Method for qualifying the effective modal bandwidth of a multimode fiber over a wide wavelength range from a single wavelength DMD measurement and method for selecting a high effective modal bandwidth multimode fiber from a batch of multimode fibers

Abstract

The invention relates to a method for qualifying the actual effective modal bandwidth of a multimode optical fiber over a predetermined wavelength range, comprising the steps of: carrying out (30) a Dispersion Modal Delay (DMD) measurement of the multimode optical fiber at a single wavelength to obtain an actual DMD plot; generating (32) at least two distinct modified DMD plots from the actual DMD plot, each modified DMD plot being generated by applying to the recorded traces a temporal delay t that increases in absolute values with the radial offset value r.sub.offset, each modified DMD plot being associated with a predetermined bandwidth threshold (S1; S2); for each modified DMD plot, computing (33) an effective modal bandwidth as a function of said modified DMD plot and comparing (34) the computed effective modal bandwidth (EMBc.sub.1; EMBc.sub.2) with the bandwidth threshold value to which the modified DMD plot is associated; (35) qualifying the actual effective modal bandwidth as a function of results from the comparing step.

Claims

1. A method for qualifying effective modal bandwidth (EMB) of a multimode optical fiber over a predetermined wavelength range, the method comprising: injecting a pulsed light of a single wavelength (.sub.0) into a multimode optical fiber with a radial offset between each successive pulse; measuring, from the injected pulsed light, Dispersion Modal Delay (DMD) of said multimode optical fiber to obtain an actual DMD plot, said actual DMD plot comprising a plurality of traces recorded at different radial offset values r.sub.offset, from an axis of said multimode optical fiber where r.sub.offset=0 to a radial offset value r.sub.offset=a where a is a core radius of said multimode optical fiber; generating, with a processor, at least two distinct modified DMD plots from said actual DMD plot, each modified DMD plot being generated by applying to the recorded traces a temporal delay t that increases in absolute values with said radial offset value r.sub.offset, each modified DMD plot being associated with a predetermined bandwidth threshold (S.sub.1; S.sub.2); and for each of said modified DMD plots: estimating, with a processor, an effective modal bandwidth (EMBc.sub.1; EMBc.sub.2) of said multimode optical fiber as a function of said modified DMD plot; and comparing, with a processor, said estimated effective modal bandwidth (EMBc.sub.1; EMBc.sub.2) with the corresponding predetermined bandwidth threshold (S.sub.1; S.sub.2) to which said modified DMD plot is associated.

2. The method according to claim 1, wherein each modified DMD plot is generated by applying the temporal delay t satisfying the following equation: $t\left(r_{\mathrm{offset}}\right)=.Math.L.Math.\frac{r_{\mathrm{offset}}}{a}$ where: is a non-zero integer representative of a wavelength shift relative radial delay, which is associated with the corresponding predetermined bandwidth threshold to which said modified DMD plot is associated; L is the length of said multimode optical fiber; a is the core radius of said multimode optical fiber; and r.sub.offset is the radial offset value, from the axis of said multimode optical fiber where r.sub.offset=0 to r.sub.offset=a, at which is injected a light pulse at said single wavelength during the DMD measurement.

3. The method according to claim 1, wherein first and second modified DMD plots are generated from said actual DMD plot respectively on the basis of: a first wavelength shift relative radial delay (.sub.1), equal to 180 ps/km, which is associated with a first bandwidth threshold (S.sub.1), equal to 6,700 MHz-km; and a second wavelength shift relative radial delay (.sub.2), equal to 220 ps/km, which is associated with a second bandwidth threshold (S.sub.2), equal to 5,200 MHz-km.

4. The method according to claim 1, further comprising: computing an initial effective modal bandwidth (EMB.sub.0) of said multimode optical fiber directly as a function of said actual DMD plot; and comparing said initial effective modal bandwidth (EMB.sub.0) with an initial predetermined bandwidth threshold equal to 4,700 MHz-km.

5. The method according to claim 1, wherein said step of estimating an effective modal bandwidth is carried out by means of a transfer function.

