Evaluation of improvements in preforms with non-step refractive index distribution (RIP)

Abstract

This invention provides a method for determining the RIP when the refractive index distribution of a preform is not substantially a step refractive index sample. (a) Measure the preform deflection function and transform it into a measured RIP. (b) Assume the RI level and radius of the preform layer being evaluated and calculate the compensation level RIP. (c) Generate a theoretical deflection function corresponding to the assumed RI level and radius and transform the generated data into a fitted RIP. (d) Compare the fitted RIP with the measured RIP and evaluate the comparison against a predetermined accuracy level for the preform layer being evaluated. (e) Iteratively repeat steps (b) and (c) until the predetermined accuracy level has been achieved. Repeat steps (b) to (e) for each preform layer requiring compensation. Finally, calculate the refractive index distribution for measurement artifact compensation of the preform.

Description

Technical Field

[0001] The present disclosure generally relates to refractive index measurements, and more particularly to methods for 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 pipes, light tubes, 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 pulling the molten end into a thin glass wire. 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 (particularly a preform for an optical fiber). A cylindrical optical object typically has a longitudinal axis of the cylinder, with at least one layer k having a layer radius r k and a layer refractive index n k radially extending symmetrically around the longitudinal axis of the cylinder (however, of course, there are also many objects with an asymmetric RIP). The deflection angle distribution ψ(y) is measured and the RIP is reconstructed from this deflection angle distribution. The radial RIP, also known as the radial refractive index profile, is denoted by the symbol n(r).

[0004] Unfortunately, the refractive index profile cannot be measured directly. The refractive index profile is typically determined indirectly as the deflection or interference of a light beam transmitted through a volume region of an optical element, and the step-by-step transmission is also referred to as "scanning". The spatial refractive index profile in the optical element can be inferred based on the interference or deflection of the outgoing beam (the outgoing beam) from the beam direction at the beam incidence point (the incident beam). A series of deflection angles ψ measured during the scanning of the beam in a direction transverse to the longitudinal axis of the cylinder (in the y direction) forms the deflection angle distribution ψ(y).

[0005] For better observation and illustration, Figure 1A the geometric relationships are schematically shown in. Depicted is an object having a homogeneous refractive index n1, which is surrounded by a refractive index adjusting fluid having 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 the Abel inverse transform.

[0006] For a radially symmetric object with a step refractive index distribution, the deflection angle distribution ψ(y) can be mathematically described by the following equation (1):

[0007]

[0008] In equation (1), m is the number of layers of the object, n0 is the refractive index of the surrounding medium, and n k It is the refractive index of the k-th layer, and r k It is the radius of the k-th layer. According to equation (1), the known mathematical method for calculating the refractive index distribution from the deflection angle distribution based on measurement data is based on the well-known "Abel transform":

[0009]

[0010] Where r is the shortest distance from the longitudinal axis of the object's cylinder to the bundle path, i.e.,

[0011]

[0012] And R is the reference point for the refractive index distribution, 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 derivative of ψ from the position Δt, the formula becomes the shape of the mathematically well-known inverse Abel transform. In principle, the Abel transform can be applied to any kind of deflection angle distribution, not just the ideal case of a step refractive index distribution as reflected in equation (1).

[0013] U.S. Patent 4,227,806 describes a method for nondestructively determining parameters of an optical fiber preform. The preform is scanned with a laser beam laterally entering the core-cladding structure, and the deflection angle of the outgoing beam is measured and subsequently compared to 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 to prevent the deflection angle from becoming too large.

[0014] U.S. Patent 4,441,811 describes a method and apparatus for determining the refractive index distribution of a cylindrical transparent optical preform. In this case, the preform, inserted in a refractive index adjusting fluid, is also scanned by a transversely entering 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 distribution is calculated from the deflection angle distribution using numerical integration. Other preform parameters, such as preform diameter, core diameter, eccentricity, and CCDR (cladding-to-core diameter ratio), can also be determined from the deflection angle distribution.

[0015] Methods for reconstructing the RIP from the distribution of lateral measured deflection angles using Abel transformation can also be found in U.S. Patents 4,744,654, 5,078,488, and 4,515,475. This method is also described in the following two technical papers: Michael R. Hutsel and Thomas K. Gaylord, “Concurrent three-dimensional characterization of the refractive-index and residual-stress distributions in optical fibers”, Applied Optics, Optical Society of America, Washington, DC; Vol. 51, No. 22, pp. 5442-5452 (August 1, 2012) (ISSN: 0003-6935, DOI: 10.1364 / A0.51.005442); and S. Fleming et al., “Nondestructive Measurement for Arbitrary RIP Distribution of Optical Fiber Preforms”, Journal of Lightwave Technology, IEEE Service Center, New York. York, NY, Vol. 22, No. 2, pp. 478-486 (February 1, 2004) (ISSN: 0733-8724, DOI: 10.1109 / JLT.2004.824464).

[0016] However, simply reconstructing the RIP or refractive index distribution n(r) from the lateral measured deflection angle distribution using the Abel transform does not cause negligible differences relative to the true RIP. This is due to known measurement artifacts that occur at the boundary between a transparent object and its environment, or at refractive index discontinuities at the boundary between radial refractive index steps. Measurements taken at the boundary of refractive index jumps from low to high refractive index (when viewed from the outside in) in the near-boundary volume region of an optical object produce areas that are, in principle, unmeasurable. Typical differences and errors in reconstructing the RIP from step refractive index distributions, for example, are due to the undersized distribution and rounding of the step height. Werner J. Glantschnig's publication "Index profile reconstruction of fiber preforms form data containing a surface refractive component," Applied Optics, Vol. 29, No. 19, pp. 2899–2907 (July 1, 1990) ("Glantschnig Publication," which is incorporated herein by reference) is a publication that addresses the problems caused by unmeasurable regions. Glantschnig showed that the actual missing deflection angle in the unmeasurable region can be inferred by interpolation based on three internal measurement points of the deflection angle distribution just before the discontinuity.

[0017] Interpolation based on three measurement points does not always yield good results. Therefore, some methods for measuring RIP cannot provide accurate measurements of the RIP of a simple, homogeneous rod. One reason for this drawback is the presence of refractive index discontinuities at the boundaries or edges of the rod, which results in the measurement of the surface refractive component. The Glantschnig publication explains why these refractive index discontinuities cannot be accurately reconstructed from the deflection function data. While the Glantschnig publication proposes a method for measuring RIP, it requires precise measurement of the deflection angle at the object's edge, which is impractical.

[0018] To address these issues, U.S. Patent No. 8,013,985 to Corning Incorporated (incorporated herein by reference) proposes a modified version of this reconstruction method, in which, to measure the RIP of a transparent cylindrical object such as an optical fiber preform, a beam deflection angle function is measured and the RIP is mathematically reconstructed from the measurement data based on paraxial ray theory. In the measurement, the optical fiber preform to be measured is positioned between a laser and a transformation lens. The preform has a central axis defining a preform radius R and a cylindrical surface. An incident beam incident on the cylindrical surface at height x is deflected within the preform and exits again as an outgoing beam at a different angle, which is detected by a photodetector and processed by a controller. The deflection angle is defined as the angle between the outgoing and incident beams and is varied by changing the laser beam height x, and the deflection angle distribution is measured. A numerical model is used to adapt the estimated RIP, representing the actual RIP, to the measured deflection angle distribution.

[0019] Therefore, a symmetric correlation is performed on the measured deflection function to define the center coordinates. The measured deflection function is divided into two halves about the center coordinates, and a refractive index semi-distribution is calculated for each half to obtain the estimated refractive index distribution for each half. The correlation parameters used for RIP calculation are the preform radius R and the refractive index of the preform. Target angular distribution ψ t Iteratively adapts to the measured deflection function, where measurement points near the boundary (where the refractive index discontinuities are located) are omitted within or on the edge of the preform. This method of arithmetic iterative adaptation of the mathematical function can be called "fitting".

