**sensors**

**sensors**

Article

**Performance Analysis of Scattering-Level**

**Multiplexing (SLMux) in Distributed Fiber-Optic** **Backscatter Reflectometry Physical Sensors**

**Daniele Tosi**^{1,2,}*** , Carlo Molardi**^{1} **, Wilfried Blanc**^{3} **, Tiago Paixão**^{4} **, Paulo Antunes**^{4}
**and Carlos Marques**^{4}

1 School of Engineering and Digital Sciences, Nazarbayev University, Nur-Sultan 010000, Kazakhstan;

carlo.molardi@nu.edu.kz

2 Laboratory of Biosensors and Bioinstruments, National Laboratory Astana, Nur-Sultan 010000, Kazakhstan

3 INPHYNI–CNRS UMR 7010, UniversitéCôte d’Azur, Parc Valrose, 06108 Nice, France;

wilfried.blanc@inphyni.cnrs.fr

4 Physics Department, I3N & University of Aveiro, 3810-193 Aveiro, Portugal; tiagopaixao@ua.pt (T.P.);

pantunes@ua.pt (P.A.); carlos.marques@ua.pt (C.M.)

***** Correspondence: daniele.tosi@nu.edu.kz

Received: 15 January 2020; Accepted: 5 March 2020; Published: 2 May 2020 ^{}^{}^{}
**Abstract:** Optical backscatter reflectometry (OBR) is a method for the interrogation of Rayleigh
scattering occurring in each section of an optical fiber, resulting in a single-fiber-distributed sensor
with sub-millimeter spatial resolution. The use of high-scattering fibers, doped with MgO-based
nanoparticles in the core section, provides a scattering increase which can overcome 40 dB. Using
a configuration-labeled Scattering-Level Multiplexing (SLMux), we can arrange a network of
high-scattering fibers to perform a simultaneous scan of multiple fiber sections, therefore extending
the OBR method from a single fiber to multiple fibers. In this work, we analyze the performance and
boundary limits of SLMux, drawing the limits of detection of N-channel SLMux, and evaluating the
performance of scattering-enhancement methods in optical fibers.

**Keywords:** optical fiber sensors; optical backscatter reflectometry (OBR); distributed sensors;

scattering-level multiplexing; Rayleigh scattering

**1. Introduction**

Optical fiber sensors have been consolidated in the past decades, and they are now an established technology in several applicative fields [1–4]. The key advantage of optical fiber sensors, with respect to other sensing technologies, such as piezoelectric, microelectromechanical systems (MEMS), or other mechanical or electronic sensors, is the possibility of interrogating multiple sensors placed upon a single fiber [2,3]. In this case, a single optical fiber sensing system can host several sensors, and therefore it is possible to perform a simultaneous detection of hundreds [2], thousands [5], or even up to a million sensing points [6]. This possibility outperforms wireless sensor networks in terms of sensing distribution [3].

Multiplexing is the key to access advanced sensing applications, and it represents the current frontier of fiber optic sensing. By multiplexing, we define the act of allocating a single optical fiber cable to a plurality of sensors, and disambiguating their detection by means of a “diversity” feature.

Each sensor must be orthogonal, or quasi-orthogonal, to the other sensors, making it possible to simultaneously detect a plurality of sensing data, and then isolate the contribution of each sensor.

In this sense, the definition of multiplexing in sensor networks is similar to its implementation in telecommunications, and research trends often intersect in these two areas [1].

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Time-division multiplexing (TDM) and wavelength-division multiplexing (WDM) represent the golden standard of multiplexing in optical fiber sensors, as they apply to Fiber Bragg Grating (FBG) sensors [1,2]. The FBG is the most popular optical fiber sensor, as it can be inscribed virtually on any fiber [7], and FBG arrays can be easily fabricated, with spacing ranging from several kilometers down to the millimeter [8]. TDM is implemented through an optical switch (1×T), which commutes to select a single channel from a network of T channels. WDM is implemented by inscribing FBGs at different wavelengths, dividing the bandwidth of an interrogator into W individual slots. TDM and WDM are used by modern FBG interrogators, which can interrogate a network up to T×W FBG sensors [2,8]; for example, an 8-channel interrogator with a 100 nm bandwidth can interrogate up to 400 FBGs spaced by 2 nm, which is a “safe” spacing between adjacent wavelength elements.

Building on this result, recently, several advanced multiplexing techniques have been presented and applied to fiber optic sensors, exploiting different degrees of diversity. Gasulla et al. [9] presented a spatial division multiplexing (SDM) method based on a multi-core fiber, where in this work, the diversity is given by seven well-spaced fiber cores, each hosting a set of sensors, considering that the separation between the cores does not lead to modal interference. The two fiber polarizations have been exploited by Oh et al., using FBG sensors [10]; this configuration, based on polarization-division multiplexing (PDM), exploits the different sensitivity of the fast/slow-axis polarized light in an FBG to interrogate a single FBG for both strain and temperature. Recently, multiplexing has been extended to Fabry–Perot sensors in the cepstrum domain [11], and even to smartphone-based optical sensors using an SDM method applied to the phone camera [12].

Distributed optical fiber sensors represent the main alternative to the network of multiplexed sensors [5]. Distributed sensors interrogate the multiple reflections, due to scattering events, occurring in an optical fiber cable. Optical backscatter reflectometry (OBR) is one of the most important methods, and as demonstrated first by Froggatt et al. [13], OBR interrogates the Rayleigh spectral signals, usually labeled as “signatures” of the fiber in each location, with a theoretical resolution of 10µm. OBR has found initial applications in the monitoring of optical systems [14], and has been subsequently extended to sensors, with particular applications in biomedical engineering [15].

OBR is inherently a single-fiber system, whereas a fiber span connected to the OBR is interrogated;

TDM is possible by using an optical switch that selects multiple fibers, but that process hampers the rapid detection of signals due to the need to acquire multiple triggers [16,17]. Since the OBR method has a spatial resolution, it is possible to arbitrarily displace the fiber in order to detect strain or temperature in multiple arrangements; for example, Macchi et al. [15] reported a planar temperature detection with a fiber disposed along eight radii during an ex-vivo radiofrequency ablation, while Parent et al. [17] reported a shape sensing method based upon a fiber triplet.

