#
Optofluidic Micromachined Platform for Refractive Index Measurement^{ †}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

^{−3}for 100 km length. Liu et al. [12] designed an integrated RI and temperature sensor that combines a Fabry–Perot interferometer (FPI) and a fiber Bragg grating in a common FPI-FBG sensor structure. The RI sensitivity of 1210.490 nm/RIU was achieved by measuring refractive index of sucrose solution in the range of 1.335 to 1.344. Zhang et al. [13] proposed an all-optical-fiber temperature-insensitive RI sensor also based on the LPG inscribed in a cobalt-doped optical fiber (COF). A part of the COF fiber was spliced between the two common single-mode fibers (SMF). Two FBGs were inscribed in the COF and photosensitive regions of SMF acting as two in-line temperature sensors. The LPG sensor was tested by measuring the RI of sucrose solutions of different concentrations. A maximum sensitivity of about 1100 nm/RIU was achieved over the refractive index from 1.32 to 1.45.

^{−5}and temperature sensitivity of 4.16 nm/°C. Wang et al. [15] demonstrated a high-accuracy hybrid fiber-optic FP sensor based on MEMS for the simultaneous measurement of RI and temperature of gas sample. The sensor is made of silicone FP cavity aimed for temperature measurement and a glass FP cavity for the gas RI measurement. The experimental results show the sensitivity of temperature measurement of about 80 pm/°C and sensitivity of RI measurement of 1535.8 nm/RIU over the gas refraction index from 1.0000248 to 1.0007681.

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Method

_{1}, I

_{2}, and I

_{3}are irradiances of light beams in three interferometric arms; ΔL

_{ij}= L

_{j}− L

_{i}is the optical paths difference (OPD) between the beams in arms i and j (the indices i and j correspond to three light paths: i, j = 1, 2, 3); γ

_{11}(ΔL

_{ij}) is the degree of coherence of the light source employed at the optical distance ΔL

_{ij}. Optical paths L

_{1,2,3}are obtained by integration along three separated paths, from the first fiber-optical coupler (1 × 3), throughout fibers and gaps between, defined by the micromachined platform, till the second-combining optical coupler (3 × 3):

_{core}—is the refractive index of core of the optical fiber; n

_{air}is air index, equal to 1; n

_{liquid}—the refractive index of the examined liquid; L

_{1,2,3(1 × 3)}—lengths of 1 × 3 fiber-optic coupler arms; L

_{1,2,3(3 × 3)}—lengths of 3 × 3 fiber-optic coupler arms; and L

_{1,2,3}

_{GAP}are widths of micromachined platform channels. OPDs are Equation (3):

_{11}has non-zero values only when the argument is close to zero, the signal on the photodetector originating from the variable interferometric terms in Equation (3) occurs if $\Delta {L}_{12}\approx 0\mathrm{or}\Delta {L}_{13}\approx 0\text{}\mathrm{or}\Delta {L}_{23}\approx 0$, described by (4):

_{1GAP}scan time two zones of coherence signal appear when the 1st and 2nd conditions in Equation (4) are satisfied, in the extent of the light source coherence length. The 3rd condition in Equation (4) does not contain the scanning gap L

_{1GAP}, so it cannot give an interferometric signal. The fulfillment of the 3rd condition must be avoided, otherwise a severe spurious signal will occur. Also, the zones with satisfied 1st and 2nd conditions should not be overlapped.

_{air}= 1.

_{liquid}of fluid in the MFP2 microchannel is:

_{2GAP}= L

_{3GAP}), ∆K = K

_{1}− K

_{2}is a constant value and ΔL

_{1GAP}is the difference between the two maxima of the interferometric signals described by Equation (8):

_{liquid}, it is necessary, in addition to measuring ∆, to also know two constants: the microchannel width L

_{3GAP}and ∆K, determined by the differences of the coupler arms lengths. L

_{3GAP}is the distance between the opposing tips of the optical fibers and should be equal to the width of the micromachined channel of 125 µm. However, it cannot be taken as known due to the possible pullback of the fibers, caused by curing of the glue fixing the fiber in the positions. The difference between the fiber arms ∆K is specific for one measurement set-up and does not change during the measurement. Its value, however, is unknown at the beginning of the measurement. Thus, two constants, ∆K and L

_{3GAP}should be determined firstly using two reference fluids of known refractive indices.

