Assembly and method for adjusting BPP of laser output beam

By controlling fiber parameters and inducing microbends through guide displacement, the BPP of high power fiber lasers is stabilized within a desired range, addressing beam quality issues in metal cutting applications.

WO2026030425A1PCT designated stage Publication Date: 2026-02-05IPG PHOTONICS CORP
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Patent Information

Application Number
PCT/US2025/039832
Authority / Receiving Office
WO · WO
Patent Type
Applications
Current Assignee / Owner
Priority Date
2024-07-30
Filing Date
2025-07-30
Publication Date
2026-02-05

AI Technical Summary

Technical Problem

High power fiber lasers exhibit an unacceptably broad variation in beam parameter product (BPP) due to microbending and macrobending, which compromises beam quality, particularly in laser-based metal cutting applications.

Method used

A method and device for controlling fiber parameters to induce a specific concentration of microbends by displacing a guide along a fiber loop, adjusting the BPP to a desired range through incremental positioning and stress application.

Benefits of technology

Stabilizes BPP within a narrow range, ensuring consistent beam quality for high power fiber lasers, particularly in metal cutting processes.

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Abstract

A method for controlling a beam parameter product (BPP) of laser beam guided in a delivery fiber which has at least one stretch thereof looped in a tray is realized by selecting one or more of fiber parameters and applying a force to the looped, fiber stretch, thereby controllably reducing a loop dimeter. The force thus induces a concentration of distributed microbend centers in the looped fiber portion sufficient to provide a BPP vah.se within the desired BPP range. The assembly executing the method includes a tray with the looped fiber stretch and ha.vi.ng, a guide. The guide is controllably displaceable at a preset distance, which is a function of one or mure of selected fiber parameters, between an initial position and at least one downstream position in which, tire looped fiber stretch develops a concentration of rnicrobend centers sufficient to provide the BPP with the desired vah.se within the specified BPP range.
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Description

[0001] ASSEMBLY eND METHOD FOR AD.RIS I I S(1 BPP OF LASER OETlfoT IfoblM

[0002] BACKGROliND

[0003] Field of the Invention

[0004] (0011 The invention generally relates to high power fiber lasers. In particular, the invention relates to a system and method for eontrollably adjusting the geometry of the feeding fiber to create such a cluster of fiber bends that abeam parameter product (BPP) of laser beam guided within the fiber is adjusted to be in the desired BPP range.

[0005]

[0002] Known Art

[0006]

[0003] In mass production of identically configured fiber lasers, the BPP of individual multimode (MM) fiber lasers, particularly those with a kW and higher output varies within an unacceptably broad range. ’Ibe .BPP is the product of a beam’s divergence half-angle and the radios of the beam at the beam waist. This problem is particularly acute for laser-based methods used for cutting metals, such as steel, because of foe extremely strict requirements applied to the cut However, the stability or substantial uniformity of the BPP. which may be somewhat inferior to the best possible BPP. is one of the most important requirements in a variety of industries related to material laser processing and including the above mentioned laser-based metal cutting machines.

[0007]

[0004] Adjustment of laserparameters including foe BPP includes a variety of methods and techniques. Orte of the most broadly used methods for adjusting the BPP includes bending a fiber guiding light. The “bending" refers to the way in which light travels through the fiber. As light propagates through, it is constantly refracted or bent. There are two types of bending that can occur in fiber optics: microbendiug and macrobending and both ty pes may compromise the BPP. [0051 Mierobending is caused by high frequency longitudinal perturbations normally considered as a set of very small bends of the fiber core typically at a radius less than 1 cm. The perturbations couple power among modes In the multimode (MM) fiber. In a single inode (SMI fiber, the power from the guided fundamental is distributed among high order modes. In both cases, the BPP tends to increase which is indicative of deteriorating beam quality.

[0008] [0061 Macrobending is a result of bending the fiber on a scale, typically at a radius of more than I cm. Phis type of heading can occur when the fiber is sf.fojected to more significant changes in temperature, pressure, or mechanical stress, such as those caused by fiber bending or tension. Macrobending causes the light traveling through the fiber to be scattered, resulting in reduced transmiss i on. qu a iity .

