned along the first optical axis 15 and modifies the properties of the laser beams. The beams emitted by the beam conditioner 3 travel along a first optical axis 15 and enter an off-axis parabolic reflector having a pair of mirrors 4 and an aperture (or "pinhole") 5. The first mirror 4 produces collimated beams that pass through the aperture 5. The second mirror 4 focuses these beams along a second optical axis 15.

[0042] The focused beam reflected from the off-axis parabolic reflector second mirror 4 passes through an optical shutter 6 and enters a measurement cell 9. As long as the control voltage to the shutter 6 remains high, however, the shutter 6 remains open; as soon as the voltage goes low, however, the shutter 6 closes, providing inherent "fail-safe" operation, i.e. security.

[0043] The measurement cell 9 is planar and has opposing sides that are perpendicular to the second optical axis 15. Within the measurement cell 9, a transparent cylindrical object 11 with a uniform or step-shaped RIP to be measured is placed, typically in the form of a fiber preform with a core with a higher refractive index surrounded by at least one cladding layer with a lower refractive index. An index-matching fluid 10 surrounds the object 11 within the measurement cell 9. In one exemplary embodiment, the index-matching fluid 10 is an oil with a refractive index close to, but not the same as, that of the object 11. However, for simplicity, the refractive index of the index-matching fluid 10 is matched to the measurement cell 9, so that no additional deflection at the entrance and exit points occurs in the illustrated embodiment.

[0044] As an alternative to the widely used paraffin RI refractive index matching oil, a glycerol-water mixture can also be used. The mixture ratio allows for relatively easy and precise adjustment or tuning of the RI to a desired RI level within the range of 1.333 (water RI) to 1.48 (glycerol RI).

[0045] The laser beam enters the measurement cell 9 and first impinges on the object 11 at a first edge of the object 11 and undergoes a first refraction. The first refracted laser beam then travels through the object 11 and exits from the opposite edge of the object 11 where the laser beam exits the object 11 through a second refraction. The deflection angle, identified by the Greek letter Ψ (psi), is defined by the angle of the outgoing laser beam with respect to the incoming laser beam. The outgoing laser beam then passes through a filter (e.g., an infrared long-pass filter) 12 and is detected by a photodetector unit. The filter 12 serves to prevent ambient light from adversely affecting the measurement. A suitable photodetector unit includes a line-scan camera 13 with an optically active sensor 14. (Alternatives to line scan cameras can also be used. Among other suitable cameras are 2D cameras and time-delay-integration or "TDI" line scan cameras. A TDI line scan camera is somewhat of a hybrid, being a 2D sensor having, for example, 16,384 x 256 pixels, although its architecture and sensor, like the line scan camera, is extended in one dimension.) The photodetector unit then transmits the corresponding detector signal via data connection 17 to controller 16 for processing.

[0046] The measurement cell 9 is mounted on a linear stage 7 configured to support the measurement cell 9 and move the measurement cell 9 in a movement direction 8 (e.g., up and down as shown in FIG. 4). By performing measurements of the deflection angle over a range of heights of the laser beam relative to the central horizontal axis of the measurement cell 9 and the object 11 in the measurement cell 9, the corresponding detector signals received and processed by the controller 16 generate a measured deflection angle, as will be explained in more detail below. In other words, the movement of the linear stage 7 allows the height of the laser beam to be changed relative to the measurement cell 9 and the object 11 such that the measured deflection function includes a range of radii of the object 11. Of course, it is also possible to move the camera relative to the laser beam so that it remains aligned with the laser beam, and vice versa.

[0047] In the embodiment shown in FIG. 4, the object 11 in the measurement cell 9 is moved (e.g., scanned), however in another embodiment, all other components (such as the laser diodes 1a, 1b, 1c and the photodetector unit) may be moved (e.g., scanned) simultaneously relative to the object 11 (which is held stationary) so that the height of the laser beam can be changed to send the laser beam through different parts of the object 11.

[0048] The controller 16 is, for example, a computer including a processor unit (e.g., CPU), a memory unit, and support circuits, all operatively interconnected. The processor may be or include any form of general-purpose computer processor that can be used in an industrial environment. The memory unit includes a computer-readable medium that can store instructions (e.g., software) that instruct the processor to perform the methods described in detail below. The memory unit may be, for example, a random access memory, a read-only memory, a floppy or hard disk drive, or other form of digital storage device. In an exemplary embodiment, the instructions stored in the memory unit are in the form of software that, when executed by the processor, transforms the processor into an application-specific processor that controls (i.e., directs or causes) the system 100 to perform one or more of the methods described below. The support circuits are operatively (e.g., electrically) coupled to the processor and may include cache, clock circuits, input / output subsystems, power supplies, control circuits, etc.

[0049] Laser diodes 1a, 1b, 1c, shutter 6, linear stage 7, and line scan camera 13 are each configured to transmit signals and data to, and receive signals and data from, controller 16 along a number of data connections 17. Data connections 17 may be wired or wireless, and any conventional data connections 17 known to those of skill in the art are suitable.

[0050] Many other deflection function measurement systems similar to those described above can be used to obtain the deflection function. Regardless of the system used, several methods are possible for determining the RIP of the cylindrical optical object 11. The deflection angle is calculated by the formula: ψ=arctan(projection onto camera / distance to camera).

[0051] As mentioned above, CT is based on the well-known inverse Radon transform, which when applied to the RIP field can be written as:

[0052]

number

[0053] In contrast to interferometric RI profiling, the phase shift diagram η(ρ,θ) is typically not directly measurable. Instead, the deflection function ψ(ρ,θ) is accessible and can be converted to the phase shift diagram η(ρ,θ) by the approximation given in equation (5).