6. The method according to claim 1, wherein the predetermined wavelength range is between 850 nm and 950 nm.

7. The method according to claim 1, wherein the actual effective modal bandwidth measured in situ on said multimode optical fiber is greater than 4,700 MHz-km for a wavelength of 850 nm, greater than 3,800 MHz-km for a wavelength of 875 nm, greater than 3,300 MHz-km for a wavelength of 900 nm, greater than 3,100 MHz-km for a wavelength of 925 nm, and greater than 2,900 MHz-km for a wavelength of 950 nm.

8. A method for selecting a high effective modal bandwidth multimode optical fiber from a batch of multimode optical fibers, the method comprising: selecting a batch of multimode optical fibers; for each multimode optical fiber of the batch: injecting a pulsed light of a single wavelength (.sub.0) into the multimode optical fiber with a radial offset between each successive pulse; measuring, from the injected pulsed light, Dispersion Modal Delay (DMD) of said multimode optical fiber to obtain an actual DMD plot, the actual DMD plot comprising a plurality of traces recorded at different radial offset values r.sub.offset, from an axis of said multimode optical fiber where r.sub.offset=0 to a radial offset value r.sub.offset=a where a is a core radius of said multimode optical fiber; generating, with a processor, at least two distinct modified DMD plots from said actual DMD plot, each modified DMD plot being generated by applying to the recorded traces a temporal delay t that increases in absolute values with said radial offset value r.sub.offset, each modified DMD plot being associated with a predetermined bandwidth threshold (S.sub.1; S.sub.2); and for each of said modified DMD plots: estimating, with a processor, an effective modal bandwidth (EMBc.sub.1; EMBc.sub.2) of said multimode optical fiber as a function of said modified DMD plot; and comparing, with a processor, the estimated effective modal bandwidth (EMBc.sub.1; EMBc.sub.2) with the corresponding predetermined bandwidth threshold (S.sub.1; S.sub.2) to which said modified DMD plot is associated; and selecting only those multimode optical fibers of the batch for which, for each modified DMD plot, said estimated effective modal bandwidth is greater than the predetermined bandwidth threshold to which said modified DMD plot is associated.

9. A computer program product characterized in that it comprises program code instructions for implementing the method according to claim 1, when said program is executed on a computer or a processor.

10. A non-transitory computer-readable carrier medium storing a computer program product according to claim 9.

11. The method according to claim 8, wherein each modified DMD plot is generated by applying the temporal delay t satisfying the following equation: $t\left(r_{\mathrm{offset}}\right)=.Math.L.Math.\frac{r_{\mathrm{offset}}}{a}$ where: is a non-zero integer representative of a wavelength shift relative radial delay, which is associated with the corresponding predetermined bandwidth threshold to which said modified DMD plot is associated; L is the length of said multimode optical fiber; a is the core radius of said multimode optical fiber; and r.sub.offset is the radial offset value, from the axis of said multimode optical fiber where r.sub.offset=0 to r.sub.offset=a, at which is injected a light pulse at said single wavelength during the DMD measurement.

12. The method according to claim 8, wherein first and second modified DMD plots are generated from said actual DMD plot respectively on the basis of: a first wavelength shift relative radial delay (.sub.1), equal to 180 ps/km, which is associated with a first bandwidth threshold (S.sub.1), equal to 6,700 MHz-km; and a second wavelength shift relative radial delay (.sub.2), equal to 220 ps/km, which is associated with a second bandwidth threshold (S.sub.2), equal to 5,200 MHz-km.

13. The method according to claim 8, further comprising: computing an initial effective modal bandwidth (EMB.sub.0) of said multimode optical fiber directly as a function of said actual DMD plot; and comparing said initial effective modal bandwidth (EMB.sub.0) with an initial predetermined bandwidth threshold equal to 4,700 MHz-km.

14. The method according to claim 8, wherein said step of estimating an effective modal bandwidth is carried out by means of a transfer function.

15. The method according to claim 8, wherein the predetermined wavelength range is between 850 nm and 950 nm.

16. The method according to claim 8, wherein the actual effective modal bandwidth measured in situ on said multimode optical fiber is greater than 4,700 MHz-km for a wavelength of 850 nm, greater than 3,800 MHz-km for a wavelength of 875 nm, greater than 3,300 MHz-km for a wavelength of 900 nm, greater than 3,100 MHz-km for a wavelength of 925 nm, and greater than 2,900 MHz-km for a wavelength of 950 nm.