However, in some applications, particularly involving medical applications which require a high-density sensing in planar or tridimensional structures [4], it is simply not possible, or not convenient, to use a single fiber, and multiple fibers are needed. To circumvent this stalemate, Beisenova et al. recently pioneered a configuration labeled scattering-level multiplexing (SLMux) [18,19], which makes use of high-scattering fibers characterized by MgO-based nanoparticle doping in the fiber core [20]. This architecture uses, as a diversity element, the amount of scattered power in each location, and can interrogate multiple locations on different fibers. This approach has been, so far, reported for the measurement of strain [18] and shape [21] on a medical needle, and for a planar temperature measurement in a mini-invasive thermotherapy [19]. This scenario is sketched in Figure1, while OBR has been presently used with fibers arranged in an arbitrary shape, or using a switch to multiplex multiple fibers in time [17,22], SLMux is the only method that allows a simultaneous scan of multiple sensing fibers.

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findings; Section 5 analyzes a range-extension to high-scattering fibers using FBGs; Section 6 discusses the results of the performance analysis in the light of the biomedical applications; finally, Section 7 draws the conclusions.

**Figure 1. **Schematic of the optical backscatter reflectometry (OBR) setup for the measurement of
planar (2D) or tridimensional (3D) arrangements. (**a**) The fiber is displaced in a 2D/3D configuration,
as in [15]; this is impractical for several medical devices, due to limited spacing, tight bending and
excessive mechanical torsions of the fiber. (**b**) The alternative is to use a 1 × N switch (TDM
arrangement), to single out each individual channel [17,22]; in this arrangement, the OBR loses a large
portion of real-time sensing, due to the significant increase of measurement time (N-fold increase,
with ideal switches and optimal software), well over 1 s. (**c**) The SLMux setup [18,19], presented in
this work; the switch is substituted by a splitter, hence the detection is simultaneous and real-time
(0.3 s). A network of single-mode fiber delayers and high-scattering fiber multiplex from a single fiber
to the N-size sensing network, each constituted by a distributed sensor.

**2. Scattering Level Multiplexing: Method and Implementation **

*2.1. Principle of Operation *

The principle of operation of the SLMux is sketched in Figure 2, and is designed to multiplex an OBR instrument into multiple sensing regions, based on the scattering amount and length of fibers [19]. The OBR source used in our experiments, and for which all scattering power levels are referenced, is the Luna OBR4600 (Luna Inc., Roanoke, VA, US), which is the most common implementation of OBR. The instrument, used in Figure 2a as the light source and detector, is sketched in Figure 2c. The OBR is a swept laser interferometer which has a measurement arm (the upper circuitry) and a trigger that serves as a delay line [13,16].

The OBR is connected to a 1 × N splitter, to *N* separate channels. A network of single-mode fibers
(SMFs), each having length *L*^{i}, *i* = 1,…, *N*, is used to separate the sensing fibers. The sensing fibers are
required to have a higher scattering than the SMF, in order to make the system operate without
interference, and they are connected to the tail of the SMF by means of splicing. Within the high-
scattering sensing fibers, the OBR works as a distributed sensor, with spatial resolution
corresponding to *c*/(2 *n*^{eff} Δ*f*) [5], *c* = speed of light, *n*^{eff} = effective refractive index of the fiber, Δ*f* = the
frequency range of the swept laser. The length of the i-th sensing fiber is *S*^{i}.

The scattering trace *P*(*z*), *z* = fiber length, *P* = backscattered power, is shown in Figure 2b in dB
units, and appears different from the standard OBR traces. Unlike the standard OBR arrangements
of Figure 1a,b, the SLMux system is not engineered to work on the whole fiber chain, but only on the
high-scattering fibers. The implication, looking at the scattering trace, is that the distributed sensing
works only on the green portions of the trace of Figure 2b, which correspond to the specific sensing
fibers, and does not work on the SMF chain, in the red portions of the trace. The chart explains the
function of the network of SMF fibers, here acting as delay lines or spacers to shift the position of
each sensing fiber at a different length along *z*.

The scattering trace has a sawtooth shape [18]; when moving from the SMF to a high-scattering
fiber, the increased amount of scattering provides an increment of signal on the OBR, which we define
as the scattering gain (*G*). On the other hand, given that Rayleigh scattering is much stronger in these
fiber elements, the losses are much higher, and they appear as a linear decrease with −2α*z* with the
two-way fiber attenuation (2α).

**Figure 1.**Schematic of the optical backscatter reflectometry (OBR) setup for the measurement of planar
(2D) or tridimensional (3D) arrangements. (**a**) The fiber is displaced in a 2D/3D configuration, as in [15];

this is impractical for several medical devices, due to limited spacing, tight bending and excessive
mechanical torsions of the fiber. (**b**) The alternative is to use a 1×N switch (TDM arrangement),
to single out each individual channel [17,22]; in this arrangement, the OBR loses a large portion of
real-time sensing, due to the significant increase of measurement time (N-fold increase, with ideal
switches and optimal software), well over 1 s. (**c**) The SLMux setup [18,19], presented in this work;

the switch is substituted by a splitter, hence the detection is simultaneous and real-time (0.3 s). A network of single-mode fiber delayers and high-scattering fiber multiplex from a single fiber to the N-size sensing network, each constituted by a distributed sensor.

In this work, we provide for the first time a quantitative evaluation of the performance of SLMux, taking into account the multiple factors that affect performance. Our analysis is based on the evaluation of all factors that affect the propagation of light into high-scattering fibers, evaluating the key performance indicators, and thus the maximum lengths of those fibers used for sensing.

The paper is arranged as follows: Section2describes the principle of the operation of SLMux, and of the MgO-based nanoparticle-doped fibers that implement it; Section3provides a model for the implementation and analysis of SLMux based on fiber performance, and draws the performance parameters; Section4evaluates the performance boundaries of the SLMux, and presents the main findings; Section5analyzes a range-extension to high-scattering fibers using FBGs; Section6discusses the results of the performance analysis in the light of the biomedical applications; finally, Section7 draws the conclusions.

**2. Scattering Level Multiplexing: Method and Implementation**

2.1. Principle of Operation

The principle of operation of the SLMux is sketched in Figure2, and is designed to multiplex an OBR instrument into multiple sensing regions, based on the scattering amount and length of fibers [19].

The OBR source used in our experiments, and for which all scattering power levels are referenced, is the Luna OBR4600 (Luna Inc., Roanoke, VA, US), which is the most common implementation of OBR.

The instrument, used in Figure2a as the light source and detector, is sketched in Figure2c. The OBR is a swept laser interferometer which has a measurement arm (the upper circuitry) and a trigger that serves as a delay line [13,16].