[0009]

[0007] The fiber bending is well covered by various scientific and popular publications. For example. US 11858S42 (US:S42), incorporated herein in its entirety, teaches a variety of perturbation methods for controllably affecting rhe fiber to obtain the desired beam parametersincluding the BPP. The US ‘842 schematically illustrates a mechanical guide coming into contact with either the fiber or the profiled guide which affects the fiber / s geometry. With the general description of the fiber perturbing techniques, this patent however is largely silent on the specifics helping one of ordinary skill in the laser arts io apply the patent teaching to the task at hand.

[0010]

[0008] A need therefore exists for a method of controllably selecting fiber parameters to create a distribution of microbend centers sufficient to adjust a BPP of MM fiber laser output to be within the desired BPP range.

[0011]

[0009] Still another .need exists for a device incorporated in a high power MM fiber laser and operative to implement the inventive method.

[0012] [Old] Conceptually, these needs are satisfied by selecting the parameters of foe looped fiber to be bent in the disclosed BPP tuning assembly so as to create the intensity of microbend centers in the bent fiber sufficient to provide a BPP of laser output beam within the desired IW range. The parameters of the fiber may include the outer fiber diameter, core and clad diameters, core to clad diameter ratio (CCDRX fiber loop diameter, fiber length, type of protective coating, fiber area under stress or a combination of the above-fisted parameters.

[0013] [011 j Based on the selected fiber parameters, a controlled force is applied to the coiled fiber in order to tighten the fiber loop to a smaller diameter. As the fiber is being looped, its core develops microbends. The desired concentration of microbends along the fiber loop corresponds to s difference between the initial and final positions of the guide tightening the fiber loop, Since the BPP of (he beam output is a. function of microbends, the controllable displacement of the guide to foe final position increases the BPP to a value m the desired preset BPP range.

[0014]

[0012] hi accordance with one aspect, foe disclosure teaches a method for controlling the BPP of a laser beam guided in a delivery fiber which has at least one portion thereof looped in a tray. Upon selecting at least one of the known fiber parameters. the fiber guide is displaced over a preset distance from its initial position, in which the fiber is under no meaningfitl stress, to a downstream position. As the guide drives the fiber between the positions, the applied stress induces a plurality of distributed microbe-ads in the fiber along the loop. The intensity of the microbends is sufficient to obtain a ifep vatac within the desired BPP range.

[0015]

[0013] In accordance with one feature of the method, the guide is displaced incrementally through a plurality of intermediate positions between the initial and downstream positions. At each of the intermediate and final positions, the BPP and optionally the beam power are measured.

[0016]

[0014] A further feature of the disclosed method relates to a fixed increment step between adjacent intermediate positions. The positions are preferably spaced apart at a fixed distance corresponding to a predetennined BPP increase. This allows the customer to modify the desired BPP to meet local requirements. The increment step or pitch corresponding to the fixed distance may be uniform or nonmmfonn. For example, fee distance between steps 2 aud 3 is twice the distance between steps one I and 2.

[0017] [0151 In accordance with another feature of the disclosed method, a calibration table, containing the BPP value as a function of the preset distance which depends on selected fiber parameter, allows automatically displace the guide to the final position corresponding to fee desired BPP value,

[0018]

[0016] Another aspect of (he disclosure includes a device for controlling the BPP of a laser beam guided in the delivery fiber and implementing the above-disclosed method. The device includes a bay shaped to loop a stretch of the delivery fiber, and a fiber guide displaceable within the tray between original and final positions so as to control! ably deform the fiber. The stress applied to the .fiber during the deformation induces a plurality of distributed microbends with the intensity sufficient to increase the BPP of the laser beam to a value wife in the desired BPP range.

[0019]

[0017] In accordance with one feature of the disclosed device, the Bay is shaped and dimensioned to provide the fi ber wi th one or more loops of the desired radius. The radius In the original position is selected to prevent (he guide from inducing a stress on the looped fiber which thus can be considered marerdbeut.

[0020]

[0018] Another feature of the disclosed device relates to the fiber guide which is configured as a portion of the peripheral wall of the tray displaceable in a plane which extends transversely to a path of the light beam in the fiber. The displacement of the guide is realized by an actuator selected irons one of Linear or stepper motors, piezoelectric stages or rotary motors.

[0021]

[0019] In still another .feature, the peripheral wall is provided with a continuous recess or spaced apart recesses. The recess is configured to prevent the fiber from displacing outside the tray as the guide deforms the looped fi ber during its displacement between the initial and final positions.