Description

6. LIST OF FIGURES

(1) Other features and advantages of embodiments of the invention shall appear from the following description, given by way of indicative and non-exhaustive examples and from the appended drawings, of which:

(2) FIG. 1 shows an example of an optical communication system implementing a multimode optical fiber;

(3) FIG. 2 provides a schematic illustration of a classical DMD measurement technique;

(4) FIG. 3 provides a flowchart of a particular embodiment of the method for assessing the EMB of a multimode fiber according to the invention;

(5) FIGS. 4A-4E illustrate an example of transformation of a DMD graph into a modified DMD graph for a multimode optical fiber according to a particular embodiment of the invention;

(6) FIG. 5 graphically depicts the actual Effective Modal Bandwidth of several multimode fibers as a function of the wavelength;

(7) FIGS. 6a and 6b graphically depict the actual Effective Modal Bandwidth of a multimode fiber measured and modeled respectively at wavelengths of 874 nm and of 947 nm as a function of the computed Effective Modal Bandwidth;

(8) FIG. 7 illustrates an example of actual DMD measurements performed for different wavelengths for two multimode optical fibers;

(9) FIG. 8 shows the simplified structure of an assessing device according to a particular embodiment of the invention.

7. DETAILED DESCRIPTION

(10) In all of the figures of the present document, identical elements and steps are designated by the same numerical reference sign.

(11) The general principle of the invention relies on a method of assessing the Effective Modal Bandwidth (EMB) of multimode fibers over a predetermined wavelength range based on DMD measurement results obtained only at a single wavelength. The invention enables maximizing the probability that the effective modal bandwidth meets a predefined specification over a wide wavelength range from one DMD measurement at a single wavelength.

(12) FIG. 1 shows an example of an optical communication system including a multimode fiber, which may be assessed according to the present disclosure. A multi-Gigabits Ethernet optical communication system successively comprises a driver 8 of a transmitter 1, a VCSEL source 9 of a transmitter 1, a launch cord 2, a connector 3, a multimode fiber 4, a connector 3, a launch cord 2, a PIN diode 6 of a receiver 5, and an amplifier 7 of a receiver 5. A digital signal at 10 Gbps or 25 Gbps is generated by the driver 8, which directly modulates the VCSEL source 9.

(13) FIG. 3 illustrates by a synoptic diagram the method of assessing the EMB of a multimode fiber according to a particular embodiment of the invention.

(14) In step 30, a characterization of the multimode fiber is carried out using a differential-mode-delay measurement technique, hereafter called DMD measurement (e.g., as set forth in the FOTP-220 standard).

(15) FIG. 2 illustrates the principle of the DMD measurement technique. This technique consists of successively injecting into the multimode fiber a light pulse (ultrafast laser pulse) having a given single mode wavelength (.sub.0=850 nm, for example), with a radial offset between each successive pulse. Delay of each pulse is then measured after a given length (L) of fiber. Multiple identical light pulses are injected at different radial offset values (r.sub.offset) (offset launch), from an axis of the fiber where r.sub.offset=0 (optical core's center) to r.sub.offset=a, with a the core radius of the fiber.

(16) More precisely, an optical reference pulse at 850 nm is emitted by a source and launched into the core 10 of a single-mode launch fiber with a core diameter of 5 m. From the end of the single-mode fiber, it is stepped across the core of a multimode fiber (MMF) 20 under test. The multimode fiber 20 has typically a core diameter of 50 m. For each offset across the core (0 to 25 microns by increment of 1 micron, for example), the propagation delay of the resultant output pulse is recorded by a high bandwidth optical receiver 30, giving the shape of the transmitted pulse, hereafter called a DMD measurement. The y-axis depicts the radial offset (or radial launch) in micrometers with respect to the optical core's center and the x-axis depicts the time in picoseconds.

(17) DMD values can be obtained from the DMD measurement or DMD plot by measuring the difference in delay using the leading edge of the fastest pulse and the trailing edge of the slowest pulse. From this difference, the temporal width is subtracted from the launch pulse, which yields the modal dispersion of the multimode fiber 30.

(18) The graph of FIG. 4A illustrates an example of DMD graph performed on the 50-m multimode optical fiber at .sub.0=850 nm. In this example, the DMD measurement (or DMD plot) comprises a set of sixteen recorded traces, also hereafter called DMD traces. Each recorded trace corresponds to a measurement carried out to a radial offset value (r.sub.offset) with respect to the optical core's center.

