Stranded and non-stranded cable designs for hollow core fiber

Abstract

An optical fiber cable includes a hollow-core optical fiber. The cable is configured to have a low excess fiber length (EFL) of the hollow-core fiber. The cable is further configured to maintain a high minimum bending radius of the hollow-core fiber to prevent permanent damage to the hollow-core fiber during installation and operation of the cable.

Description

Title: STRANDED AND NON-STRANDED CABLE DESIGNS FOR HOLLOW CORE FIBERCROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of priority of U.S. Provisional Application No. 63 / 673,367, filed on July 19, 2024, the content of which is relied upon and incorporated herein by reference in its entirety.BACKGROUND

[0002] Optical fiber cables generally include one or more optical fibers that are disposed within a cable jacket. Such optical fiber cables may include any of various additional elements such as strength members, water-blocking elements, buffer tubes, or the like, depending upon an application of the optical fiber cable.

[0003] Conventionally, an optical fiber includes a core, a cladding, and one or more coatings that are applied to the cladding in order to protect the optical fiber from damage or stresses that may induce attenuation of an optical signal that propagates in the core. In a conventional optical fiber, the core is a solid, glass element within which an optical signal will propagate.

[0004] More recently, hollow-core fibers have been developed. Hollow-core fibers have various constructions, but are generally characterized in that an optical signal propagates through non-solid free space in air or a vacuum (i.e., a “hollow core”). Due to the propagation of an optical signal in air or vacuum rather than a solid glass core of a conventional optical fiber (a “solid-core fiber”), the latency of an optical signal propagating in a hollow-core fiber is typically lower than the latency of an optical signal propagating in a solid-core fiber.SUMMARY OF THE DISCLOSURE

[0005] The following is a brief summary of subject matter that is described in greater detail herein. This summary is not intended to be limiting as to the scope of the claims.

[0006] Various technologies pertaining to an optical fiber cable that includes at least one hollow-core fiber are described herein. An exemplary optical fiber cable includes a cable jacket having an interior cavity disposed therein. The cable further includes a hollow-core optical fiber disposed in a longitudinal manner (i.e., not stranded). The hollow-core fiber can have an excess fiber length (EFL) of less than or equal to 0.2% in order to maintain a sufficient minimum radius of curvature to avoid permanent damage to the hollow-core fiber.

[0007] Another exemplary optical fiber cable includes a cable jacket having an interior cavity disposed therein. In this cable, a hollow-core fiber is disposed within a buffer tube that is helically stranded around a central strength member. In such cable, a diameter of the central strength member and a lay length of the buffer tube can be selected so as to maintain a minimum radius of curvature of 200 mm when the cable lays straight at a temperature of 20°C.

[0008] The above summary presents a simplified summary in order to provide a basic understanding of some aspects of the systems and / or methods discussed herein. This summary is not an extensive overview of the systems and / or methods discussed herein. It is not intended to identify key or critical elements or to delineate the scope of such systems and / or methods. Its sole purpose is to present some concepts in a simplified form as a prelude to the more detailed description that is presented later.BRIEF DESCRIPTION OF THE DRAWINGS

[0009] The accompanying drawings are included to provide a further understanding, and are incorporated in and constitute a part of this specification. The drawings illustrate one or more embodiments, and together with the description serve to explain principles and operation of the various embodiments.

[0010] FIG. 1 depicts an exemplary hollow-core optical fiber.

[0011] FIG. 2 is a cross-sectional view of an exemplary optical fiber cable that includes a hollow-core fiber.

[0012] FIG. 3 is a cross-sectional view of another exemplary optical fiber cable that includes a hollow-core fiber.

[0013] FIG. 4 is a plot illustrating relationships among various construction parameters of an optical fiber cable and a radius of curvature of an optical fiber.

[0014] FIG. 5 is a cross-sectional view of still another exemplary optical fiber cable.

[0015] FIG. 6 is a plot illustrating relationships among various construction parameters of another optical fiber cable and a radius of curvature of an optical fiber.

