Improved tomographic refractive index profile assessment of asymmetric glass fiber preforms and fibers themselves

Abstract

A method for determining a refractive index profile (RIP) when the refractive index profile of a preform is substantially asymmetric. (i) scanning the preform from a first projection angle and creating raw data representing the object from the measurement data. (ii) optionally, rotating the object and iteratively repeating step (i) until all projection angles have been scanned and all measurement data have been created. (iii) processing the measurement data to form a sinogram, and if the optional step (ii) has been completed, then the method proceeds to step (v). (iv) rotating the object and iteratively repeating steps (i) and (iii) until all projection angles have been scanned. And (v) calculating the 2D RIP. (vi) selecting a line segment of interest within the 2D RIP. (vii) applying a fitting process to the line segment of interest. And (viii) finally, determining the step / gradient and size of the refractive index.

Description

Technical Field

[0001] The present disclosure relates generally to refractive index measurement, and more particularly to methods of measuring the refractive index profile of a transparent cylindrical object such as an optical fiber preform. Background Art

[0002] Transparent cylindrical objects, such as optical fiber preforms, optical fibers, light guides, light pipes, etc., are used in a variety of optical applications. In many cases, it is desirable to know the refractive index profile (RIP) of such an object. For example, an optical fiber is formed by heating an optical fiber preform and drawing the molten end into a thin glass strand. The RIP of the preform defines the RIP of the resulting optical fiber, which in turn determines the waveguide properties of the optical fiber. Therefore, it is important to be able to accurately measure the RIP of an optical fiber preform.

[0003] There are various methods for determining the radial RIP of a cylindrical optical object, in particular a preform for an optical fiber. A cylindrical optical object generally has a cylindrical longitudinal axis with a layer radius r k and has a layer refractive index n k At least one layer k of may extend radially around the longitudinal axis of the cylinder, symmetrically around the axis, and uniformly. Of course, there are many objects with non-radial, asymmetric or gradient RIPs, and the present 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 (where ρ is the scan position and θ is the measured projection angle). The RIP is also called the refractive index profile and is represented by the symbol n(x, y), where x and y are Cartesian coordinates.

[0004] A Cartesian coordinate system uniquely specifies each point in three-dimensional space by three Cartesian numerical coordinates (x, y, z), which are the signed distances from three fixed, mutually perpendicular oriented lines to the point measured in the same units of length. Each reference line is called a coordinate axis or just an axis of the system, and the point where they meet is its origin, usually at the ordered triple (0,0,0). A coordinate can also be defined as the position of the perpendicular projection of a point on the three axes, expressed as a signed distance from the origin.

[0005] Unfortunately, the refractive index distribution cannot be measured directly. The refractive index distribution is typically determined indirectly as the deflection or interference of a light beam that travels through a volume region of the optical element. The step-by-step transmission of the light beam relative to the optical element is referred to as "scanning" and is in the ρ direction. The spatial refractive index distribution in the optical element can be inferred from the interference or deflection of the outgoing light beam (the outgoing beam) based on the direction of the beam at the beam incidence point (the incident beam). During the light beam scanning, a series of deflection angles ψ measured in a direction transverse to the longitudinal axis (in the ρ direction) for a single fixed projection angle θ form a deflection angle distribution ψ(ρ,θ) (where θ is fixed).

[0006] For better visualization and illustration, Figure 1 the geometric relationships are schematically shown in. Depicted is an object with a homogeneous refractive index n1, which is surrounded by a refractive index adjusting fluid with a refractive index n0 such that n0 < n1. The radius of the object is r1. The deflection angle ψ is defined as the angle between the outgoing beam and the incident beam, and y is defined as the distance between the longitudinal axis of the cylinder and the incidence point of the incident beam. When scanning the object, the beam refracts as soon as it touches 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* that appears later in the formula for numerical integration (commonly referred to as the Abel inverse transform in the literature).

[0007] For an axially symmetric object with a fully step-like refractive index distribution, the deflection angle distribution ψ(y) can be described mathematically with reference to the following equation (1):

[0008]

[0009] In equation (1), m is the number of layers of the object, n0 is the refractive index of the surrounding medium, n k is the refractive index of the k-th layer, and r k is the radius of the k-th layer. The known mathematical method for calculating the refractive index distribution from the deflection angle distribution based on the measurement data according to equation (1) is based on a well-known numerical integration (referred to as the "Abel inverse transform" in the literature) calculated by the following equation (2)

[0010]

[0011] where r is the shortest distance from the longitudinal axis of the cylinder of the object to the beam path, i.e., as defined in equation (3)

[0012]

[0013] and R is the reference point of the refractive index profile, i.e. the radial position of the reference refractive index (the atmosphere surrounding the object, the refractive index adjusting fluid or the reference glass plate). By applying the partial derivatives of ψ from the position Δt, the formula becomes the shape of the well-known in mathematics inverse Abel transform. In principle, the inverse Abel transform can be applied to any kind of deflection angle distribution of an axially symmetric RIP, not just the ideal case of a step-index-like distribution as reflected in equation (1).

[0014] U.S. Patent No. 4,227,806 describes a method for non-destructively determining parameters of an optical fiber preform. The preform is scanned with a laser beam that enters the core-cladding structure transversely, and the deflection angle of the exiting beam is measured and then compared with a theoretical or empirical deflection angle distribution for a preform with a known refractive index distribution. During the measurement, the preform is positioned in a bath containing a refractive index adjusting fluid in order to prevent the deflection angle from becoming too large.

[0015] U.S. Patent No. 4,441,811 describes a method and apparatus for determining the refractive index profile of a cylindrical transparent optical preform. In this case, the preform inserted into the refractive index adjusting fluid is also scanned by a transverse incoming beam extending perpendicular to the optical axis. The beam is deflected by the glass of the preform and imaged onto a positionable detector using an optical device. The refractive index profile is calculated from the deflection angle distribution using 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.

[0016] Tomography performs imaging by using segments or sections of any kind of penetrating waves, such as light waves.The use of computed tomography (CT) to determine the RIP of an optical fiber preform is well known. See, for example, Y. Zhao et al., "Nondestructive Measurement for Arbitrary RIP Distribution of Optical Fiber Preforms," ​​Journal of Lightwave Technology, Vol. 22, No. 2, pp. 478-486 (2004); Y. Zhao et al., "Nondestructive Measurement of Refractive Index Profile for Holey Fiber Preforms," ​​Optics Express, Vol. 11, No. 20, pp. 2474-2479 (2003); Y. Zhao et al., "Tomographic Reconstruction for Arbitrary Refractive Index Distribution of Optical Fiber Preforms," ​​Symposium on Optical Fiber Measurements, pp. 51-54 (2004); and A. Novozámsky, "Tomography Reconstruction of Geometry and Refractive Index Profile of Highly Asymmetric Optical Fiber Preforms,” Proc. SPIE, vol. 7746, pp. 77461O-1–77461O-6 (2010).

[0017] Methods for reconstructing the RIP from the measured lateral deflection angle distribution using an inverse Abel transform can also be found in U.S. Pat. No. 4,744,654, U.S. Pat. No. 5,078,488, and U.S. Pat. No. 4,515,475. The following technical articles describe methods using an 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. 5442-5452 (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. 478-486 (2004).

[0018] P. Chu et al., "Nondestructive Determination of Refractive Index Profile of an Optical Fiber: Fast Fourier Transform Method," Applied Optics, Vol. 18, No. 7, pp. 1117-1122 (1979) (incorporated by reference in this document) proposed another method using fringe patterns. This method uses a fast Fourier transform (FFT) to solve the Abel inverse transform and convert the path length into a refractive index profile. The advantage of the FFT method is that it can speed up the calculation.

[0019] However, simply reconstructing the RIP or the refractive index distribution n(r) (for symmetric cases) or n(x,y) (for asymmetric cases) from the transversely measured deflection angle distribution using Abel's inverse transform or Radon's inverse transform does not result in a negligible difference with respect to the true RIP. One reason for this error is the known measurement artifacts that occur at the refractive index discontinuities at the boundaries between the transparent object and the environment or between the radial refractive index steps. Measurements made at the boundary of the refractive index jump from a low refractive index to a high refractive index (when viewed from outside to inside) in the near-boundary volume region of the optical object create regions that are not illuminated or characterized in principle. The occurrence of unmeasurable regions caused by the measurement method in the case of an upward refractive index jump is typical for optical fibers where the core has a relatively higher refractive index than the cladding.