(19) In step 31, a value of Effective Modal Bandwidth, EMB.sub.0, of the optical fiber is determined from this DMD plot. More particularly, this value EMB.sub.0, called initial Effective Modal Bandwidth, is derived from a transfer function, which depends on the set of DMD traces obtained in step 30 (plot illustrated in FIG. 4A) by generating a fiber response as a linear combination of the DMD traces. It should be noted that this particular step is optional to the implementation of the assessing method according to the invention. It can lead the assessing method to have better EMB predictive capabilities. Usually, one generates several transfer functions to compute a series of EMB values, typically ten values, and assesses the minimum EMB obtain as the EMB of the fiber.

(20) The step 32 consists of modifying the actual DMD plot obtained in step 30 by applying a temporal delay t to the recorded traces of the DMD plot, (FIG. 4A) so as to generate a modified DMD plot (i.e., a DMD measurement delayed in time as a function of the radial offset value with a given delay), the temporal delay t satisfying the following equation:

(21) $\begin{array}{cc}{t}_i\left(r_{\mathrm{offset}}\right)={}_i.Math.L.Math.\frac{r_{\mathrm{offset}}}{a}& \left(1\right)\end{array}$
where: .sub.i is a non-zero (positive or negative) integer representative of a wavelength shift relative radial delay (hereafter called WSRD), the index i being a positive integer; L is the length of the multimode fiber used during the DMD measurements (e.g., 550 m); a is the core radius of said multimode optical fiber (e.g., 25 m); r.sub.offset is the radial offset, from an axis of said multimode optical fiber where r.sub.offset=0 to r.sub.offset=a, at which is injected a light pulse at said single wavelength (.sub.0=850 nm) during the DMD measurement.

(22) According to this equation, the modified DMD plot is thus generated by applying a temporal delay t to the recorded traces of the original DMD plot, which increases in absolute values with the radial offset value r.sub.offset. The step 32 is carried out for i values of wavelength shift relative radial delay to generate i modified DMD plots.

(23) In the exemplary embodiment here illustrated, the temporal delay t is applied to the actual DMD plot for two distinct wavelength shift relative radial delays, .sub.1 and .sub.2, to generate two modified DMD plots. Each wavelength shift relative radial delay .sub.i is associated with a predetermined bandwidth threshold value S.sub.i according to a threshold calibration process described below in relation to FIGS. 6a and 6b.

(24) In this exemplary embodiment, the first WSRD .sub.1 is equal to 180 ps/km and is associated with a first bandwidth thresholds S.sub.1 equal to 6,700 MHz-km (FIG. 6a). The second WSRD .sub.2 is equal to 220 ps/km and is associated with a second bandwidth thresholds S.sub.2 equal to 5,200 MHz-km (FIG. 6b).

(25) Thus, after applying, for each WSRD, the temporal delay t to the DMD plot resulting from the single wavelength DMD characterization, the algorithm generates, at the end of the step 32, a first modified DMD plot for the WSRD .sub.1, as illustrated on the graph of FIG. 4B, and a second modified DMD plot for the WSRD .sub.2, as illustrated on the graph of FIG. 4C.

(26) Regarding the graph of FIG. 4B, the first modified DMD plot has been obtained from the graph of FIG. 4A using the above equation (1) with the coefficient .sub.1 (i=1). The first modified plot is associated with the first bandwidth thresholds S.sub.1.

(27) Regarding the graph of FIG. 4C, the second modified DMD plot has been obtained from the graph of FIG. 4B, using the above equation (1) with the coefficient .sub.2 (i=2). The second modified plot is associated with the second bandwidth thresholds S.sub.2.

(28) Of course, the principle of defining discussed above can be extended to a greater number of wavelength shift relative radial delays. The number of wavelength shift relative radial delays taken into account in the present example is limited purely for the purposes of pedagogical description. Of course, in order to ensure a better assessment of the actual EMB of the multimode fiber, a greater number of wavelength shift relative radial delays and associated bandwidth thresholds can be provided.

