D-type fiber optic sensor used as a refractometer based on total-internal reflection heterodyne interferometry

Sensors and Actuators B 101 (2004) 322–327

D-type fiber optic sensor used as a refractometer based on total-internal reflection heterodyne interferometry Ming-Hung Chiu a,∗ , Shao-Nan Hsu b , Hsiharng Yang b a

Department of Optoelectronics, National Huwei Institute of Technology, 64 Wunhua Road, Huwei, Yunlin 632, Taiwan b Institute of Precision Engineering, National Chung Hsing University, Taichung 402, Taiwan Received 24 September 2003; received in revised form 31 January 2004; accepted 1 April 2004 Available online 18 May 2004

Abstract A new type of fiber optic sensor (FOS) based on total-internal reflection heterodyne interferometry (TIRHI) is proposed. It can be used as a liquid refractometer. The phase shift difference due to the TIR effects between the P- and S-polarizations is measured using heterodyne interferometry with a D-type fiber optic sensor. Substituting the phase shift difference into Fresnel’s equations, the refractive index can be calculated. It has some merits, such as, high sensitivity and stability, small size and real-time measurement. © 2004 Elsevier B.V. All rights reserved. Keywords: Fiber optic sensor; refractometer; heterodyne interferometry

1. Introduction Fiber optic sensor (FOS) is used in the optical industry for measurement applications, such as, refractive index, stress, pressure, and temperature measurements, etc. Many types of FOSs are used as refractometers. Suhadolnik et al. [1] and Chaudhari and Shaligram [2] presented an optical fiber liquid refractometry based on intensity modulation. The sensing probe acted as a fiber-optic displacement sensor. Ilev [3] proposed a fiber optic refractometer that acted as an autocollimator with a single mode fiber. Meriaudeau et al. [4] and Slavik et al. [5,6] presented a gold island fiber optic sensor based on the surface plasma resonance (SPR) theory for refractive index sensing. Other technique for refractive index or concentration measurements with fiber optical Bragg gratings was presented in previous papers [7,8]. Lo et al. [9] developed a stable optical fiber refractometer using path-matching differential interferometries (PMDI) with two parallel Fabry-Perots sensing cavities. Shribak [10] proposed another optical fiber refractometer method based on the differential phase shift between the P and S components introduced after total-internal reflection. However, these methods are intensity methods making their resolutions often be decreased by the light source influence. ∗ Corresponding author. Tel.: +886-5-6329643x575/18; fax: +886-5-6329257. E-mail address: [email protected] (M.-H. Chiu).

0925-4005/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.snb.2004.04.002

In this paper, a new type of liquid refractometer based on total-internal reflection heterodyne interferometry (TIRHI) with a D-type fiber optic sensor is proposed. The phase shift difference between the S- and P-polarizations is a function of the refractive index, incident angle and the number of TIRs. If the angle of incidence and number of TIRs are known, and the phase shift differences are measured using the common-path heterodyne interferometry with a lock-in amplifier, the refractive indices of liquids will be achieved. In our results, the phase resolution had a value of 0.01◦ and the measuring sensitivity of refractive index was about 3 × 10−5 for the number 31 TIRs. Because the optical structure is a common path configuration with a large number of TIRs, it has merits such as high resolution and stability, small size and real-time measurement.

2. Principle 2.1. The phase shifts due to TIR effects From Fig. 1, a light from medium 1 is incident into medium 2, where n1 and n2 are the refractive indices of the reference medium and test medium, respectively, and n1 > n2 . If TIR is occurred, the beam after TIR will be induced into phase shifts in the P- and S-polarizations, respectively. According to Fresnel’s equation [11] the phase shift differ-

M.-H. Chiu et al. / Sensors and Actuators B 101 (2004) 322–327

323

dyne light source expressed by Jones matrix can be given by   EP eiw1 t , (3) E in = ES eiw2 t

Fig. 1. A light from medium 1 is incident into medium 2.

ence between the P- and S-polarizations is given using
  sin2 θi − n2 −1 δ = δP − δS = 2 tan , (1) tan θi sin θi where θi is the angle of incidence, δP and δS the phase shifts for the P- and S-polarizations and n the ratio of n2 to n1 . The relation curves between the phase shift differences δ and the angles of incidence θi for different n values are shown in Fig. 2. As θi or n increases, δ will decrease in a range of the incident angle from 86 to 90◦ . From these relations, Eq. (1) can be rewritten as   2 (2) n = sin θi 1 − tan 21 δ tan θi . From Eq. (2), if θi , δ and n1 are known, the refractive index n2 of the test medium could be calculated. 2.2. Total-internal-reflection heterodyne interferometry (TIRHI) From Fig. 1, a heterodyne light source has two linearly orthogonal polarizations which are the P- and S-polarizations with the frequencies w1 and w2 , respectively. The hetero-