[0020] In Figure 2 the sketch, the error source is illustrated by referring to a simple case, namely, a rod with a homogeneous refractive index distribution n1 that is inserted into a refractive index adjusting fluid (also called refractive index adaptive liquid or immersion liquid) with a refractive index n0, where n0 is less than n1. During the scanning of the rod, a beam incident tangentially at the entry point is refracted towards the center of the rod and exits the rod as an outgoing beam with a different propagation direction, thus generating a beam path as shown in Figure 2 . Therefore, there are regions or areas in the object through which no beam can be transmitted tangentially (i.e., are never illuminated by the beam during measurement). This region is shaded in Figure 2 and is marked with a radius r* and an angle β (beta), where the angle β = 90° - ψ / 2. Therefore, the deflection angle in the unmeasurable region r* < r < r1 cannot be measured, and it is obvious that due to this measurement error, the reconstructed refractive index value is lower than the true refractive index.

[0021] Typical differences and errors in the reconstructed RIP for, for example, a step refractive index distribution are an undersized distribution and rounding of the step height. The publication "Index profile reconstruction of fiber preforms from data containing a surface refraction component," by Werner J. Glantschnig, Applied Optics, Vol. 29, No. 19, pp. 2899 - 2907 (1990) ("Glantschnig publication", which is incorporated herein by reference) is one publication that addresses the problem caused by the unmeasurable regions. Glantschnig showed that by interpolating based on three internal measurement points of the deflection angle distribution just before the discontinuity, the actually missing deflection angle can be inferred in the unmeasurable region.

[0022] Interpolation based on three measurement points does not always produce good results. Therefore, some of the methods for measuring RIP cannot provide accurate measurements 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 the refractive index discontinuities are not accurately reconstructed from the deflection function data. Although the Glantschnig publication proposes a method for measuring RIP, it requires accurate measurement of the deflection angle at the edge of the object, which is difficult to the point of being impractical.

[0023] To address these issues, U.S. Pat. No. 8,013,985 to Corning Incorporated (which is incorporated by reference in this document) proposes a modification of this reconstruction method. In order to measure the RIP of a transparent cylindrical object such as an optical fiber preform, a beam deflection angle function is measured. The estimated RIP representing the actual RIP is adaptively measured to the deflection angle distribution by a numerical model. In the measurement, the optical fiber preform to be measured is arranged between the laser and the transformation lens. The preform has a central axis and a cylindrical surface that defines the preform radius R. The incident beam incident on the cylindrical surface at a height x is deflected in the preform and emitted again at another angle as an exit beam, which is detected by a photodetector and processed by a controller. The deflection angle is defined as the angle between the exit beam and the incident beam and is changed by changing the laser beam height x, and the deflection angle distribution is measured.

[0024] To this end, a symmetric correlation is performed on the measured deflection function to define the central coordinate. The measured deflection function is divided into two halves about the central coordinate, and a refractive index half profile is obtained for each of the two halves to produce a resulting estimated refractive index profile for each half. The relevant parameters for the RIP calculation are the preform radius r k and the refractive index n of the layer k Target angular distribution ψ t Iterative adaptation to the measured deflection function, wherein measurement points close to the boundaries (refractive index discontinuities) in or on the edge of the preform are omitted. This method of arithmetic iterative adaptation of a mathematical function may be called "fitting".

[0025] According to U.S. Pat. No. 8,013,985, a fit is performed such that the above equation (1) (however, without taking into account the arccos part indicated in the second line of the equation) has inserted into the equation the yet unknown parameters of the RIP, namely the value of the preform radius R (or the value of the radius at the refractive index discontinuity) and the yet unknown refractive index value, wherein the yet unknown parameters are varied so that the target angular distribution ψ is obtained t Best match to the measured deflection angle distribution ψ mTherefore, the target angular distribution is adapted (fitted) to the measured deflection angular distribution with as yet unknown parameters.

[0026] On the basis of the simulated target angular distribution thus adapted, a reconstructed refractive index distribution is obtained. This distribution extends up to a reconstructed preform radius R* that is greater than the radius of the inner object region. For cylindrical objects with at least one discontinuity in the RIP, the method is applied to each object region defined by the discontinuity, respectively.

[0027] In this method, the simulated target angular distribution ψ is obtained by fitting the unknown parameters. t Adaptive to measure the deflection angle distribution ψ m , and a radial refractive index distribution is derived from the simulated target angular distribution, which can extend up to the boundary of the discontinuity of the refractive index distribution located further outward.

[0028] Therefore, the detection of the complete RIP of an optical object having several layers radially separated by refractive index discontinuities requires continuous measurement, calculation and estimation from the outside to the inside of the layers defined by the corresponding discontinuities. Systematic and numerical errors may result in the fit of the simulated target angular distribution. In addition, it has been found that the comparison of the deflection angle distributions (i.e. the simulated deflection angle distribution and the measured deflection angle distribution) is not very illustrative and requires a high degree of expertise to determine whether the fit is optimal and optionally how the fit is optimal, or whether and optionally which values ​​require post-correction or further change.

[0029] As with the '985 patent, U.S. Patent No. 10,508,973, issued to the assignee of the present application (Heraeus Quarzglas GmbH & Co. KG, Hanau, Germany) and incorporated by reference herein, discloses a fitting process for axially symmetric preforms. The '973 patent teaches a method for determining the refractive index profile of a cylindrical optical object, particularly a preform for an optical fiber. The method comprises: (a) preparing a measured deflection angle distribution, including determination of the extreme values ​​of the deflection angle distribution, to obtain a prepared deflection angle distribution; (b) transforming the prepared deflection angle distribution into a prepared refractive index distribution; (c) evaluating the prepared refractive index distribution for fixing the orientation values ​​of the layer radius and the layer refractive index of the assumed refractive index distribution; (d) generating a simulated deflection angle distribution based on the assumed refractive index distribution with the orientation values, and transforming the deflection angle distribution into the simulated refractive index distribution; (e) fitting the simulated refractive index distribution to the prepared refractive index distribution by iterative adaptation of parameters to obtain a fitted simulated refractive index distribution defined by adaptive parameters; and (f) obtaining the refractive index distribution as a hypothetical refractive index distribution with adaptive parameters. The method represents the prior art for determining the RIP when the RIP is substantially or completely step-index-like.

[0030] Prior 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 two-dimensional or 2D RIPs) have typical profile measurement artifacts (underestimated refractive index steps, distorted profiles, rounded edges, etc.) that make accurate evaluation impossible. The second type of error is systematic error due to asymmetry. Ignoring the asymmetry of an almost symmetrical preform by simply fitting a symmetric distribution (which is usually able to handle measurement artifacts in the symmetric case) leads to a large number of systematic errors.

[0031] Therefore, there is still a need for a method for determining the RIP of a cylindrical transparent object that does not have an axially symmetric or approximately axially symmetric refractive index distribution. The RIP may or may not be substantially or completely step-index-like. There is also a need for a method that minimizes measurement artifact errors. Of course, the method must also be improved in terms of rationality, accuracy, reliability and reproducibility. A related need is a method for improving preform assemblies and meeting the needs of preform consumers, especially for preforms that are increasingly complex in design. Summary of the invention

[0032] To meet these and other needs, and in view of its purpose, the present disclosure provides a method for determining the refractive index profile of an object such as a preform, especially when the RIP is substantially asymmetric. The method includes the following steps: (a) providing an object, the object comprising an optical object having a longitudinal axis, at least one layer extending outwardly about the longitudinal axis, wherein at least one layer lacks complete rotational symmetry in cross section; (b) scanning the object with a beam starting from a first projection angle, and creating raw data representing the object from 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 created; (d) processing the measurement data to form a sinogram, and if optional step (c) has been completed, 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 segment of interest within the 2D RIP; (h) applying a fitting process to the line segment of interest; and (i) determining the refractive index step / gradient and size.