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Signal demodulation is performed as described in [16]. Cross-correlation between the Rayleigh
signatures (i.e. the spectral reflectivity values acquired at each location), acquired in reference and
measurement conditions, are calculated for each point along *z* [4], selecting a window that comprises
all of the sensing fibers. Then, the individual contribution of each sensor is isolated, since the
scattering at the location is larger than the surrounding fiber.

**Figure 2. **Principle of operation of the Scattering-Level Multiplexing (SLMux) setup. (**a**) Experimental
setup implementing the SLMux, in the N-channel system; (**b**) power scattering trace, reporting the
power P at each location z measured on the OBR in the SLMux setup; (**c**) detail of the swept-laser
interferometer included in the OBR instrument (PD: photodetector, PBS: polarization beam splitter).

*2.2. High Scattering Fibers *

Rayleigh scattering is known to be a primary factor for losses in optical fibers, and therefore SMF fibers are engineered to minimize its contribution in order to reduce the fiber attenuation, which is necessary for long-haul communications. The latest research carried out in OBR-distributed sensing, however, has almost the opposite trend, namely, developing new methods to enhance scattering events in an optical fiber, in order to have a strong scattering gain. Loranger et al. [23] presented a method based on the UV exposure of a single-mode fiber, obtaining a scattering enhancement of approximately 20 dB. Yan et al. [24] showed a scattering enhancement of 40 dB by inscribing a nanograting in the fiber through a femtosecond laser.

The solution proposed by the authors, instead, makes use of a fiber doped with nanoparticles based on MgO (MgO-NP) within the core as the sensing fiber, which guarantees a scattering gain up to 49 dB. A detail of the fabrication of the fiber was previously reported by Blanc et al. [20,25] and subsequently by Beisenova et al. [18,19,21], while Section 4 of this work describes the specific scattering performance of the fiber in the context of SLMux.

In short, the MgO-NP fiber is designed to have the same core and cladding size of the SMF (10/125 μm inner/outer diameter), while having a higher density of scattering sources in the proximity of the fiber core, giving rise to a much higher Rayleigh scattering. Fibers have been drawn from silica preforms made with modified chemical vapor deposition (MCVD) [25]. The addition of

**Figure 2.**Principle of operation of the Scattering-Level Multiplexing (SLMux) setup. (**a**) Experimental
setup implementing the SLMux, in the N-channel system; (**b**) power scattering trace, reporting the
power P at each location z measured on the OBR in the SLMux setup; (**c**) detail of the swept-laser
interferometer included in the OBR instrument (PD: photodetector, PBS: polarization beam splitter).

The OBR is connected to a 1×N splitter, toNseparate channels. A network of single-mode
fibers (SMFs), each having lengthLi,i=1,. . .,N, is used to separate the sensing fibers. The sensing
fibers are required to have a higher scattering than the SMF, in order to make the system operate
without interference, and they are connected to the tail of the SMF by means of splicing. Within
the high-scattering sensing fibers, the OBR works as a distributed sensor, with spatial resolution
corresponding toc/(2n_{eff}∆f) [5],c=speed of light,n_{eff}=effective refractive index of the fiber,∆f =the
frequency range of the swept laser. The length of the i-th sensing fiber isS_{i}.

The scattering traceP(z),z=fiber length,P=backscattered power, is shown in Figure2b in dB units, and appears different from the standard OBR traces. Unlike the standard OBR arrangements of Figure1a,b, the SLMux system is not engineered to work on the whole fiber chain, but only on the high-scattering fibers. The implication, looking at the scattering trace, is that the distributed sensing works only on the green portions of the trace of Figure2b, which correspond to the specific sensing fibers, and does not work on the SMF chain, in the red portions of the trace. The chart explains the function of the network of SMF fibers, here acting as delay lines or spacers to shift the position of each sensing fiber at a different length alongz.

The scattering trace has a sawtooth shape [18]; when moving from the SMF to a high-scattering fiber, the increased amount of scattering provides an increment of signal on the OBR, which we define as the scattering gain (G). On the other hand, given that Rayleigh scattering is much stronger in these fiber elements, the losses are much higher, and they appear as a linear decrease with−2αzwith the two-way fiber attenuation (2α).

Signal demodulation is performed as described in [16]. Cross-correlation between the Rayleigh signatures (i.e., the spectral reflectivity values acquired at each location), acquired in reference and measurement conditions, are calculated for each point alongz[4], selecting a window that comprises

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all of the sensing fibers. Then, the individual contribution of each sensor is isolated, since the scattering at the location is larger than the surrounding fiber.

2.2. High Scattering Fibers

Rayleigh scattering is known to be a primary factor for losses in optical fibers, and therefore SMF fibers are engineered to minimize its contribution in order to reduce the fiber attenuation, which is necessary for long-haul communications. The latest research carried out in OBR-distributed sensing, however, has almost the opposite trend, namely, developing new methods to enhance scattering events in an optical fiber, in order to have a strong scattering gain. Loranger et al. [23] presented a method based on the UV exposure of a single-mode fiber, obtaining a scattering enhancement of approximately 20 dB. Yan et al. [24] showed a scattering enhancement of 40 dB by inscribing a nanograting in the fiber through a femtosecond laser.

The solution proposed by the authors, instead, makes use of a fiber doped with nanoparticles based on MgO (MgO-NP) within the core as the sensing fiber, which guarantees a scattering gain up to 49 dB. A detail of the fabrication of the fiber was previously reported by Blanc et al. [20,25] and subsequently by Beisenova et al. [18,19,21], while Section4of this work describes the specific scattering performance of the fiber in the context of SLMux.

In short, the MgO-NP fiber is designed to have the same core and cladding size of the SMF (10/125µm inner/outer diameter), while having a higher density of scattering sources in the proximity of the fiber core, giving rise to a much higher Rayleigh scattering. Fibers have been drawn from silica preforms made with modified chemical vapor deposition (MCVD) [25]. The addition of magnesium during the fabrication activates the formation of Mg-silicate nanoparticles [26], as reported by Blanc et al. [20], which act as a scattering source for input signals.