[0020] According to U.S. Patent No. 8,013,985, a fitting was performed such that the above equation (1) (however, disregarding the arccos part indicated in the second line of the equation) has incorporated the 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 unknown refractive index value, wherein the unknown parameter variation results in the obtained target angular distribution ψ t Optimally match the measured deflection angle distribution ψ m Therefore, the target angle distribution is adaptively (fitted) with the measured deflection angle distribution using unknown parameters.

[0021] Based on this adaptive simulated target angular distribution, a reconstructed refractive index distribution is obtained. This distribution extends up to the reconstructed preform radius R*, which is greater than the radius of the internal object region. For cylindrical objects with at least one discontinuity in the RIP, the method is applied to the respective object regions defined by that discontinuity.

[0022] In this method, the simulated target angular distribution ψ is obtained by fitting unknown parameters. tAdaptive to the measured deflection angle distribution ψ m Furthermore, a radial refractive index distribution is derived from the simulated target angular distribution, which extends to the boundary of the refractive index distribution at a more external discontinuity.

[0023] Therefore, the detection of a complete RIP (Reflection Indicator) 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 can lead to a poor fit of the simulated target angular distribution. Furthermore, it has been found that comparing deflection angular distributions (i.e., simulated and measured deflection angular distributions) is not very indicative and requires a high degree of expertise to determine whether the fit is optimal and, optionally, how optimal, whether the values ​​require post-correction or further variation, and optionally, which values ​​require post-correction or further variation.

[0024] The assignee of this application (Heraeus Quarzglas GmbH & Co. KG of Heraeus ... U.S. Patent No. 10,508,973 (Hanau, Germany) and incorporated herein by reference teaches a method for determining the refractive index distribution of a cylindrical optical object, particularly a preform for optical fibers. The method includes: (a) preparing a measured deflection angle distribution, including determining the extrema 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 orientation values ​​of the layer radius and layer refractive index to fix a hypothetical refractive index distribution; (d) generating a simulated deflection angle distribution based on the hypothetical refractive index distribution with orientation values, and transforming the deflection angle distribution into a simulated refractive index distribution; (e) fitting the simulated refractive index distribution to the prepared refractive index distribution through 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. This method represents the prior art regarding the determination of a RIP when the RIP is substantially or entirely a step-index sample.

[0025] However, a method is still needed to determine the RIP when the RIP of a cylindrical transparent object (usually, but not necessarily, has a radially symmetric or approximately radially symmetric refractive index distribution) is substantially or completely not a step-index sample. Of course, this method must also be improved in terms of reasonableness, accuracy, reliability, and reproducibility. A related need is for a method to improve preform assemblies and meet the demands of preform consumers, especially for preforms with increasingly complex designs. Summary of the Invention

[0026] To meet these and other needs, and for their purposes, this disclosure provides a method for determining the RIP, particularly when the refractive index distribution of an object such as a preform is not substantially a step refractive index sample. The method includes the following steps: (a) providing a cylindrical optical object having a longitudinal axis of cylinder and a layer radius r. k And has a layer refractive index n k (a) At least one layer k extends radially symmetrically about the longitudinal axis of the cylinder, wherein the at least one layer is not substantially of a step refractive index. (b) Next, the deflection function of the object is measured and the measurement data is transformed into a measured refractive index distribution. (c) The refractive index level and radius of the layer (initially the outer layer) of the object being evaluated are assumed and a compensation level refractive index distribution is calculated. (d) A theoretical deflection function corresponding to the assumed refractive index level and radius is generated and the generated data is transformed into a fitted refractive index distribution. (e) The fitted refractive index distribution is compared with the measured refractive index distribution and the comparison is evaluated against a predetermined accuracy level for the layer of the object being evaluated. (f) Steps (c) and (d) are repeated iteratively until the predetermined accuracy level has been achieved. (g) It is determined whether the object has another layer to be compensated. (h) Steps (c) to (f) are repeated for each layer of the object until the object has no other layers to be evaluated and compensated. (i) Finally, the refractive index distribution for measurement artifact compensation of the object is calculated.

[0027] It should be understood that the above general description and the following detailed description are exemplary and not intended to limit this disclosure. Attached Figure Description

[0028] This disclosure is best understood from the following detailed description when read in conjunction with the accompanying drawings. It is emphasized that, by convention, the features in the drawings are not to scale. Rather, for clarity, the dimensions of the features have been arbitrarily enlarged or reduced. The following figures are included in the drawings:

[0029] Figure 1A The radiation path through an object with a homogeneous refractive index distribution is shown, and various geometric relationships are schematically illustrated.

[0030] Figure 1B The radiation path through an object with a homogeneous refractive index distribution is shown, along with the measurement artifacts in the refractive index distribution caused by a shadowed, unmeasurable region in which tangential radiation cannot be detected.

[0031] Figure 2 This is a schematic diagram of the deflection function measurement system;

[0032] Figure 3 A segment of the measured deflection angle function with associated spline functions for various smoothing parameters p is shown;

[0033] Figure 4 It shows from Figure 3 The refractive index distribution is calculated from the measured deflection angle distribution (p=1);

[0034] Figure 5 A graph showing different refractive index distributions is provided to illustrate the effect of the offset at the origin of the bottom deflection angle distribution.

[0035] Figure 6 A plot is shown of the prepared refractive index distribution n'(r) of a preform with a step distribution and the hypothetical refractive index distribution n*(r) modeled by the evaluation of this distribution;

[0036] Figure 7 This is a flowchart illustrating the steps of a method for providing an improved accurate refractive index distribution for an object that does not have a step refractive index or at least has a substantially step refractive index;

[0037] Figure 8 This is a graph showing the calculated refractive index distribution, plotted as the refractive index difference (n(r) - n0) against position r in millimeters, to explain the application of an implementation scheme for calculating the refractive index distribution for measurement artifact compensation in a real fluorine-doped quartz glass tube.

[0038] Figure 9 In such Figure 8 A comparison between the measured distribution curves of the fluorine-doped quartz glass tube and the curves obtained using the new evaluation method;

[0039] Figure 10 This is a graph showing the calculated refractive index distribution, plotted as the refractive index difference (n(r) - n0) against position r in millimeters, to explain the application of an implementation scheme of the method for calculating the refractive index distribution of a real mandrel for measurement artifact compensation in a stepless RIP sample; and

[0040] Figure 11 In such Figure 10 The comparison between the measured distribution curve of the mandrel and the curve obtained using the new evaluation method is shown. Detailed Implementation

[0041] The description of this method refers to a transparent cylindrical object in the form of an optical fiber preform. However, those skilled in the art will understand that the method is generally applicable to any cylindrical object with a refractive index at a given radiation wavelength, wherein the corresponding deflection angle distribution can be measured via the lateral transmission of radiation at a certain wavelength, and there exists a target deflection angle distribution function that can be expressed as a function fit to the measurement data. Referring now to the accompanying drawings, where the same reference numerals refer to the same elements throughout the various figures constituting the drawings, Figure 2This is a schematic diagram illustrating an exemplary embodiment of a basic deflection angle distribution function measurement system 100, which can be used to establish a measurement deflection angle distribution function.

[0042] System 100 has a first optical axis 15A, a second optical axis 15B, and a third optical axis (not shown) between a pair of off-axis mirrors 4A, 4B. A laser source, such as a laser diode 1, generates a laser beam (or "beam") and provides it to a single-mode optical fiber 2, which delivers the laser beam to a beam conditioner 3. (In optical fiber communication, a single-mode optical fiber is an optical fiber designed to carry only single-mode light: transverse mode. Standard G.652 defines the most widely used form of single-mode optical fiber.) The beam conditioner 3 aligns the laser beam along the first optical axis 15A and modulates the properties of the laser beam. The beam emitted by the beam conditioner 3 travels along the first optical axis 15A and engages with an off-axis parabolic reflector having a pair of mirrors 4A, 4B and an aperture (or "pinhole") 5. The first mirror 4A generates a parallel beam that passes through the aperture 5; the second mirror 4B focuses these beams along the second optical axis 15B.