[0054]

number

[0055] Usually in tomography, the measurement data are typically pre-processed to improve the quality of the reconstruction. Such pre-processing also applies in the field of RI profiling, where the importance of a precisely defined deflection function origin is well known. Regardless of how precisely all the mechanical parts and components of the measurement system 100 are manufactured and assembled, it is always beneficial to numerically fine-tune the origin. For the evaluation of radially symmetric profiles, there exist different approaches to achieve so-called prepared deflection functions, which are defined as a measured deflection function ψ with a finely adjusted origin. prepared (y)=ψ measured (yy shift )-ψ Offset The two parameters ψ Offset and y shift is very small, but typically non-zero, for any particular measurement system 100. Several approaches for defining these two parameters for a radially symmetric RIP are described in U.S. Pat. No. 10,508,973.

[0056] In asymmetric RIP, the deflection function for a fixed projection angle θ can be complex. Such complexity is due to the prepared deflection function ψ prepared / (ρ,θ)=ψ measured / (ρ-ρ shift )-ψ Offset However, in tomography in general, there are many techniques to improve the quality of the reconstructed image. Although most of the research and algorithms to improve the reconstructed image quality have focused on X-ray and NMR-CT, some of the methods are applicable in the field of tomography RIP. For simplicity, only a few examples for improving the quality of the reconstructed image are given in the following disclosure, and those skilled in the art can choose additional or alternative methods.

[0057] For each measured deflection angle distribution ψ(ρ,θ), shiftProperly defining ρ can be understood as the well-known radial runout correction in tomography. Radial runout occurs when an orbital translation occurs instead of a simple rotation along the Z axis that changes the projection angle θ. Mathematically, this adds a shift for each projection angle θ. A tomographic reconstructed image affected by radial runout typically has smeared edges, unclear features or transitions, etc. As a result, radial runout correction can be achieved by minimizing the entropy of the reconstructed image. In this case, ρ for each single projection is shift and then compute the reconstruction. This iterative process is not very efficient as it requires many time-consuming computations of the reconstruction. An alternative approach, which is preferred, is described below.

[0058] In most cases, one or more features within the measured sample can be used for radial runout correction. A person skilled in the art can identify suitable features by the following criteria: A feature has a sharp RI step (at least 10 over several micrometers). -3 The feature should have an RI difference of preferably 0.01 to 0.01 mm (preferably 0.01 to 0.1 mm) so that any edge detection algorithm works well. The feature should also preferably define or enclose a region of interest in the reconstructed 2D RIP. This criterion ensures that the edges of the feature are not distorted by the bias of the outer RI variations. In practice, the measurements for each projection angle θ are calculated using an individual ρ shift The columns are shifted by a factor of 10, so that the features are aligned concentrically around the origin, regardless of how chaotic the interior may appear. As shown in the sinogram included in the figure, this means that each column is shifted vertically so that feature pairs are aligned. Figure 17 shows, for example, that a circular feature is

number

[0059] ρ shiftMeasured deflection function ψ by measured In addition to proper alignment of , the quality of the reconstructed 2D RIP depends on the degree of accuracy of ψ for each measured projection. Offset 4 uses two beam perpendicular planes and a surrounding reference material with a constant refractive index, so that both sides (ρ=0 and ρ=ρ ref ) criterion, the resulting phase shifts η must be equal. This constraint is satisfied by the fact that for each measured projection, ψ Offset In particular, the deflection function offset ψ Offset is the integral over the reference material on both sides (the upper integration limit ρ in Eq. (5) is the reference position ρ ref ), so η(ρ=0)=η(ρ=ρ ref ρ shift and ψ Offset By appropriately defining prepared (ρ,θ), and therefore the prepared phase shift diagram η prepared It becomes possible to calculate (ρ,θ).

[0060] In addition to RIP-specific mathematical tools to improve the quality of the reconstruction, more general CT tools exist as well. The number of tools is not limited to the following given example for sinogram interpolation. The inverse Radon transform involves an integral over the scan position ρ and the projection angle θ. Ideally, both step sizes dρ and dθ are very small. However, a trade-off exists, since a finer mesh size defined by dρ and dθ increases the overall measurement time required.

[0061] In addition to reducing the mesh size by using smaller step sizes dρ, dθ, or both dρ and dθ, it is possible to interpolate within the sinogram. Interpolation of additional projection angles θ gives particularly good results in terms of improving the reconstruction quality. The reason is that the sinogram typically does not change much in the direction of dθ at small scales. In contrast, discontinuities typically exist in the direction of dρ. Starting with one or several additional interpolated projection angles θ between the measured projections, the number of projections in the prepared sinogram can reach 10, 20, or even more times the number of measured projections. Many different methods can be applied for two-dimensional interpolation, including but not limited to nearest neighbor, bilinear, cubic, and spline interpolation.

[0062] A frequency domain filter needs to be used to apply the inverse Radon transform to the prepared phase shift diagram η(ρ,θ). Different types of filters are suitable for image reconstruction. Among such filters are the Ram-Lak filter, the Shepp-Logan filter, the Cosine filter, the Hamming window filter, and the Hann window filter. The Ram-Lak filter is also known as the Ramp filter. Since this filter is sensitive to noise, it is multiplied with an appropriate window to improve the results. The Shepp-Logan filter is obtained by multiplying the Ram-Lak filter with a sinc or sampling function. The Cosine filter is obtained by multiplying the Ram-Lak filter with a cosine function. Similarly, the Hamming and Hann filters are obtained by multiplying the Ram-Lak filter with a Hamming window and a Hann window, respectively. The Ram-Lak and Shepp-Logan filters are high-pass filters, which keep the edge information intact. The Cosine, Hamming and Hann filters are band-pass filters. They are used to smooth the image and remove the extra edges from the image.

