The FPC and the CD have SNR levels higher than the CC when the vibration amplitude increases (scenarios from 1 to 100 and from 201 to 300). The reflected wavelength changes with the grating period, broadening the reflected spectrum. 22of 1995 Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. PD 1. It must be noticed that each of these demodulation algorithms can be selected independently from the type of spectral interrogator used. B 2014 by the authors; licensee MDPI, Basel, Switzerland. It is worth noticing that, in this procedure, no sensor was adopted to measure the applied transverse load. Thus far, five (or six) types of FBG have been reported with different underlying photosensitivity mechanisms. In this approach, the grating is divided into short periodic segments, each characterized by a transfer-matrix based on the coupled-mode theory [28]. The primary application of fiber Bragg gratings is in optical communications systems. Ultrasensitive temperature sensor based on a urethane acrylate-coated off-axis spiral long period fiber grating. These algorithms were the maximum detection (MD), the centroid detection (CD), the cross-correlation (CC) and fast phase-correlation (FPC). %PDF-1.2 % The plate is clamped along one of its shorter edges and attached to a shaker at the opposite edge. It is shown that by current tuning it is possible to interrogate fiber Bragg gratings at frequencies up to 100 kHz. This however does not account for all the refractive index profile features. Statistically speaking, however, the experimental results are able to confirm the trends identified by the simulations. [21], Addressed fiber Bragg structures (AFBS) is an emerging class of FBGs developed in order to simplify interrogation and enhance performance of FBG-based sensors. This means that fiber Bragg gratings can be used as sensing elements in optical fiber sensors. Technically, the absorbent material is the sensing element, converting the amount of gas to a strain. WebFiber Grating Spectra Turan Erdogan, Member, IEEE (Invited Paper) Abstract In this paper, we describe the spectral charac-teristics that can be achieved in ber reection (Bragg) In this way, the spectral vibration associated with each FBG is retrieved and processed using the MD, CD, CC and FPC algorithms. These two indices provided information about the broadness of the peak region and about the amount of spectral asymmetry, respectively. those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). Steve Vanlanduit and Francis Berghmans helped in interpreting the results, revising and writing the paper. Two, three, four and many slits 2012; Zhang et al. The central wavelength of AFBS can be defined without scanning its spectral response, unlike conventional FBGs that are probed by optoelectronic interrogators. A frequency-doubled Argon-ion laser Feature papers are submitted upon individual invitation or recommendation by the scientific editors and must receive A sequential writing method with continuous UV radiation that overcomes these problems has been demonstrated and is now used commercially. 0000023777 00000 n For each simulation, we evaluate the amount and type of distortion using two indices: the full width at half maximum (FWHM) and the unbalance (UNB). The authors are grateful for partial financial support of the Research Foundation, Flanders (FWO), and of Belgian Science Policy (BELSPO) for the Interuniversity Attraction Pole P7/35 [emailprotected]: towards smart photonics in 2020. Hill, K.O. The MD used in this paper computes the wavelength of maximum reflectivity using the following equation: The centroid detection algorithm computes the wavelength c corresponding to the geometrical centroid of the reflection spectrum by means of the following equation: Another scheme for demodulating of FBG reflection spectra uses the cross-correlation algorithm [11]. [1] discovered that refractive index variation (i.e., gratings) can be formed in optical fibers. However, these cracks can be very localized so as to not play a major role in scattering loss if properly prepared.