[0043] The focused beam, deflected by the second mirror 4B of the off-axis parabolic reflector, passes through the optical shutter 6 and enters the measurement unit 9. During operation, the shutter 6 remains in the closed position and then opens when a pulse control signal is applied. The shutter 6 remains open as long as the control voltage of the shutter 6 remains high. However, once the voltage drops, the shutter 6 closes, thus providing inherent "fail-safe" operation, i.e., safety.

[0044] The measuring unit 9 has a planar, opposite side perpendicular to the second optical axis 15B. Arranged within the measuring unit 9 is a transparent cylindrical object 20, which has the homogeneous or stepped 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 20 within the measuring unit 9 is a refractive index adjusting fluid 18. In an exemplary embodiment, the refractive index adjusting fluid 18 is an oil having a refractive index close to but different from that of the measuring unit 9.

[0045] A laser beam enters the measurement unit 9 and initially strikes the object 20 at its first edge, undergoing a first refraction. The first-refracted laser beam then travels through the object 20 and exits at a reverse edge, where it undergoes a second refraction and exits again. The deflection angle, identified by the Greek letter ψ (Pussy), is defined by the path of the outgoing laser beam relative to the direction of the incident laser beam. The outgoing laser beam then passes through a filter (e.g., an infrared long-pass filter) 10 and is detected by a photodetector unit. The filter 10 helps to eliminate the adverse effects of ambient light on the measurement. A suitable photodetector unit includes a line-scan camera 11 with an optically active sensor 12. The photodetector unit then sends a corresponding detector signal to a controller 13 for processing.

[0046] The measuring unit 9 is mounted on a linear stage 7, which is configured to support the measuring unit 9 and in the direction of movement 8 (e.g., as shown in the figure). Figure 2 The measuring unit 9 is moved along the vertical direction shown. A measurement of the deflection angle is performed relative to the horizontal axis of the center of the measuring unit 9 and the object 20 within the measuring unit 9, over a range of laser beam height. The corresponding detector signal received and processed by the controller 13 generates 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 vary relative to the measuring unit 9 and the object 20, such that the measured deflection function encompasses a range of the radius of the object 20.

[0047] Despite Figure 2 In the illustrated embodiment, the object 20 in the measuring unit 9 moves (e.g., scans), but in another embodiment, other components (such as the laser diode 1 and the photodetector unit) can simultaneously move (e.g., scan) relative to the object 20 (which remains stationary), such that the laser beam height can be varied to send the laser beam through different parts of the object 20.

[0048] Controller 13 is, for example, a computer including a processor unit (e.g., CPU), a memory unit, and support circuitry, all of which are operatively interconnected. The processor can be or includes any form of general-purpose computer processor that can be used in an industrial environment. The memory unit includes a computer-readable medium capable of storing instructions (e.g., software) that instruct the processor to perform the methods described in detail below. The memory unit can be, for example, random access memory, read-only memory, floppy disk or hard disk drive, or other forms of digital storage device. In an exemplary embodiment, the instructions stored in the memory unit are in the form of software that, when executed by the processor, transforms the processor into a dedicated processor that controls (i.e., instructs or causes) system 100 to perform one or more of the methods described below. The support circuitry is operatively (e.g., electrically) coupled to the processor and may include caches, clock circuitry, input / output subsystems, power supplies, control circuitry, etc.

[0049] The laser diode 1, shutter 6, linear stage 7, and line scan camera 11 are each configured to send signals and data to and receive signals and data from a controller 13 via multiple data connections 14. The data connections 14 can be wired or wireless; any conventional data connection 14 known to those skilled in the art is suitable.

[0050] The deflection function can be obtained using many other deflection function measurement systems similar to those described above. Regardless of the system used, a variety of methods are possible for determining the RIP of the cylindrical optical object 20.

[0051] In one method, a preparatory deflection angle distribution ψ'(y) is generated in a first step based on a measured deflection angle distribution ψ(y). To do this, the measured deflection angle distribution ψ(y) is analyzed and extrema are determined. These extrema always occur in regions of refractive index jumps, such as on the inner boundary of the optical object 20 or on the surface of a cylinder. For simplicity, the following explanation will refer to an optical preform with a step refractive index distribution, having at least two layers and thus having one or more refractive index jumps.

[0052] A radially symmetric object exhibits a deflection angle distribution with at least two extrema, caused by a refractive index jump on the same layer k. When determining these extrema, the extrema y of the measured deflection angle distribution are determined. k,max The location is approximately at the edges on either side of the refractive index jump (numerically defined by the radius of the corresponding layer). This determination of the extremum is called "edge detection".

[0053] Measurements of the deflection angle distribution should be taken with reference to a Cartesian coordinate system (X, Y, Z). This coordinate system uniquely identifies each point in three-dimensional space using three Cartesian numerical coordinates, which are signed distances from the point to three fixed, mutually perpendicular orientation lines, measured in units of equal length. Each reference line is called a coordinate axis or simply the axis of the system, and the point where they meet is its origin, typically at the ordered triplet (0, 0, 0). Coordinates can also be defined as the position of a point's perpendicular projection onto the three axes, expressed as a signed distance from the origin.

[0054] The measured data of the deflection angle distribution are indicated as dependent on the y-axis of the Cartesian coordinate system, while the radius of the layer is usually referred to in a different coordinate system (radial system) and indicated as dependent on the radius r. In the case of small refractive index differences and weak refraction, this difference can be so small that the y and r values ​​are usually indistinguishable, which is referred to in the literature as the "approximation method," "linear approximation method," or "non-refractive approximation method."

[0055] In edge detection, the risk of incorrectly assuming edges due to outliers or measurement noise should be avoided as much as possible. It has been found that using spline functions with several different smoothing parameters to smooth the distribution of measured deflection angles is particularly suitable for this purpose. Spline functions are several higher-order constituent polynomials. By iteratively applying weaker smoothing parameters, the corresponding extrema gradually shift towards the actual extrema in each iteration.

[0056] Therefore, in edge detection, it is preferable to determine the innermost rightmost extreme value y. k,右 and the innermost left extreme value y k,左 As discussed above, these values ​​approximately correspond to the corresponding edge of the k-th layer of the RIP. For example, this is the outer edge of the core or the outer edge of the cladding (note that the refractive index increases from the outside to the inside). The right and left edges determined in this way are particularly suitable for defining the actual center point of object 20.

[0057] Furthermore, the preparation for measuring the deflection angle distribution preferably includes adjustment (fine-tuning), in which the origin of the deflection angle distribution is adjusted.

[0058] The origin of the deflection angle distribution in the Cartesian coordinate system (at y = 0) is called the origin, through which the longitudinal axis of the cylinder of object 20 is to be extended. A shift along the y-axis may occur because, when measuring the deflection angle distribution using system 100, the y-axis only passes through the geometry defined by the measuring unit 9. However, the center of the measuring unit 9 does not automatically correspond to the longitudinal axis of object 20. Therefore, adjusting the origin of the deflection angle distribution involves, for example, shifting it in the direction of the y-axis of the coordinate system to the innermost right extremum y. k,右 With the innermost left extreme value y k,左 In the middle of the middle.

[0059] Furthermore, the entire angular distribution may include a shift from the origin in the form of a displacement along the vertical axis (which is the ψ-axis in the coordinate system of the deflection angular distribution). To eliminate the shift, the deflection angular distribution is shifted a distance in the direction of the ψ-axis of the coordinate system, determined in this way.

[0060] Generally speaking, accurately defining or determining the origin of ψ is crucial for achieving accurate RIP calculations and therefore all subsequent steps. Unfortunately, determining ψ = 0° (no deflection) is not straightforward. Differences within a range of only 0.01° can significantly impact the calculated RIP. Simply defining the origin by the set geometry is insufficient. In practice, several methods can be used to fine-tune or determine the deflection origin where ψ = 0°. Unfortunately, some of these methods are sample-dependent and not always applicable.