The MgO-NP method to enhance Rayleigh scattering is the most interesting from the application standpoint, because it leads to the fabrication of a proper optical fiber, rather than exposing a portion of a pre-existing fiber. The MgO-NP can be spooled like a normal fiber, and can be spliced in a standard fusion splicer; in all of the following characterization, MgO-NP fibers have been spliced to standard SMF in a low-cost splicer (Fujikura 12S, SMF-SMF recipe). Since the fiber can be spooled, spliced and treated as a normal fiber, it also does not require removing the protective jacket around the fiber, as instead done in previous works [22–24]. The fiber used in experiments, having a standard 250µm jacket, is much more suitable for working on medical devices such as epidural (Tuohy) [21] or Chiba [18] needles, without any recoating that would increase the fiber thickness.

**3. Theoretical Analysis of Scattering-Level Multiplexing**

3.1. Definitions

Table1shows the parameters used in the following theoretical analysis. For simplicity, all power values are reported in dBm units, all attenuation and gains in dB, and fiber attenuation in dB/m. In calculations, attenuations and losses are always referred as two-way, i.e., accounting both the forward and backward propagation. Here, gain terms refer to the increment of the scattering level with respect to standard SMF fibers, and they do not imply an amplification of optical power.

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**Table 1.**List of the main parameters used in the performance analysis of SLMux.

**Parameter** **Label** **Unit** **Value**

Scattering gain G dB 37.2–49.3 (Table2)

Two-way fiber losses 2α dB/m 22.1–298.0 (Table2)

Number of SLMux channels N - 2–64

SMF backscattered power PSMF dBm −102.7

OBR noise power level P_{N} dBm −110.7

Total interference power P_{INT} dBm =P_{SMF}+10log_{10}(N−1) (max)

MgO-NP sensing fiber length S m See Section3.7

Maximum MgO-NP sensing length Smax m See Table3

Total MgO-NP sensing length Stot m =NSmax

Extra two-way attenuations A dB 4.5–11

Maximum loss imbalance ∆A dB 0.4–5

Signal-to-noise ratio, ideal SNR_{network} dB See Section3.4

Signal-to-noise ratio, real SNR dB See Section3.5

Signal-to-interference ratio, ideal SIRnetwork dB See Section3.4

Signal-to- interference ratio, real SIR dB See Section3.5

Extra FBG power gain F dB 9.5–28.0

Maximum FBG chain length S_{FBG} m

Range-extended max. SLMux length S_{extended} m =Smax+S_{FBG}

3.2. Scattering Diversity and Power Propagation

The key principle of SLMux is avoiding the overlap between two sensing regions, at any given space; in this case, we can imply that the power backscattered by the MgO-NP sensor is much larger than the combination of the other SMF fibers overlapping in the same location, since the scattering gain is large. We can label this condition as the “scattering diversity”, the underlying process of SLMux. In formula, as derived from Figure2:

[(LS+Li)^{÷}(LS+Li+Si)] _{,} ^{h}LS+Lj

÷

LS+Lj+Sj

i (1)

for any pair (i,j)=1,. . ., N. Here the diversity symbol (,) refers to the entire range of extension of the i-th andj-th sensing regions, which have to avoid any overlap.

With this parameter layout, and considering that the OBR works only in the sensing regions corresponding to high-scattering fibers, for eachi-th channel, we can then express the backscattered power, in ideal conditions, as:

P(z) =P_{SMF}−10 log_{10}N+G−2α(z−L_{S}−L_{i}). (2)
for from the location (L_{S}+L_{i})≤z≤(L_{S} +L_{i} +S_{i}). The power follows the sawtooth shape shown
in Figure2: the baseline power scattered by the SMF (PSMF) suffers the attenuation term 10log10N
that takes into account the optical splitter, then it is enhanced by the MgO-NP, and decreases linearly
following the fiber attenuation.

3.3. Underlying Considerations

In order to analyze the SLMux performance, we provide the following considerations, that are mostly verified experimentally. Several of these statements have been previously presented by Beisenova et al. [19]; The appendices contain specific elements and experiments aimed at the verification of the most critical assumptions.

1. The SMF fibers have a constant backscattered powerP_{SMF}, and are lossless. Typical attenuation
values for SMF fibers (e.g., Corning SMF-28) are around 0.36–0.48 dB/km two-ways, hence the
attenuation on a short span of few meters is negligible.

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2. The noise power corresponds to the average power due to the electrical and optical noise at the
photodetector of the OBR. This value, labeledP_{N}, is measured in dark conditions, when no fiber
is connected to the OBR [16].

3. Since the scattering level from a MgO-NP fiber is high, we operate the OBR with no amplification (e.g., 0 dB electrical amplification set on the OBR instrument). This is necessary to avoid the nonlinearities in the scattering peaks.

4. With these conditions, we can measurePSMF=−102.7 dBm, andPN=−110.7 dBm for the OBR instrument used in experiments. The power is here expressed in absolute units, which depend on the input power launched by the OBR laser source. Noise and interference are always calculated as differential terms, hence the results are independent on the power launched by the OBR.

5. We neglect the reflective effect of connectors, which induce a reflective spike on the OBR. That is because connectors are located at SMF-SMF junctions which are not overlapping to any of the sensing fiber, and hence are irrelevant. Connector losses are treated as impairments.

6. Since commercial splitters are mainly 1×2^{x}, we consider the operative cases of 1×2, 1×4, 1×8,
1×16, 1×32 and 1×64 splitters. We assume the splitter to have an insertion loss of 10log10(N)
in dB, while the excess loss is treated as an impairment. We assume the length of the splitter to be
equal for all channels; adjusting the length of each SMF span it is possible to satisfy the scattering
diversity outlined in Equation (1). In this case, the performances of the system are scaled to the
upper number of channels, e.g., a 1×12 system will have the same performance of a 1×16.

7. MgO-NP fibers have a gain scatteringG(defined as the increment of scattered power with respect to the SMF fiber), and two-way attenuation 2α. ThenGandαare assumed to be constant on the whole network. Although different portions of the MgO-NP might have uneven scattering performance, in general these values tend to be similar on fibers drawn from the same process, hence we can simply account for the local variability ofGandαas an impairment.

8. MgO-NPs are spliced to the SMF matching the mode profile, in a quasi-lossless splice. This way, we can treat the splice loss as an impairment, but without alteration of the scattering signatures.

Splice losses have always been estimated as<0.1 dB per splice for any MgO-NP.

9. The scattering signature, i.e., the spectral response of the Rayleigh scattering back-reflection evaluated at each locationz, is a random signal. We approximate the scattering signature of MgO-NP fibers, like SMF fibers, as a random signal having mean power equal toP(z). Although the signals are not completely flat, their profile is similar to a white noise (see AppendixA).