[0033] It is to be understood that both the foregoing general description and the following detailed description are exemplary and not restrictive of the disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The present disclosure is best understood from the following detailed description when read in conjunction with the accompanying drawings. It is emphasized that, according to common practice, the various features of the drawings are not to scale. Rather, the dimensions of the various features are arbitrarily expanded or reduced for clarity. This patent or application file contains at least one color drawing. Copies of this patent or patent application publication and color drawings included in the drawings will be provided by the Patent Office upon request and payment of the necessary fee. Included in the drawings are the following figures:

[0035] Figure 1 shows the path of radiation through an object having a homogeneous refractive index profile, schematically illustrating various geometric relationships;

[0036] Figure 2 shows a radiation path through an object having a homogeneous refractive index profile, illustrating measurement artifacts in the refractive index profile caused by shadowed, unmeasurable areas where no tangential radiation can be detected;

[0037] Figure 3 Variables applicable to determining a refractive index profile using computerized tomography are illustrated;

[0038] Figure 4 is a schematic diagram of the deflection function measurement system;

[0039] Figure 5A is a graph of an exemplary deflection angle distribution ψ(ρ) (in degrees) plotted against position along the ρ axis (in millimeters) after measuring the deflection function for different orientations for a given launch angle (e.g., θ=8°) during the first stage of the improved method for evaluating an asymmetric glass fiber preform;

[0040] Figure 5B is to highlight using decreasing scale along the horizontal and vertical axes Figure 5A A graph of the central portion of a graph of ;

[0041] Figure 6 illustrates a Radon transform that may be used to calculate data during the first stage of an improved method for evaluating an asymmetric glass fiber preform;

[0042] Figure 7 is the sinusoidal diagram obtained by calculating the phase shift and stacking the measured data presented in Figure 5;

[0043] Figure 8 It is shown that when the inverse Radon transform is applied to Figure 7 a graph of the relative refractive index in the xy plane (i.e., for a line segment of the preform) following a sinusoidal plot of ;

[0044] Fig. 9is a flow chart illustrating steps of a particular embodiment of an improved method for evaluating an asymmetric glass fiber preform;

[0045] Fig.10 is outlined in Fig. 9 A flow chart of the steps of a specific embodiment of the fitting process applied in one step of the illustrated improved method;

[0046] Fig.11 Graphs of the relative refractive index n(r)-1.4587 plotted against the radius r (in millimeters) are shown for a prepared refractive index profile n'(r) of a preform having a step profile and a hypothetical refractive index profile n*(r) modeled by evaluation of the profile;

[0047] Fig.12 is a graph of the relative refractive index n(r)-1.4587 plotted against radius r (in millimeters), illustrating the generalized fitting process;

[0048] Figures 13 to 16 Depicted is an example of applying an embodiment of the method of the present disclosure to a preform having a single oval core, and in particular, Fig.13 is the sinogram created by this method;

[0049] Fig.14 is a graph of the relative refractive index n(x,y)-1.446 in the xy plane, illustrating the reconstructed 2D RIP of a preform with a single elliptical core;

[0050] Fig.15 is an example along the way Fig.14 The core of the graph is a curve graph of the line segment fitting process of the data intercepted by the line segment drawn;

[0051] Fig.16 is a graph of the relative refractive index n(x,y)-1.446 of a preform having a single elliptical core versus the position r in millimeters and comparing two different line segments and single shot and tomographic measurements;

[0052] Figures 17 to 20 Depicted is an example of applying an embodiment of the method of the present disclosure to a preform having a single core with a cladding having an octagonal shape, and specifically, Fig.17 is the sinogram created by this method;

[0053] Fig.18 is a graph of the relative refractive index n(x,y)-1.446 in the xy plane, illustrating a reconstructed 2D RIP of a preform having a single core with an octagonal-shaped cladding;

[0054] Fig.19 is an example along the way Fig.18 A graph of the line segment fitting process of the data intercepted by the first line segment drawn at the core of the graph;

[0055] Fig. 20 is an example along the way Fig.18 A curve graph of the line segment fitting process of the data intercepted by the second line segment drawn at the core of the graph;

[0056] Figure 21 to Figure 24 Depicted is an example of applying an embodiment of the method of the present disclosure to a preform having seven cores, and in particular, Fig.21 is the sinogram created by this method;

[0057] Fig. 22 is a graph of the relative refractive index n(x,y)-1.4587 in the xy plane, illustrating the reconstructed 2D RIP of a preform with seven cores;

[0058] Fig.23 is an example along the way Fig. 22 A curve graph of the line segment fitting process of the data intercepted by the first line segment drawn at the center core of the graph;

[0059] Fig.24 is an example along the way Fig. 22 A curve graph of the line segment fitting process of the data intercepted by the second line segment drawn at the center core of the graph;

[0060] Figure 25 to Figure 28 Depicted is an example of applying an embodiment of the method of the present disclosure to a preform having six cores, and in particular, Fig.25 is the sinogram created by this method;

[0061] Fig.26 is a graph of the relative refractive index n(x,y)-1.4587 in the xy plane, illustrating the reconstructed 2D RIP of a preform with six cores;

[0062] Fig. 27 is an example along the way Fig.26 A first core of the graph is a graph of a line segment fitting process of the data intercepted by the line segment; and

[0063] Fig.28 is an example along the way Fig.26 The other core of the chart is a graph of the line segment fitting process that plots the line segment intercepting the data. DETAILED DESCRIPTION

[0064] In this specification and the claims that follow, reference will be made to a number of terms which will be defined to have the following meanings ascribed to them. "Include," "have," "include," and the like are meant to cover but not be limited to, i.e., be inclusive rather than exclusive. The term "substantially" as used in this document is a descriptive term indicating approximation, and means "to a considerable extent" or "to a large extent but not entirely as specified," and is intended to avoid strict numerical boundaries for specified parameters.

[0065] The term "about" (or "approximately") means that the amount, size, formula, parameter and other quantities and characteristics are not and need not be exact, but may be approximate and / or larger or smaller as needed, thereby reflecting tolerances, conversion factors, rounding, measurement errors, etc., and other factors known to those skilled in the art. When a value is described as being about or approximately equal to a number, the value is within ±10% of the number. For example, a value of about 10 refers to a value between 9 and 11, including the end values. When the term "about" is used in describing a value or an endpoint of a range, the disclosure should be understood to include the specific value or endpoint. Regardless of whether the endpoint of a numerical value or range in this specification states "about", the endpoint of the numerical value or range is intended to include two embodiments: one modified by "about" and one not modified by "about". It will also be understood that the endpoints of each range in the range are meaningful relative to the other endpoint and independently of the other endpoint.

[0066] The term "about" also refers to all terms within a range unless otherwise stated. For example, about 1, 2, or 3 is equivalent to about 1, about 2, or about 3, and also includes from about 1 to 3, from about 1 to 2, and from about 2 to 3. The specific values ​​and preferred values ​​disclosed for compositions, components, ingredients, additives, and the like, and their ranges are for illustration only; they do not exclude other defined values ​​or other values ​​within defined ranges. The compositions and methods of the present disclosure include those compositions and methods having any value or any combination of the described values, specific values, more specific values, and preferred values.

[0067] 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. Directional terms used in this disclosure - such as up, down, right, left, front, back, top, bottom - refer only to the drawings as drawn and those accompanying Figure 1 The coordinates are provided with respect to the axes and are not intended to imply an absolute orientation.

[0068] The use of computed tomography (CT) to determine the refractive index profile (RIP) of an optical fiber preform is well known. The variables applicable to determining the RIP using CT are given by Figure 3It is defined by the illustration provided in []. Depicted is an object with a refractive index distribution n(x,y), which is surrounded by a refractive index adjustment fluid with a refractive index n0 such that n0 < n(x,y). The Cartesian coordinates x and y belong to the physical object (e.g., a vitreous body). When scanning the object, the beam refracts upon contact with the object and is directed towards the center of the object along the path shown by the arrow. The deflection angle ψ is defined as the angle between the outgoing beam and the incoming beam.

[0069] During CT, the object is rotated. For simplicity, Figure 4 the mechanism for holding and rotating the sample (usually a rotating turntable) is not shown in []. However, tomography requires an accurate way to rotate the sample. Although manual rotation is possible, it is not practical. An electrically driven rotating turntable with an encoder is more suitable.

[0070] The rotation of the object through an angle θ (referred to as the projection angle) results in Cartesian coordinate axes x' and y'. The scanning process is performed along the scanning position ρ in the y' direction. For a given and fixed projection angle, such a scan results in a measured deflection angle ψ(ρ, θ = fixed). A large set of projection angles θ need to be measured for the deflection angle distribution ψ(ρ, θ) to determine the accurate RIP. Therefore, the deflection angle distribution ψ(ρ, θ) is measured, and the RIP is reconstructed from the deflection angle distribution (where ρ is the scanning position and θ is the measured projection angle).

[0071] The description of this method is made with reference to a transparent cylindrical object in the form of an optical fiber preform. However, those skilled in the art will understand that the described method can generally be applied to any cylindrical object having a refractive index at a given radiation wavelength, where the corresponding deflection angle distribution can be measured via the lateral transmission of radiation of a certain wavelength, and there exists a target deflection angle distribution function that can be expressed as a function that can be fitted to the measured data. Now refer to the accompanying drawings, in which throughout the various figures constituting the drawings, the same reference numerals refer to the same elements, Figure 4 is a schematic diagram illustrating an exemplary embodiment of a basic deflection angle distribution measurement system 100, which can be used to establish a measured deflection angle distribution function. The deflection angle is calculated by the following equation: ψ = arctan(projection on the camera / distance to the camera).