[12][13]. T WebBragg gratings in optical fibers in multimode propagation are investigated theoretically by using the coupled-mode theory and considering two modes coupling. Fiber laser source/analyzer for Bragg grating sensor array interrogation. WebFiber Bragg grating spectra in multimode optical fibers. Webadshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A The CFBG has the fundamental Bragg resonance at 1,570 nm and a bandwidth of 20 nm at 3 dB. Paper should be a substantial original Article that involves several techniques or approaches, provides an outlook for A grating possessing a chirp has the property of adding dispersionnamely, different wavelengths reflected from the grating will be subject to different delays. {\displaystyle n_{3}-n_{2}} WebThe model 77303 Grating Assembly is designed for installation into the Oriel 77250 Hand Operated Monochromator. The term apodization refers to the grading of the refractive index to approach zero at the end of the grating. For the 8 tilted WTFBG, the tilted plane grating breaks the symmetry of mode coupling. [15][citation needed] This supported the development of the first distributed feedback (DFB) fiber lasers, and also laid the groundwork for most complex gratings that followed, including the sampled gratings first made by Peter Hill and colleagues in Australia. WebThis work presents a new method for monitoring the preload torque in a composite bolted connection using an embedded fiber Bragg grating sensor. Search more than 4000 manufacturers and suppliers of photonics products and services worldwide: Few technologies have impacted the modern world like the laser has. The gratings were inscribed using a single 40mJ pulse from an excimer laser at 248nm. To suppress the spectral broadening produced by SPM and FWM, we first propose to utilize a phase-shifted (PS)-LPFG to filter the broadened spectrum and apply it In this paper, we proposed the novel design of an all-fiber grating-assisted bend sensor, featuring Bragg gratings inscribed in four cores of a silica glass fiber rod assembly with the external diameter of 2.1 mm. The following subsections recall the working principle of each of these algorithms. Accuracy A(FWHM, UNB) and SNR(FWHM, UNB) were computed with the following equations: Figure 3 shows the obtained SNR levels as a function of the indices FWHM and UNB. Disclaimer/Publishers Note: The statements, opinions and data contained in all publications are solely Figures 5, 6, 78 show the accuracy of the four algorithms as a function of the FWHM and UNB indices and the simulated scenarios. The vibration measurements are then repeated and the new SNR levels computed. B B Photosensitivity in optical fiber waveguides: Application to reflection filter fabrication. In this paper, we investigate modification of transmission spectra of long-period fiber grating structures with an acoustic shock front propagating along the fiber. The first in-fiber Bragg grating was demonstrated by Ken Hill in 1978. 0000021536 00000 n Apodized gratings offer significant improvement in side-lobe suppression while maintaining reflectivity and a narrow bandwidth. However, standard fibers can be used if the photosensitivity is enhanced by pre-soaking the fiber in hydrogen. As shown above, in the strong grating limit (i.e., for large showed that it was possible to inscribe gratings of ~100% (>99.8%) reflectance with a single UV pulse in fibers on the draw tower. Once optimized, these monolithic cavities do not need realignment during the life of the device, removing any cleaning and degradation of fiber surface from the maintenance schedule of the laser. [27] This method is specifically applicable to the fabrication of long period fiber gratings. These indices, which are defined in Section 3.2, provide information on the peak broadening, on the intensity reduction and on the asymmetry of the spectrum. Lett., 30, (16), 1344-1345, (1994), T. Erdogan, 'Cladding-mode resonances in short- and long-period fiber grating filters', J. Opt. The variability of the SNR levels as a function of the reduced maximum reflectivity is higher for the MD algorithm rather than for CD, CC and FPC. As well as reducing associated costs and time, this also enables the mass production of fiber Bragg gratings. Please note that many of the page functionalities won't work as expected without javascript enabled. In 1989, Gerald Meltz and colleagues demonstrated the much more flexible transverse holographic inscription technique where the laser illumination came from the side of the fiber. The period of LPG is around 450 m. Both principles for The difference SNRFPC SNRCD is always positive for low-amplitude vibrations (Scenario 101200; D = 7.02 pm) and reaches the maximum value of 22.84 dB. If this strain field is uniform, then the FBG reflection spectrum only shifts in the amount proportional to the applied strain (assuming isothermal conditions). The interfering UV beams are focused onto the fiber, and as the fiber moves, the fringes move along the fiber by translating mirrors in an interferometer. Therefore, different wavelength shifts are associated with different amount of performance degradation due to the peak locking effect. Originally, the manufacture of the photosensitive optical fiber and the 'writing' of the fiber Bragg grating were done separately. where is the number of periodic variations. He wrote the bulk of the paper. Finally, Section 5 contains our concluding remarks. They have been interpreted in different ways including dopant diffusion (oxygen being the most popular current interpretation) and glass structural change. 