10. Scattering signatures from different sections of fibers are statistically independent of each other [19]

(see AppendixA).

11. For simplicity, we assume all sensing lengths of the MgO-NP fibers have equal valueS. In most applications [4], sensors have equal lengths, since they are often mounted on a medical device having a defined length.

3.4. Noise and Interference Contribution

We introduce two quality factors for the SLMux, which define its performance across the whole sensing network. The first condition relates to the signal-to-noise ratio (SNR), and measures the amount of signal, i.e., power scattered by the fiber, over the noise level of the OBR; the SNR condition exists for any OBR system, and is defined asSNR(z)=P(z)−PN. Unfolding the power propagation law, since the MgO-NP fiber suffers from progressive losses, the worst-case scenario occurs at the far end of the longest sensing channel, which has the weakest overall signal power. Since this is the worst-case scenario, we can then define the network SNR as:

SNR_{network}=P_{SMF}−10 log_{10}N+G−2αS−P_{N} (3)

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where “network” refers to the SNR related to the simple optical sensing network, as laid out in Figure2, without the contribution of an additional excess loss of components and power unbalances, that will be treated in the next section.

The second quality factor is specific of the SLMux configuration, and relates to the signal over
interference ratio (SIR). We define the SIR at the generic locationzasSIR(z)=P(z)−PINT, i.e., as the ratio
between the signal powerP(z) and interference powerP_{INT}due to the presence of several SMF fiber
signatures overlapping to the main signature coming from the MgO-NP fiber. As visually expressed in
Figure2, thei-th sensing fiber interferes with (i−1) SMF fibers, each carrying a contribution equal to
P_{SMF}. As by assumptions 9–10, multiple overlapping signatures are statistically independent, hence
we combine their average power. With these considerations, the lowest value of network SIR can be
derived for the shortest fiber, which has (N−1) interferents:

SIRnetwork=^{−}10 log_{10}(N−1) +G−2αS. (4)

Comparing Equation (4) with Equation (3), and approximating log10(N−1)≈log10N, we notice
that the system, at least in ideal conditions, is dominated by the SIR; in fact, since the OBR is designed
in order to haveP_{SMF}well larger thanP_{N}(8.0 dB higher as by measured in assumption 4), we obtain
that the SIR is significantly lower than the SNR, and therefore the interference is the limiting factor on
SLMux performance. This consideration however can be mitigated when looking at the non-idealities
of the system.

3.5. Effect of Impairments

SNR and SIR undergo different typologies of impairments, which account for the non-idealities of the system. The SNR is affected by all the losses in addition to the circuit losses, such as excess loss of splitter, connector and splice losses, and the additional attenuations that compose the power budget.

The additional losses reduce the signal power, consequentially lowering the SNR by the same amount;

we can therefore write the real SNR as:

SNR=_{SNR}_{network}^{−}_{A}=_{P}_{SMF}^{−}_{10 log}_{10}_{N}+_{G}^{−}_{2αS}^{−}_{P}_{N}^{−}_{A} _{(5)}
whereAis the contribution of the excess losses. Even in a well-designed SLMux, excess losses of
connectors, fibers, splitter and splices can account for several dB, particularly considering that losses
are experienced both by forward and backward waves. For example, the design reported by Beisenova
et al., which introduces an additional splitter, shows additional excess losses [18,19].

The SIR is not vulnerable to most of the loss terms, since the attenuations affect in the same way the MgO-NP fiber, and the SMF fibers overlapping to it. Instead, the SIR is vulnerable to the loss imbalances, i.e., the deviation of the excess of attenuations or to the local variations of scattering properties from their baseline values. For example, if the splitter has the same excess and connector loss on each channel, both signal and interference terms suffer the same attenuation and their ratio would remain the same. The attenuation of MgO-NP fibers is in general repeatable over fiber samples drawn from the same preform, so the attenuation deviations are also treated as impairments. The parameter that impairs the SIR is the maximum change of the attenuation of the MgO-NP fiber with respect to the imbalances of the interference. This term, labeled∆A, has in general a smaller value than A, and we can write the effective SIR as:

SIR=SIR_{network}−∆A=^{−}10 log_{10}(N−1) +G−2αS−∆A. (6)
3.6. Quantification of the Quality of Detection

OBR detection is based on the cross-correlation between Rayleigh scattering signatures [13], which is known to be a noise-resilient operation when applied to spectral detection [14,27,28]. Due to the overlap of scattering signals, statistically independent on each other, and approximated as a white

Sensors**2020**,20, 2595 9 of 21

stochastic process [13,23], we need to quantify the limit of SNR and SIR at which the system is operating.

A Monte Carlo simulation (M=1000 order) has been performed by combining signatures at different SIR and SNR levels, and evaluating the percentage of detected correlations. The result is shown in Figure3.

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loss on each channel, both signal and interference terms suffer the same attenuation and their ratio
would remain the same. The attenuation of MgO-NP fibers is in general repeatable over fiber samples
drawn from the same preform, so the attenuation deviations are also treated as impairments. The
parameter that impairs the SIR is the maximum change of the attenuation of the MgO-NP fiber with
respect to the imbalances of the interference. This term, labeled Δ*A*, has in general a smaller value
than *A*, and we can write the effective SIR as:

= − Δ = −10 log − 1 + − 2 − Δ . (6)

*3.6. Quantification of the Quality of Detection *

OBR detection is based on the cross-correlation between Rayleigh scattering signatures [13], which is known to be a noise-resilient operation when applied to spectral detection [14,27,28]. Due to the overlap of scattering signals, statistically independent on each other, and approximated as a white stochastic process [13,23], we need to quantify the limit of SNR and SIR at which the system is operating.

A Monte Carlo simulation (M = 1000 order) has been performed by combining signatures at different SIR and SNR levels, and evaluating the percentage of detected correlations. The result is shown in Figure 3.

**Figure 3. **Percentage of correctly detected correlations, as a function of signal over interference ratio
(SIR) and signal-to-noise ratio (SNR), by means of a Monte Carlo simulation applied on Rayleigh
scattering signatures.

In order to account for 100% correct detection, with an operative margin, we can see the boundary limits for SIR and SNR. The system is limited by either SIR or SNR at the limit of −11.5 dB, with a transition region which can be approximated as a linear trend. In formulas, we can express the three conditions to be met in order to meet the OBR cross-correlation limits:

*SIR *> −11.5 dB (7)

*SNR *> −11.5 dB* * (8)

*SIR + SNR *> −17.5 dB* * (9)

where SIR and SNR are expressed in dB units.