[0072] The system 100 has a pair of optical axes 15 and a third optical axis (not shown) between a pair of off-axis reflectors 4. One or more laser sources (such as laser diodes 1a, 1b, and 1c) each generate a laser beam (or "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 single-mode light: the 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 Y-shaped fibers with two inputs and one output, or X-shaped fibers with crosstalk in the splicing area. The beam conditioner 3 aligns and changes the properties of the laser beam along the first optical axis 15. The beam emitted by the beam conditioner 3 travels along the first optical axis 15 and is joined to an off-axis parabolic reflector having a pair of reflectors 4 and an aperture (or "pinhole") 5. The first reflector 4 produces parallel beams that pass through the aperture 5; the second reflector 4 focuses the beams along the second optical axis 15.

[0073] The focused beam reflected from the second mirror 4 of the off-axis parabolic reflector passes through an optical shutter 6 and enters a measuring unit 9. As long as the control voltage of the shutter 6 remains high, the shutter 6 remains open. However, as soon as the voltage goes low, the shutter 6 closes, thereby providing an inherent "fail-safe" operation, i.e. safety.

[0074] The measuring cell 9 has a reverse side which is planar and at right angles to the second optical axis 15. Arranged in the measuring cell 9 is a transparent cylindrical object 11 having a homogeneous or step RIP to be measured, typically in the form of an optical fiber preform having a core with a higher refractive index surrounded by at least one cladding with a lower refractive index. Surrounding the object 11 in the measuring cell 9 is a refractive index adjusting fluid 10. In the exemplary embodiment, the refractive index adjusting fluid 10 is an oil having a refractive index close to but different from that of the object 11. However, for simplicity, the refractive index of the refractive index adjusting fluid 10 is matched to the measuring cell 9 so that no additional deflections occur at the entry and exit points in the illustrated embodiment.

[0075] As an alternative to the widespread and commonly used paraffin RI index matching oils, glycerol-water mixtures can also be used. The mixing ratio allows the RI to be adjusted or tuned relatively easily and accurately to the desired RI level within the range of 1.333 (water RI) and 1.48 (glycerol RI).

[0076] The laser beam enters the measuring unit 9 and is first incident 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 leaves the object 11 at the opposite edge, where it undergoes a second refraction and leaves the object 11. The deflection angle identified by the Greek letter ψ (psi) is defined by the angle of the outgoing laser beam relative to the incident 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 helps to exclude adverse effects of ambient light on the measurement. A suitable photodetector unit includes a line scan camera 13 with an optically active sensor 14. (Alternatives to line scan cameras may 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: it is a 2D sensor with, for example, 16,384×256 pixels, but its architecture and sensor are extended in one dimension more like a line scan camera.) The photodetector unit then sends the corresponding detector signal to the controller 16 via data connection 17 for processing.

[0077] The measuring unit 9 is mounted on a linear stage 7, which is configured to support the measuring unit 9 and move in a moving direction 8 (e.g., Figure 4 The measurement unit 9 is moved in the vertical direction (in the up and down direction shown). By performing the measurement of the deflection angle over a range of laser beam heights relative to the central horizontal axis of the measurement unit 9 and the object 11 in the measurement unit 9, the corresponding detector signal received and processed by the controller 16 produces the measured deflection angle, as described in more detail below. In other words, the movement of the linear stage 7 allows the height of the laser beam to be varied relative to the measurement unit 9 and the object 11, so that the measured deflection function includes a range of radii of the object 11. Of course, the camera can be moved relative to the laser beam so that the camera also remains aligned with the laser beam, and vice versa.

[0078] Despite Figure 4 In the illustrated embodiment, the object 11 in the measuring unit 9 moves (e.g., scanned), but in another embodiment, other components (such as laser diodes 1a, 1b and 1c and photodetector units) can be simultaneously moved (e.g., scanned) relative to the object 11 (which remains stationary) so that the laser beam height can be varied in order to send the laser beam through different parts of the object 11.

[0079] The controller 16 is, for example, a computer including a processor unit (e.g., CPU), a memory unit, and support circuits, all of which are operably interconnected. The processor may be or include any form of general-purpose computer processor that may be used in an industrial environment. The memory unit includes a computer-readable medium capable of storing instructions (e.g., software) that direct the processor to perform a method as described in detail below. The memory unit may be, for example, a random access memory, a read-only memory, a floppy disk or a hard disk drive, or other forms of digital storage. 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 a dedicated processor that controls (i.e., directs or causes) the system 100 to perform one or more of the methods described below. The support circuits may be operably (e.g., electrically) coupled to the processor and may include caches, clock circuits, input / output subsystems, power supplies, control circuits, and the like.

[0080] The laser diodes 1a, 1b, 1c, shutter 6, linear stage 7 and line scan camera 13 are each configured to send and receive signals and data to and from a controller 16 along a plurality of data connections 17. The data connections 17 may be wired or wireless; any conventional data connection 17 as known to the skilled person is suitable.

[0081] Many other deflection function measurement systems similar to those described above may be used to obtain the deflection function. Regardless of the system used, a variety of methods for determining the RIP of the cylindrical optical object 11 are possible. The deflection angle is calculated by the following equation: ψ = arctan (projection on camera / distance to camera).

[0082] As mentioned above, CT is based on the well-known inverse Radon transform. When applied in the RIP domain, this transform can be written as equation (4) where θ is the projection angle and ρ is the scanning position (e.g. Figure 3 exemplified and discussed above), and η is the wavefront phase shift caused by the object under investigation. (Note that in X-ray CT, η(ρ,θ) will be the absorption distribution, which leads to the reconstruction of the density distribution.) As always, the result of the Radon transform is given in polar coordinates (r,φ), which are related to Cartesian coordinates by:

[0083] x = r(cosφ) and y = r(sinφ). The resulting distribution is typically numerically converted from n(r,φ) to n(x,y). Because the grids of polar and Cartesian coordinates do not match, the reconstructed 2D RIP n(r,φ) can be converted to n(x,y) by using interpolation including but not limited to nearest neighbor, bilinear, cubic, and spline.

[0084] In contrast to the interferometric RI distribution, the phase shift map η(ρ,θ) is usually not directly measurable. Instead, the deflection function ψ(ρ,θ) is available and can be converted into the phase shift map η(ρ,θ) by the approximation given in equation (5):

[0085]

[0086] where n0 is the reference refractive index at ρ=0.

[0087] Typically for tomography, the measured data are usually preprocessed to improve the quality of the reconstruction. Such preprocessing is also true in the field of RI distributions, where the importance of a precisely defined deflection function origin is well known. Regardless of how carefully all 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 distributions, there are different methods to achieve a so-called prepared deflection function, which is a measured deflection function ψ with a fine-tuned origin. 准备 (y) = ψ 测量 (yy 移位 )-ψ 偏移 For any particular measurement system 100, the two parameters ψ 偏移 and 移位 Very small, but usually non-zero. Several methods of defining these two parameters for radius-symmetric RIP are mentioned in US Pat. No. 10,508,973.

[0088] For asymmetric RIP, the deflection function for a fixed projection angle θ can be complex. This complexity reduces the implementation of the prepared deflection function ψ 准备 (ρ,θ)=ψ 测量 (ρ-ρ 移位 )-ψ 偏移 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 quality of the reconstructed image focus on X-ray and NMR-CT, some methods can be applied to 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; additional or alternative methods can be picked and selected by those skilled in the art.

[0089] For each measured deflection angle distribution ψ(ρ,θ) appropriately define ρ 移位can be understood as the well-known radius deviation correction in tomography. Radius deviation occurs when the trajectory shift occurs not only along the Z axis but also by the rotation of the projection angle θ. Mathematically, this adds a shift of each projection angle θ. The tomographic reconstructed images affected by radius deviation usually have blurred edges, unclear features or transitions, etc. Therefore, radius deviation correction can be achieved by minimizing the entropy of the reconstructed image. In this case, it is necessary to change ρ for each single projection 移位 and calculate the reconstruction. Because this iterative process requires many time-consuming reconstruction calculations, it is not very efficient. A preferred alternative method is explained below.

[0090] In most cases, one or even more features within the measurement sample can be used for radius deviation correction. A person skilled in the art can identify a suitable feature by the following criteria. The feature should have a sharp RI step (RI difference of at least 10 μm over a few microns).