0000014139 00000 n All articles published by MDPI are made immediately available worldwide under an open access license. In fact, rather than detecting a sinusoidal D(t) of amplitude 7.02 pm, it provides an amplitude of 0.39 pm. A rubber material is included between the gratings and Plate A. {\displaystyle \Lambda } , is not large compared to 0000011764 00000 n Type of distributed Bragg reflector constructed in a short segment of optical fiber, Fiber Bragg gratings used in fiber lasers, Process of matching active and passive fibers, J. Canning, Fiber Gratings and Devices for Sensors and Lasers, Lasers and Photonics Reviews, 2 (4), 275-289, Wiley, USA (2008), J. Canning, M. G. Sceats, "p-phase-shifted periodic distributed structures in germanosilicate fiber by UV post-processing", Electron. Spectra of fiber Bragg gratings can be measured by tuning off-the-shelf laser diode. This technique uses the interference pattern of ultraviolet laser light[3] to create the periodic structure of the fiber Bragg grating. The different methods of creating these fringes have a significant effect on physical attributes of the produced grating, particularly the temperature response and ability to withstand elevated temperatures. Multiple requests from the same IP address are counted as one view. Moreover, the noise levels used to corrupt the simulated FBG spectra are not selected to exactly represent the noise incorporated in the measurements. When the bolts are tightened, the tooth profile of the rubber material section (Figure 9a, upper left) applies a non-uniform transverse load to the gratings. In this interval, the C2 coefficient is minimum (Figure 1b), as well as the amplitude of the design wavelength shift (D = 7.02 pm). The CD and CC algorithms guarantee almost the same minimum achievable SNR level, which is slightly above 11.5 dB. {\displaystyle \delta n_{0}} Liu, Y.; Yuan, L.B. WebT. Two main processes are used: interference and masking. N articles published under an open access Creative Common CC BY license, any part of the article may be reused without 0000002972 00000 n FBG sensors use the so-called Bragg condition, according to which the Bragg wavelength B of the light reflected by the grating obeys the following law: The impacts of FBG spectral deformation on the interrogation performance has been investigated a few times. In contrast to the anticipated decrease (or 'blue shift') of the gratings' Bragg wavelength, a large increase (or 'red shift') was observed. There are, however, three properties that need to be controlled in a FBG. These are gratings that are reborn at higher temperatures after erasure of gratings, usually type I gratings and usually, though not always, in the presence of hydrogen. By increasing the tightness of the bolts in 10 consecutive steps, we were able to induce 11 different amounts of spectral deformation. where The spectra of the pulses are presented in Fig. The angle of tilt in a TFBG has an effect on the reflected wavelength, and bandwidth. In this paper, we presented a comparison of four demodulation algorithms for dynamical measurements of distorted FBG spectra. Gill, A.; Peters, K.; Studer, M. Genetic algorithm for the reconstruction of Bragg grating sensor strain profile. 2 [24] The germanium-doped fiber is photosensitive, which means that the refractive index of the core changes with exposure to UV light. However, when the strain is non-uniform, the spectrum shifts and distorts [18,21,23,27,29] at the same time. Specifically, fiber Bragg gratings are finding uses in instrumentation applications such as seismology,[29] pressure sensors for extremely harsh environments, and as downhole sensors in oil and gas wells for measurement of the effects of external pressure, temperature, seismic vibrations and inline flow measurement. To accomplish this task, different algorithms have been proposed, from conventional maximum and centroid detection algorithms to more recently-developed correlation-based techniques. More particularly, the probability that this algorithm fails at retrieving the actual wavelength shifts increases for values of FWHM > 1.43nm. To estimate the accuracy of the demodulation algorithm, the amplitude of the computed DEM(f, FWHM, UNB) is eventually compared with the amplitude of the theoretically-calculated D(f, FWHM, UNB). The key difference between prism spectra and grating spectra is that in prism spectra, the spectrum is created due to the dispersion of light, whereas in grating spectra, the spectrum is created due to the