[0063] In modern CT, many methods exist to improve the quality of the reconstruction, which can be applied here by anyone skilled in the art. However, such improvements always depend on the particular object under investigation, and a particular method may be beneficial for a particular object, or may simply result in additional computation time, or may even worsen the results. In the case of large deflections due to large refractive index steps in the object, it may be beneficial to apply backpropagation instead of linear backprojection. However, this iterative procedure requires many resources and results in longer computation times.

[0064] The measurement of the RIP of optical fiber preforms is important for the inspection of the quality of the optical fiber waveguide and also for the specification of additional treatments of the preforms (e.g. overcoating or etching) before drawing the fiber. In the case of preforms, non-destructive techniques are particularly useful. The method disclosed in this document is based on the measurement of the deflection of a transversely directed light beam scanned through the preform. The method is further based on the numerical processing of a set of measured deflection functions at many angular projections. The method disclosed above calculates the RIP further based on the assumption that the preform is circular. However, a method for the tomographic reconstruction of the RIP for preforms with highly asymmetric cross sections is desired.

[0065] Attempts have been made to address the RI characteristics of asymmetric fiber preforms. See, for example, K. Toga et al., "Microscopic Computer Tomography Measurement of Nonaxisymmetrically Distributed Optical Fiber Refractive Index," Journal of Lightwave Technology, Vol. 6, No. 1, pp. 73-79 (1988), and B. Bachim et al., "Microinterferometric Optical Phase Tomography for Measuring Small, Asymmetric Refractive-Index Differences in the Profiles of Optical Fibers and Fiber Devices," Applied Optics, Vol. 44, No. 3, pp. 316-27 (2005). These two references are incorporated herein by reference.

[0066] The following disclosure describes steps of an improved method that provides accurate RIP of objects that are not symmetric or at least not substantially symmetric. Such preforms may be preforms with unintended asymmetries. Furthermore, the method can be used with multi-core preforms, Panda preforms (used to make a common style of polarization-maintaining fiber that has circular, symmetric stress rods on either side of the core to induce polarization), or preforms for fiber lasers with non-circular interfaces.

[0067] The improved method for evaluating asymmetric glass fiber preforms has two main steps. The first step involves the determination of the tomographic refractive index. The second step involves the correction of measurement artifacts.

[0068] In the first stage of the method, the deflection function is measured for different orientations (a single scan provides useless information for asymmetric preforms). The number of measurements taken must balance the accuracy of the data (more measurements are desired to give higher resolution) against the time required to make the measurements (fewer measurements are quicker). For example, the system 100 may take about 18 minutes to scan the preform every 2° using one light source, or about 3.6 hours to scan the preform every 0.5° using three light sources (scanning every 0.5° means that 720 measurements are made for the entire 360° around the preform). The measurements yield a deflection angle distribution ψ(ρ,θ). FIG. 5A is a graph of an exemplary deflection angle distribution ψ(ρ,θ) (in degrees) for a simplified case plotted against the position (in millimeters) along the ρ axis for a given projection angle (θ=8°). FIG. 5B is a graph emphasizing the central portion of the graph of FIG. 5A using a reduced scale along both the abscissa and ordinate.

[0069] Once the measurements are taken, they are subjected to tomographic evaluation. Such evaluation includes calculating the phase shift and stacking to form a sinogram. The sinogram provides a convenient way of representing the complete set of data acquired during a scan and is useful for checking systematic errors during data acquisition or for verifying that pre-processing steps (e.g. radial runout correction) are working correctly.

[0070] As shown in Figure 6, the Radon transform is an integral transform that transforms a function f defined on the xy plane into a function Rf defined on the two-dimensional (θ,s) space of lines in the plane (i.e., the Radon transform), whose value at a particular line is equal to the line integral of the function over that line. The parameter ρ is the length of a portion of the line A-A', s is the distance of the line from the origin, and θ is the angle that the normal or perpendicular to the line makes with the x-axis. This transform was introduced by Johann Radon in 1917, who also provided a formula for the inverse transform. Radon further included a formula for the transform in three dimensions, where the integral is over a plane (integration over a line is known as the x-ray transform). This was later generalized to higher dimensional Euclidean spaces and more broadly in the context of integral geometry. The inverse Radon transform is widely applicable to tomography, which creates images from projection data associated with cross-sectional scans of an object.

[0071] If the function f represents the unknowns, then the inverse Radon transform represents the projection data obtained as the output of a tomographic scan. The inverse of the Radon transform can therefore be used to reconstruct the original quantities from the projection data, and thus forms the mathematical basis for tomographic reconstruction, also known as iterative reconstruction. Because the inverse Radon transform of an off-center point source is a sine wave, a representation of the inverse Radon transform data is often called a sinogram. As a result, the inverse Radon transform of multiple scans appears graphically as multiple sine waves with different amplitudes and phases, called a sinogram.

[0072] FIG. 7 is a sinogram resulting from calculating the phase shift and stacking the measurement data shown in FIG. 5A. The phase shift is expressed in arbitrary units (abbreviated as au). Arbitrary units are relative units of measurement to indicate the ratio of a quantity of a quantity to a predetermined reference measurement. "Predetermined" means pre-determined, and therefore the predetermined characteristic must be determined, i.e. selected or at least known, prior to any event. FIG. 8 shows a diagram of the relative refractive index in the xy plane (i.e. for a cross section of the preform) after applying the inverse Radon transform. The refractive index is shown in relative values ​​based on the refractive index of the surrounding reference glass plate (n0=1.4587).