[0061] One method for determining the origin of ψ is to fit a straight line (or odd polynomial) to a sub-region of the innermost region (approximately 10% to 20% of the core diameter). This region needs to have a substantially homogeneous refractive index and be centered. Generally, this process is effective for tubes (due to the air-core region) and homogeneous fused silica cores. (In practice, this is most effective only for undoped cores. Tubes are extremely dependent on perfect geometry. Doping usually introduces minute variations.) Alternatively, and because it is also recommended for heterogeneous cores, this method limits ψ to 0° by evaluating the calculated RIP. In practice, the range of the origin is defined, the RIP is calculated, and based on comparison, the most reasonable RIP is selected. The origin can also be automatically or iteratively corrected by a technician by examining the RIP calculated for each offset step. Figure 5 Miscentering is demonstrated. Choosing the optimal origin based on RIP is relatively easy.

[0062] The result of the evaluation and preparation is the preparation deflection angle distribution ψ'(y) that is adaptive to the origin of the coordinate system relative to its origin.

[0063] In the next step, a RIP called the prepared refractive index distribution n'(r) is generated from the prepared deflection angle distribution ψ'(y) by transformation. This step can be completed without generating the RIP from the original measured deflection angle distribution. Prior adaptation of the origin of the deflection angle distribution is very helpful for this transformation, which is performed, for example, using the Abel transform. Without adaptation, small deviations from the actual origin cause errors in the transformed refractive index distribution (i.e., unreliable defects).

[0064] The prepared refractive index distribution n'(r) still lacks refractive index and radius values ​​from unmeasurable regions, meaning that this prepared refractive index distribution does not reflect the expected RIP of the preform in reality. However, the prepared refractive index distribution represents an illustrative orientation guide from which suitable orientation values ​​for the assumed refractive index distribution n*(r) can be derived relatively explicitly. This assumed refractive index distribution forms the basis for subsequent methodological steps. The orientation values ​​to be derived include the orientation value r*k of the layer radius and the orientation value n*k of the layer refractive index of the assumed refractive index distribution n*(r). Especially for the refractive index, empirical values ​​and data are typically stored in a database, which can also be used to determine the refractive index.

[0065] In the simplest case, use the determined extreme value y. k,右 and y k,左 The orientation value r*k is fixed in the evaluation of the prepared refractive index distribution n'(r). However, as explained above in conjunction with the approximation method, this is only approximately correct. In a particularly preferred variant of the method, the determined extreme value y k,右 and y k,左 Therefore, they are respectively transformed into layer radius r k,右 and r k,左 Furthermore, the calculated layer radius is used to fix the orientation value r*k.

[0066] The transformation of the extreme values ​​of the layer radius is preferably accomplished based on one of the following two equations.

[0067] Equation (2): r* k =n0 / n k-1 *y k,max ;or

[0068] Equation (3): r* k =n0 / n k *y k,max Where n0 = the refractive index of the surrounding medium, n k-1 = The refractive index of the outer adjacent layer k, n k = the refractive index of layer k, and y k,max = The position of the deflection angle of layer k with the largest absolute value. Equation (2) at r k Equation (3) applies if total internal reflection does not occur at the boundary; otherwise, equation (3) applies.

[0069] Assume the RIP is based on a prepared refractive index distribution n'(r) and orientation values ​​derived from that distribution, which in turn include estimates of the refractive index and radius from unmeasurable regions. Assume the RIP has depicted the expected refractive index distribution of the preform in reality, or a distribution close to it. The iterations explained in the following paragraphs are applied layer by layer to the object.

[0070] In the next method step, a simulated deflection angle distribution ψ""y" is generated from the assumed refractive index distribution n*(r). Equation (1) mentioned above applies to the generation of the simulated deflection angle distribution ψ""y". Therefore, the simulated deflection angle distribution ψ""y" is based on the assumption of the RIP of object 20 (i.e., the assumed refractive index distribution n*(r)), which is derived from the prepared refractive index distribution n'(r) after correcting and evaluating the original measurements. The simulated refractive index distribution n""r" is obtained again through a transformation of the simulated deflection angle distribution ψ""y".

[0071] Therefore, the simulated refractive index distribution n"(r) is obtained by simulation constructed with the aid of the prepared refractive index distribution n'(r) via the assumed refractive index distribution n*(r). The more similar the simulated refractive index distribution n"(r) is to the prepared refractive index distribution n'(r), the closer the assumption on which the assumed refractive index distribution n*(r) is to reality, i.e., the true refractive index distribution n(r) of object 20.

[0072] Ideally, if the simulated refractive index distribution n"(r) and the prepared refractive index distribution n'(r) match, then the hypothetical refractive index distribution n*(r) on which the simulation is based will thus reflect the true refractive index distribution of object 20. However, in practice, an exact match cannot be achieved. However, sufficiently accurate adaptation can be achieved by iteratively fitting the simulated refractive index distribution n"(r) to the prepared refractive index distribution n'(r). The iteration includes at least one run of the simulation according to the following methodological steps: based on the orientation value r* k and n* k The assumed refractive index distribution n*(r) is used to generate a simulated deflection angle distribution ψ(y), and this deflection angle distribution is transformed into a simulated refractive index distribution n(r). The result is obtained by adapting the parameters r* in an optimal or appropriate manner. k,fit and n* k,fit A sufficiently accurate fit to simulate the refractive index distribution n(r) fit Therefore, this simulation is based on a model with adaptive parameters r*. kfit and n* kfit The assumption is that the RIP simultaneously represents the reconstructed real RIP of object 20.

[0073] The simulated refractive index distribution n*(r) is used to determine whether a sufficient fit has been achieved. fit The mathematical standard for calculating whether the deviation between the simulated refractive index distribution n(r) and the prepared refractive index distribution n'(r) is below a given threshold is used. The deviation is preferably calculated based on the minimum absolute residual or the least squares method. In the case of equidistant radii, the absolute residual corresponds to the so-called best-fit region.

[0074] Because, according to the implementation plan of the method, the optimization parameter r* k,fit and n*k,fit The determination of the refractive index distribution and the level of the deflection angle distribution are based on the refractive index distribution rather than the level of the deflection angle distribution, thus simplifying and improving the rationality, accuracy and reproducibility of the measurement results.

[0075] Ideally, each layer of the optical object 20 is within the entire layer radius r. k The inner layer exhibits a given refractive index n k However, in reality, things deviate from this ideal situation. The refractive index n of the layer... k It can vary around the nominal value, and its evolution may differ from a constant value. The reconstruction of the RIP based on the method according to the disclosed embodiment does not presuppose an ideal step distribution. The deviation is consistent with the mean of the true layer's refractive index. This also applies to layers with a preset refractive index gradient.

[0076] In a particularly preferred embodiment of the method, in addition to fitting the simulated refractive index distribution n"(r) to the prepared refractive index distribution n'(r) according to the following method steps, the parameter r* is also used. k and n* k The iterative adaptive process (using the methods and steps discussed above) completes the fitting of the simulated deflection angle distribution ψ*(y) to the prepared deflection angle distribution ψ'(y): through the parameter r* k and n* k The iterative adaptive method is used to fit the simulated refractive index distribution n"(r) to the prepared refractive index distribution n'(r), where the fitted simulated refractive index distribution n*(r) is obtained. fit The fitted simulation of the refractive index distribution is determined by the adaptive parameter r* k,fit and n* k,fit Limitations. Obtain the fitted simulated deflection angle distribution ψ'*(y). fit The fitted simulation of the deflection angle distribution is determined by the adaptive parameter r'* k,fit and n'* k,fit Limited. The refractive index distribution n*(r) is fitted using a weighting factor G. fit The simulated deflection angle distribution ψ'*(y) is fitted with a weighted factor (1-G). fit When combining, the RIP is obtained as having adaptive parameters r* k,fit and n* k,fit The assumed refractive index distribution, where 0 <G<1。

[0077] To reconstruct the true refractive index distribution n(r), a weighted parameter is used, which is obtained by observing the fitted simulated refractive index distribution n(r). fit The refractive index plane, and on the other hand, by observing the simulated deflection angle distribution ψ'*(y) through fitting, fitThe resulting angular plane is obtained. This eliminates random measurement variations or conversion errors, and thus achieves higher accuracy in reconstructing the true refractive index distribution.