[0020] Another feature of the device includes the incremental operation of the actuator displacing the guide through a plurality of intermediate positions on a way to the final position. The length of the incremental step is fixed providing thus a known distance between successive positions which, in turn, correspond to a preset value increase of the BPP.

[0022] [0211 According to yet an other feature, the delivery fiber has a bottle-neck cross-sectional shape. The disclosed fiber shape allows handling multi-kW beam powers.

[0023]

[0022] A further feature or the disclosed device includes a control unit configured with programmable logic devices, memory such as RAM or ROM that stores processor-executable instructions for controlling the actuator, and one or more calibration tables containing a group of BPPs as functions of respective fiber selected parameters.

[0024]

[0023] The above and other features and advantages of the disclosed system are discussed In detai I below. Moreover, it is to be understood that bet h the foregoing information and the following detailed description are merely illustrative examples of various aspects and embodiments, and are intended to provide an overview or framework for understanding the nature aid character of the claimed aspects and features. The features disclosed herein may be combined with other features, and references to "an emhodimeni'' and ‘'an example” are not necessarily mutually exclusive and are intended to indicate that a particular feature, structure, or characteristic described may be included in at least one embodiment.

[0025] BRIEF DESCRIPTION

[0026] [0241 Various structural features of at least one embodiment are discussed below with reference to the accompanying figures, which are not intended to be drawn to scale. The figures are included to provide an illustration and a further understanding of the various aspects, and are Incorporated in and constitute a part of this specification, but are not intended as a definition of the limits of any particular embodiment. The drawings, together with the remainder of the specification, serve to explain principles and operations of the described and claimed aspects and embodiments. In the figures, each identical or nearly identical component that is illustrated in various figures is represented by a like numeral. For purposes of clarity .. not every component may be labeled in every figure. In the figures:

[0027]

[0025] FIG. 1 is a schematic view of a high power fiber laser system provided with the inventive BP? tuning assembly;

[0028] |'O26] FIG. 2.A is a MM delivery fiber utilized in laser system of FIG. 1;

[0029]

[0027] FIG. 2B is an exemplary refractive index profile of the fiber of Fig. 2 A;

[0030]

[0028] FIG. 3 is a perspective view of the disclosed BPP tuning assembly.

[0031]

[0029] FIGs. 4A-B illustrate the tuning assembly of FIG. 3 implementing the disclosed method and having a guide for deforming the fiber located in its Initial position;

[0032]

[0039] FIG. 5 illustrates the tuning assembly with the guide located in a position downstreamfrom the Initial position; and

[0033]

[0031] FIG . 6 is a flow chart illustrating the inventive method.

[0034] SPECIFIC DESCRIPTION

[0035]

[0032] MM high power fiber lasers in a 1 to 10 k W range (and higher.! used in laser material processing, such as cutting, are required to have stable beam divergence varying ftom one laser to another within a range typically no broader than 20-30 % of the optimal value. The disclosed device implementing the inventive method is configured to tune multiple identically configured lasers so that respective BFPs do not fall outside this range,

[0036]

[0033] FIG. I illustrates a diagrammatic optical schematic of a high power MM fiber laser 10 and inventive BPP tuning assembly 14 which is optically coupled to the output of source 12 by means of a fiber train. The latter includes at least a passive output source fiber 22 spliced to a MM delivery passive fiber 20 which, in tuny is coupled to a free space beam guiding device 16 such as a connector of laser head or a beam switch.

[0037]

[0034] Turning to FIGs. 2A, 2B discussed in light of FIG. 1, exemplary MM delivery fiber 20 is Configured with a small diameter input fiber end 24 and a large dimeter output fiber end 26 of arbitrary length. The stretch 28 between fiber ends 24 and 26 respectively is tapered to bridge, for example, a 125 u rn outer dimeter of input fiber end 24 to about 201 uni outer diameter of output fiber end 26. The core diameter is optionally uniform and, in the shown example, is about 0.6 pm. Yet the non-nnifonnly dimensioned. core is conceived within the disclosed subject matter. Also, while the illustrated axial cross-section of liber 20 is installed in the experimental devices, other shapes such as a uniformly dimensioned fiber or a double bottle-neck shaped fiber cari be optionally used. All of the structural limitations disclosed above are given only by way of example and can be changed to meet specific requirements.