[0073] The refractive index profile is then determined using known techniques (the inverse Radon transform is preferred). These steps complete the first "tomographic" stage of the improved method for evaluating asymmetric glass fiber preforms. Unfortunately, the results show typical measurement artifacts such as underestimated refractive index steps, distorted profiles, and rounded edges.

[0074] Measurement artifacts are corrected in the second stage of the method. Correction of the artifacts is achieved by applying a method such as that of '973 described above to a selected line section of the 2D RIP (i.e., the "start RIP") obtained from the tomographic data. A "modeled RIP" is created after assuming a symmetric preform based on several parameters (which are to be varied). A "distorted RIP" is calculated from the modeled RIP by (i) simulating the deflection angle distribution of the modeled RIP and (ii) calculating the distorted RIP from the simulated distribution. The parameters are varied relative to the modeled RIP until the distorted RIP approaches the starting RIP. This approach is approximate. The calculation of the corrections is performed as if the starting RIP was measured on a preform with rotational symmetry, which is not the case. The key underlying assumption is that the measurement artifacts for a real specimen are similar for a rotationally symmetric preform.

[0075] The starting point of the improved evaluation method is a 2D-RIP based on tomographic measurements and reconstructions (including all CT techniques available today for improved imaging). One or more line sections of the region of interest (core, side pits, edges, etc.) are selected. According to each of the selected line sections, an abstract, imaginary but symmetric preform is "fitted" to the selected line sections. For a simplified explanation, it is assumed that an abstract, imaginary symmetric profile can be directly fitted. However, the profile cannot be directly fitted, since no analytical expression exists for such a RIP (including typical measurement artifacts). The fitting procedure therefore includes the following steps for each iteration: (i) assuming a symmetric preform based on several parameters (to be changed), (ii) simulating the deflection angle distribution, (iii) reconstructing the symmetric RIP, and (iv) calculating the deviations of the selected cross sections. With this measurement and evaluation procedure, the tomographic 2D RIP reconstruction first takes care of all asymmetries (so that no systematic errors are introduced) and the line section fitting procedure does the rest, especially to address typical measurement artifacts in refractive index profiling.

[0076] 9 is a flow diagram showing steps of a particular embodiment of an improved method 500 for providing an accurate refractive index profile of an object that does not have a symmetrical cross section, or at least does not have a substantially symmetrical cross section. The method 500 determines the radial RIP of a cylindrical optical object 11 having a cylindrical longitudinal axis about which at least one layer extends asymmetrically. In step 501 of the method 500, a deflection function is measured starting from a projection angle (theta) 0. In step 502, the object 11 is scanned. After completion of step 502, it is possible to proceed directly to step 504 of the method 500.

[0077] Optionally, but not required, a raw image can be created from the scan. In optional step 503, one or more of a variety of techniques can be used to improve the quality of the raw image. For example, scanning cameras have an "image ROI" feature that allows an operator to specify the portion of the sensor array to be used for image acquisition. ROI is an acronym for "region of interest." If an image ROI is specified, the camera will only transmit pixel data from within that region. In most cameras, this specification significantly increases the maximum frame rate of the camera. The ROI can be brightened. Another technique can be applied to collect several images of different exposures.

[0078] As another example of a technique to improve the quality of the raw image, a scanning camera with high dynamic range (or HDR) can be used. In essence, HDR helps to produce "better" pixels. HDR expands the range of brightness levels, which allows for enhanced distinction between white and black. The color range is also expanded, allowing colors to be more detailed.

[0079] As yet another example of a technique to improve the quality of the raw image, filtering algorithms can be used to remove OVD diffraction. Outside vapor deposition (OVD) is a process in which glass is deposited in layers to produce a porous deposit (glass soot). The porous glass deposit can be cleaned, for example, by flowing chlorine gas (dehydrogenation) to reduce the OH percentage. At the same time, the porous deposit becomes a glass preform (vitrification). Despite further processing steps such as vitrification, microlayer structures related to the process can remain and can also affect RI variations at the microscale. These very frequent RI variations lead to diffraction when scanned with a laser and even non-coherent light beams.

[0080] Higher diffraction orders reduce the accuracy of the determination of the deflection angle, up to the very severe case where the zeroth order beam cannot be distinguished by the higher orders. Because the high-frequency RI microlayer structure caused by the OVD manufacturing process is typically non-periodic and curved, the diffraction pattern can be very irregular, to the point where the higher diffraction orders can be brighter than the diffraction orders from the zeroth order beam. It is well known to those skilled in the art that only the evaluation of the zeroth order beam will yield a useful deflection angle distribution and a reasonable RIP reconstruction. Depending on the level of OVD diffraction severity (i.e., the intensity of light in the higher diffraction orders), additional pre-processing by applying an OVD filter algorithm may be required.

[0081] After step 502, which involves scanning the object 11 with the light beam (starting from a first projection angle) and creating raw data representing the object through measurement data, the method 500 can proceed along one of two alternative paths. The first alternative path involves rotating the object 11 by a small angle (theta), such as π / 180, and iteratively repeating step 502 until all projection angles in the entire range (0-2π) have been scanned and all measurement data has been acquired. The method then processes and stacks the measurement data to create a phase-shifted sinogram and proceeds to step 508.

[0082] A second alternative path after step 502 is shown in FIG. 9. In step 504 of method 500, the deflection function and the phase shift diagram are calculated (as described above). It is also possible to directly calculate the phase shift diagram without the intermediate step of calculating the deflection function (i.e., the intermediate step is optional). The phase shift diagrams are exported and stacked as described above to form a sinogram in step 505. Then, in step 506, method 500 asks whether all projections in the entire range (0 to 2π) have been measured. If the entire range has not yet been measured, method 500 performs step 507. In step 507, the object 11 is rotated by a small angle (theta), such as π / 180, and method 500 returns to step 502 to scan the object 11. Steps 502 , 503 (optional), 504 , 505 , 506 , and 507 are repeated iteratively until all projections in the entire range (0 to 2π) have been measured, and method 500 may proceed to step 508 .