[0091] 10 -3 is preferred) so that any edge detection algorithm works well. It is also preferred that the feature defines or even surrounds the region of interest within the reconstructed 2D RIP. This criterion ensures that the edges of the feature are not distorted by deflections from external RI variations. In practice, the measurement of each projection angle θ will be shifted by a separate ρ 移位 , so that the features are aligned concentrically around the origin, regardless of how chaotic the interior may appear. As illustrated on the sinusoidal diagram included in the accompanying drawings, this means that each column is shifted vertically so that the feature pairs are aligned. For example, Fig.17 It is illustrated that a circular feature appears as a horizontal straight line in the sinusoidal graph at ρ≈±12 mm. A non-circular feature appears as a mirror image pair of a sine wave in the sinusoidal graph, where the mirror axis is ρ=0 mm.

[0092] In addition to 移位 The measured deflection function ψ 测量 In addition to proper alignment, ψ can be defined appropriately for each measured projection. 偏移 to improve the quality of reconstructed 2D RIP. Figure 4 The illustrated measurement system 100 uses an ambient reference material with two beam-perpendicular surfaces and a constant refractive index, so the resulting phase shift η through the reference on the two opposing sides must be equal (ρ=0 and ρ=ρ 参考 ). This constraint can be used to fix ψ for each measurement projection. 偏移 In particular, the deflection function shifts ψ 偏移 is changed so that the integral across the reference material on both sides (setting the upper limit of the integral ρ in equation (5) to the reference position ρ 参考 ) leads to η(ρ=0)=η(ρ=ρ 参考). Define ρ appropriately. 移位 and ψ 偏移 Allows calculation of the prepared deflection function ψ 准备 (ρ,θ) and the phase shift map η prepared thereby 准备 (ρ,θ).

[0093] In addition to RIP-specific mathematical tools that improve reconstruction quality, more general CT tools also exist. Regarding sinogram interpolation, the number of tools is not limited to the examples given below. The inverse Radon transform has an integral over the scan position ρ and over the projection angle θ. Ideally, the step sizes dρ and dθ are both very small. However, there is a tradeoff, as a finer mesh size defined by dρ and dθ increases the total measurement time required.

[0094] In addition to reducing the grid size by using smaller step sizes dρ, dθ, or both dρ and dθ, interpolation can also be performed within the sinogram. Interpolation of additional projection angles θ produces particularly good results in improving reconstruction quality. The reason is that the sinogram usually does not change much on a small scale in the direction of dθ. In contrast, discontinuities usually exist in the dρ direction. Starting from one or several additional interpolated projection angles θ between the measured projections, the number of projections within the prepared sinogram can reach 10, 20 or even more times the number of measured projections. Many different methods can be applied to two-dimensional interpolation, including but not limited to nearest neighbor, bilinear, cubic and spline.

[0095] Frequency domain filters are required to apply the inverse Radon transform to the prepared phase shift map η(ρ,θ). Different types of filters are suitable for image reconstruction. Among such filters are Ram-Lak filter, Shepp-Logan filter, cosine filter, Hamming window filter, and Hann window filter. Ram-Lak filter is also known as Ramp filter. This filter is sensitive to noise, so it is multiplied by an appropriate window to improve the result. Shepp-Logan filter is obtained by multiplying the Ram-Lak filter by a sinc or sampling function. Cosine filter is obtained by multiplying the Ram-Lak filter by a cosine function. Similarly, Hamming and Hann filters are obtained by multiplying the Ram-Lak filter by Hamming and Hann windows respectively. Ram-Lak and Shepp-Logan filters are high-pass filters, which keep the edge information intact. Cosine, Hamming, and Hann filters are band-pass filters. They are used to smooth images and remove extra edges from the image.

[0096] In modern CT, there are many methods to improve the quality of the reconstruction, which can also be applied by the skilled person here. However, this improvement always depends on the specific object studied: a specific method may be beneficial for a specific object, or may simply lead to additional computing time or may even worsen the results. In the case of large deflections due to large refractive index steps within the object, it may be beneficial to apply backpropagation instead of rectilinear backprojection. However, this iterative process requires a lot of resources, resulting in longer computing times.

[0097] The measurement of the RIP of an optical fiber preform is important for checking the quality of the optical fiber waveguide and for the specification of additional treatments of the preform before drawing the optical fiber (e.g., coating or etching). For preforms, non-destructive techniques are particularly useful. The method disclosed in this document is based on the measurement of the deflection of a transverse guided 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 also calculates the RIP based on the assumption that the preform is circular. However, a method for tomographic reconstruction of the RIP of a preform with a highly asymmetric cross-section is needed.

[0098] Attempts have been made to address the RI characteristics of asymmetric optical 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. 316-327 (2005). Both references are incorporated by reference in this document.

[0099] The following disclosure describes steps of an improved method that provides accurate RIP for an asymmetric or at least substantially asymmetric object. Such a preform may be a preform with an unexpected asymmetry. Additionally, the method may be used for a multicore preform, a Panda preform (used to form a common type of polarization-maintaining fiber with circular and symmetrical stress rods on either side of the core to induce polarization), or a preform for a fiber laser with a non-circular interface.

[0100] The improved method for evaluating asymmetric glass fiber preforms has two main stages. The first stage involves tomographic refractive index determination. The second stage involves correction of measurement artifacts.

[0101] 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 performed must balance the accuracy of the data (more measurements are desired to give higher resolution) with the time required to perform the measurements (fewer measurements are faster). For example, the system 100 can scan a preform every 2° for about 18 minutes using one light source, or scan a preform every 0.5° for about 3.6 hours using three light sources (scanning in steps of 0.5° means 720 measurements for a full 360° around the preform). This measurement produces a deflection angle distribution ψ(ρ,θ). Figure 5A is a graph of an exemplary deflection angle distribution ψ(ρ,θ) (in degrees) for a simplified case plotted against position along the ρ axis (in millimeters) for a given projection angle (θ=8°). Figure 5B is to highlight using decreasing scale along the horizontal and vertical axes Figure 5A The graph of the central part of the graph.

[0102] Once the measurements are taken, they are tomographically evaluated. This evaluation involves calculating phase shifts and stacking to form a sinogram. The sinogram provides a convenient way to represent the complete data set acquired during the scan and can be used to check for systematic errors during data acquisition or to verify that pre-processing steps (e.g., radius deviation correction) are working correctly.

[0103] like Figure 6As illustrated, the Radon transform is an integral transform that takes a function f defined on the xy plane to be a function Rf defined on a 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 on the 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 between the normal or perpendicular to the line and the x-axis. The transform was introduced in 1917 by Johann Radon, who also provided formulas for the inverse transform. Radon also included formulas for three-dimensional transforms, where integration is performed on a plane (integration on a line is called an X-ray transform). It was subsequently generalized to higher-dimensional Euclidean spaces and more widely generalized in the context of integral geometry. The inverse Radon transform is widely used in tomography to create images from projection data associated with cross-sectional scans of an object.

[0104] If the function f represents an unknown, then the inverse Radon transform represents the projection data obtained as the output of a tomographic scan. Therefore, the inverse transform of the Radon transform can be used to reconstruct the original quantity from the projection data, and therefore it forms the mathematical basis of tomographic reconstruction (also called iterative reconstruction). Because the inverse Radon transform of an eccentric point source is a sine curve, the depiction of the inverse Radon transform data is often called a sinogram. Therefore, the inverse Radon transform of multiple scans is graphically represented as multiple sine waves with different amplitudes and phases, called a sinogram.

[0105] Figure 7 is by calculating the phase shift and stacking Figure 5A Sine diagram obtained from the measured data presented in . Phase shifts are expressed in arbitrary units (abbreviated au). Arbitrary units are relative units of measurement to show the ratio of a quantity to a predetermined reference measurement. "Predetermined" means predetermined, so that the predetermined characteristic must be determined, i.e. chosen or at least known, prior to some event. Figure 8 A graph of the relative refractive index in the xy plane (ie for a cross section of a preform) after applying the inverse of the Radon transform is shown. The refractive index is indicated as a relative value based on the refractive index of the surrounding reference glass sheet (n0 = 1.4587).

[0106] Thus, the refractive index profile is determined using known techniques (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 will show typical measurement artifacts of under-estimated refractive index steps, distorted profiles, rounded edges, etc.

[0107] In the second stage of the method, measurement artifacts are corrected. Correction of artifacts is achieved by applying a method similar to the '973 method described above to a selected line segment of a 2D RIP obtained from the tomographic data (i.e., the "starting RIP"). A "modeled RIP" is created after assuming a symmetrical preform based on several parameters (which will be varied). The "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. Parameters are varied for the modeled RIP until the distorted RIP approaches the starting RIP. This method is an approximation. The correction calculations are performed as if the starting RIP were measured at a preform with rotational symmetry, which is not the case. An important underlying assumption is that the measurement artifacts of the actual sample are similar for a rotationally symmetric preform.