(29) The invention is not limited to this exemplary embodiment, and the person skilled may also envisage other implementations of the step 32. He may envisage, for example, obtaining, first, a set of wavelength shift relative radial delays (each being associated with a bandwidth threshold value according to the above principle), then applying this set of WSRD values to the above formula (1). Another possible implementation could consist of obtaining one value of wavelength shift relative radial delay, then applying this value to the above formula (1) and repeating these two phases iteratively for each remaining value of wavelength shift relative radial delay. For example, the wavelength shift relative radial delays provided as the algorithm progresses are raising or lowering values.

(30) In step 33, the algorithm calculates, for the first generated modified DMD plot (illustrated in FIG. 4B), a first Effective Modal Bandwidth of the multimode fiber, EMBc.sub.1. The algorithm also calculates, for the second generated modified DMD plot (illustrated in FIG. 4C), a second Effective Modal Bandwidth of the multimode fiber, EMBc.sub.2.

(31) In step 34, the algorithm then compares the first calculated Effective Modal Bandwidth EMBc.sub.1 with the first bandwidth threshold value S.sub.1 to which the first wavelength shift relative radial delay .sub.1 is associated, and the second calculated Effective Modal Bandwidth EMBc.sub.2 with the second bandwidth threshold value S.sub.2 to which the second wavelength shift relative radial delay .sub.2 is associated, in order to qualify the actual EMB of the fiber over the wavelength range comprised between 850 nm and 950 nm. This step is illustrated in Table 1 below.

(32) TABLE-US-00001 TABLE 1 .sub.0 = 850 nm EMB.sub.0 >4,700 MHz-km .sub.0 = 850 nm EMBc.sub.1 (.sub.1 = 180 ps/km) >6,700 MHz-km .sub.0 = 850 nm EMBc.sub.2 (.sub.2 = 220 ps/km) >5,200 MHz-km .sub.0 = 850 nm . . .

(33) Optionally, the method also compares the Effective Modal Bandwidth EMBc.sub.0 calculated directly from the raw DMD measurement (obtained in step 31) with the bandwidth threshold of 4,700 MHz-km.

(34) As a function of the results of the step 34, the algorithm delivers an estimate of potential performance in terms of EMB of the multimode fiber over the wavelength range 850 nm-950 nm. As a function of that estimate, in step 35, the fiber being processed is either pre-selected to undergo an in situ EMB measurement or rejected.

(35) If the above set of criteria illustrated in Table 1 is met, this means that the multimode fiber is likely to meet the following actual EMB requirements:

(36) TABLE-US-00002 TABLE 2 Wavelength EMB requirements 850 nm EMB >4,700 MHz-km 875 nm EMB >3,800 MHz-km 900 nm EMB >3,300 MHz-km 925 nm EMB >3,100 MHz-km 950 nm EMB >2,900 MHz-km

(37) The inventors discovered that if a multimode fiber has a first calculated Effective Bandwidth, EMBc.sub.1, higher than 6,700 MHz-km and a second calculated Effective Bandwidth, EMBc.sub.2, higher than 5,200 MHz-km, for first and second wavelength shift relative radial delays equal to 180 ps/km and 220 ps/km respectively, such a fiber is then likely to meet these EMB requirements that are expected to be compliant with 425 Gbps (WDM) error free transmission over 150 m.

(38) As an example, the inventors take a batch of multimode optical fibers, whose actual EMB is assessed according to the qualifying method of the present disclosure. The principle here consists of pre-selecting the fiber or fibers meeting the above criteria.

(39) In that context, each multimode fiber that meets the aforesaid criteria then can be pre-selected, because it is expected to ensure meeting the actual EMB requirement over the wavelength range 850 nm-950 nm. Thus, by pre-selecting only the potentially interesting multimode fibers for in situ EMB measurements, the number of additional actual EMB measurements at other wavelengths over 850 nm to 950 nm is reduced, thereby reducing costs of measuring.

(40) Thus, the invention relies on an adequate adjustment of the EMB thresholds and wavelength shift relative radial delay (Table 1) to guarantee the fiber meets the above actual EMB requirements (Table 2).

(41) It should be noted that the values of EMB threshold and wavelength shift relative radial delay may depend on the chemistry of the refractive index profile of the fiber and the nominal refractive index profile. In the exemplary embodiment described here above, the inventors are focused on 50-micrometer multimode fibers of the type OM4 doped with Germanium and/or Fluorine and/or Phosphorus.