[0016] FIG. 7 is a plot illustrating relationships among various construction parameters of yet another optical fiber cable and a radius of curvature of an optical fiber.DETAILED DESCRIPTION

[0017] Various technologies pertaining to an optical fiber cable including at least onehollow-core fiber are now described with reference to the drawings, wherein like reference numerals are used to refer to like elements throughout. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of one or more aspects. It may be evident, however, that such aspect(s) may be practiced without these specific details. In other instances, well-known structures and devices may be shown in block diagram form in order to facilitate describing one or more aspects. Further, it is to be understood that functionality that is described as being carried out by certain system components may be performed by multiple components. Similarly, for instance, a component may be configured to perform functionality that is described as being carried out by multiple components.

[0018] Moreover, the term “or” is intended to mean an inclusive “or” rather than an exclusive “or”. That is, unless specified otherwise, or clear from the context, the phrase “X employs A or B” is intended to mean any of the natural inclusive permutations. That is, the phrase “X employs A or B” is satisfied by any of the following instances: X employs A; X employs B; or X employs both A and B. In addition, the articles “a” and “an” as used in this application and the appended claims should generally be construed to mean “one or more” unless specified otherwise or clear from the context to be directed to a singular form. Additionally, as used herein, the term “exemplary” is intended to mean serving as an illustration or example of something, and is not intended to indicate a preference.

[0019] While hollow-core fibers may be suitable for transmitting optical signals with lower latency than conventional solid-core fibers, various hollow-core fiber designs may be more susceptible than solid-core fibers to damage and / or stress-induced attenuation. Accordingly, optical fiber cables incorporating hollow-core fibers are subject to different design considerations and constraints than cables that include only solid-core fibers.

[0020] Referring now to Fig. 1, a cross-sectional view of an exemplary hollow-core fiber 100 is illustrated. The hollow-core fiber 100 comprises an outer cladding 102, a plurality of capillary tubes 104, and a hollow core region 106 defined by the plurality of capillary tubes 104. The outer cladding 102 can comprise or consist of a silica-based glass. Moreover, each of the capillary tubes 104 can comprise or consist of a silica-based glass. The capillary tubes 104 are each depicted in the hollow-core fiber 100 as having a plurality of nested capillaries 108, wherein a nested capillary 108 is a tube that is disposed within an interior cavity 110 of its respective capillary tube 104. The nested capillaries 108 can each comprise or consist of a silica-based glass. The hollow-core fiber 100 depicted in Fig. 1 is shown as having six of thecapillary tubes 104, but it is to be appreciated that a hollow-core fiber can have various numbers of capillary tubes (e.g., 2, 4, 6, or 8 capillary tubes). Furthermore, the hollow-core fiber 100 depicted in Fig. 1 is shown as having three nested capillaries 108 in each of the capillary tubes 104, but it is to be appreciated that a hollow-core fiber can have various numbers of nested capillaries disposed within a single capillary tube (e.g., 1, 2, 3, 4, or 5 nested capillaries). It is further to be appreciated that in embodiments wherein the hollow-core fiber 100 has a plurality of the nested capillaries 108 within a single capillary tube 104, the nested capillaries 108 within a same capillary tube 104 may be the same size or different sizes.

[0021] In exemplary embodiments, the hollow-core fiber 100 can include one or more coating layers (not shown) on the exterior surface of the outer cladding 102. In some embodiments, these coatings may be substantially similar to the primary and secondary coatings of conventional solid-core fibers. In further embodiments, one or more of the coatings can be or include a colorant to facilitate identification of the hollow-core fiber from among a group of optical fibers.

[0022] The hollow-core fiber 100 depicted in Fig. 1 is one example of a category of hollow-core fibers that is referred to as an anti-resonant hollow-core fiber. It is to be appreciated, however, that optical fiber cables described herein that include a hollow-core fiber are not so-limited. For instance, an optical fiber cable described herein can incorporate types of hollow-core fibers other than anti-resonant hollow-core fibers. In another example, an optical fiber cable described herein can incorporate an anti-resonant hollow-core fiber that has a design differing from that shown in Fig. 1. Various additional aspects relating to hollowcore optical fibers are described in at least United States Patent Application Publication No. 2024 / 0036252, the disclosure of which is incorporated herein by reference.

[0023] Generally, when an optical fiber disposed within an optical fiber cable is longer than the cable itself, the optical fiber will exhibit bending even when the cable is positioned in a substantially straight manner. The amount by which a length of an optical fiber exceeds the length of the cable in which it is disposed is referred to as excess fiber length, or EFL. The EFL of an optical fiber in a cable is typically expressed as a percentage of the length of the cable by which the length of the optical fiber exceeds the length of the cable.