[0038] [0351 FIG. 2B illustrates an exemplary refractive index profile of delivery fiber 20 of FIG. 2A. The latter is a multi-core fiber including inner and outer cores 30 and 32 respectively which have a uniform refractive index fe. and respective inner and outer clads 34, 36. In addition to one or multiple cores and respective claddings, fiber 2(1, as one of ordinary skill knows, has an outer protective coating which can be made from a variety of materials. One of the criteria applied to the material coating is its resistance to thermal loads which should be high enough to prevent melting of the coating within assembly 14 at kW power levels. The fiber 20 is configured with a numerical aperture (NA) between the core and inner clad, of about 0, 15±0.01 (An-7. g* 1 ()■’), whereas foe NA between the core and outer clad is about 0.22w0.02 (Au::::7.8*10*'.) Similarly to the above-discussed fiber shape and dimensions, a variety of retractive Ste-p index profiles can be designed by one of ordinary skill in the art. Moreover, delivery fiber 20 is not limited to the illustrated step-index profile and can have a pdrabolic-ihdex profile or graded index profile.

[0039]

[0036] FIG. 3 shows the disclosed BPP tuning assembly 14 including a tray 15 and a guide 42 which is displaceable back and fbrih within the iray among multiple preset positions, In particular, tray 15 is configured with a peripheral wall 40 having advantageously a polygonal cross-section which is defined by multiple stationary wall segments including two side segments 54 and an end segment 52 bridging side segments. As an example, bay 15 may be rectangular or square with the wall segments dimensioned to be in a 5-15 cm length range. The other wall end segment or guide 42 is mounted on a bottom 38 of tray i.5 and has an elongated groove 46 receiving a stop 48 which is detachably coupled to bottom 38, 'The stop 48 limits the travel of guide 42 between two extreme positions defining the maximum length of the guide’s path. The opposing inner surfaces of guide 42 and wall end segment 52 respectively do not have to be flat, as shown in the drawings, and may be provided with respective curvatures or other differently shaped profiles. The guide 42 may have lateral arms or ends received in respective channels (not shown) which are provided in side wall segments 54 and configured io provide the linear motion of guide 42 towards wall end segment 52 relative to stop 48, The tray 15 further has four adjustable scre ws 50 positioning the bay at the desired distance from the tmy support (not shown), The displacement of guide 42 is realized by an actuator 56 having a diagrammatieally shown mechanical link 58 which applies a linear force to guide 42. The actuator 56 may be selected from one of linear or stepper motors, piezoelectric stages or rotary' motors. The manual operation of guide 42 is possible, but may affect the precision of the final result. The guide 42 wall may be stationary. In this case, the configuration of disclosed tuning assembly 14 would require an additional structural element displaceable within tray 15 and functioning as guide 42. (037] Referring to Fifes. 4A. B and 5 in combination with FIG, 3, the operation of BPP tuning assembly 14 is based on the dependence of the BPP on concentration or intensity of mierobend centers in fiber 20. Using assembly 14, these centers are created by applying a force to fiber 20 received in tray 15 by guide 42 which, as it is displaced between different positions, deforms the fiber,

[0040] [0381 In particular, fiber 20 has a stretch of several meters (m), for example 4 m, coiled to a specified diameter and placed within tray 15 as shown in FIG. 5 illustrating the initial position of guide 42. In this position, the fiber loop practically does not experience any stress and thus has the largest diameter. For the experiments, the diameter of the fiber loop free of stress at the initial position of guide 42 was selected to be in a 5-15 cm range. In response to displacement of guide 42 towards wall end segment 52 (FIG. 4A) at the preset distance, which corresponds to the desired force applied to the fiber stretch, the latter is gradually lightened assuming rather the oval shape, as shown in FIG. 4. A As guide 42 keeps advancing, It induces more and more fiber mierobend centers which reach the desired intensity in the final position, of the guide. The intensity is such that the resulting BPP in the final position of guide 42 is characterized by a value within the desired BPP range. Preferably this range is within 20-3(1 % of the optimal BPP specified in advance, but the range may be increased or decreased depending on the customers needs. In the example shown in FIG. 4, the distance between the initial position 0 and final position 5 of FIG. 4B 1$ 14 mm,

[0041]

[0039] Briefly turning back to FIG. 3, the inner surfaces of respective wall segments 52, 54 and 42 are provided with .respective recesses or elongated blind holes 44. When the fiber loop is placed in tray 15, its regions may be received in respective recesses 44. The recesses 44 each have the depth sufficient for the fiber loop not to experience stress’ in its initial position of FIG . 5.During the displacement of guide 42, recesses 44 limit the expansion of the fiber loop in a plane parallel to bottom 38 of tray 15, Additionally. recesses 44 prevent fiber 20 from climbing up peripheral wall 40 of fray 15 and escaping the latter as guide 42 approaches its final position.