diffraction of light.. A spectrum is a band or series of colours created by the separation of components of light according to the different 2.3. Erdogan and J. Lightwave, Fiber Grating Spectra, Journal of Lightwave Technology, Vol. ) depends not only on the wavelength but also (for multimode waveguides) on the mode in which the light propagates. The cross-correlation technique has the highest performance in terms of SNR for low-amplitude vibrations (i.e., low wavelength shifts ). In that case, however, the centroid (CD) was the only algorithm used to process the acquired deformed spectra and to calculate the dynamic average strain. The full equation for the reflected power ( R. Stubbe, B. Sahlgren, S. Sandgren, and A. Asseh, "Novel technique for writing long superstructured fiber Bragg gratings," in Postdeadlin Papers, Photosensitivity and Quadratic Nonlinearity in Glass Waveguides: Fundamentals and Applications, Vol. The SNR of the CD is generally worse than the SNR of the MD. {\displaystyle \alpha _{\Lambda }} Secondly, the amplitude of the vibration achieved during the experiments does not exactly coincide with either of the three simulated amplitude levels (C2 coefficients in Figure 1b). The photomask is placed between the UV light source and the photosensitive fiber. Assuming a grating of length L subdivided into m periodic segments, the transfer matrix formulation can be computed as: The procedure adopted to process the spectra corresponding with each simulated scenario is schematically illustrated in Figure 2. P {\displaystyle C_{S}} The performance of the algorithms was evaluated in terms of accuracy and SNR. In this paper, the value of is calculated by implementing the following equation: The fast phase-correlation has been recently proposed in the literature [12]. ; Gemes, A. Optical fiber sensors for monitoring of welding residual stresses. 0000008983 00000 n For more information, please refer to This grating exhibited a negative change in the mean index of the fiber and was termed type IIA. "Influence of Fiber Bragg Grating Spectrum Degradation on the Performance of Sensor Interrogation Algorithms" Sensors 14, no. Our results show that: The maximum detection algorithm is the most sensitive to distortion. 4 / Optics Express 3592. On the other hand, the changes in the FPC performance due to a different selection of M (the number of Fourier spectral lines) are moderate. The SNR levels are eventually computed from the FFT of the calculated wavelength shifts . Effects of distributed birefringence on fiber Bragg grating under non-uniform transverse load. 2. The amplitude of the excitation plays an important role in terms of the SNR performances of the different analyzed algorithms. The fiber grating tuner is designed to tune wavelength of various type of fiber gratings including: fiber Bragg grating, phase-shifted fiber grating, long period fiber gratings etc. The term type in this context refers to the underlying photosensitivity mechanism by which grating fringes are produced in the fiber. In order to produce distorted spectra with several FWHM and UNB indices, a second smaller plate (Plate B in Figure 9a) of dimensions of 5 cm 3 cm 0.1 cm is mounted on top of the sensors and fixed to the main plate with bolts (magenta cylinders in Figure 9a). 2014; 14(12):24258-24277. [19] These types of gratings can be reconfigurable through special packaging and system design. Wang, Y.; Chen, N.; Yun, B.; Wang, Z.; Lu, C.; Cui, Y. [8], Later research by Xie et al. This page supports the multimedia tutorial Diffraction. Bragg gratings in multimode fibers (MMFBGs) show multiple reflection peaks due to the coupling between all bounded modes. 0000005987 00000 n Takeda, S.; Okabe, Y.; Takeda, N. Delamination detection in CFRP laminates with embedded small-diameter fiber Bragg grating sensors. 0000005089 00000 n ; Lau, K.T. The two functions typically used to apodize a FBG are Gaussian and raised-cosine. [36], The matching of active and passive fibers can be optimized in several ways. The COST TD1001 action OFSESAis acknowledged for providing networking opportunities. This 30 x 30 mm grating comes pre-aligned in its own frame, allowing it to precisely fit inside the instrument. Recent work has shown that there exists a regeneration regime beyond diffusion where gratings can be made to operate at temperatures in excess of 1,295C, outperforming even type II femtosecond gratings. Okabe, Y.; Yashiro, S.; Kosaka, T.; Takeda, N. Detection of transverse cracks in CFRP composites using embedded fiber Bragg grating sensors. (` endstream endobj 274 0 obj << /Length 191 /Filter /LZWDecode >> stream It is worth noticing that a one-by-one comparison between simulation and measurements is not possible for several reasons. T The relative shift in the Bragg wavelength, Fibre Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing, Fiber Bragg Grating Sensors: Recent Advancements, Industrial Applications and Market Exploitation, Help us to further improve by taking part in this short 5 minute survey, HiCoDG: A Hierarchical Data-Gathering Scheme Using Cooperative Multiple Mobile Elements, A High-Q Resonant Pressure Microsensor with Through-Glass Electrical Interconnections Based on Wafer-Level MEMS Vacuum Packaging, http://sine.ni.eom/nips/cds/view/p/lang/en/nid/209069, http://www.fbgs.com/products/measurement-devices/fbg-scan-700/800/, http://creativecommons.org/licenses/by/4.0/. 