(42) FIG. 4D and FIG. 4E depict the actual DMD measurements performed at 874 nm and at 947 nm, respectively. They enable comparing the modified DMD measurement at the single wavelength 850 nm obtained for .sub.1 equal to 180 ps/km and .sub.2 equal to 220 ps/km, and the actual DMD measurements. It shows that .sub.1 (FIG. 4B) is correlated to the actual DMD measurements performed at 874 nm (FIG. 4D) and .sub.2 (FIG. 4C) is correlated to the actual DMD measurements performed at 874 nm (FIG. 4E). It should be noted that the wavelength shift relative radial delays applied here are positive integers. This enables predicting the actual EMB for wavelengths higher than 850 nm (for example, 874 nm, 899 nm, 926 nm, 947 nm, and 980 nm as illustrated in FIG. 7). Of course, negative integers can be applied so as to predict actual EMB for wavelengths lower than 850 nm (for example, 820 nm, as illustrated in FIG. 7).

(43) FIG. 5 graphically depicts the EMB measured for ten multimode fibers over a wide wavelength range comprised between 850 nm and 950 nm. The requirement curve illustrates the evolution of the aforesaid EMBc.sub.i criteria (see Table 2).

(44) This graph highlights that the fibers for which the curve is higher than the requirement curve are likely to meet the expected EMB requirements for this kind of fiber.

(45) FIGS. 6a and 6b graphically depict the actual EMB of a multimode fiber measured and modeled at a wavelength of 874 nm and of 947 nm, respectively, as a function of the computed effective modal bandwidth (EMBc.sub.i). The dashed vertical lines at 6,700 MHz-km and 5,200 MHz-km represent, respectively, the first and second bandwidth thresholds S.sub.1 and S.sub.2 established in the exemplary embodiment of FIG. 3.

(46) It shows that the calculated Effective Modal Bandwidths EMBc.sub.1 (.sub.1=180 ps/km) and EMBc.sub.2 (.sub.2=220 ps/km) are correlated to the measured Effective Modal Bandwidths at the wavelengths of 874 nm and 947 nm, respectively.

(47) The bandwidth thresholds according to the invention are thus established by comparing the actual values of effective modal bandwidth with the computed values of effective modal bandwidth at the other wavelengths.

(48) FIG. 7 illustrates an example of actual DMD measurements performed at a wavelength of 820, 874, 899, 926, 947, and 980 nm for two multimode optical fibers: Fiber 1 and Fiber 2.

(49) FIG. 8 shows the simplified structure of an assessing device 60 according to a particular embodiment of the invention, which carries out the method shown in FIG. 3 for example.

(50) The device 60 comprises a non-volatile memory 61 (e.g., a read-only memory (ROM) or a hard disk), a volatile memory 63 (e.g., a random access memory or RAM), and a processor 62. The non-volatile memory 61 is a non-transitory computer-readable carrier medium. It stores executable program code instructions, which are executed by the processor 62 in order to enable implementation of the qualifying method described above in relation to FIG. 3.

(51) Upon initialization, the aforementioned program code instructions are transferred from the non-volatile memory 61 to the volatile memory 63 so as to be executed by the processor 62. The volatile memory 63 likewise includes registers for storing the variables and parameters required for this execution.

(52) The device 60 receives as inputs the DMD measurement data 64a, a plurality of wavelength shift relative radial delays 64b, and a plurality of corresponding predetermined bandwidth thresholds 64c. The device 60 generates as outputs an estimate 65 of potential performance in terms of EMB of the multimode fiber over a predetermined wavelength range.

(53) All the steps of the above steering method can be implemented equally well: by the execution of a set of program code instructions executed by a reprogrammable computing machine, such as a PC type apparatus, a DSP (digital signal processor), or a microcontroller. These program code instructions can be stored in a non-transitory computer-readable carrier medium that is detachable (for example, a floppy disk, a CD-ROM, or a DVD-ROM) or non-detachable; or by a dedicated machine or component, such as an FPGA (Field Programmable Gate Array), an ASIC (Application-Specific Integrated Circuit), or any dedicated hardware component.

(54) In other words, the invention is not limited to a purely software-based implementation, in the form of computer program instructions, but it can also be implemented in hardware form or any form combining a hardware portion and a software portion.

(55) Although the present disclosure has been described with reference to one or more examples, workers skilled in the art will recognize that changes may be made in form and detail without departing from the scope of the disclosure and/or the appended claims.