[0108] The starting point of the improved evaluation method is a 2D-RIP based on tomographic measurement and reconstruction (including all CT technologies currently available for improved imaging). One or more line segments of the region of interest are selected (core, side pits, edges, etc.). According to each of the selected line segments, an abstract, imaginary, but symmetrical preform is "fitted" to the selected line segment. In order to simplify the description, it is assumed that the abstract, imaginary, symmetrical distribution can be directly fitted. However, this distribution cannot be directly fitted because there is no analytical expression for such a RIP (which includes typical measurement artifacts). Therefore, for each iteration, the fitting process includes the following steps: (i) assuming a symmetrical preform based on several parameters (which will be changed); (ii) simulating the deflection angle distribution; (iii) reconstructing a symmetrical RIP; and (iv) calculating the deviation of the selected cross section. Through this measurement and evaluation process, the tomographic 2D RIP reconstruction first handles all asymmetries (so that no systematic errors occur), and the fitting process of the line segment performs the rest, especially solving the typical measurement artifacts in the refractive index distribution.

[0109] Fig. 9 1 is a flow chart illustrating steps of a particular embodiment of a method 500 for providing an improvement in an accurate refractive index profile for an object that does not have a symmetrical cross section or at least has a substantially symmetrical cross section. The method 500 determines a radial RIP of a cylindrical optical object 11 having a cylindrical longitudinal axis about which at least one layer extends axially asymmetrically. In step 501 of the method 500, a deflection function is measured starting from a projection angle (θ) of zero. In step 502, the object 11 is scanned. Step 504 of the method 500 may be performed directly after completing step 502.

[0110] Optionally, although 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 the operator to specify a portion of the sensor array to be used for image acquisition. ROI is an acronym for "region of interest." If an image ROI has been specified, the camera will only transmit pixel data from within that region. On most cameras, this specification significantly increases the maximum frame rate of the camera. The ROI can be brightened. Applying another technique, several images can be collected using different exposures.

[0111] As another example of a technique to improve the quality of raw images, a scanning camera with high dynamic range (or HDR) can be used. In short, HDR helps produce "better" pixels. The range of brightness levels has been increased via HDR, making it possible to enhance the distinction between white and black. The range of colors has also been increased, making even colors more detailed.

[0112] As another example of a technique to improve the quality of the original image, a filtering algorithm can be used to remove OVD diffraction. Outside vapor deposition (OVD) is a process in which glass is deposited in layers to form a porous deposit (glass soot). The porous glass deposit can be cleaned, for example, by flushing with chlorine (dehydrogenation) to reduce the OH percentage. At the same time, the porous deposit becomes a glass preform (vitrification). Regardless of further processing steps such as vitrification, the processing-related micro-layer structure can remain and can also affect RI variations on a microscopic scale. These high-frequency RI variations lead to diffraction when scanned with a laser, even an incoherent beam.

[0113] Higher diffraction orders reduce the accuracy of determining the deflection angle, up to a really severe case where the zero-order beam cannot be distinguished from 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, up to the point where higher diffraction orders can become brighter than the diffraction orders from the zero-order beam. It is well known to those skilled in the art that evaluation of only the zero-order beam leads to a useful deflection angle distribution and a plausible RIP reconstruction. Depending on the severity level of the OVD diffraction (i.e., the intensity of the light within the higher diffraction orders), additional pre-processing by applying the OVD filter algorithm may be required.

[0114] After step 502, which includes scanning the object 11 with the beam (starting from a first projection angle) and creating raw data representing the object from the 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 (θ), such as π / 180, and iteratively repeating step 502 until all projection angles within the full range (zero to 2π) have been scanned and all measurement data have been obtained. The method then processes and stacks the measured data to create a phase shift sinusoidal diagram and proceeds to step 508.

[0115] Fig. 9 , a second alternative path after step 502 is illustrated in . In step 504 of method 500, the deflection function and phase shift map are calculated (as described above). The phase shift map can also be calculated directly without the intermediate step of calculating the deflection function (i.e., the intermediate step is optional). Also as described above, the phase shift map is output and stacked in step 505 to form a sinogram. Method 500 then asks in step 506 whether all projections within the full range (zero to 2π) have been measured. If the full range has not been measured, method 500 implements step 507. In step 507, object 11 is rotated by a small angle (θ) such as π / 180, and method 500 returns to step 502 and scans object 11. Steps 502, 503 (optional), 504, 505, 506, and 507 are iteratively repeated until all projections within the full range (zero to 2π) have been measured and method 500 can proceed to step 508.

[0116] In optional step 508, one or more of a variety of techniques may be used to improve the quality of the sinogram. For one example, radius deviation may be corrected. As another example, the sinogram may be interpolated to a fine grid.

[0117] In step 509 , a 2D RIP is calculated from the sinogram by applying an inverse Radon transform. This calculation is described above. Step 509 completes the first stage of method 500 .

[0118] Step 510 begins the second phase of method 500 and inquires whether there are any significant RIP measurement artifacts in the 2D RIP. Measurement artifacts occur when the refractive index step transitions from a lower value to a higher value (in the direction from the outside to the inside). For each selected line segment, this transition is relatively easy to determine. The word "significant" can specify, for example, the sharpness of the RI step (i.e., the sharper the step, the more significant the artifact). If the step is a gradient and not sharp (such as for a germanium-doped core with a parabolic RI), the artifact does not exist or can be ignored.

[0119] If the RIP measurement artifacts are not significant, then the method 500 implements step 520. In step 520, certain geometries and refractive index steps are determined before the method 500 ends in step 580. If there are significant RIP measurement artifacts in the 2D RIP, then the method 500 proceeds to step 530. In step 530, a line segment of interest (also referred to as a region of interest or ROI) is selected within the 2D RIP. Then, in step 540, a fitting process is applied to the selected line segment. Fig.10 Provides more details about the fitting process.

[0120] Once the fitting process 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 results of the fitting process to a predetermined level of accuracy for the selected line segment of the object 11 being evaluated. The predetermined level of accuracy may depend on the particular application. A typical predetermined accuracy is about 90%, an additional 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.

[0121] In step 560, the fitting parameters, such as RI step, geometry, gradient, and size, are derived. The method 500 then asks in step 570 whether all regions of interest within the preform have been characterized. If fewer than all regions of interest have been characterized, the method 500 returns to step 530 and selects a new line segment of interest within the 2D RIP. Steps 530, 540, and 560 are iteratively repeated until all regions of interest have been characterized, and the method 500 can proceed to step 580 and end.

[0122] Fig.10 5 is a flowchart outlining the steps of a specific embodiment of the fitting process applied in step 540 of the improved method 500. The line segment of interest (or ROI) selected within the 2D RIP in step 530 is used as the start of the fitting process in step 541. The starting parameters for the fitting process are then extracted from the line segment in step 542, and the first fitting region is defined in step 543. The method 500 then asks in step 544 whether the actual layer is step-shaped. 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, the fitting region is moved to the next inner layer in step 546, and the method 500 returns to step 544. Thus, a loop including steps 544, 545, and 546 is created until the question posed in step 544 is answered affirmatively or the question posed in step 545 is answered negatively.

[0123] If the answer to the question posed in step 545 is negative, the method 500 inquires whether the line segment is step-shaped in step 547. If the answer to the question posed in step 547 is positive, the measurement artifact compensation parameters and line segment have been implemented in step 548, and the fitting process 540 ends. If the answer to the question posed in step 547 is negative, the measurement artifact compensated RIP is determined in step 549, and the measurement artifact compensated line segment is implemented in step 550.

[0124] If the answer to the question posed in step 544 is affirmative, then an analytical deflection curve of an axially symmetric RIP designed to simulate the measurement artifact as an equivalent axially symmetric RIP is generated in step 551. In step 552, the deflection is transformed into a deflected RIP. Next, in step 553, the accuracy of the deflected RIP is calculated compared to the initial line segment. Accuracy can be measured by the R-squared statistic, which quantifies the predictive accuracy of the statistical model. The statistic shows the proportion of the variance in the outcome variable that is explained by the prediction. It is also called the coefficient of determination, R 2 、r 2 and r squared. R 2 Typically has values ​​in the range of 0 to 1 (or 100%). A value of 1 means that the prediction is the same as the observation; it is not possible to have an R greater than 1. 2 A value of 0 indicates that there is no linear relationship between the observed and predicted values, where "linear" in this context means that there may still be 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 R 2 Expressed as a percentage (eg, 50%).