*3.7. Maximum Sensing Fiber Length *

By replacing Equations (5–6) into Equations (7–9), and solving for the maximum value of *S*, we
can obtain an estimate of the maximum length of each sensing region, for the MgO-NP fiber having

**Figure 3.**Percentage of correctly detected correlations, as a function of signal over interference ratio
(SIR) and signal-to-noise ratio (SNR), by means of a Monte Carlo simulation applied on Rayleigh
scattering signatures.

In order to account for 100% correct detection, with an operative margin, we can see the boundary limits for SIR and SNR. The system is limited by either SIR or SNR at the limit of−11.5 dB, with a transition region which can be approximated as a linear trend. In formulas, we can express the three conditions to be met in order to meet the OBR cross-correlation limits:

SIR>−11.5 dB (7)

SNR>−11.5 dB (8)

SIR+SNR>−17.5 dB (9)

where SIR and SNR are expressed in dB units.

3.7. Maximum Sensing Fiber Length

By replacing Equations (5–6) into Equations (7–9), and solving for the maximum value ofS, we can obtain an estimate of the maximum length of each sensing region, for the MgO-NP fiber having (G, 2α) scattering characteristics. Hence, we can evaluate the maximum length of a sensing regionSmaxas the minimum value ofSthat satisfies the SNR/SIR conditions:

Smax=min

_{11.5}_{−}_{10 log}

10N+G−∆A

2α ;^{11.5}^{−}^{10 log}^{10}^{N}^{+}_{2α}^{G}^{−}^{A}^{+}^{P}^{sm f}^{−}^{P}^{N};^{17.5}^{−}^{20 log}^{10}^{N}^{+}^{2G}_{4α}^{−}^{A}^{−}^{∆A}^{+}^{P}^{sm f}^{−}^{P}^{N}

(10) using the approximation log10(N−1)≈log10N, which is effective for high values ofN.

The result in Equation (10) provides a closed-form expression for the upper bound of a SLMux system, i.e., the relationship between the maximum length achievable,Smax, for a system withN channels, given a high-scattering fiber with gain Gand losses 2α, taking into account the effect of impairments.

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**4. Performance Analysis**

Several high-scattering fibers have been drawn, having different density and positioning of MgO-NP with respect to the fiber core. The scattering traces, measured with the OBR in different instances, show the estimate of the scattering parameters. Figure4shows the scattering traces of three different MgO-NP fibers, recorded on the OBR (using different gage length values). The trace appears very close to the sawtooth shape of Figure2a, with an instantaneous rise of scattering level and a linear drop following the attenuation pattern. The first two fibers have similar gain and loss numbers, while the third fiber has similar gain, but much more significant losses.

*Sensors ***2019**, *19*, x FOR PEER REVIEW 9 of 20

(*G*, 2α) scattering characteristics. Hence, we can evaluate the maximum length of a sensing region
*S**max* as the minimum value of *S* that satisfies the SNR/SIR conditions:

= 11.5 − 10 log + − ∆

2 ;11.5 − 10 log + − + −

2 ;17.5 − 20 log + 2 − − ∆ + −

4 (10)

using the approximation log10(*N*−1) ≈ log10*N*, which is effective for high values of *N*.

The result in Equation (10) provides a closed-form expression for the upper bound of a SLMux
system, i.e. the relationship between the maximum length achievable, *S*^{max}, for a system with *N*
channels, given a high-scattering fiber with gain *G* and losses 2α, taking into account the effect of
impairments.

**4. Performance Analysis **

Several high-scattering fibers have been drawn, having different density and positioning of MgO-NP with respect to the fiber core. The scattering traces, measured with the OBR in different instances, show the estimate of the scattering parameters. Figure 4 shows the scattering traces of three different MgO-NP fibers, recorded on the OBR (using different gage length values). The trace appears very close to the sawtooth shape of Figure 2a, with an instantaneous rise of scattering level and a linear drop following the attenuation pattern. The first two fibers have similar gain and loss numbers, while the third fiber has similar gain, but much more significant losses.

**Figure 4. **Scattering traces measured on the OBR instruments for three different MgO-NP fibers; data
show the estimation of gain and two-way losses. (**a**) Fiber M01 used in [18]; (**b**) fiber M01 used in [19];

(**c**) fiber R04.

Table 2 shows the parameters of all fibers used in the analysis.

**Table 2. **Scattering parameters and fiber characteristics of MgO-NP specialty fibers.

**Fiber **^{1}** Reference Preform Type **^{2}** G [dB] 2**α** [dB] **

1 Figure 4a [18] M01 38.6 30.8

2 Figure 4b [19] M01 42.9 29.7

3 Figure 4c R04 40.0 134.0

4 G22 47.5 298.0

5 [29] G22 46.1 292.0

6 [30] M01 37.2 22.1

7 G22 49.3 273.3

1 Fibers are listed in chronological order of testing. ^{2} The preform type characterizes the label used by
INPHYNI Institute to characterize the fibers.

Multiple fibers have been drawn, according to the methods described in [18–21,25], and the scattering parameters of seven fibers drawn with these methods, and reported on the OBR instrument, are reported in Table 2. Data report multiple fibers, drawn in different preforms that account for different location and distribution of elongated nanoparticles in the core.

Length (m)

23 23.5 24 24.5

Power (dBm)

-110 -100 -90 -80 -70

-60 (a) F ib er 1

OBR trace Attenuation slope

Length (m)

5.5 6 6.5 7

Power (dBm)

-110 -100 -90 -80 -70

-60 (b ) F ib er 2 OBR trace Attenuation slope

Length (m)

5.4 5.5 5.6 5.7

Power (dBm)

-110 -100 -90 -80 -70

-60 (c) F ib er 3

OBR trace Attenuation slope

30.8 dB/m 29.7 dB/m

38.6 dB

42.9 dB 134.0 dB/m

40.0 dB

**Figure 4.**Scattering traces measured on the OBR instruments for three different MgO-NP fibers; data
show the estimation of gain and two-way losses. (**a**) Fiber M01 used in [18]; (**b**) fiber M01 used in [19];

(**c**) fiber R04.

Table2shows the parameters of all fibers used in the analysis.