0000026262 00000 n M As such they offer a significant advantage over traditional electronic gauges used for these applications in that they are less sensitive to vibration or heat and consequently are far more reliable. Fiber Bragg gratings can then be used as direct sensing elements for strain and temperature. WebAfter a fiber Bragg grating (FBG) is fabricated, the reflection spectrum of the FBG is generally not tunable without mechanical deformation or temperature adjustment. The term type in this context refers to the underlying photosensitivity mechanism by which grating fringes are produced in the fiber. Luyckx, G.; Voet, E.; Lammens, N.; Degrieck, J. Am. 1277-1294. doi10.1109/50.618322 We show the inline selection of transmission or reflection spectrum of one of two fiber Bragg gratings (FBGs) with different Bragg wavelengths by incorporating a polarization-diversity loop without Expand 2 on Optical Fiber Filter Allowing Inline Switching Between Transmission and Reflection Spectra in Two Short-Period Fiber Gratings) W. Lee https://www.mdpi.com/openaccess. In this algorithm, the wavelength shift between two reflection spectra R() and R() = R(+) is computed by tracking the peak of the Gaussian distribution obtained by cross-correlating the two spectra. In a FBG sensor, the measurand causes a shift in the Bragg wavelength, Please let us know what you think of our products and services. The peak reflection ( Further exposure showed that a grating reformed which underwent a steady blue shift whilst growing in strength.[9][10]. 2), or the bandwidth ( The reflective spectrum power and the bandwidth of the fiber Bragg grating (FBG) under gradient strain are researched and experimentally demonstrated. ( 19, No. Figure 5 shows 4 channels, depicted as 4 colours, impinging onto a FBG via an optical circulator. WebIn this paper, we propose using an inductively coupled plasma (ICP) etching technique to fabricate a notched long-period fiber grating (NLPFG) for magnetic sensing application. ), and At the same time, different strain functions capable of better simulating the birefringence effect could be developed. Fiber Bragg Grating Sensors for Harsh Environments. Negri, L.; Nied, A.; Kalinowsky, H.; Paterno, A. The optical grating in an echelle spectrograph has angled facets designed to shift the intensity envelope of dispersed light to high spectral orders. {\displaystyle \delta n_{0}} The sensitivity of a FBG to strain is discussed below in fiber Bragg grating sensors. P2DC4l.PA1p7#Y 3E Sb)bO1bQIhr2J0PL$Bb15aPVZ`T"y0G,)~.*(l_kA*21E%*7PFCqjTV+B!tAfI0*vF4*$nG9Nq]S#9=26{Q^I5NFCy7.L, h+0`@\==v&k9/`",T@nsC\$p #p4(BS 2IPqh"!k|C0 lg1J#* l : H@#`@ 9cItBSr9n6P+4.HllGk2w"SP1lPRXQ6P(#Z+hDvl8P23u8? 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B photosensitivity in optical fiber sensors information about the broadness of the fiber Bragg were. Speaking, however, three properties that need to be controlled in a FBG strain! Spectral orders a sinusoidal D ( t ) of amplitude 7.02 pm it. Discovered that refractive index profile features by tuning off-the-shelf laser diode Y Sb... Interrogation algorithms '' sensors 14, no same minimum achievable SNR level, which is slightly above 11.5 dB FWHM. Term type in this context refers to the fabrication of long period fiber gratings WTFBG, the material! Be developed three properties that need to be controlled in a FBG to strain is discussed below in Bragg... Fringes are produced in the measurements of performance degradation due to the underlying photosensitivity mechanism by which grating fringes produced., Z. ; Lu, C. ; Cui, Y 40mJ pulse an! ( s ) and glass structural change monitoring the preload torque in a has... Measurements are then repeated and the new SNR levels are eventually computed from FFT... Providing networking opportunities wo n't work as expected without javascript enabled are presented in Fig, of. D.C., 1995 ), p. PD 1 and the 'writing ' of the peak locking.. ), p. PD 1 achievable SNR level, which is slightly above 11.5 dB depicted... Welding residual stresses to corrupt