[0078] The parameters determined based on the reconstruction of the true refractive index distribution n(r), especially the adaptive parameter r* k,fit and n* k,fit It is preferably used for adaptive processes in the manufacturing of preforms.

[0079] The method according to the embodiment is used to determine the refractive index distribution of a cylindrical optical object 20 (e.g., such as an optical preform). The RIP of the preform cannot be directly measured and is therefore indirectly determined as the deflection of the light beam transmitted through the volume region of the preform. The refractive index distribution of the preform can be derived from the deflection distribution of the outgoing light beam.

[0080] Figure 3 The figure uses an example of a preform in which an undoped quartz glass mandrel is surrounded by an inner cladding of fluorine-doped quartz glass and an outer cladding of undoped quartz glass to illustrate a segment of a typical deflection angle function as measured above. The deflection angle ψ (in degrees) is plotted against the position along the y-axis (in millimeters). The curve specified by "p=1" corresponds to the measurement curve. Several spline functions for various smoothing parameters p<1 are also plotted in this figure. These curves illustrate the effects of various smoothing steps and will be explained in more detail below.

[0081] The refractive index distribution n(r) is calculated from the deflection angle distribution using the Abel transform. Figure 4 The corresponding graph shows the relative refractive index n(r) = 1.446 against radius r (in millimeters). The curves shown are illustrated using numerical integration. Figure 3 The measured deflection angle distribution (p=1) is calculated. The curve in region 21 represents the core rod; the curve in region 22 represents the inner cladding; and the curve in region 23 represents the outer cladding.

[0082] These measurement results are incorrect. As explained above, one reason for the error is the appearance of unmeasurable regions caused by the measurement method in cases of upward refractive index jumps, as is typical of optical fibers with a relatively higher refractive index in the core than in the cladding. Figure 1B The sketch illustrates the error source by referring to a simplified case: a rod with a homogeneous refractive index distribution n1 is inserted into a refractive index-adjusting fluid (also known as a refractive index adaptive liquid or immersion liquid) with a refractive index number n0, where n0 is less than n1. During the scanning of the rod, the tangentially incident beam at the incident point is refracted toward the center of the rod and exits the rod again as an outgoing beam with a different propagation direction, thus producing an error source such as... Figure 1BThe beam path shown. Thus, there are regions or areas in the object through which the light beam cannot be tangentially transmitted (i.e., is never irradiated by the beam during the measurement). This region is Figure 1B shown shaded in and marked with a radius r* and an angle β (beta), where the angle β = 90° - ψ / 2. Thus, the deflection angle in the 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.

[0083] The goal of the method explained below with the evaluation and modeling of the measured deflection angle distribution is the compensation of this system measurement error and the substantial reconstruction of the true refractive index distribution n(r).

[0084] At the start of the evaluation, the positions of the extrema y k,max of the measured deflection angle distribution are determined. These are already approximately the radii of the individual layers. In principle, the exact positions on the positive and negative y-axes at the edge of the mandrel can be determined by simple manual reading, especially in the case of ideal noise-free data.

[0085] The implementation of the method is explained with reference to Figure 3 For the implementation, the measurement data corresponds to the curve p = 1. To ensure that the edge is not wrongly placed on remote measurement points or secondary extrema caused by noise, the measured deflection angle distribution is strongly smoothed at the start using a spline function. The spline function is a number of composed higher-order polynomials, for example of the third order. The smoothing parameter p represents a compromise, for example, between p = 1 (piecewise fitting of cubic polynomials), 0 < p < 1 (piecewise fitting of a smoothed curve), and p = 0 (fitting of a straight line).

[0086] The method starts with p = 0.9, i.e., strong smoothing. The absolute value of the deflection angle increases from the inside outwards towards the edge within a wide region. The strongly smoothed deflection angle curve shows a maximum or minimum in this region, depending on the sign of the deflection angle. A few outlier data points produce small (if any) extrema. The extrema are determined on the strongly smoothed curve. Subsequently, smoothing is carried out for p = 0.99 (less smoothing). This step is repeated with gradually decreasing smoothing for p = 0.999; p = 0.9999; p = 0.99999; and finally, for the original measurement data (p = 1). There is no more smoothing in the sixth and final iteration (p = 1). Indeed, the choice of p = 1 corresponds to cubic interpolation, but if it is evaluated especially at the support points, the original points are actually obtained again. Thus, the curve p = 1 represents a segment of the measurement data.

[0087] Therefore, the extrema previously determined based on strong smoothing gradually shift towards the actual extrema of the deflection angle distribution with each iteration, and thus tend to move towards the true refractive index edge as well. Thus, the true location of the refractive index edge is best approximated by the highest smoothing parameter. The true edge location is at the bottom of the maximum value in the case of a downward refractive index jump, and conversely, at the peak of the maximum value in the case of an upward refractive index jump.

[0088] In another evaluation, the innermost extremum y of the deflection angle distribution, which had already been found using this evaluation, was used. k,右 and y k,左 They are specifically used for the correction of the origin in the y-direction within the deflection angle distribution.

[0089] Before performing the Abel transformation, the origin of the deflection angle distribution ψ(y) must be correctly determined. Specifically, the y-axis of the coordinate system for the angle distribution is determined solely by the geometry of the measuring unit 9. Here, the center of the measuring unit 9 does not necessarily have to coincide with the center of the preform, which causes a shift towards the y-axis. Furthermore, the entire angle distribution may have an angular offset, which has a displacement contribution in the ψ direction of the coordinate system. This offset may be caused, for example, by inaccurate referencing of the angle of the rotating disk in the measuring system 100.

[0090] Figure 5 The effect of the offset of the origin of the bottom deflection angle distribution on the refractive index distribution calculated from this bottom deflection angle distribution is shown. For this purpose, two distributions consisting of 4,401 data points are plotted using equation (1), and the calculation is then performed. Distribution curve 41 is the assumed step distribution with a refractive index jump Δn = ±0.01. The remaining curves show the calculation of the refractive index distribution, which is plotted as the refractive index difference (n(r) - n0) in relative units (ru) against position r: curve 42 is from the correct deflection angle distribution, curve 43 is the incorrectly positioned origin with 0.1 mm in the y direction, and curve 44 is the origin with -0.02° (approximately 3.5 × 10⁻⁶) (approximately 3.5 × 10⁻⁶). -4 The angular offset of rad is incorrectly positioned, and curve 45 is the case of two shifts together.

[0091] Curve 42 illustrates the typical systematic error results of the conversion of the measured deflection angle distribution in the refractive index distribution. The total refractive index level is significantly lower than the true level. Furthermore, there is rounding of the refractive index distribution towards the edges. Curves 43 to 45 show the effect of incorrect origin positioning.

[0092] For substantially radially symmetrical optical preforms, the previously determined mandrel edges in the deflection angle distribution are particularly suitable for determining the preform's center point and, therefore, the coordinate origin. If necessary, the y-axis is shifted along a corresponding path so that the origin lies exactly midway between the mandrel edges.

[0093] Offset corrections are performed to vertically shift the deflection angle distribution accordingly. To do this, the line is fitted to the innermost right extreme value y using the sum of least squares. k,右 and the innermost left extreme value y k,左 The area to be fitted extends within 20% of the mandrel diameter. Finally, the measurement data is moved vertically around the y-axis segment of the straight line, causing the line to extend through the origin.

[0094] In alternative variations of the method used to determine the offset, a higher-order polynomial (e.g., 9th order) is fitted to the innermost right extremum y. k,右 With the innermost left extreme value y k,左 The middle between. Then, it is also possible to choose a sub-route or the entire route between the edges. In another alternative method variant for determining the offset, the deflection angle distribution is shifted such that the sum of the deflection angles of all equidistant measurements equals zero.

[0095] The result of the evaluation and preparation is to prepare a deflection angle distribution ψ'(y) that is adaptive to the origin of the coordinate system relative to its origin.