_{3GAP}, which is the distance between the two centers of the coherence domain. Then, the actual length of the channel L

_{3GAP}can be found using a known fluid introduced into the microchannel. We were using Isopropanol (IPA) as a reference fluid, which has the refraction index ${n}_{IPA}^{lit}=$ 1.375 at 1298 nm and 22 °C, according to [24]. After two calibrating measurements, the index of the unknown liquid n

_{liquid}can be calculated by:

_{liquid}, but their difference $\Delta {L}_{1GAP}^{liquid}$, which is used in Equation (9). It means that there is no need to determine the exact start of the scan and resetting the gap width to zero before scanning, as it was the case in our previous experiments reported in [25], in which there was no reference microchannel.

_{liquid}) measurement is determined by the accuracy of the determination of distance between the two centers of the coherence area ($\Delta {L}_{1GAP}^{IPA}$, $\Delta {L}_{1GAP}^{air}$) which, in turn, relates to the accuracy of determining the two positions of the center of the coherence area (L

_{1GAP}). We assume that the refractive index of the reference fluid (${n}_{IPA}^{lit})$ is known from the literature with sufficient accuracy and precision, so it can be considered as an accurate constant.

_{1GAP}) is employed. This is done mechanically, by moving the tip of the optical fiber of the 1 × 3 coupler against the opposite optical fiber of the 3 × 3 coupler. These small-step movements were performed using a motorized stage and the position was read out using the built-in encoder.

_{11}(ΔL

_{ij}), decreases rapidly when ΔL

_{ij}rises for several micrometers. The maximum of interferometric term is reached when γ

_{11}(ΔL

_{ij}) equals one, i.e., when the interferometer OPD equals zero. Scanning the air gap in the reference arm, this position (denoted as L

_{1GAP}), where the interferometer OPD equals zero, can be found as the highest local maximum of interferometric term.

- The centroid algorithm, where the position of the center of coherence zone in the fringe pattern was calculated using the following equation [32]:$${L}_{1GAP}^{I,II}=\frac{{{\displaystyle \sum}}_{\left|I\left({L}_{p}\right)\right|\ge 0.3{I}_{max}}{L}_{p}\xb7\left|I\left({L}_{p}\right)\right|}{{{\displaystyle \sum}}_{\left|I\left({L}_{p}\right)\right|\ge 0.3{I}_{max}}\left|I\left({L}_{p}\right)\right|}$$
- The envelope fitting, where the set of local maxima of interferometric signal is fitted by Gaussian curve with its four parameters—center, width, height, and offset. Among them, the parameter center, that defines ${L}_{1GAP}^{I,II},$ is the only one of importance.

#### 2.3. Design of the Optofluidic Platform

^{3}and viscosity ν = 0.001 Pa⋅s. The simulation is done for four different values of the relative pressure at the inlet [0.001, 0.005, 0.01, 0.05] bar.

- D
_{H}is the hydraulic diameter of the pipe; - Q is the volumetric flow rate (m
^{3}/s); - A is the pipe cross-sectional area (m
^{2}); - u is the mean velocity of the fluid (SI units: m/s);
- μ is the dynamic viscosity of the fluid (Pa·s);
- ν is the kinematic viscosity (m
^{2}/s); and - ρ is the density of the fluid (kg/m
^{3}).

_{H}, defined as D

_{H}= 4A/P, where A is the cross-sectional area and P is the wetted perimeter. The wetted perimeter for a channel is the total perimeter of all channel walls that are in contact with the fluid.

_{e}< 1 is fulfilled for fluid speeds below ~1 cm/s. Since the critical value of R

_{e}is about 2000, for fluid speeds of several cm/s and lower, the use of the LF user interface is justified.