[0024] A positive EFL of an optical fiber in a cable generally causes that optical fiber to bend to take a shape approximating a sinusoid within a cavity in which the optical fiber is disposed (absent constraint on the fiber such as encapsulation in a cable jacket). Solid-corefibers commonly used in optical fiber cables today are often capable of some amount of this EFL-induced bending without exhibiting unacceptable attenuation. Excessive bending of this kind can cause attenuation of signals propagating in the optical fiber that exceeds desired performance thresholds for an optical fiber cable. However, the EFL of the optical fiber can also allow the optical fiber to move to lower-stress positions during bending of the cable than would be possible with a low or zero EFL. Thus, to tolerate tighter bends of a cable than would be possible with a lower EFL, various cables incorporating conventional solid-core fibers are designed to target a positive, non-zero EFL.

[0025] Referring now to Fig. 2, an exemplary optical fiber cable 200 is illustrated, wherein the optical fiber cable 200 is configured to mitigate the potential for optical signal attenuation due to stresses on a hollow-core fiber. In particular, the optical fiber cable 200 is configured to include one or more hollow-core fibers having a low or zero EFL. While hollowcore fiber designs vary, many hollow-core fibers are far less robust to attenuation than conventional solid-core fibers. Further, below a certain minimum radius of curvature, even conventional solid-core fibers are prone to break, rendering the fibers permanently unusable for transmission of an optical signal.

[0026] It is expected that many hollow-core fiber designs will exhibit relatively large minimum bending radii prior to structural failure. In other words, it is expected that hollowcore fibers will break or be rendered irreversibly unable to transmit an optical signal without undue attenuation after being subjected to bends that are commonly tolerated by solid-core fibers today. Further, it is expected that while some hollow-core fiber designs will endure sharp bends without sustaining structural damage, many such designs will nevertheless will display higher than desired attenuation at bends tolerated by solid-core fibers. Whereas various solid-core fibers today are capable of a minimum radius of curvature before break or unacceptable attenuation of less than 7.5mm, current hollow-core fiber designs may have minimum a minimum radius of curvature before break or higher than acceptable attenuation of 200mm or greater.

[0027] Accordingly, the optical fiber cable 200 is designed to ensure that a hollowcore fiber disposed therein maintains a minimum radius of curvature that is greater than 200 mm. The optical fiber cable 200 comprises a cable jacket 202 having an interior cavity 204 disposed therein. The cable jacket 202 is formed in a shape that has a major axis 206 and a minor axis 208, such that in exterior profile the cable jacket 202 is wider than it is tall. In exemplary embodiments, the cable jacket 202 is formed as a rectangle with curved ends 209disposed on opposite sides of the interior cavity 204 along the major axis 206. The cavity 204 can be rectangular in shape, with a major axis of the cavity 204 aligned along the major axis 206 of the cable 200.

[0028] The optical fiber cable 200 further comprises a plurality of optical fibers 212. The plurality of optical fibers 212 includes at least one hollow-core fiber. In exemplary embodiments, each of the plurality of optical fibers 212 can be a hollow-core fiber, or the plurality of optical fibers 212 can include a mix of hollow-core fibers and conventional solidcore fibers. As used herein, the term “solid-core fiber” is intended to include not only singlecore single-mode optical fiber but multimode optical fiber, multi-core optical fiber, and substantially any other optical fiber for which a solid is the medium of transmission of an optical signal from one end of the optical fiber to the other.

[0029] In exemplary embodiments, the optical fibers 212 are configured as a rigid, planar ribbon of optical fibers. By way of example, the optical fibers 212 can be encapsulated in a cured matrix material (not shown) that is configured to maintain a planar configuration of the optical fibers 212 when the optical fibers 212 are subjected to stresses. In various embodiments, the optical fibers 212 can be configured as a rigid, planar ribbon that comprises a plurality of ribbon matrix layers. In such embodiments, each of the ribbon matrix layers can have different physical properties such as hardness or elastic modulus, thereby providing protection from different kinds of stresses, impacts, or the like. In some embodiments, the optical fibers 212 can be encapsulated in an extruded polymer material to form the rigid, planar ribbon.