[0125] The method 500 then asks in step 554 whether a particular stopping criterion has been met (e.g., a particular R-squared value calculated in step 553). With each iteration of the fitting process, the change in the initial parameters (n k and r k ) becomes smaller and smaller. Once the change becomes small enough that it drops below a certain threshold, no further fitting iterations are needed. In practice, let n k The change is less than, for example, 10 -5 is meaningless because there are other inherent errors that limit the accuracy. The same observation applies to the layer radius r k .

[0126] If the answer to the question posed in step 554 is negative, then method 500 proceeds to step 555 where the actual fitting parameter n is changed before method 500 returns to step 551. m and r mThus, a loop is created that includes steps 551, 552, 553, 554, and 555 until the question asked in step 554 is answered affirmatively. When the answer to the question asked in step 554 is affirmative, the method returns to step 545.

[0127] Fig.11 The graph of shows the prepared refractive index profile n'(r) of a preform with a simple step profile and the hypothetical refractive index profile n*(r) modeled by its evaluation. The refractive index is indicated as a relative value based on the refractive index of the refractive index adjusting fluid (n0=1.4587). In the graph, the relative refractive index n(r)-1.4587 is plotted against the radius r (in millimeters).

[0128] The assumed refractive index profile n*(r) already depicts the refractive index profile of the preform that would be expected in reality, or it is close to that refractive index profile. The assumed refractive index profile is based on the prepared refractive index profile n'(r) and orientation values ​​derived from that profile, which in turn include estimates of the refractive index and radius from unmeasurable regions.

[0129] Using equation (1), in a next method step, a simulated deflection angle distribution ψ"(y) is generated based on the assumed refractive index distribution n*(r). The simulated deflection angle distribution ψ*(y) thus obtained is therefore based on an assumption of the refractive index distribution of the preform (i.e. the assumed refractive index distribution n*(r)), which in turn is derived from the prepared refractive index distribution n'(r) after correction and evaluation of the original measured values.

[0130] By transforming the simulated deflection angle distribution ψ" (y) according to the numerical integration of equation (2), the simulated refractive index distribution n" (r) is again obtained, which is Fig.11 51. The profile has a rounded region 53 between the cladding region 52 and the core region 51. (As mentioned above, the core rod is usually surrounded by an inner cladding of fluorine or germanium doped silica glass and an outer cladding of undoped silica glass in the preform.) Except for this rounded region 53, the simulated refractive index n'(r) is almost consistent with the prepared refractive index profile n'(r). This is remarkable considering that the assumed refractive index profile n*(r) is very different from it. This similarity suggests that the assumptions on which the assumed refractive index profile n*(r) is based are already very close to the true refractive index profile n(r) of the preform. That is, Fig.11 The assumed refractive index distribution n*(r) in reflects the real refractive index distribution n(r) accurately or at least accurately enough.

[0131] In practice, an exact match between the simulated refractive index profile n"(r) and the prepared refractive index profile n'(r) cannot be achieved. However, a sufficient and arbitrarily accurate adaptation can be achieved by iteratively fitting the simulated refractive index profile n"(r) to the prepared refractive index profile n'(r). Fig.12 Explain alternative and generalized fitting procedures.

[0132] The alternative fitting procedure allows for a more accurate assessment of the RIP which is not completely step-like but has current measurement artifacts due to sharp RI steps from low to high (in the out-to-in direction). Fig.12 , the relative refractive index n(r)-1.4587 is plotted against the radius r (in millimeters). The measurement data 301 are depicted with "X". Typical measurement artifacts of the RIP occur at r=±22 mm, causing the reconstructed measurement to differ from the true RIP in this area. The goal of the fitting process is to determine the RI step and its associated artifact errors, which can be used to later correct the measurement data 301. For this purpose and similar to the fitting process explained previously, a simulation aid 302 and an associated simulation fit or fitting curve 303 are given. The simulation aid 302 is a hypothetical RIP, which is generated with the goal of estimating and covering the RI step at r=±22 mm. The hypothetical RIP of the simulation aid 302 allows the deflection function to be generated by using equation (1). The fitting curve 303 is generated by transforming the deflection function using equation (2).

[0133] For a fixed range (e.g., 21 mm <|r|), the parameters of the simulation aid 302 are changed so that the fitting curve 303 matches the measured data 301 around the RI step. This region must be small enough so that any internal RI gradients do not affect the fit, but also wide enough so that the rounded curve shape can be fit robustly enough. Based on visual feedback, one skilled in the art can tune the selected region to improve the fitting process.

[0134] Adding the difference between the simulation aid 302 and the fitting curve 303 to the measured data 301 results in a fitting result 304. The result is more accurate than the measured RIP. For more complex preforms, the fitting process can be repeated as needed on each RI step that occurs. In this case, the RIP of the simulation aid 302, the fitting curve 303 and the fitting result 304 are stitched together accordingly for each of the different regions.

[0135] Even in the specific case where the characterized preform itself does not have such a described RI step, but rather has an RI of undoped fused silica near the outer surface, this method is very useful for the following reasons. A setup similar to apparatus 100 typically has an undoped fused silica measurement cell 9, because this material is homogeneously available and the absolute RI is well known, including its dispersion, temperature dependence and other properties. The prior art also uses a refractive index adjustment fluid 10 to keep the deflection angles that occur small enough so that the apparatus 100 can capture them. If the RI of the refractive index adjustment fluid 10 is above the measurement cell 9 and the RI is at the outer region of the glass object 11, then measurement artifacts will appear at the boundary of the measurement cell 9 and the refractive index adjustment fluid 10 and will also affect the entire inner region. The only way to completely avoid such artifacts would be for the refractive index adjustment fluid 10 to completely match the measurement cell 9 and the outer region of the glass object 11. Apart from the usual 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 a distinction between glass object 9, refractive index adjusting fluid 10 and measurement cell 11 would be impossible.

[0136] Example

[0137] The following examples are included to more clearly demonstrate the general nature of the present disclosure.These examples of the present disclosure are exemplary and not limiting.

[0138] Figures 13 to 16 Example 1 of a preform having a single oval core is depicted. Fig.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 waveform reflecting a single core is depicted before the Radon transform is applied. Note that the vertical lines reflect the first line segment 310 and the second line segment 312. The sinogram shows the magnitude of the deflection angle distribution ψ(ρ, θ) in arbitrary units in the ρ-θ plane.

[0139] Fig.14 31 is a graph of the relative refractive index n(x,y)-1.446 in the xy plane, illustrating a reconstructed 2D RIP of a preform having a single elliptical core. A first line segment 310 is taken along the major axis (longest diameter) of the ellipse between the two vertices of the ellipse. A second line segment 312 is taken along the minor axis or shortest diameter of the ellipse.

[0140] Along the way Fig.14 The data obtained by drawing the second line segment 312 at the core of the chart is presented in Fig.15The line segment fitting process is illustrated in the graph of , which plots the relative refractive index n(r)-1.446 versus the position r in millimeters. Fig.15 The main concepts of method 500 are illustrated. Fig.15 The graph of includes three curves: a curve 320 of the picked, tomographically reconstructed line segment data, a simulated fitting curve 321, and a fitting result (or assumption) curve 322. The assumed RI steps are 0.002 and 0.01, which can be evaluated very well by the method 500.

[0141] Fig.16 The use of the first line segment 310 and the second line segment 312 highlights the need for tomographic measurements and evaluation methods therein. Fig.16 The graph of plots the relative refractive index n(r)-1.446 of a preform having a single elliptical core versus the position r in millimeters and compares two different tomographic line segments with a single related measurement. Curve 330 depicts a single measurement along the first line segment 310; curve 332 depicts a single measurement along the second line segment 312. Curve 334 depicts tomographic measurements along the first line segment 310; curve 336 depicts tomographic measurements along the second line segment 312. Thus, method 500 can be compared with direct 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 selected line segment. The fitting function and the resulting distribution of method 500 are omitted to avoid overloading the graph.

[0142] Figures 17 to 20 Example 2 depicts a preform having a single core with an octagonal shaped cladding which can be considered to be almost radially symmetrical. The core was manufactured by Heraeus Quarzglas GmbH & Co. KG, Germany under the registered trademark Made of fluorine-doped quartz glass for sale. Fig.17 is a sinogram created by applying method 500 (i.e., rotating the preform, taking measurements, and stacking the measurements from left to right). Note that the vertical lines reflect the first line segment 340 and the second line segment 342. The sinogram shows the magnitude of the deflection angle distribution ψ(ρ,θ) in arbitrary units in the ρ-θ plane.