[0096] In the next step, the prepared refractive index distribution n'(r) is generated from the prepared deflection angle distribution ψ'(y) using the Abel transform. (See reference...) Figure 5 As shown, prior adaptation of the origin of the deflection angle distribution is very helpful because without this adaptation, small deviations from the actual origin will cause errors in the transformed refractive index distribution.

[0097] Indeed, the prepared refractive index distribution n'(r) does not reflect the refractive index distribution that the preform will realistically expect. However, the prepared refractive index distribution n'(r) represents an illustrative orientation guide from which suitable orientation values ​​for the assumed refractive index distribution n*(r) can be derived relatively explicitly, forming the basis for subsequent methodological steps. The orientation values ​​to be derived include the orientation value r*k of the layer radius and the orientation value n*k of the layer refractive index of the assumed refractive index distribution n*(r). Especially for the refractive index, empirical values ​​and data are typically stored in a database and can be used to determine the refractive index.

[0098] In this assessment, the previously determined extreme value y k,右 and y k,左 It is also used to determine the orientation value r*k. However, since these positions only approximately correspond to the radius of the refractive index distribution, the determined extrema y are... k,右 and y k,左 Transformed into layer radius r respectively k,右 and r k,左 The calculated layer radius is used to fix the orientation value r*k. When r kWhen total internal reflection does not occur at the boundary, the transformation from extremum to layer radius is based on the second equation in the Abel transform, and when at r k When total internal reflection occurs at the boundary, the conversion from the extremum to the layer radius is based on equation (3).

[0099] Figure 6 The figure illustrates the prepared refractive index distribution n'(r) of a preform with a simple step distribution and the hypothetical refractive index distribution n*(r) modeled through its evaluation. The refractive index is indicated as a relative value based on the refractive index of the fluid (n0 = 1.446).

[0100] Assume that the refractive index distribution n*(r) already depicts the refractive index distribution that the preform is expected to have in reality, or is close to that refractive index distribution. Assume that the refractive index distribution is based on the prepared refractive index distribution n'(r) and the orientation values ​​derived from that distribution, which in turn include estimates of the refractive index and radius from unmeasurable regions.

[0101] Using equation (1), in the next method step, a simulated deflection angle distribution ψ"(y) is generated based on the assumed refractive index distribution n*(r). Thus, the simulated deflection angle distribution ψ*(y) obtained is based on the assumption of the refractive index distribution of the preform (i.e., the assumed refractive index distribution n*(r)), which is derived from the prepared refractive index distribution n'(r) after correcting and evaluating the original measurements.

[0102] By transforming the simulated deflection angle distribution ψ(y) based on the first equation in the Abel transform, the simulated refractive index distribution n(r) is obtained again. This simulated refractive index distribution is... Figure 6 This is illustrated using this notation. The distribution has a rounded region 53 between the cladding region 52 and the core region 51. Except for this rounded region 53, the simulated refractive index n'(r) is almost identical to the prepared refractive index distribution n'(r). This is noteworthy considering that the assumed refractive index distribution n*(r) differs significantly from it. This similarity suggests that the assumptions upon which the refractive index distribution n*(r) is based are very close to the actual refractive index distribution n(r) of the preform. That is, Figure 6 The assumed refractive index distribution n*(r) in the model accurately or at least sufficiently accurately reflects the true refractive index distribution n(r).

[0103] In practice, an exact match between the simulated refractive index distribution n"(r) and the prepared refractive index distribution n'(r) cannot be achieved. However, sufficient and arbitrarily accurate adaptation can be achieved by iteratively fitting the simulated refractive index distribution n"(r) to the prepared refractive index distribution n'(r).

[0104] During the iterative fitting, the parameter r* k and n* kThe changes over a long period of time allow for a sufficiently accurate fitting of the simulated refractive index distribution n(r). fit The parameter r* used here k,fit and n* k,fit This forms the basis for the corresponding hypothetical refractive index distribution n*(r), and thus, these parameters simultaneously represent the reconstructed true refractive index distribution of the preform.

[0105] Does a sufficiently well-fit simulated refractive index distribution n*(r) exist? fit The standard is the minimum deviation between the simulated refractive index distribution n(r) and the prepared refractive index distribution n'(r), which is determined, for example, based on the sum of the minimum absolute residuals. This measurement method yields good results even in the case of a rather complex refractive index distribution in a preform with eight layers. The fitting of the layer parameters is preferably performed from the outer layer to the inner layer.

[0106] In use for reconstruction Figure 6 In the model explained above for the true refractive index distribution, the simulated refractive index distribution n"(r) is fitted to the prepared refractive index distribution n'(r). In the modified form used for this reconstruction process, a weighting parameter is additionally used, which, on the one hand, takes into account the fitted simulated refractive index distribution n"(r). fit The refractive index plane, and on the other hand, by considering the deflection angle distribution ψ'*(y) in the fitting simulation. fit The resulting angular plane is obtained. This eliminates random measurement variations and conversion errors, and thus achieves higher accuracy in reconstructing the true refractive index distribution.

[0107] Therefore, the simulated deflection angle distribution ψ*(y) is additionally fitted to the prepared deflection angle distribution ψ'(y). The fitting process is based on the parameter r*. k and n* k The process involves iterative adaptation, changing parameters until a sufficiently accurate fit is obtained to simulate the deflection angle distribution ψ(r). fit The optimal adaptive parameter r'* used here. k,fit and n'* k,fit This forms the basis for the corresponding assumed refractive index distribution n*(r), but these may differ from the optimal adaptive parameter value r*. k,fit and n* k,fit The refractive index distribution n*(r) is simulated by fitting a weighted average with G = 0.5. fit The fitted simulation of the deflection angle distribution ψ'*(y) fit (Similarly, G = 0.5) The information obtained therefrom is additionally considered in the reconstruction of the refractive index distribution.

[0108] In order to more accurately determine the refractive index r of each layer k and nk It is recommended to use the least squares method or the least absolute residual method for fitting.

[0109] A key problem is that the fitting function n(r) lacks an analytical expression. Therefore, a roundabout approach is used to construct the fitting function. Within each iteration, the parameter r is adjusted... k and n k The change is generated by equation (1) to produce the deflection angle distribution, and the Abel transformation is performed to finally compare the distribution n(r) obtained by the least squares standard or by the least absolute residual method with the measured refractive index distribution. Therefore, the calculation of the transformation is a fixed component in each iteration, which prolongs the computation time.

[0110] To ensure fitting within a shorter time period, the following constraints can be imposed: (i) Origin correction (due to origin correction, the offsets in the ψ direction and shifts in the y direction that would otherwise be independent fitting parameters are omitted, and the number of independent fitting parameters is thus reduced by two); (ii) Lateral fitting (to even consider the minimum deviation of radial symmetry within the preform about the fitting, various layer parameters r are allowed within the layer for both the positive and negative y axes). k and n k However, this fit can be divided into two fits with only half the number of free fitting parameters, which results in a considerable reduction in the number of required iterations and thus saves time; and (iii) hierarchical fitting (starting from the basic idea of ​​dividing a fit with many free parameters into several fits with a few free parameters, hierarchical fitting is also possible in addition to lateral fitting; however, it should be noted that the parameter r to be determined must be determined from the outside in). k and n k This allows the number of layers considered to increase continuously, and the area considered for fitting to increase layer by layer; together with the previously explained lateral fitting, 2k fittings with two unknown parameters to be determined are obtained in a preform with k layers, instead of one fitting with 4k unknown parameters to be determined, and thus, the required computation time is significantly reduced.

[0111] As outlined above, the timeline of development of methods for evaluating refractive index distribution (RIP) is as follows. Initially, the direct Abel transform was applied. However, the Abel transform does not account for the typical measurement artifacts in RIPs. Next, U.S. Patent 8,013,985, granted to Corning Incorporated, provided an improved method, the '985 method, but it was intended solely for research and development purposes (unlike commercial ones). Finally, the applicant's own U.S. Patent 10,508,973 teaches a method, the '973 method, which represents the current prior art for determining RIPs when they are substantially or entirely step-index samples. The '973 method accounts for well-known measurement artifacts in refractive index distributions (underestimated step-index and rounded distributions).