[0083] In optional step 508, the quality of the sinogram may be improved using one or more of a variety of techniques. As one example, radial runout may be corrected. As another example, the sinogram may be interpolated to a finer mesh.

[0084] In step 509, the 2D RIP is calculated from the sinogram by applying the inverse Radon transform, which was described above. Step 509 completes the first stage of the method 500.

[0085] Step 510 starts the second phase of the method 500 and asks whether any significant RIP measurement artifacts are present in the 2D RIP. Measurement artifacts occur when the refractive index step transitions from a low value to a high value (in the direction from outside to inside). This transition is relatively easy to determine for each selected line section. The term "significant" can refer, for example, to the sharpness of the RI step (i.e., the sharper the step, the more significant the artifact). If the step is gradient and not steep, as in the case of a germanium doped core with a parabolic shaped RI), the artifact is not present or can be ignored.

[0086] If the RIP measurement artifacts are not significant, method 500 performs step 520. In step 520, a particular geometric shape and refractive index step is determined before method 500 ends in step 580. If significant RIP measurement artifacts are present in the 2D RIP, method 500 proceeds to step 530. In step 530, a line section of interest (also called a region of interest or ROI) is selected within the 2D RIP. A fitting procedure is then applied to the selected line section in step 540. Further details regarding the fitting procedure are provided in connection with FIG. 10 below.

[0087] If the fitting procedure applied in step 540 satisfies one or more stopping criteria, the method 500 proceeds to step 560. The stopping criteria may be determined by comparing the result of the fitting procedure to a predetermined accuracy level for the selected line section of the object 11 being evaluated. The predetermined accuracy level may depend on the particular application. A typical predetermined accuracy is about 90%, a further predetermined accuracy is about 92%, a preferred predetermined accuracy is about 95%, a more preferred predetermined accuracy is about 97%, and a most preferred predetermined accuracy is about 99% or higher.

[0088] In step 560, fitting parameters such as RI step, geometry, gradient, and dimensions are exported. Next, method 500 asks in step 570 whether all regions of interest in the preform have been characterized. If less than all regions of interest have been characterized, method 500 returns to step 530 and a new line section of interest is selected in the 2D RIP. Steps 530, 540, and 560 are repeated iteratively until all regions of interest have been characterized, and method 500 can proceed to step 580 to complete.

[0089] FIG. 10 is a flow diagram summarizing the steps of a particular embodiment of the fitting procedure applied in step 540 of the improved method 500. The line section (or ROI) of interest selected in the 2D RIP in step 530 is used as the start of the fitting procedure in step 541. Then, in step 542, starting parameters for the fitting procedure are extracted from the line section and in step 543, a first fitting region is defined. Next, the method 500 asks in step 544 whether the actual layer is stepped. If the answer to the question posed in step 544 is negative, the method 500 asks in step 545 whether there is another inner layer. If the answer to the question posed in step 545 is positive, in step 546, the fit region is moved to the next inner layer and the method 500 returns to step 544. Thus, a loop including steps 544, 545, and 546 is created until either the question posed in step 544 is answered in the affirmative or the question posed in step 545 is answered in the negative.

[0090] If the question posed in step 545 is answered in the negative, then the method 500 asks whether the line section is stepped in step 547. If the question posed in step 547 is answered in the positive, then measurement artifact compensated parameters and line section have been achieved in step 548 and the fitting procedure 540 ends. If the question posed in step 547 is answered in the negative, then a measurement artifact compensated RIP is determined in step 549 and a measurement artifact compensated line section is achieved in step 550.

[0091] If the question posed in step 544 is answered in the affirmative, then in step 551 an analytical deflection curve of an axisymmetric RIP intended to mimic the measurement artifact as an equivalent axisymmetric RIP is generated. In step 552 the deflection is converted to a deflected RIP. Then in step 553 the accuracy of the deflected RIP compared to the initial line section is calculated. The accuracy can be measured by the R-squared statistic which quantifies the predictive accuracy of the statistical model. The statistic indicates the proportion of variance in the outcome variable that is explained by the prediction. This is known as the coefficient of determination R 2 , r 2 , and is also known as r-squared. 2 Typically, R has a value ranging from 0 to 1 (or 100%). A value of 1 indicates that the prediction is identical to the observed value. 2 It is not possible to have a value of 0. A value of 0 indicates that there is no linear relationship between the observed and predicted values, and "linear" in this context means that there is still the possibility of a nonlinear relationship between the observed and predicted values. Finally, a value of 0.5 means that half of the variance in the outcome variable is explained by the model. Sometimes, the R 2 is expressed as a percentage (e.g., 50%).

[0092] Next, the method 500 asks in step 554 whether a particular stopping criterion has been met (e.g., a particular R-squared value was calculated in step 553). For each iteration of the fitting procedure, the initial parameters (n k and r k ) becomes smaller and smaller. Once the variation is small enough, below a certain threshold, further fitting iterations are not necessary. In practice, there are other inherent errors that limit the accuracy, e.g., 10 -5 Smaller than n k The same observation can be made with respect to the layer radius r k also applies.

[0093] If the answer to the question posed in step 554 is no, then the method 500 proceeds to step 555, where the actual fitting parameters n m and r m is changed. Thus, a loop including steps 551, 552, 553, 554, and 555 is created until the question posed in step 554 is answered in the affirmative. If the answer to the question posed in step 554 is yes, the method returns to step 545.