**Table 2.**Scattering parameters and fiber characteristics of MgO-NP specialty fibers.

**Fiber**^{1} **Reference** **Preform Type**^{2} **G [dB]** **2**α**[dB]**

1 Figure4a [18] M01 38.6 30.8

2 Figure4b [19] M01 42.9 29.7

3 Figure4c R04 40.0 134.0

4 G22 47.5 298.0

5 [29] G22 46.1 292.0

6 [30] M01 37.2 22.1

7 G22 49.3 273.3

1Fibers are listed in chronological order of testing.^{2}The preform type characterizes the label used by INPHYNI
Institute to characterize the fibers.

Multiple fibers have been drawn, according to the methods described in [18–21,25], and the scattering parameters of seven fibers drawn with these methods, and reported on the OBR instrument, are reported in Table2. Data report multiple fibers, drawn in different preforms that account for different location and distribution of elongated nanoparticles in the core.

The scattering gain recorded with the M01 preform, which appears as the most interesting method for SLMux, has a range of 5.7 dB (37.2–42.9 dB), while the two-way loss achieves a minimum of 22.1 dB/m and a maximum of 30.8 dB/m. This fiber has been used by Beisenova et al. and Molardi et al. [18,19,30], and the data are in agreement with Table2, with some fluctuations also due to the random nature of nanoparticle distribution. Conversely, fibers drawn from the G22 fiber, achieve a higher gain (47.5–49.3 dB), but losses fall with a 10×higher rate, up to almost 300 dB/m [30]. In the middle between the two preforms, the R04 fiber pattern achieves a gain of 40.0 dB and losses of 134.0 dB/m.

The performance of the seven fibers listed in Table2, in ideal conditions (i.e., excess losses A=0 dB, loss variation∆A=0 dB), is listed in Figure5; in the chart, the maximum sensing length for

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the MgO-NP fibers is reported for each channel number. M01 fibers, having a smaller attenuation, have the best performance figure, due to the lower attenuation. The 6th fiber is the best performing method, achieving 206.7 cm of maximum sensing length in 2-channel configurations, down to 138.6 cm for 64 channels. The other M01 fibers have lower length, approximately 16% less for the 2nd fiber, and 26% lower for the 3rd fiber, with a similar slope. The R04 performance is lower; the maximum length is 36.2 cm for two channels, down to 25.0 cm for 64 channels. The G22 fiber type yields the lowest performance rating, where the maximum length achievable with this preform ranges from 18.7 cm to 21.1 cm for two channels, falling to 13.5–15.6 cm for the 64 channels.

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The scattering gain recorded with the M01 preform, which appears as the most interesting method for SLMux, has a range of 5.7 dB (37.2–42.9 dB), while the two-way loss achieves a minimum of 22.1 dB/m and a maximum of 30.8 dB/m. This fiber has been used by Beisenova et al. and Molardi et al. [18,19,30], and the data are in agreement with Table 2, with some fluctuations also due to the random nature of nanoparticle distribution. Conversely, fibers drawn from the G22 fiber, achieve a higher gain (47.5–49.3 dB), but losses fall with a 10× higher rate, up to almost 300 dB/m [30]. In the middle between the two preforms, the R04 fiber pattern achieves a gain of 40.0 dB and losses of 134.0 dB/m.

The performance of the seven fibers listed in Table 2, in ideal conditions (i.e. excess losses *A* = 0
dB, loss variation Δ*A* = 0 dB), is listed in Figure 5; in the chart, the maximum sensing length for the
MgO-NP fibers is reported for each channel number. M01 fibers, having a smaller attenuation, have
the best performance figure, due to the lower attenuation. The 6th fiber is the best performing
method, achieving 206.7 cm of maximum sensing length in 2-channel configurations, down to 138.6
cm for 64 channels. The other M01 fibers have lower length, approximately 16% less for the 2nd fiber,
and 26% lower for the 3rd fiber, with a similar slope. The R04 performance is lower; the maximum
length is 36.2 cm for two channels, down to 25.0 cm for 64 channels. The G22 fiber type yields the
lowest performance rating, where the maximum length achievable with this preform ranges from
18.7 cm to 21.1 cm for two channels, falling to 13.5–15.6 cm for the 64 channels.

**Figure 5. **Maximum sensor length *S*^{max}, as a function of number of channel *N*, in ideal conditions (*A* =
0 dB, Δ*A* = 0 dB), for the fibers listed in Table 2.

The performances are dominated by the attenuation term: the increase of gain observed for G22 fibers does not suffice to cope with the higher losses, hence the performances of M01 fibers appear to always outperform other methods.

The impact of impairments has to be assessed, for a system to take into account all effects.

Considering, for simplicity, the 6th fiber as the most performing SLMux sensing fiber, we can
evaluate the joint impact of impairments (*A*, Δ*A*), on the whole fiber length, evaluating the reduction
of *S*^{max} due to impairments. Results are shown in Figure 6, reporting the reduction of the maximum
length as *A* and Δ*A* increase. We identify three regions: on the left and right parts of the curve, the
maximum length is limited by Δ*A* and *A*, respectively, showing a saturation effect; in the inner region,
the maximum length has a linear dependence on both impairments.

### Number of channels, N

2 4 8 16 32 64

### Maxim um se nsor length, S

max### (cm)

10 12 15 20 25 30 40 50 60 80 100 120 150 200 250Fiber1 (M01) Fiber2 (M01) Fiber3 (R04) Fiber4 (G22) Fiber5 (G22) Fiber6 (M01) Fiber7 (G22)

**Figure 5.** Maximum sensor lengthSmax, as a function of number of channelN, in ideal conditions
(A=0 dB,∆A=0 dB), for the fibers listed in Table2.

The performances are dominated by the attenuation term: the increase of gain observed for G22 fibers does not suffice to cope with the higher losses, hence the performances of M01 fibers appear to always outperform other methods.

The impact of impairments has to be assessed, for a system to take into account all effects.

Considering, for simplicity, the 6th fiber as the most performing SLMux sensing fiber, we can evaluate the joint impact of impairments (A,∆A), on the whole fiber length, evaluating the reduction ofSmaxdue to impairments. Results are shown in Figure6, reporting the reduction of the maximum length asAand

∆Aincrease. We identify three regions: on the left and right parts of the curve, the maximum length is limited by∆AandA, respectively, showing a saturation effect; in the inner region, the maximum length has a linear dependence on both impairments.

Sensors**2020**,20, 2595 12 of 21

1

**Figure 6.**Maximum lengthSmaxof the sensing region (text, in centimeters) for the 6th fiber, M01 type,
as a function of the impairments parametersAand∆A, evaluated for (**a**) 4 channels; (**b**) 16 channels;

(**c**) 64 channels.