[0030] In embodiments wherein the optical fibers 212 are configured in a rigid, planar ribbon, the ribbon can have any of various fiber counts such as, but not limited to, 8, 12, 16, 24, 32, 36, or 48 fibers. The ribbon has a height of one fiber. In some embodiments, the optical fibers 212 of the cable 200 can be arranged in a plurality of such ribbons that are then arranged on top of one another, thereby forming a ribbon stack. In general, a wider ribbon yields a shorter ribbon stack for a same number of the optical fibers 212. Thus, it may be desirable to employ wide ribbons in the optical fiber cable 200 to maintain a small distance between the optical fibers 212 and a neutral bending axis of the cable 200, which typically yields less attenuation than when the optical fibers 212 are positioned further away from the neutral axis.

[0031] The optical fiber cable 200 further comprises strength elements 210 that aredisposed on opposite sides of the cavity 204 along the major axis 206. The strength elements 210 extend along a length of the cable 200 (i.e., looking into the page in Fig. 2). In various exemplary embodiments, the strength elements 210 can be glass-reinforced plastic elements (GRPs), aramid-reinforced plastic elements (ARPs), steel wires, etc. Furthermore, while the optical fiber cable 200 is illustrated with two strength elements 210, it is to be appreciated that each of the depicted strength elements 210 can instead comprise a plurality of strength elements. The strength elements 210 provide tensile strength to the cable 200, but also resist thermal contraction of the cable jacket 202 at low temperature that can otherwise cause an increase in the EFL of the fibers 212.

[0032] In the embodiment depicted in Fig. 2, a height, A, of the cavity 204 along the minor axis 208 is greater than a diameter, d, of the strength elements 210. Setting h to be greater than d can facilitate access to the fibers 210 by an installer of the cable 200 in the field. For instance, the installer can align a tool with one or more of the strength elements 210. However, it is to be appreciated that in other embodiments, the height h of the cavity 204 can be selected to be less than the diameter d of the strength elements 210. In these embodiments, the strength elements 210 can prevent stresses that are applied to the cable 200 during installation from being transmitted to the cavity 204 and a hollow-core fiber in the optical fibers 212. The optical fiber cable 200 is depicted as including foam layers 214, 216 within the cavity 204. In exemplary embodiments, the foam layers 214, 216 are disposed on opposite sides of the cavity 204 along the minor axis 208 such that the optical fibers 212 are disposed between the foam layers 214, 216. The foam layers 214, 216 can provide additional cushioning for the optical fibers 212 during bending of the cable 200. In various embodiments, the foam layers 214, 216 can have a water-blocking material disposed thereon / therein (e.g., SAP powder).

[0033] In some embodiments, an optical fiber cable can include buffer tubes. Referring now to Fig. 3, another exemplary optical fiber cable 300 is illustrated in which a hollow-core fiber is disposed within a buffer tube. The optical fiber cable 300 is similar in construction to the optical fiber cable 200 and includes the cable jacket 202 having the cavity 204 formed therein with a major axis 206 and minor axis 208 such that the cable jacket 202 is wider than it is tall. The cable 300 further includes the strength elements 210 and the optical fibers 212, including one or more hollow-core fibers.

[0034] The cable 300 further comprises one or more buffer tubes 302 disposed within the cavity 204. Each of the buffer tubes 302 has one or more of the optical fibers 212 disposedtherein. The buffer tubes 302 can be formed of various extrudable polymers such as polyethylene (PE) or polypropylene (PP). In exemplary embodiments, the buffer tubes 302 can be a two-layer construction wherein a first layer comprises polycarbonate and a second layer comprises polybutylene terephthalate (PBT). Such two-layer construction can provide additional mechanical protection for the hollow-core fibers in the optical fibers 212 beyond that provided by PE or PP buffer tubes 302.

[0035] The inventors have identified that, in a cable constructed in similar fashion to the optical cables 200, 300, the EFL of the optical fibers 212 and the height h of the cavity 204 are factors that should be controlled to maintain a necessary minimum radius of curvature for a hollow-core optical fiber. In particular, the inventors conducted an analysis of a cable constructed in similar manner to the optical fiber cable 200 depicted in Fig. 2 and established relationships among EFL of the fibers 212, height h of the cavity 204, and minimum radius of curvature of the fibers 212.