[0112] In summary, the method taught in '973 Patent determines the radial RIP of a cylindrical optical object having a longitudinal axis of cylinder and a layer radius r. k and layer refractive index n k At least one layer k extends radially symmetrically around the longitudinal axis of the cylinder. The method includes the following steps: measuring a deflection angle distribution ψ(y) by introducing an incident beam at an incident point into the cylindrical optical object in a direction transverse to the longitudinal axis of the cylinder, wherein the 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; and reconstructing the RIP based on a model. The model includes the following steps: (a) adjusting the measured deflection angle distribution ψ(y), including determining the extrema of the deflection angle distribution and including the region of refractive index step, wherein an adjusted deflection angle distribution ψ'(y) is obtained, and wherein the adjustment of the measured deflection angle distribution includes correction of the origin of the adjusted deflection angle distribution, (b) transforming the adjusted deflection angle distribution ψ'(y) into an adjusted refractive index distribution n'(r), and (c) evaluating the adjusted refractive index distribution n'(r) to fix an orientation value, which includes an orientation value r* of the layer radius of the assumed refractive index distribution n*(r). k Orientation value n* of the refractive index of the layer k (d) By using an orientation value r* k and n* k The assumed refractive index distribution n*(r) generates a simulated deflection angle distribution ψ(y) to produce a simulated refractive index distribution n(r), and this deflection angle distribution is transformed into a simulated refractive index distribution n(r). (e) Through the orientation value r* k and n* k The iterative adaptive method is used to fit the simulated refractive index distribution n"(r) to the adjusted refractive index distribution n'(r), where the fitted simulated refractive index distribution n*(r) is obtained. fit The fitted simulation of the refractive index distribution is determined by the adaptive parameter r* k,fitand n* k,fit The constraints, and (f) obtain this refractive index distribution as having adaptive parameters r* k,fit and n* k,fit The assumed refractive index distribution.

[0113] Both the '985 and '973 methods are suitable only for step-index or at least substantially step-index preforms. A step-index preform is defined as a preform that produces a multimode or single-mode optical fiber with a uniform refractive index throughout the core. (Step-index multiclad fibers also exist, in which additional light, in addition to propagation within the core, propagates as a multimode within the cladding.) This step involves a shift between the core and a cladding with a lower refractive index than the core. The term "substantially" as used in this document is an approximate descriptive term and means "quite large in degree" or "largely but not exactly specified," and is intended to avoid strict numerical boundaries for specified parameters. Thus, a substantially step-index preform is a preform that produces a multimode or single-mode optical fiber with a core having a refractive index that is, if not entirely, substantially uniform.

[0114] Neither the '985 method nor the '973 method, or any other known method for this purpose, can accurately provide the RIP for objects that are not perfectly step-index, but rather require compensation for previously described measurement artifacts in the refractive index distribution. The '985 method employs the measured deflection function ψ(y) and fits the ideal refractive index deflection curve to the measured deflection function. Therefore, the calculation is performed in the deflection function space. In contrast, the '973 method performs the calculation in the refractive index distribution space.

[0115] The remainder of this document describes the steps of a method for improving the accurate RIP of objects that do not have a step refractive index or at least have a substantially step refractive index. This improvement method takes into account well-known measurement artifacts (underestimated refractive index step and rounding distribution) in the refractive index distribution. Object 20 may have one, two, or up to ten layers to compensate for measurement artifacts in the refractive index distribution.

[0116] Figure 7 The flowchart illustrates the steps of the improved method 110. Method 110 determines the radial RIP of a cylindrical optical object 20, which has a cylindrical longitudinal axis and a layer radius r. k and layer refractive index n kAt least one layer k extends radially symmetrically around the longitudinal axis of the cylinder. In step 101 of method 110, the deflection function is measured and the measurement data is transformed into a refractive index distribution using an Abel transform. (This RIP is reflected in curves 201 and 301 labeled “Measurement Curves” in the following examples.) As discussed above, step 101 typically involves measuring the deflection angle distribution ψ(y) by introducing the incident beam at the point of incidence into the cylindrical optical object 20 in a direction transverse to the longitudinal axis of the cylinder, where the 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 point of incidence of the incident beam in a Cartesian coordinate system.

[0117] In step 102 of method 110, the refractive index level of the outer region (or layer) of object 20 is assumed. (The resulting RIP is reflected in curves 202 and 302 labeled "compensation level" in the following example.) In step 103, a corresponding theoretical deflection function is generated and transformed using an Abel transform. (The resulting RIP is reflected in curves 203 and 303 labeled "fitting curve" in the following example.) In step 104, the transformed theoretical deflection function generated in step 103 is compared with the transformed measured deflection function from step 101. In step 104a, this comparison is evaluated against a predetermined accuracy level for the region of object 20 being evaluated. "Predetermined" means predetermined, such that predetermined characteristics must be determined before the start of the method steps, i.e., selected or at least known. The predetermined accuracy level may depend on the specific application. Typical pre-determined accuracy is about 90%, other pre-determined accuracy is about 92%, preferred pre-determined accuracy is about 95%, more preferred pre-determined accuracy is about 97%, and most preferred pre-determined accuracy is about 99% or higher.

[0118] If the transformed theoretical deflection function generated in step 103 is determined to be sufficiently close to the transformed measured deflection function of step 101 (i.e., the accuracy level is at or above a predetermined level), then method 110 proceeds to step 105. (In the following example, fitted curves 203, 303 will substantially match measured distribution curves 201, 301.) If not, method 110 returns to step 102. Steps 102 and 103 are repeated iteratively until the accuracy level is at or above the predetermined level, and method 110 may proceed to step 105.

[0119] In step 105 of method 110, it is determined whether object 20 has another region (or layer) to be compensated. Typically, a region of object 20 is defined as a region or layer between the boundary or edge of the object and a discontinuity in refractive index, or between two discontinuities in refractive index. Compensation always begins at the outer edge of object 20 and proceeds inward toward the center of object 20 through a series of one or more regions or layers. When it is determined that no region of object 20 still needs to be evaluated and compensated, method 110 proceeds to step 106. If there is still another region of object 20 to be evaluated and compensated, method 110 returns to step 102, and steps 102, 103, 104, 104a, and 105 are repeated for each additional region until no more regions still need to be evaluated and compensated.

[0120] The difference between the assumed RIP in step 102 (compensation level curves 202 and 302 in the following examples) and the RIP corresponding to the transformed theoretical deflection function generated in step 103 (fitting curves 203 and 303 in the following examples) is an error, shift, or offset caused by measurement artifacts of the refractive index distribution. This error accumulates as more layers are compensated. In step 106 of method 110, this difference is added to the measured and transformed RIP of step 101 (measurement distribution curves 201 and 301 in the following examples) to calculate the measurement artifact-compensated RIP (curves 204 and 304 labeled "new evaluation method" in the following examples). Therefore, the mathematical calculation rule is: New evaluation method curve = Measurement distribution curve + Compensation level curve - Fitting curve. The measurement artifact-compensated RIP curves 204 and 304 include the true absolute refractive index value. The improved method 110 provides an accurate and reliable RIP, even for objects 20 that are not step-index samples or are substantially step-index samples.

[0121] Example

[0122] The following two embodiments are included to more clearly illustrate the overall nature of this disclosure. These two embodiments are exemplary and not restrictive.

[0123] Figure 8 The graph shows the calculated refractive index distribution, plotted as the refractive index difference (n(r) - n0) against position r in millimeters, to explain the application of Method 110 to a practical fluorine-doped quartz glass tube. As mentioned above, such tubes are typically used to form an inner cladding that surrounds an undoped quartz glass core rod in a preform. Figure 8 The figure depicts the measurement distribution curve 201, the compensation level curve 202, the fitting curve 203, and the new evaluation method curve 204. The new evaluation method curve 204 is the RIP that applies method 110 to the tube and represents the measurement artifact compensation of the tube.