[0094] FIG. 11 shows the relationship between the adjusted refractive index profile n'(r) and the hypothetical refractive index profile n(r) modeled by its evaluation for a preform with a simple step profile. * The refractive index is shown as a relative value based on the refractive index of the refractive index matching fluid (n0=1.4587). In the figure, the relative refractive index n(r)-1.4587 is plotted against the radius r (in millimeters).

[0095] Virtual refractive index profile n *(r) already represents or is close to the actual expected refractive index profile of the preform. The hypothetical refractive index profile is based on the tailored refractive index profile n'(r) and orientation values ​​derived from the profile, which include estimates of the refractive index and radius from unmeasured regions.

[0096] Using equation (1), the simulated deflection angle distribution Ψ″(y) is converted in the next method step into a virtual refractive index profile n * (r) is generated. Therefore, the simulated deflection angle distribution ψ * (y) is the assumed refractive index profile of the preform (i.e., the hypothetical refractive index profile n * (r)), which is then derived from the adjusted refractive index profile n′(r) after correction and evaluation of the original measurements.

[0097] The simulated refractive index profile n″(r), plotted in this specification in FIG. 11, is again obtained by transforming the simulated deflection angle distribution ψ″(y) by numerical integration of equation (2). The profile has a rounded region 53 between the cladding region 52 and the core region 51. (As mentioned above, such core rods are often surrounded in preforms by an inner cladding layer of fluorine-doped or germanium-doped silica glass and an outer cladding layer of undoped silica glass.) Except for this rounded region 53, the simulated refractive index n″(r) closely matches the tailored refractive index profile n'(r). The assumed refractive index distribution n * This is remarkable considering that (r) is significantly different. This similarity is due to the fact that the hypothetical refractive index profile n * This suggests that the assumptions underlying n(r) are already very close to the actual refractive index profile of the preform, n(r). That is, the hypothetical refractive index profile n(r) in FIG. * (r) accurately or at least accurately enough reflects the actual refractive index profile n(r).

[0098] In practice, an exact match between the simulated refractive index profile n"(r) and the tuned refractive index profile n'(r) cannot be achieved. However, by iteratively fitting the simulated refractive index profile n"(r) to the tuned refractive index profile n'(r), it is possible to achieve a suitable and arbitrarily accurate fit. An alternative generalized fitting procedure can be described with reference to FIG. 12.

[0099] The alternative fitting procedure allows for a more accurate assessment of a RIP that is not perfectly step-like, but has the current measurement artifacts due to the steep RI step from low to high (in the outside-to-inside direction). In FIG. 12, a specific relative refractive index n(r)-1.4587 is plotted against the radius r (in millimeters). The measurement data 301 is indicated with an "X". A typical measurement artifact of a RIP appears at r=±22 mm, so that the reconstructed measurement differs from the actual RIP in that region. The goal of the fitting procedure is to determine the RI step and its associated artifact error, which can later be used to correct the measurement data 301. For this purpose, similar to the fitting procedure described previously, a simulation helper 302 and an associated simulation fit or fitting curve 303 are provided. The simulation helper 302 is an assumed RIP that was generated with the goal of estimating and covering the RI step at r=±22 mm. The assumed RIP of the simulation helper 302 allows for the generation of a deflection function by using equation (1). By transforming this deflection function using equation (2), a fitting curve 303 is obtained.

[0100] The parameters of the simulation helper 302 are changed so that for a fixed range (e.g., 21 mm<|r|), the fitting curve 303 matches the measured data 301 around the RI step. The region must be small enough so that any inner RI gradient does not affect the fit, but wide enough so that this rounded curve shape can be fitted robustly enough. In response to visual feedback, one skilled in the art can adjust the selected region to improve the fitting procedure.

[0101] Adding the difference between the simulation helper 302 and the fitting curve 303 to the measurement data 301 results in a fit result 304. The result is more accurate than the measured RIP. For more complex preforms, this fitting procedure can be repeated as necessary for each RI step that occurs. In this case, the RIP of the simulation helper 302, the fitting curve 303, and the fit result 304 are stitched together according to each of the different regions.

[0102] Even in the specific case where the characterized preform itself does not have such a described RI step, but has the RI of undoped fused silica near the outer surface, this method is also very useful for the following reasons: A setup like the device 100 usually has an undoped fused silica measurement cell 9, since this material is available homogeneously and the absolute RI is well known, including its dispersion, temperature dependence, and other properties. It is also state of the art to use a refractive index-adjusting fluid 10 to keep the occurring deflection angles small enough so that the device 100 can capture them. If the RI of the refractive index-adjusting fluid 10 is above the measurement cell 9 and the RI is in the outer region of the glass object 11, a measurement artifact will appear at the boundary between the measurement cell 9 and the refractive index-adjusting fluid 10, affecting the entire inner region as well. The only way to completely avoid this artifact is for the refractive index-adjusting fluid 10 to perfectly match the measurement cell 9 and the outer region of the glass object 11. In addition to general practical problems (due to the strong temperature dependence of liquids suitable as refractive index adjusting fluid 10), this would completely eliminate the boundary, so that no distinction between the glass object 9, the refractive index adjusting fluid 10 and the measurement cell 11 is possible. EXAMPLES

[0103] In order to more clearly demonstrate the general nature of the present disclosure, the following examples are included which are intended to illustrate, but not limit, the disclosure.