[0036] A plot 400 depicting results of this analysis is depicted in Fig. 4. Along the x- axis of the plot 400 is the bending pitch of the optical fibers 212 in millimeters, where the bending pitch refers to the period of sinusoidal bending of the optical fibers 212 due to EFL of the fibers 212. Along the y-axis of the plot 400 is the height h of the cavity 204. The cavity height h and the EFL of the fibers 112 are design parameters that may be selected by a designer of the cable 200. The blue lines along the plot 400 indicate the relationship between cavity height and pitch for various levels of EFL. In other words, the blue lines of plot 400 indicate a bending pitch to which the fibers 212 are subjected for various heights of the cavity 204. The green lines along the plot 400 indicate the relationship among minimum radius of curvature of the fibers 212, the cavity height, and the pitch. In other words, for each green line, points above the green line indicate combinations of cavity height and pitch that will cause the optical fibers 212 to experience a radius of curvature below the minimum radius of curvature specified for such green line. The plot 400 assumes that the cable 200 is straight (i.e., lying flat) at a temperature of 20°C.

[0037] A minimum radius of curvature of 200 mm is likely to be required for many hollow-core fiber designs. Accordingly, combinations of cavity height and bending pitch that would cause the optical fibers 212 to experience a radius of curvature below 200 mm are shaded in red in the plot 400. As can be observed from the plot 400, as EFL exceeds about 0.2%, a minimum cavity height necessary to maintain a fiber radius of curvature below 200 mm rapidly increases. Accordingly, in various embodiments, an optical fiber cable (e.g., thecables 200, 300) that incorporates a hollow-core fiber has an EFL of less than or equal to 0.2%. In exemplary embodiments, the optical fiber cable 200 can be configured to have an EFL of less than or equal to 0.1% when the height h of the cavity 204 is less than or equal to 1.75 mm. In further exemplary embodiments, the optical fiber cable 200 can be configured to have a cavity height of greater than or equal to 3.25 mm, so that the optical fibers 212 do not experience a minimum radius of curvature less than 200 mm at 0.2% EFL.

[0038] Referring now to Fig. 5, another exemplary optical fiber cable 500 is illustrated in cross-section. The cable 500 includes a cable jacket 502 having an interior cavity 504. The cable jacket 502 has a substantially circular outside profile in cross-section. In exemplary embodiments, the interior cavity 504 may have a substantially circular cross-section. The cable 500 comprises a plurality of buffer tubes 506 and a central strength member 508 that are disposed within the interior cavity 504. The cable 500 further comprises a plurality of optical fibers 510, wherein each of the optical fibers 510 are disposed within one of the buffer tubes 506. At least one of the optical fibers 510 is a hollow-core fiber.

[0039] In exemplary embodiments, the buffer tubes 506 can be helically stranded about the central strength member 508. The inventors have determined that a radius of curvature of a hollow-core fiber disposed within one of the buffer tubes 506 is a function of a diameter of the central strength member 508, an outside diameter of the buffer tubes 506 (assuming that the buffer tubes 506 have substantially identical outside diameters), and a lay length of the helical stranding of the buffer tubes 506.

[0040] Referring now to Fig. 6, a plot 600 illustrating a relationship between lay length of the buffer tubes 506, diameter of the central strength member 508, and radius of curvature of a hollow-core fiber in the optical fibers 510 is illustrated. In the plot 600, lay length in millimeters is shown along the x-axis and diameter of the central strength member 508 is shown along the -axis. In the plot 600, a curve is shown for each of several radii of curvature of a hollow-core fiber in the fibers 510, wherein each curve indicates combinations of lay length and central strength member diameter that yield the indicated radius of curvature. The plot 600 assumes zero EFL for the optical fibers 510 and a 1.5 mm outside diameter of the buffer tubes 506. As in the plot 400, combinations of lay length and central strength member diameter that yield a radius of curvature for a hollow-core fiber of less than 200 mm are shaded red to indicate the likelihood of permanent damage to the hollow-core fiber for such combinations. In general, the inventors have observed that embodiments of the cable 500 that satisfy the inequality d < 0.092 / - 10.5, where d is the diameter of the centralstrength member 508 and I is the lay length of the buffer tubes 506, are likely to maintain the hollow-core fiber with a necessary minimum radius of curvature to avoid fiber breaks when the buffer tubes 506 have an outside diameter of 1.5 mm ±5%.