## 3. Experiment

_{1(1 × 3)}(see Figure 1). The photodetector signals from two pigtailed InGaAs photodiodes (Roithner Lasertechnik, Austria) were amplified by a pair of transimpedance amplifiers and acquired by National Instruments 16-bit/100kHz DAQ card. Simultaneously, the encoder (associated to the motorized Z600 actuators) digital signals were captured by the same card. The processing of the signals was made using the software package MATLAB (MathWorks, Natick, MA, USA).

## 4. Results and Discussion

_{Δ}in Equation (11), of 0.304 µm. Applying Equation (10), the standard deviation in refraction index measurement is calculated as σ

_{n}= 0.0031. This value can be considered as the precision of the index measurement.

_{3GAP}). The sensitivity of the method increases linearly with increasing channel width, because the difference in the position of the centers of the coherence region is equal to the product of the channel width and the measured index, see Equation (6). It can be seen in Figure 7 that in our experiment it is possible to observe changes in ΔL

_{1GAP}less than 0.2 µm. This value gives a sensitivity in determining the refraction index of about 0.0016, because the channel width is 125 µm. However, the measuring range decreases with increasing channel width. The intensity of interferometric signal decreases with increasing distance between the fiber tips, due to weaker optical coupling. Experiments show that it is possible to measure the position of center of the coherence region with a declared accuracy at a distance of about 800 µm, giving an unnecessarily wide range of refractive index measurements (up to 5). If we would like to measure refractive indices up to e.g., value 2, the channel width should not exceed about 300 µm.

_{1GAP}was declared as the zero, where the refractive index equals to 1. Thus, the accuracy of the measurement of L

_{1GAP}(mean value) is absolute by definition. Results of the measurement of the refractive index of the aforementioned fluids are shown in Figure 8, along with the literature data [24,34,35].

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic presentation of fiber-optic Mach–Zehnder interferometer sensing configuration and micromachined platforms: MFP1,2—microfluidic platform; LSC—low coherence source, 1 × 3; 3 × 3—single-mode fiber-optic couplers; PD1,2—photodetectors; and ADC—analog to digital convertors.

**Figure 2.**(

**a**) Overall view and dimensions (in mm) of the micromachined structure; (

**b**) the cross-section of the microchannels for both fluid flow and fiber insertion; and (

**c**) top view of the cross-over of the microchannels.

**Figure 3.**3D distribution of velocity in the part of the structure given in Figure 2a for an applied pressure at the inlet of 0.01 bar.

**Figure 4.**(

**a**) Velocity intensity distribution along the middle line of the channel for a relative pressure of 0.01 bar applied at the inlet; and (

**b**) dependence of velocity intensity in a point in the middle of the channel on the pressure applied at the inlet.

**Figure 5.**Low-coherence interferograms acquired by scanning of microchannel of both optofluidic platforms. LCI1 belongs to MFP1, with air in the microchannel and LCI2 belongs to MFP2, the microchannel filled with air (lower curve) and Isopropanol (IPA) (upper curve).

**Figure 6.**Two low-coherence interferogram after band-pass filtration and local maxima detection, fitted by the double Gaussian curve.

**Figure 8.**Refractive index of subjected fluids obtained by our Mach–Zehnder interferometric configuration (light blue) and literature data for same fluids at 1300 nm (dark blue, patterned).

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**MDPI and ACS Style**

Djinović, Z.; Tomić, M.; Kocsis, A.
Optofluidic Micromachined Platform for Refractive Index Measurement. *Chemosensors* **2022**, *10*, 197.
https://doi.org/10.3390/chemosensors10050197

**AMA Style**

Djinović Z, Tomić M, Kocsis A.
Optofluidic Micromachined Platform for Refractive Index Measurement. *Chemosensors*. 2022; 10(5):197.
https://doi.org/10.3390/chemosensors10050197

**Chicago/Turabian Style**

Djinović, Zoran, Miloš Tomić, and Agnes Kocsis.
2022. "Optofluidic Micromachined Platform for Refractive Index Measurement" *Chemosensors* 10, no. 5: 197.
https://doi.org/10.3390/chemosensors10050197