[0104] Figures 13-16 show Example 1 of a preform with a single elliptical core. Figure 13 is a sinogram created by applying method 500, i.e., rotating the preform, taking measurements, and stacking the measurements from left to right. A single sinusoidal shape is shown reflecting the single core, prior to application of the Radon transform. Note that the vertical lines reflect the first line section 310 and the second line section 312. The sinogram shows the magnitude of the deflection angle distribution ψ(ρ,θ) in the ρ-θ plane in arbitrary units.

[0105] 14 is a diagram of the relative refractive index n(x,y)-1.446 in the xy plane showing a reconstructed 2D RIP of a preform with a single elliptical core. A first line section 310 is taken along the major axis (longest diameter) of the ellipse between the two vertices of the ellipse. A second line section 312 is taken along the minor axis or shortest diameter of the ellipse.

[0106] Data taken along a second line section 312 drawn through the core of the diagram of FIG. 14 is shown in the graph of FIG. 15 illustrating the line section fitting procedure. The graph plots the relative refractive index n(r)-1.446 versus position r in millimeters. FIG. 15 illustrates the main concept of the method 500. The graph of FIG. 15 includes three curves: a curve 320 through the selected tomographically reconstructed line section data, a simulated fit curve 321, and a fit result (or assumed) curve 322. The assumed RI steps are 0.002 and 0.01, which can be very well estimated with the method 500.

[0107] FIG. 16 highlights the need for tomographic measurements and evaluation methods therein using the first line section 310 and the second line section 312. The graph in FIG. 16 plots the relative refractive index n(r)-1.446 versus the position r in millimeters for a preform with a single elliptical core, comparing two different tomographic line sections with a single related measurement. Curve 330 shows a single measurement along the first line section 310, and curve 332 shows a single measurement along the second line section 312. Curve 334 shows a tomographic measurement along the first line section 310, and curve 336 shows a tomographic measurement along the second line section 312. Thus, method 500 can be compared to a simple evaluation (basic inverse Abel transformation). Depending on the orientation during the single measurement, the results can vary greatly. In contrast, the level of RIP is independent of the line section selected. The fit function and resulting profile of method 500 are omitted to avoid overloading the graph.

[0108] 17-20 show a preform example 2 with a single core with an octagonal cladding that can be considered approximately radially symmetric. The core is made of fluorine-doped quartz glass sold under the trademark Fluosil® by Heraeus Quarzglas GmbH & Co.KG of Germany. FIG. 17 is a sinogram created by applying the method 500, i.e., by rotating the preform, taking measurements, and stacking the measurements from left to right. Note that the vertical lines reflect the first line section 340 and the second line section 342. The sinogram shows the magnitude of the deflection angle distribution ψ(ρ,θ) in the ρ-θ plane in arbitrary units.

[0109] 18 is a diagram of the relative refractive index, n(x,y)-1.446, in the xy plane showing a reconstructed 2D RIP of a preform with an octagonal cladding. A first line section 340 is taken along the major axis through the opposing vertices of the octagonal cladding. A second line section 342 is taken along the minor axis through the opposing flat sections between the vertices of the octagonal cladding.

[0110] Data taken along a line section 342 drawn through the core of the diagram of Figure 18 is shown in the graph of Figure 19 illustrating the line section fitting procedure. The graph plots the relative refractive index n(r)-1.446 versus position r in millimeters. The graph of Figure 19 includes four curves: a curve 350 through the measured line section data, a simulated fit curve 351, a fit result (or assumed) curve 352, and a single measurement reconstruction curve 353. The graph shows the advantages of the method 500 and highlights the need for tomographic evaluation compared to single measurements.

[0111] Data taken along a line section 340 drawn through the core of the diagram of Figure 18 is shown in the graph of Figure 20 illustrating the line section fitting procedure. The graph plots the relative refractive index n(r)-1.446 versus position r in millimeters. The graph of Figure 20 includes four curves: a curve 360 ​​through the measured line section data, a simulated fit curve 361, a fit result (or assumed) curve 362, and a single measurement reconstruction curve 363. The graph shows the advantages of the method 500 and highlights the need for tomographic evaluation compared to single measurements.

[0112] Figures 21-24 show Example 3 of a more complex preform with seven cores. Figure 21 is a sinogram created by applying method 500, i.e., rotating the preform, taking measurements, and stacking the measurements from left to right. Six sinusoidal shapes are shown, one for each of the non-central cores. Note that the vertical lines reflect the first line section 370 and the second line section 372. The sinogram shows the magnitude of the deflection angle distribution ψ(ρ,θ) in the ρ-θ plane in arbitrary units.

[0113] 22 is a diagram of the relative refractive index n(x,y)-1.4587 in the xy plane showing a reconstructed 2D RIP of a preform with seven cores. A first line section 370 is a shorter line section taken through the central core. A second line section 372 is a longer line section taken through the central core.

[0114] Data taken along a longer line section 372 drawn through the central core of the diagram of FIG. 22 is shown in the graph of FIG. 23 illustrating the line section fitting procedure. The graph plots the relative refractive index n(r)-1.4587 versus position r in millimeters. The graph of FIG. 23 includes three curves: a curve 380 through the measured line section data, a simulated fit curve 381, and a fit result (or hypothetical) curve 382. This graph illustrates the advantages of the method 500. The Radon transform and its inverse can be applied to transition between the sinogram of FIG. 21 and the graph of FIG. 23.

[0115] Data taken along a shorter line section 370 drawn through the central core of the diagram of Figure 22 is shown in the graph of Figure 24 illustrating the line section fitting procedure. The graph plots the relative refractive index n(r)-1.4587 versus position r in millimeters. The graph of Figure 24 includes three curves: a curve 384 through the measured line section data, a simulated fit curve 385, and a fit result (or hypothetical) curve 386. This graph illustrates the advantages of the method 500.