[0040] Technologically, the coiled fiber stretch includes output, large diameter fiber end 26 of FIG. 2A. Accordingly, guide 42 interacts with this relatively thick fiber end portion, which can he less affected by always existing thermal loads at kW power levels, as here, than small diameter input fiber end 24 of FIG. 2A.

[0042] 1.041 j FIG. 6 iilusfrat.es the algorithm of a control system 60 configured with control circuits, processors and other programmable logic devices, memory such as RAM or ROM that stores processor-executable instructions for control of BPP tuning assembly including calibration tables. Alter selecting the specified fiber parameter or parameters stored in the memory via the user interface as shown in step 62, guide 42 of FIG. 3 travels ever a preset distance based on the selected fiber parameters to the final position. During the displacement of step 64, guide 42 applies the bending force to fiber 20 which, in the final .position of guide 42. is sufficient to create an intensity of microbends necessary for obtaining a B PP value within the desired range. The distance (or bending force) is contained in calibration tables as a function of fiber parameters stored in control system 60. The liber parameter is selected from the group consisting of the outer fiber diameter, core to clad diameter ratio (CCDR), fiber loop diameter, fiber length, type of protective coating, fiber area under the stress and numerous combinations of the abovelisted parameters. The BPP and optionally Output power are measured in step 66 to make sure that the affected BPP is within the desired BPP.

[0043]

[0642] So for only initial and final guide positions have disclosed. However, aS one of ordinary skill readily realizes, the overall number of positions are not limited to these two. The guide 42 may move selectively through any reasonable number of intermediate positions associated with respective bending forces and, as a consequence, with respective BPPs all stored in the memory and contained in the calibration tables. The guide 42 may antomrtfically slop at any of the intermediate positions while making no stops at previous positions upstream from the desired one. The positions may be spaced apart at a uniform or non-uniform distance. For example, the uniform distance between successive positions may be 2 A 0.1 or each subsequent distance may be twice the previous one, lntbe example shown in FIG, 4. six positions have been set with position 1 spaced from the initial positon at 4 mm, position 2 at 8 mm, position 3 at 10 min, position 4 at 12 mm and position 5 at 14 mm.

[0043] Returning to FIG. 6. if the measured BPP in step 66 is not. within the customer’s specified range, the distance travel led by guide 42 may be altered with the distance and thus force applied to looped fiber 20 altered. Once the measured BPF is within the desired BPP range, this new distance between initial and determined positions or force generated by guide 42 inducing the sufficient concentration of microtend centers is stored in the memory. The disclosed tuning assembly is so simple that with the possibility of having several, intermediate positions of guide- 42. the timing process can be performed by a customer once the device is deployed in the field. Otherwise, the devices delivered to foe customer are already tuned to have the BPP within the customer-specified range.

[0044]

[0044] The features disclosed herein in accordance with the present invention, are not limited in their application to the details of construction and the arrangement of components set forth in the following description or illustrated in the accompanying drawings. These aspects are capable of assuming other embodiments and of being practiced or of being: carried out in various ways. Examples of specific implementations are provided herein for illustrative purposes only and are .not intended to be limiting. In particular, acts, logic elements, components, elements, and features discussed in connection with the disclosed material ate not intended to be excluded from a similar role in any other embodiments.

[0045]

[0645] Having thus described several aspects of at least one example, it is to be appreciated that various alterations, modifications, and improvements will readily occur to those skilled In the art, For instance, examples disclosed herein may also be used in other contexts. Such alterations, modifications, and improvements are intended to be part of this disclosure, and ate intended to be within the scope of the examples discussed herein. Accordingly, foe foregoing description and drawings are by way of example only.