A well-designed SLMux, which operates to minimize the losses, minimizing the number of components, can count on the following excess losses, two-way (with numbers taken from component datasheets or splicer estimates): splice losses 0.05 dB±0.04 dB; connector losses 0.36 dB±0.08 dB for each pair of FC/APC connectors through a mating sleeve; excess losses of the splitter ranging from 0.9 dB to 6.6 dB; variation of splitting ratio per channel up to 15%, which corresponds to−0.15 dB to +0.15 dB. Hence, for a well-designed SLMux network, we can estimateA~ 4.5 dB, and∆A~ 0.4 dB.

In a worst-case scenario the imbalance was estimated as∆A~ 5 dB and a distribution network with multiple splitters was used, bringing the excess losses to about 11 dB [18]. In practical cases, among the several SLMux systems implemented by the authors, the∆Aparameter is the easiest to be controlled, since the user can assign the weakest port of the splitter to theN-th channel (longest), and the strongest signal to the first port, as it is more resilient to interferences. Conversely, splitter losses and excess losses are hard to be controlled. Empirically, we observe thatA=7 dB, and∆A=2 dB, are realistic parameters for the typical SLMux system. Hence, we can consider these three cases as benchmark:

best case scenarioA=4.5 dB and∆A=0.4 dB; typical scenarioA=7 dB and∆A=2 dB; worst case scenarioA=11 dB and∆A=5 dB.

Figure7evaluates the penalty due to impairments for fibers 6 (M01), 3 (R04) and 7 (G22). For the M01 fiber, we observe a penalty of 5.4 cm in the best case, 14.7 cm in the typical case and 30.5 cm in the worst case with respect to the ideal case. For the R04 fiber, the penalties are 0.9 cm, 2.4 cm and 5.0 cm, respectively. For the G22 fiber, the penalties are 0.4 cm, 1.2 cm and 2.5 cm respectively, about half of the R04 fiber. The chart shows that the inclusion of impairments does not alter the logarithmic dependence of the maximum sensing length with the number of channels, adding a penalty that can be quantified as a constant margin.

Sensors**2020**,20, 2595 13 of 21

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**Figure 7. **Maximum sensor length as a function of number of channels, accounting the impairments:

(**a**) Fiber 6, M01; (**b**) Fiber 3, R04; (**c**) Fiber 7, G22.

**Figure 8. **Total sensing length *S*^{tot} for each fiber (fiber 6, M01; fiber 3, R04; fiber 7, G22), as a function
of the number of SLMux channels.

The results of the performance analysis are recapped in Table 3, reporting *S*^{max} and *S*^{tot} for all the
MgO-NP fibers, in all the working conditions. We can observe the multiple trade-off existing between
the maximum total active length of SLMux, and the length per sensing channel; the first element
increases linearly with *N*, while the second term decreases logarithmically with *N*.

# channels, N

2 4 8 16 32 64

Max sensor length, Smax (cm) 110 120 130 140 150 160 170 180 190 200

(a) F ib er 6 (M 01)

Theoretical Best case Typical case Worst case

# channels, N

2 4 8 16 32 64

Max sensor length, S max (cm) 20 22 24 26 28 30 32 34

36 (b ) F ib er 3 (R 04)

Theoretical Best case Typical case Worst case

# channels, N

2 4 8 16 32 64

Max sensor length, S max (cm) 14 15 16 17 18 19 20

21 (c) F ib er 7 (G 22)

Theoretical Best case Typical case Worst case

### Number of channels, N

2 4 8 16 32 64

### Tota l sensing leng th, S

tot### (cm)

10^{1}
10^{2}
10^{3}
10^{4}

M01 (best) M01 (typ.) M01 (worst) R04 (best) R04 (typ.) R04 (worst) G22 (best) G22 (typ.) G22 (worst) G22

M01

R04

**Figure 7.**Maximum sensor length as a function of number of channels, accounting the impairments:

(**a**) Fiber 6, M01; (**b**) Fiber 3, R04; (**c**) Fiber 7, G22.

The total sensing length that can be interrogatedStot, which corresponds to the sum of all the lengths associated to each channelStot=NSmax, is shown in Figure8. The M01 fiber, having the best performance rating for multiplexing, can achieve a sensing length of up to 85 m, using all the 64 channels, or up to 7.5 m for four channels, which is a length that covers a wide array of sensing applications. Even considering their length limitations, R04 and G22 fibers can achieve total sensing lengths of 132 cm and 78 cm, respectively, for four channels, and 15 m and 9 m for the maximum number of channels.

*Sensors ***2019**, *19*, x FOR PEER REVIEW 12 of 20

**Figure 7. **Maximum sensor length as a function of number of channels, accounting the impairments:

(**a**) Fiber 6, M01; (**b**) Fiber 3, R04; (**c**) Fiber 7, G22.

**Figure 8. **Total sensing length *S*^{tot} for each fiber (fiber 6, M01; fiber 3, R04; fiber 7, G22), as a function
of the number of SLMux channels.

The results of the performance analysis are recapped in Table 3, reporting *S*^{max} and *S*^{tot} for all the
MgO-NP fibers, in all the working conditions. We can observe the multiple trade-off existing between
the maximum total active length of SLMux, and the length per sensing channel; the first element
increases linearly with *N*, while the second term decreases logarithmically with *N*.

# channels, N

2 4 8 16 32 64

Max sensor length, Smax (cm) 110 120 130 140 150 160 170 180 190 200

(a) F ib er 6 (M 01)

Theoretical Best case Typical case Worst case

# channels, N

2 4 8 16 32 64

Max sensor length, S max (cm) 20 22 24 26 28 30 32 34

36 (b ) F ib er 3 (R 04)

Theoretical Best case Typical case Worst case

# channels, N

2 4 8 16 32 64

Max sensor length, S max (cm) 14 15 16 17 18 19 20

21 (c) F ib er 7 (G 22)

Theoretical Best case Typical case Worst case

### Number of channels, N

2 4 8 16 32 64

### Tota l sensing leng th, S

tot### (cm)

10^{1}
10^{2}
10^{3}
10^{4}

M01 (best) M01 (typ.) M01 (worst) R04 (best) R04 (typ.) R04 (worst) G22 (best) G22 (typ.) G22 (worst) G22

M01

R04

**Figure 8.**Total sensing lengthStotfor each fiber (fiber 6, M01; fiber 3, R04; fiber 7, G22), as a function of
the number of SLMux channels.