[0124] Figure 9 This is a simple comparison between the measurement distribution curve 201 for fluorine-doped quartz glass tubes and curve 204 of the new evaluation method. It should be noted that there is a significant, non-negligible shift between these curves, but the trend characteristics are still preserved. This comparison demonstrates a high correlation between the two curves, reflecting the high level of accuracy achieved through method 110.

[0125] Figure 10 The graph shows the calculated refractive index distribution, plotted as the refractive index difference (n(r) - n0) against position r in millimeters, to explain the application of method 110 to a practical mandrel. As mentioned above, such a mandrel is typically surrounded in a preform by an inner cladding of fluorine-doped quartz glass and an outer cladding of undoped quartz glass. Figure 10 The figure depicts the measurement distribution curve 301, the compensation level curve 302, the fitting curve 303, and the new evaluation method curve 304. The new evaluation method curve 304 is the final result of applying method 110 to the mandrel and represents the RIP of measurement artifact compensation for the mandrel.

[0126] Figure 11 This is a simple comparison between the measurement distribution curve 301 used for the mandrel and the curve 304 of the new evaluation method. The comparison shows a high correlation between the two curves, reflecting the high level of accuracy achieved through method 110.

[0127] Method 110 provides a more accurate and reliable RIP evaluation than existing methods. This evaluation is essential for preform assemblies and for meeting the needs of preform consumers, especially for preforms with more complex designs. Method 110 provides improved results whenever the RIP is not a step-index sample or is substantially a step-index sample, resulting in RIP measurement artifacts.

[0128] Although the foregoing description and illustrations have reference to certain specific embodiments and examples, this disclosure is not intended to be limited to the details shown. Rather, various modifications to the details may be made to the scope of the equivalents of the claims and without departing from the spirit of this disclosure. For example, it is expressly intended that all scopes broadly enumerated in this document include, within their scope, all narrower scopes falling within the broader scope.

Claims

1. A method for determining the radial refractive index distribution of an object, the method comprising: (a) Providing the object, the object comprising a cylindrical optical object having a longitudinal axis of a cylinder and a layer radius r. k And has a layer refractive index n k At least one layer k extends radially around the longitudinal axis of the cylinder, wherein the at least one layer is not a step-index refractive index. (b) Measure the deflection function of the object and transform the measured data into a measured refractive index distribution; (c) Assume the refractive index level and radius of the layer of the object being evaluated and calculate the compensation level refractive index distribution; (d) Generate a theoretical deflection function corresponding to the assumed refractive index level and radius, and transform the generated data into a fitted refractive index distribution; (e) Compare the fitted refractive index distribution with the measured refractive index distribution and evaluate the comparison against a predetermined accuracy level for the layer of the object being evaluated; (f) Repeat steps (c) and (d) iteratively until the predetermined accuracy level has been achieved; (g) Determine whether the object has another layer to be evaluated and compensated; (h) Repeat steps (c) through (f) for each layer of the object until no other layers of the object remain to be evaluated and compensated; and (i) Calculate the refractive index distribution for measurement artifact compensation of the object. The step of calculating the refractive index distribution for measurement artifact compensation includes adding the measured refractive index distribution to the compensation level refractive index distribution and subtracting the fitted refractive index distribution.

2. The method of claim 1, wherein step (b) of measuring the deflection function comprises measuring the deflection angle distribution ψ(y) by introducing an incident beam at an incident point into the cylindrical optical object in a direction transverse to the longitudinal axis of the cylinder, wherein the 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 transformation step is based on the Abel transformation.

4. The method of claim 1, wherein the predetermined accuracy level is 99% or higher.

5. The method of claim 1, wherein the at least one layer comprises an outer layer and at least one inner layer, and the outer layer is the first layer to be evaluated in step (c).

6. The method according to claim 1, wherein, In the step of determining whether the object has another layer to be evaluated and compensated, the layer is a layer between the boundary or edge of the object and a discontinuity of refractive index or between two discontinuities of refractive index.

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

8. The method of claim 1, further comprising the step of using the refractive index distribution compensated for by the measurement artifacts to make the preform manufacturing process adaptive.

9. A method for determining the radial refractive index distribution of an object, the method comprising: (a) Providing the object, the object comprising a cylindrical optical object having a longitudinal axis of a cylinder and a layer radius r. k And has a layer refractive index n k At least one layer k extends radially around the longitudinal axis of the cylinder, wherein the at least one layer is not a step-index refractive index. (b) Measure the deflection function of the object and transform the measured data into a measured refractive index distribution via an Abel transform; (c) Assume the refractive index level and radius of the layer of the object being evaluated and calculate the compensation level refractive index distribution; (d) Generate a theoretical deflection function corresponding to the assumed refractive index level and radius, and transform the generated data into a fitted refractive index distribution via Abel transformation; (e) The fitted refractive index distribution is compared with the measured refractive index distribution and the comparison is evaluated against a predetermined accuracy level of the layer of the object being evaluated, wherein the predetermined accuracy level is 90% or higher; (f) Repeat steps (c) and (d) iteratively until the predetermined accuracy level has been achieved; (g) Determine whether the object has another layer to be evaluated and compensated, wherein the layer is between the boundary or edge of the object and the refractive index discontinuity or between two refractive index discontinuities; (h) Repeat steps (c) through (f) for each layer of the object until no other layers of the object remain to be evaluated and compensated; and (i) The refractive index distribution for measurement artifact compensation of the object is calculated by adding the measured refractive index distribution to the compensation level refractive index distribution and subtracting the fitted refractive index distribution.

10. The method of claim 9, wherein step (b) of measuring the deflection function comprises measuring the deflection angle distribution ψ(y) by introducing an incident beam at an incident point into the cylindrical optical object in a direction transverse to the longitudinal axis of the cylinder, wherein the 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.

11. The method of claim 9, wherein the at least one layer comprises an outer layer and at least one inner layer, and the outer layer is the first layer to be evaluated in step (c).

12. The method according to claim 9, wherein the object provided in step (a) is an optical fiber preform.

13. The method of claim 9, further comprising the step of using the refractive index distribution compensated for by the measurement artifacts to make the preform manufacturing process adaptive.

14. A method for determining the radial refractive index distribution of a cylindrical optical fiber preform, the method comprising: (a) Providing the preform having a cylindrical longitudinal axis and a layer radius r k And has a layer refractive index n k At least one layer k extends radially around the longitudinal axis of the cylinder, wherein the at least one layer is not a step-index refractive index. (b) Measure the deflection function of the preform and transform the measured data into a measured refractive index distribution via an Abel transform, wherein the deflection function is derived by introducing the incident beam at the incident point into the preform in a direction transverse to the longitudinal axis of the cylinder to measure the deflection angle distribution ψ(y), wherein the 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 the Cartesian coordinate system; (c) Assume the refractive index level and radius of the layers of the preform being evaluated and calculate the compensation level refractive index distribution, wherein the at least one layer comprises an outer layer and at least one inner layer, and the outer layer is the first layer to be evaluated; (d) Generate a theoretical deflection function corresponding to the assumed refractive index level and radius, and transform the generated data into a fitted refractive index distribution via Abel transformation; (e) The fitted refractive index distribution is compared with the measured refractive index distribution and the comparison is evaluated against a predetermined accuracy level of the layer of the preform being evaluated, wherein the predetermined accuracy level is 90% or higher. (f) Repeat steps (c) and (d) iteratively until the predetermined accuracy level has been achieved; (g) Determine whether the preform has another layer to be evaluated and compensated, wherein the layer is between the boundary or edge of the preform and the refractive index discontinuity or between two refractive index discontinuities; (h) Repeat steps (c) to (f) for each layer of the preform until the preform has no other layers still to be evaluated and compensated; (i) The refractive index distribution for measurement artifact compensation of the preform is calculated by adding the measured refractive index distribution to the compensated level refractive index distribution and subtracting the fitted refractive index distribution; and (j) The refractive index distribution compensated for by the measurement artifacts is used to make the preform manufacturing process adaptive.

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