Multiparameter miniature fiber-optic sensor : design and signal interrogation

Miniature, all-silica, fiber-optic sensors capable of independent measurement of at least two different parameters are presented. Sensors were produced by a micromachining process based on the selective etching of specially designed phosphorousdoped optical fibers and an assembly-procedure that included fiber cleaving, fiber splicing and etching of fiber-micro-assemblies. Furthermore, an efficient method for independent readout of parameters in sensors that are composed of multiple resonators was also developed. The method utilizes a discrete Furrier transform of sensor’s optical spectrum and allows for simultaneous, crosstalk-free and highly sensitive readout of individual resonators’ path length changes.


Introduction
Optical fiber-based sensors have received a great deal of attention over the past several decades for increased sensitivity over existing techniques, geometric versatility, immunity to harsh environments, and inherent compatibility with optical fiber communication systems.The rising complexity of sensor systems, methods often require sensing of more than one physical or chemical parameter.In particular, multi-parameter fiber-optic sensors that monitor physical, chemical, and biological parameters are of great importance in numerous areas including structural health monitoring, environmental pollution control, biochemical and biomedical applications [1][2][3][4].Miniaturization brings additional challenges in cases of small sensing devices designs, as those devices are more sensitive to oxidation and other degradation processes.A variety of multi-parameter sensors have been proposed recently including Fiber Bragg grating [5], Fabry-Perot interferometer (FPI) [6], higher-ordermode fiber based modal interferometer sensors [7], evanescent field sensors [8], surface plasmon resonance sensors [9] and combination between them [10].Beside them, there are also some other techniques involving multicore fibers, that have high potential for multiparameter sensing [11].
In this paper we present all-silica multiparameter miniature fiber-optic Fabry-Perot (FP) sensors for measuring at least two parameters simultaneously.Sensor design, signal interrogation and achieved performance is presented and discussed for following multiparameter sensors: -sensor for pressure and temperature [12] sensor for pressure and refractive index [13] https://doi.org/10.33180/InfMIDEM2018.409 -sensor for refractive index and temperature [14] -sensor for relative humidity and temperature [15] -sensor for pressure, temperature, thermal conductivity and refractive index [16] All sensors demonstrated high measurement resolution with negligible cross-talk among measured parameters.We successfully demonstrated simultaneous measurement up to four very different physical parameters.In addition, efficient method for independent readout of different parameters of multiple resonators was also presented.The method base on discrete Furrier transform of sensor's back reflected optical spectrum that allows simultaneous, crostallk-free and highly sensitive measurements of resonators' path length change.

Mathematical model and signal processing of fabry-perot multiparameter sensor
The model of the multiparameter sensor, which was used in simulations to illustrate the cross-talk between different frequency components and effect of applied Gaussian window, will be presented below.
Sensor is composed from three semi reflective surfaces, which forms three FP resonators.The first two are shown in the Fig. 1 as L 1 and L 2 , while the third resonator L 3 represents their sum.The basic principle of the operation of an individual FP resonator or interferometer can be explained by the light wave that enters the resonator, where it is reflected or interfered between the two surfaces.The magnitude of the light current or the shape of the spectral characteristic is effected by: the distance L between mirrors, the wavelength of light λ and the refractive index n of the transmission medium.Because in our case we have several FP resonators in the series, we can use one-dimensional space, where the superposition of the optical wave can be presented with a trigonometric approach.In general, the optical wavelength in some point can be described as a function of time: This can be written in the complex space as: First, three waves overlapping in space of the same frequency and speed must be add together.
The following waves are summed up after the reflection from the mirrors in the lead-in fiber: Where E 03 , E 02 , and E 01 are individual components of the electrical field strength, that are reflected from individual semi-reflective surfaces, Ev is the input amplitude of the electric field strength, r is coefficient of reflectivity and t is transmission coefficient, and the coefficient α is reserved for describing the optical losses on the splice.
The phase changes corresponded to the interferometer's optical path length variations: φ=kn=2πLn/λ, in our case, we have already defined it as a phase change due to a reflection from a distant mirror, which doubling the optical path, and thus the phase of the wave.
When optical waves travels cross the glass / air boundary, or vice versa, an additional phase shift occurs for π / 2, so in our example, when we observe the reflected wave, this is taken into account with the phase delay π (equation 4).
The current description covers only electric field strengths that do not include transmission coefficients t of individual mirrors on the way back.This is supplemented by the following terms: (1 )(1 ) Where E 3 , E 2 and E 1 represent the total electrical field strength, which is reflected from the individual semireflective mirror, as shown in Fig. 1.Furthermore, the total electrical field strength can be written as the sum of all three components: Since the reflected-light intensity I R is proportional to the square of the electric field strength, the following can be written as: When squaring, the conjugated complex value of the electric field strength must be taken into account:

t r e E r e Et r e E t t r e
For more understandable presentation, the product will be written by combining individual coefficients into groups: 1 Taking into account the Euler's equation cos sin jx e x j x ± = ± , we obtain: Since we calculate the reflected-light intensity, the reflective and transmission coefficients can be replaced by the reflectance R and the transmission T: To reduce the set of unknowns of equations (4.11), by applying the law R + T = 1, the transmission can be re-placed by the reflection and the group of coefficients can be written as follows: ) ( ) (1 (1 If we take into account the individual values of the phase angles and the fact that the reflected light intensity depends on the input light intensity, the final equation can be written as: ( ) We have shown that the total reflected-light intensity I R of FPI with three semi-reflective surfaces can be described as a linear superposition of three cosine spectral components with distinctive spectral frequencies, which are determined by the length of the resonator, the refractive index (RI) of the transmission medium and the wavelength of light.
Further presented interrogation method involve straightforward solution for independent readout of individual FP resonators path length variations.Method based on discrete Furrier transform (DFT) of sensor's optical spectrum followed by phase tracking of corresponded frequency component.Basic definition of DFT is: Where X k is Fourier transform at k-th frequency component, N is the number of samples, and x n is the n-th sample, which is then multiplied by a complex matrix of real and imaginary values.The method is especially useful because it enables us to calculate a complex matrix in advance, which depends only on the number of input samples.If we are interested only in changing the phase of a predefined frequency component, it is sufficient to calculate only the k-th component of the complex matrix, which additionally saves the processor time.When multiplying the input data with the k-th component, we obtain a complex number x+jy from which the value of the phase is calculated: The spectral characteristic in the wavelength space does not have a pure cosine characteristic, as the distance between the adjacent peaks is not constant regarding wavelength axis.To get a clean periodic cosine characteristic, the wavelength should be replaced by frequency taking into account basic law λ=c/f, where c presents speed of light in vacuum and f frequency.The mathematical model from equation ( 13) is transformed into the following form in the frequency domain: ( ) To show significance of frequency domain and of applying a Gaussian window, we simulated dual cavity FPI, calculate DFT in wavelength and frequency domain, once with and once without Gaussian window.One example of simulated spectrum is shown on Fig. 2.  The simulation results show that DFT in frequency domain with Gaussian window helps to isolate the individual frequency component to minimize crosstalk between them.The crosstalk between both components was reduced from few degrees to less than ±0.01 degree, when varying L 1 and observing phase change of L 2 .