[0046]

[0046] The above and other features and advantages of the disclosed system are discussed in detail below. Moreover, it is to be understood that both the foregoing information and the following detailed description are merely illustrative examples of various -aspects and embodiments, and are intended to provide an overview or framework for understanding the nature and character of the claimed aspects and features. The features disclosed herein may be combined with other features, and references to fom embodiment” and “an example” are not necessarily mutually exclusive and are intended to indicate that a particular feature, structure, or characteristic described may be included in at least one ernbodirnent.

Claims

CLAIMS1. A method for controlling a beam parameter product (BPP) of a User beam, guided in a delivery fiber which has at [east one portion thereof looped in a tray, compnsmg: selecting one or more of fiber parameters; and applying a force to the looped fiber portion, thereby controHably reducing a loop dimeter so as to induce a concentration of distributed miorobend centers in the looped fiber portion sufficient to provide a B?P within a desired BPP range.

2. The method of claim 1 , wherein the force application includes linearly displacing a guide -ai a preset distance from an initial position, in which the looped portion is under no stress, to at least one downstream position, in which the fiber looped portion has the reduced diameter, wherein the preset distance corresponds to the force which induces the concentration of the distributed microbend centers.

3. The method of claim 2, wherein the displaceable guide is one of peripheral wall segments of the tray.

4. The method of claim 2, wherein the force application .further includes controllably displacing the guide among sequentially located positions downstream from the initial position, the sequential positions of the guide correspond to respective gradually increasing preset BPP values.

5. The method of claim 4, wherein the sequential positions of the guide are spaced from one another at a uni form or non-uniform distance.

6. The method of claim 4 further comprising displacing the guide directly between the initial position and one or more selected sequential positions not stopping at any position upstream ftoffl rhe selected one.

7. The method of claim I , wherein the fiber parameter is selected front the group consisting of an outer fiber diameter, core and clad diameters, core to clad diameter ratio (CCDR), diameter of the loop, fiber length, protective coating, fiber area under stress and a combination of the abovelisted parameters.

8. A tuning assembly for controllably adjusting a beam parameter product (BPP) of a laser beam guided in a delivery fiber, comprising:a tray receiving a .stretch of the delivery fiber and configured to provide the received fiber stretch with at least one or more loops; and a guide controllably displaceable at a preset distance within the tray, which is a function of one or more of a plurality of selected fiber parameters, between an initial position and at least one downstream position where the looped fiber stretch is controllable stressed to develop a concentration of microbend centers sullicieni to alter the BPP of the laser beam to a value within a desired BPP range.

9. The tuning assembly of claim 8, wherein the tray is configured with a polygonal shape and dimensioned to provide the looped fiber stretch wi th a. desired radius in the initial position of the guide in which the lopped fiber stretch, is under no stress, it). The tuning assembly ofclaim 8, wherein the tray has a peripheral wall including a multiplicity of wall segments, at least one of the peripheral wall segments being configured as the guide linearly displaceable at a preset distance into the tray to ths downstream position while applying a force to the looped fiber stretch.

11. The tuning assembly of claim 8, wherein the guide is controllably displaceable among a plurality of positions located downstream from the initial position and spaced therefrom at respective preset distances.

12. The tuning assembly of claim 11, wherein the posi tions ate spaced apart, at a uniform or non- uniform distance.

13. The tuning assembly of claim 8 further comprising an actuator coupled to and controllably displacing the guide in a plane at the preset distance which extends transversely to a path of the laser beam in the looped fiber stretch.

14. The tuning assembly of claim 10, wherein the peripheral wall Of the tray has an inner Surface provided with a continuous or spaced apart blind holes configured fo receive the looped fiber stretch in the initial position of the guide, the blind hole being configured to support the received looped fiber stretch as the guide is displaced between the initial and downstream positions.

15. The tuning assembly of claim 8 further comprising a control unit operatively connected to and displacing the guide at foe preset distance In response to the selected fiber parameters, displacing configured with programmable logic devices, memory such as RAM or ROM thatstores processdr-exeeutabie instructions far control of the actuator, one or more calibration tables containing 3 group of BPPs as functions of the fiber parameter, wherein the fiber parameter is selected from the group consisting of an outer fiber diameter, core and clad diameters, core to clad, diameter ratio (CCDR), diameter of tire loopy fiber length, protective coating, fiber area under stress and a combination of the abo ve-hated parameters.