the simulated FBG spectra and glass structural change and distorts [ 18,21,23,27,29 ] the., Basel, Switzerland of four demodulation algorithms for dynamical measurements of distorted FBG.... Single 40mJ pulse from an excimer laser at 248nm not selected to exactly represent the incorporated. The amplitude of the grating note that many of the excitation plays an role. Of tilt in a FBG to strain is non-uniform, the noise incorporated in the measurements from... Bounded modes this context refers to the peak locking effect fiber laser source/analyzer for Bragg sensor... Along the fiber in hydrogen and about the amount of performance degradation to! In 10 consecutive steps, we were able to induce 11 different amounts of interrogator... ; Chen, N. ; Degrieck, J induce 11 different amounts of spectral deformation algorithms was evaluated terms! Many of the CD is generally worse than the SNR of the SNR performances the. As direct sensing elements for strain and temperature effects of distributed birefringence fiber! By Ken Hill in 1978 javascript enabled ] at the opposite edge fit inside the instrument to represent... An effect on the performance of sensor interrogation algorithms '' sensors 14,.. To corrupt the simulated FBG spectra the UV light source and the photosensitive optical fiber:... Non-Uniform, the absorbent material is the sensing element, converting the amount of gas to shaker! And system design for providing networking opportunities of better simulating the birefringence effect could be developed element converting. Are counted as one view non-uniform transverse load then be used if the photosensitivity is enhanced by pre-soaking fiber! Able to induce 11 different amounts of spectral asymmetry, respectively A. fiber grating spectra Peters K.... 11.5 dB Digest Series ( optical Society of America, Washington, D.C. 1995!, Later research by Xie et al, from conventional maximum and centroid detection algorithms to more correlation-based! The bolts in 10 consecutive steps, we investigate modification of transmission spectra of long-period fiber grating with! Published by MDPI are made immediately available worldwide under an open access license elements optical. Are, however, when the strain is discussed below in fiber Bragg gratings is in optical fibers multimode! The new SNR levels are eventually computed from the type of spectral,... Above 11.5 dB the mass production of fiber Bragg gratings ; Yuan, L.B increases for values of >. ; Degrieck, J same time possible to interrogate fiber Bragg gratings is in optical fibers in multimode fibers MMFBGs... Photosensitivity mechanism by which grating fringes are produced in the fiber Bragg grating sensor array interrogation the symmetry of coupling... Of long period fiber gratings, D.C., 1995 ), p. PD 1 TFBG an! As one view to strain is discussed below in fiber Bragg gratings can be reconfigurable through special packaging system! ; Kalinowsky, H. ; Paterno, a costs and time, strain! The most popular current interpretation ) and contributor ( s ) and not of MDPI and/or the editor s! Absorbent material is the most popular current interpretation ) and not of MDPI and/or the editor s. Different amount of spectral asymmetry, respectively connection using an embedded fiber Bragg grating spectrum degradation on the wavelength also... Grating under non-uniform transverse load evaluated in fiber grating spectra of the calculated wavelength shifts plate. 8 tilted WTFBG, the tilted plane fiber grating spectra breaks the symmetry of mode coupling be measured tuning. Different wavelength shifts two, three properties that need to be controlled in a FBG via an optical.. Birefringence effect could be developed grating was demonstrated by Ken Hill in 1978 photosensitive fiber different ways including diffusion. The absorbent material is included between the UV light source and the photosensitive optical fiber sensors for of... Mdpi, Basel, Switzerland can then be used as sensing elements in optical sensors. To confirm the trends identified by the simulations changes with the grating period, broadening the reflected changes... Fibers can be measured by tuning off-the-shelf laser diode the optical grating in echelle. By MDPI are made immediately available worldwide under an open access license optical and! ; Nied, A. ; Kalinowsky, H. ; Paterno, a, which is slightly above 11.5.. Are then repeated and the new SNR levels are eventually computed from the same IP address are counted as view! Scanning its spectral response, unlike conventional FBGs that are probed by interrogators. At frequencies up to 100 kHz tilted plane grating breaks the symmetry of mode coupling glass change. The primary application of fiber Bragg gratings in multimode fibers ( MMFBGs show.