[0116] 25-28 show Example 4 of a preform with six cores and no central core. FIG. 25 is a sinogram created by applying method 500, i.e., rotating the preform, taking measurements, and stacking the measurements from left to right. Six sinusoidal shapes are shown, one for each core. Note that the curves reflect a first line section 390 and a second line section 392. The line sections 390, 392 shown in the sinogram of FIG. 25 appear curved because the line sections 390, 392 in the 2D RIP (see FIG. 26) do not pass through the center. The sinogram shows the magnitude of the deflection angle distribution ψ(ρ,θ) in the ρ-θ plane in arbitrary units.

[0117] 26 is a diagram of the relative refractive index n(x,y)-1.4587 in the xy plane showing the reconstructed 2D RIP of a preform with six cores. A first line section 390 is a shorter line section through one of the cores. A second line section 392 is a longer line section through another of the cores but including the preform boundary of about ±32 mm.

[0118] Data taken along a longer line section 392 is shown in the graph of Figure 27 illustrating the line section fitting procedure. The graph plots the relative refractive index n(r)-1.4587 versus position r in millimeters. The graph of Figure 27 includes three curves: a curve 394 through the measured line section data, a simulated fit curve 395, and a fit result (or hypothetical) curve 396. This graph illustrates the advantages of method 500.

[0119] Data taken along a shorter line section 390 is shown in the graph of Figure 28 illustrating the line section fitting procedure. The graph plots the relative refractive index n(r)-1.4587 versus position r in millimeters. The graph of Figure 28 includes three curves: a curve 397 through the measured line section data, a simulated fit curve 398, and a fit result (or hypothetical) curve 399. This graph illustrates the advantages of the method 500.

[0120] These examples show that the calculated preform parameters, especially the refractive index step, are much more accurate with method 500. Method 500 is beneficial for customers of asymmetric preforms, including multi-core preforms, hollow core fiber preforms, Panda preforms, or preforms for fiber lasers with non-circular interfaces.

[0121] Although shown and described above with reference to certain specific embodiments and examples, the present disclosure is not intended to be limited to the details shown. Rather, various modifications in details may be made without departing from the spirit of the present disclosure, within the scope and range of equivalents of the claims. For example, all broad ranges described herein are expressly intended to include within their scope all narrow ranges that are included in the broad ranges.

Claims

1. 1. A method for determining a refractive index profile (RIP) of an object, the method comprising: (a) providing an optical object comprising an optical body having a longitudinal axis about which at least one layer extends outwardly, the at least one layer lacking perfect rotational symmetry in cross section; (b) scanning the object with a light beam starting from a first projection angle and generating raw data representative of the object through the measurement data; (c) optionally rotating the object and iteratively repeating step (b) until all projection angles have been scanned and all measurement data have been generated; (d) processing the measurement data to form a sinogram, and proceeding to step (f) if optional step (c) is completed; (e) rotating the object and iteratively repeating steps (b) and (d) until all projection angles have been scanned; (f) calculating the 2D RIP; (g) selecting a line section of interest within the 2D RIP; (h) applying a fitting procedure to the line sections of interest; (i) determining the refractive index step / gradient and dimensions; A method comprising:

2. 2. The method of claim 1, wherein the step (b) of scanning the object includes directing an incident beam at a point of incidence on the cylindrical optical object in a direction transverse to the cylindrical longitudinal axis, a deflection angle ψ being defined as the angle between an outgoing beam and the incident beam, and y being the distance between the cylindrical longitudinal axis and the point of incidence of the incident beam in a Cartesian coordinate system.

3. The method of claim 1 , wherein the step of calculating the 2D RIP is performed based on an inverse Radon transform.

4. 2. The method of claim 1, wherein the step of processing the measurement data to form a sinogram comprises the steps of calculating a deflection function, calculating a phase shift diagram, and stacking the phase shift diagrams to form the sinogram.

5. 2. The method of claim 1, wherein the raw data includes an original image, the method further comprising the steps of improving the quality of the original image by one or more of using a scanning camera with an "image ROI" function, collecting several images with different exposures, using a scanning camera with HDR, and removing OVD diffraction using a filtering algorithm.

6. The method of claim 1 , further comprising improving a quality of the sinogram by one or more of applying a radial runout correction and interpolating the sinogram to a finer mesh.

7. The method of claim 1 , wherein the object provided in step (a) is a fiber preform.

8. 8. The method of claim 7, further comprising using the determined refractive index step / gradient and dimensions to characterize the fiber preform and adapt a preform manufacturing process.

9. The method of claim 1 , further comprising, prior to step (f), determining whether all projection angles have been scanned.

10. 2. The method of claim 1, further comprising the step of determining after step (f) whether significant RIP measurement artifacts are present in the 2D RIP, and if not, determining the geometric and refractive index steps and terminating the method.

11. 2. The method of claim 1, wherein the step (h) of applying the fitting procedure to the selected line section of interest comprises the steps of extracting starting parameters for the fitting procedure from the line section, defining a first fitting region, and determining whether an actual layer is stepped.

12. 12. The method of claim 11, wherein the fitting procedure further comprises the steps of generating an analytical deflection curve if the actual layer is stepped, converting the analytical deflection curve to a deflected RIP, and calculating accuracy of the deflected RIP compared to the initial line section.

13. The method of claim 1 , further comprising, after step (i), a step (j) of determining whether all line sections of an object in the 2D RIP have been characterized.

14. 14. The method of claim 13, further comprising iteratively repeating steps (g), (h), (i), and (j) until all line sections of interest in the 2D RIP have been characterized.

15. The method of claim 14 , further comprising the step of calculating a measurement artifact-compensated refractive index profile of the object.

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