[0143] Fig.18 34 is a graph of the relative refractive index n(x,y)-1.446 in the xy plane, illustrating a reconstructed 2D RIP of a preform having an octagonal shaped cladding. A first line segment 340 is taken along the major axis through the opposite vertices of the octagonal shaped cladding. A second line segment 342 is taken along the minor axis through the relatively flat segment between the vertices of the octagonal shaped cladding.

[0144] Along the way Fig.18 The data obtained by drawing a line segment 342 at the core of the chart is presented in Fig.19 The line segment fitting process is illustrated in the graph of , which plots the relative refractive index n(r)-1.446 versus the position r in millimeters. Fig.19 The graph of includes four curves: a curve 350 through the measured segment data, a simulated fit curve 351, a fit result (or assumption) curve 352, and a single measurement reconstruction curve 353. This graph illustrates the advantages of method 500 and highlights the need for tomographic evaluation when comparing to a single measurement.

[0145] Along the way Fig.18 The data obtained by drawing a line segment 340 at the core of the chart is presented in Fig. 20 The line segment fitting process is illustrated in the graph of , which plots the relative refractive index n(r)-1.446 versus the position r in millimeters. Fig. 20 The graph of includes four curves: a curve 360 ​​through the measured segment data, a simulated fit curve 361, a fit result (or assumption) curve 362, and a single measurement reconstruction curve 363. This graph illustrates the advantages of method 500 and highlights the need for tomographic evaluation when comparing to a single measurement.

[0146] Figure 21 to Figure 24 Example 3 is depicted with an even more complex preform having seven cores. Fig.21 is a sinogram created by applying method 500 (i.e., rotating the preform, taking measurements, and stacking the measurements from left to right). Depicted are six sinusoidal waveforms, one for each of the non-center cores. Note that the vertical lines reflect the first line segment 370 and the second line segment 372. The sinogram shows the magnitude of the deflection angle distribution ψ(ρ,θ) in arbitrary units in the ρ-θ plane.

[0147] Fig. 22 is a graph of the relative refractive index n(x,y)-1.4587 in the xy plane, illustrating a reconstructed 2D RIP of a preform with seven cores. The first line segment 370 is a shorter line segment cut through the center core. The second line segment 372 is a longer line segment cut through the center core.

[0148] Along the way Fig. 22 The data obtained by drawing a longer line segment 372 from the center core of the chart is presented in Fig.23 The line segment fitting process is illustrated in the graph of , which plots the relative refractive index n(r)-1.4587 versus the position r in millimeters. Fig.23The curve graph includes three curves: a curve 380 of the measured line segment data, a simulated fitting curve 381, and a fitting result (or assumption) curve 382. The curve graph illustrates the advantages of the method 500. The Radon transform and its inverse transform can be applied to Fig.21 The sine graph of Fig.23 The transition between the curve graphs.

[0149] Along the way Fig. 22 The data obtained by drawing a shorter line segment 370 from the center core of the chart is presented in Fig.24 The line segment fitting process is illustrated in the graph of , which plots the relative refractive index n(r)-1.4587 versus the position r in millimeters. Fig.24 The graph of includes three curves: a curve 384 through measured segment data, a simulated fitting curve 385, and a fitting result (or assumption) curve 386. The graph illustrates the advantages of the method 500.

[0150] Figure 25 to Figure 28 Example 4 is depicted of a preform having six cores and without any central core. Fig.25 is a sinusoidal graph created by applying method 500 (i.e., rotating the preform, taking measurements, and stacking the measurements from left to right). Depicted are six sinusoidal waveforms, one for each of the cores. Note that the curved lines reflect the first line segment 390 and the second line segment 392. Fig.25 The line segments 390, 392 shown in the sinusoidal diagram of FIG. 4 appear to be curved because the line segments 390, 392 within the 2D RIP (see FIG. 4 ) are curved. Fig.26 ) does not pass through the center. The sinusoidal diagram shows the magnitude of the deflection angle distribution ψ(ρ,θ) in arbitrary units in the ρ-θ plane.

[0151] Fig.26 390 is a graph of the relative refractive index n(x,y)-1.4587 in the xy plane, illustrating a reconstructed 2D RIP of a preform having six cores. A first line segment 390 is a shorter line segment taken through one of the cores. A second line segment 392 is a longer line segment taken through another of the cores but including the preform boundary at about ±32 mm.

[0152] The data obtained along the longer line segment 392 are presented in Fig. 27 The line segment fitting process is illustrated in the graph of , which plots the relative refractive index n(r)-1.4587 versus the position r in millimeters. Fig. 27 The graph of includes three curves: a curve 394 through measured segment data, a simulated fitting curve 395, and a fitting result (or assumption) curve 396. The graph illustrates the advantages of the method 500.

[0153] Data taken along the shorter line segment 390 are presented in Fig.28 The line segment fitting process is illustrated in the graph of , which plots the relative refractive index n(r)-1.4587 versus the position r in millimeters. Fig.28 The graph of includes three curves: a curve 397 through measured segment data, a simulated fitting curve 398, and a fitting result (or assumption) curve 399. The graph illustrates the advantages of the method 500.

[0154] These examples demonstrate that the preform parameters, especially the refractive index step, calculated using method 500 are more accurate. Method 500 is beneficial to customers of asymmetric preforms, including multi-core preforms, hollow core fiber preforms, Panda preforms, or preforms for fiber lasers with non-circular interfaces.

[0155] Although illustrated and described above with reference to certain specific embodiments and examples, the disclosure is not intended to be limited to the details shown. Instead, various modifications may be made to the details within the scope of equivalents of the claims and without departing from the spirit of the disclosure. For example, it is expressly intended that all ranges broadly enumerated in this document include within their scope all narrower ranges that fall within the broader ranges.

Claims

1. A method for determining a refractive index profile (RIP) of an object, the method comprising: (a) providing the object, the object comprising an optical object, the optical object having a longitudinal axis, at least one layer extending outwardly about the longitudinal axis, wherein the at least one layer lacks complete 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 from 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 created; (d) processing the measurement data to form a sinogram and if the optional step (c) has been completed, proceeding to step (f); (e) rotating the object and iteratively repeating steps (b) and (d) until all projection angles have been scanned; (f) Calculate 2D RIP; (g) selecting a line segment of interest within the 2D RIP; (h) applying a fitting process to the line segment of interest; as well as (i) Determine the refractive index step / gradient and size.

2. A method according to claim 1, wherein the step (b) of scanning the object comprises introducing an incident beam into a cylindrical optical object at an incident point in a direction transverse to the longitudinal axis of the cylinder, wherein a deflection angle ψ is defined as the angle between the outgoing beam and the incident beam, and y is the distance between the longitudinal axis of the cylinder and the incident point of the incident beam in a Cartesian coordinate system. 3 . The method according to claim 1 , wherein the step of calculating the 2D RIP is performed based on an inverse Radon transform.

4. The method of claim 1, wherein the step of processing the measurement data to form a sinusoidal graph comprises calculating a deflection function, calculating a phase shift graph, and stacking the phase shift graphs to form the sinusoidal graph.

5. The method according to claim 1, wherein the original data comprises an original image, and the method further comprises the following steps: The quality of the raw image is improved by one or more of using a scanning camera with an "image ROI" feature, collecting several images with different exposures, using a scanning camera with HDR, and using a filtering algorithm to remove OVD diffraction.

6. The method according to claim 1, further comprising the steps of: The quality of the sinogram is improved by applying one or more of: radius deviation correction, and interpolating the sinogram to a fine grid.

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

8. The method according to claim 7, further comprising the steps of: The determined refractive index step / gradient and dimensions are used to characterize the optical fiber preform and adjust the preform manufacturing process.

9. The method according to claim 1, further comprising the steps of: Prior to step (f), it is determined whether all projection angles have been scanned.

10. The method according to claim 1, further comprising the steps of: After step (f) it is determined whether there are significant RIP measurement artifacts in the 2DRIP, and if not, the geometry and refractive index step are determined and the method ends.

11. A method according to claim 1, wherein the step (h) of applying the fitting process to the selected line segment of interest includes extracting starting parameters for the fitting process from the line segment, defining a first fitting region, and determining whether the actual layer is step-shaped.

12. The method according to claim 11, wherein the fitting process further comprises: If the actual layer is step-shaped, an analytical deflection curve is generated, the analytical deflection curve is transformed into a deflection RIP, and the accuracy of the deflection RIP compared to the initial line segment is calculated.

13. The method of claim 1, further comprising the step (j) of determining, after step (i), whether all line segments of interest within the 2D RIP have been characterized.

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

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

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