Multiparameter fiber optic sensors
Multiparameter fiber optic sensors are created by using micromachining technique based on selective etching [17].Selective etching is a highly effective tool for realization of various optical sensors and microdevices.In general, the creation of a microdevice based on selective-etching requires the design and manufacturing of a specially doped structure forming fiber (SFF).A short section of SFF is then spliced at the tip or in-between the lead-in single mode fibers (SMF) and then etched into the final structure.The tip of the SFF can also be directly etched into the desired microphotonic structure when the SFF incorporates a waveguide structure.
One example produced by selective etching is shown in Fig. 4. The sensor's design utilized dual all-fiber FP resonators with distinctive lengths that permitted straightforward spectrally-resolved interrogation of the sensor [12].First shorter pressure sensitive FP resonator (L 1 ) is located on the fiber tip and consists of thin silica membrane and inner reflective surface.Temperature is measured by observing the optical path length change of the second FP resonator (L 2 ), which is mainly temperature dependent due to the silica's RI dependence on the temperature (i.e.dn/dT of silica corresponds to about 10 -5 K -1 ) Temperature measurements with all-silica structure positioned between two reflective surfaces is involved almost at all further presented sensors.
The temperature and pressure were efficiently and unambiguously determined by signal processing of the reflected optical-spectra.Reflected optical spectra of typical sensor is presented in Fig. 5.The sensor can be easily modified to cover different pressure and temperature ranges.In particular, its allsilica design and miniature size provides potential opportunities for its usage in high-temperature, biomedical and micro-fluidic systems.
Another example of multiparameter sensor is shown in Fig. 6, and present a miniature, all-silica, dual-parameter FP sensor for simultaneous measurement of surrounding fluid's RI and temperature [14].Sensor consists of two stacked FPI, first FPI is U-shaped microcell for RI change measurements and second FPI is temperature sensitive segment.This sensor per mits a full temperature-compensated high resolution RI measurement in range of 10 -7 refractive index unit (RIU) as is shown on Fig. 7. High resolution measurement can be used to determine very small changes in fluid structure or composition.All-silica design provides high chemical and thermal inertness, while the miniature size provides opportunities for measuring very small (nL) fluid volumes.Next example in Fig. 8 shows one more complex multiparameter FP sensor for simultaneous measurement of pressure and refractive index [13].Sensor consists of microcell that allows surrounding fluid to freely enter inside to provide the detection of fluid's RI through the measurement of the microcell's optical path length.
Pressure measurements is realized by FPI created between thin silica diaphragm and inner reflective surface.High measurement resolutions bet ter than 0.1 mBar and 2x10 -5 RIU can be achieved by using spectral interrogation and a DFT-based measure ment algorithm.
Another example of multiparameter sensor is shown in Fig. 10, and present a miniature, all-silica, dual-parameter FP sensor for simultaneous measurement of relative humidity (RH) and temperature [15].The sensor is com posed of two cascaded FPI.The first FPI consists of a short silica micro-wire (diameter is cca.13 μm) "sandwiched" in-between two semi-reflective in-fiber mirrors (mirrors 1 and 2 in Fig. 10).Micro-wire is coated by a thin layer of porous silica, and forms a RH sensing part.The second FPI consists of section created on the sensor tip that forms a temperature measuring part.The typical total length of produced sensor is less than 2 mm, while diameter doesn't exceed 125 μm.The sensor has good dynamic performances and covers broad RH measuring range as shown in Fig. 11.Sensor has also linear characteristics for both measurement parameters with sensitivity of 0.48 degree/%RH and 3.7 degree/°C.
The last and the most complex device is multiparameter all-silica fiber optic sensor for simultaneous measurement of pressure, RI, temperature and thermal conductivity of gases [16].It is one of the few truly fiber solutions that allows measuring more than three parameters simultaneously.Sensor has high repeatability and high resolutions of all four sensed parameters (a temperature resolution of 2 mK, pressure resolution of 1 mbar, RI resolution of 5x10 -7 RIU and thermal conductivity of better than 1x10 -3 W/mK were achieved).

Conclusions
This paper presented design and interrogation of many multiparameter Fabry-Perot sensors that are all capable of measuring at least two parameters simultaneously.Experimental results regarding crosstalk confirmed that independent and simultaneous readout of stacked FP resonators on the optical fiber is possible, which is consistent with simulated results obtained from a mathematical model.
In the future, sensors could be produced with even more FP resonators (more than 3), which is entirely feasible with this kind of micromachining technology and with this kind of signal interrogation, but it however increases the complexity of the sensor and hence also the price efficiency in compared to using multiple individual sensors.

Figure 3 :
Figure 3: Simulated FP sensor with dual cavity length L 1 =100 μm, L 2 =160 μm, n=1.45, wavelength sweep was from 1510 to 1590 nm: (a) DFT in wavelength space with no applied window, (b) DFT in frequency space with Gaussian window.

Figure 7 :
Figure 7: Demonstration of system RI resolution under varying temperature conditions.

Figure 9 :
Figure 9: Sensor's response to P and RI change: (a) pressure resolution demonstration, (b) RI resolution demonstration.

Figure 11 :
Figure 11: (a) Response of produced sensor to humidity change using about a 600 nm thick porous SiO 2 layer, (b) Dynamic response of RH sensor.

Figure 12 :
Figure 12: Fabricated multiparameter sensor: (a) SEM image; (b) optical microscope image.The sensor utilizes three different FPI stacked on the tip of a lead-in optical fiber.The first FPI is made of a thinwall glass capillary and thin silica diaphragm located on the top of the sensor structure.The 2 nd FPI is open path U-shaped all-silica microcell, which allows for free access of the surrounding gas in-between the FPI's semireflective surfaces and, thus, for gas RI measurements.A short section of Vanadium-Doped Fiber placed in between an in-fiber mirror and semi-reflective surface defines the 3 rd FPI.Vanadium doping induces high optical absorption at shorter wavelengths (i.e.980 nm), while the increase in absorption near 1550 nm remains limited/low[18].This 3 rd FPI performs two functions: Temperature sensing and thermal conductivity measurement.Temperature is measured by observing the optical path length change of the 3 rd FPI.On the other hand, the thermal conductivity is measured by application of active heating of this temperature sensitive segment.