[0041] Referring now to Fig. 7, a plot 700 illustrating another relationship between lay length of the buffer tubes 506, diameter of the central strength member 508, and radius of curvature of a hollow-core fiber in the optical fibers 510 is illustrated. The plot 700 is substantially similar to the plot 600, but illustrates the relationships among lay length, central strength member diameter, and radius of curvature of the fibers 510 when the buffer tubes 506 have outside diameters of 2.5 mm. The inventors have found that embodiments of the optical fiber cable 500 wherein the buffer tubes 506 have outside diameters of 2.5 mm ±5% and that satisfy the inequality d < 0.075 / - 6.875 are likely to maintain a hollow-core fiber in the fibers 510 with a necessary minimum radius of curvature to avoid breaks of the hollowcore optical fiber.

[0042] In any of the cables 200, 300, 500, the optical fibers 212, 510 can be configured as loose fibers or intermittently-bonded, non-planar ribbons.

[0043] What has been described above includes examples of one or more embodiments. It is, of course, not possible to describe every conceivable modification or alteration of the above systems, devices, or methodologies for purposes of describing the aforementioned aspects, but one of ordinary skill in the art can recognize that many further modifications and permutations of various aspects are possible. Accordingly, the described aspects are intended to embrace all such alterations, modifications, and variations that fall within the spirit and scope of the appended claims. Furthermore, to the extent that the term “includes” is used in either the detailed description or the claims, such term is intended to be inclusive in a manner similar to the term “comprising” as “comprising” is interpreted when employed as a transitional word in a claim.

Claims

CLAIMSWhat is claimed is:

1. An optical fiber cable, comprising: a cable jacket that extends along a length of the optical fiber cable; a hollow-core optical fiber surrounded by the cable jacket, the hollow-core optical fiber extending along the length of the optical fiber cable and having an excess fiber length (EFL) of 0.2% or less.

2. The optical fiber cable of claim 1, wherein the cable jacket has a cavity formed therein, and wherein further the cavity is sized to maintain a minimum radius of curvature of the hollow-core optical fiber of greater than or equal to 200 mm when the optical fiber cable is kept straight at 20°C.

3. The optical fiber cable of claim 2, wherein the hollow-core optical fiber has an EFL of 0.1% or less and a height of the cavity is greater than or equal to 1.75 mm.

4. The optical fiber cable of claim 2, wherein a height of the cavity is greater than or equal to 3.25 mm.

5. The optical fiber cable of claim 2, further comprising a plurality of strength members, wherein the cable jacket has a major axis and a minor axis such that the cable jacket is wider than the cable jacket is tall, wherein at least two of the plurality of strength members are disposed on opposite sides of the cavity along the major axis.

6. The optical fiber cable of claim 5, wherein the plurality of strength members consists of two strength members, the two strength members disposed on the opposite sides of the cavity along the major axis, and wherein the two strength members each have a diameter that is greater than or equal to the height of the cavity.

7. The optical fiber cable of claim 2, wherein the cavity is filled with a water-blocking gel.

8. The optical fiber cable of claim 2, further comprising: a first foam layer disposed along a first side of the cavity; and a second foam layer disposed along a second side of the cavity, wherein the hollowcore optical fiber is disposed between the first foam layer and the second foam layer.

9. An optical fiber cable, comprising: a plurality of buffer tubes; a hollow-core optical fiber disposed within one of the plurality of buffer tubes; a central strength member, the plurality of buffer tubes being helically stranded about the central strength member, wherein a diameter d of the central strength member and a lay length I of the plurality of buffer tubes around the central strength member satisfy the following inequality: d < 0.075 / - 6.875 ;and a cable jacket that surrounds the plurality of buffer tubes, wherein further a minimum radius of curvature of the hollow-core optical fiber when the optical fiber cable is kept straight at a temperature of 20°C is less than or equal to 200 mm10. The optical fiber cable of claim 9, wherein each of the plurality of buffer tubes has an outside diameter of 2.5 mm ± 5%.

11. The optical fiber cable of claim 9, wherein each of the plurality of buffer tubes has an outside diameter of 1.5 mm ± 5% and wherein d and I satisfy the following inequality: d < 0.092 / - 10.5.

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