Fig. 2. The phase shift differences vs. the incident angles.

where EP and ES are the P- and S-polarization amplitudes, respectively. After TIR, the beam will be induced the phase shifts, δP and δS . Then it can be given using   EP ei(w1 t−δP ) . (4) E TIR = ES ei(w2 t−δS ) When the beam after TIR passes through an analyzer with a 45◦ transmission axis to the P- or S-polarization direction for producing an optical interference signal. Therefore, the amplitude of light at the output of the analyzer is given using  

1 1 1 1 ES ei(w2 t−δS ) + EP ei(w1 t−δP ) , E out = E TIR = 2 1 1 2 ES ei(w2 t−δS ) + EP ei(w1 t−δP ) (5) and the interference intensity is given by I = |Eout |2 = 21 {ES2 + EP2 + 2ES EP cos[(w2 − w1 )t − (δS − δP )]} = 21 {ES2 + EP2 + 2ES EP cos[(w2 − w1 )t + δ]},

(6)

where (w2 − w1 ) is the beat frequency and δ is the phase shift difference between δP and δS . This optical signal can be transformed into an electrical signal using a photodetector. The phase shift difference of δ can be achieved in real-time using a lock-in amplifier comparing a reference signal with the same beat frequency. Because these two polarizations have the same optical path, the interference signal is really stable. 2.3. D-type fiber optic sensor The refractive indices of liquids can be measured using TIRHI with a prism and a precision rotator [12], or using a special prism at a specific incident angle [13]. In the same way, in this paper, a D-type FOS with a small incident angle range replaced the prism. This D-type FOS configuration is shown in Fig. 3. Fig. 3(a) shows that, a beam with P- and S-polarizations is coupled in and out of the fiber using two objective lenses (L1, L2). The D-type FOS consists of a D-shape fiber (D) with two transmission fiber sections. It is made of the same material of a general single-mode fiber and the sensing section is polished as a D-shape probe (D), the core must be exposed to the test medium for sensing liquids. Fig. 3(b) shows that the D-shape fiber, the height of fiber core is h and its length is L. Fig. 3(c) shows that the optical path length in a D-shape fiber core is a function of h and L, if the numerical aperture (NA) of the objective lens L1 is 0.1 and the air and fiber core refractive indices are 1 and 1.47, respectively, then the maximum coupled angle is given by

324

M.-H. Chiu et al. / Sensors and Actuators B 101 (2004) 322–327

where φ = lim tan

−1




N→∞

I = lim

N 

N→∞

N i=1 Ii Vi sinφi N i=1 Ii Vi cosφi

 ,

Ii ,

i=1

N

i=1 (Ii

V 2 = lim

N→∞

+2

− V i )2 N N j>i

i=1 (Ii Vi )(Ij Vj ) cos(φi I2

− φj )

,

φi = mi δi . and mi , and δi are the number of TIRs and the light phase shift difference at the ith incident angle. Ii and Vi are the average intensity and the visibility of the ith light beam interference, respectively. If the amplitudes of the P- and S-polarizations are equal, the visibility of Vi is equal to 1.0 and the total phase difference can be written as
 N sin φ i . (11) φ = lim tan−1 Ni=1 N→∞ i=1 cos φi If the launch angle of the light out of FOS is specific, θi is selected and m a constant integer. That is φ = mδ. 2.4. The configuration of measurement system Fig. 3. The D-type fiber optic sensor. (a) A beam is coupled in and out of the D-type FOS. L1, L2, objective lens; D, D-shape fiber. (b) The scheme of the D-shape fiber. (c) Total-internal reflection in the core of the D-shape fiber.

θNA = sin−1 (NA/nair ) ≈ 5.74◦ , the maximum refraction angle is given by θ1 max = sin−1 (sin θNA /n1 ) ≈ 3.9◦ and the minimum incident angle θi min is 86.1◦ , where n1 and nair are the fiber core and air refractive indices, respectively. From Fig. 3(c), The number of TIRs is given using m=

L , 2h × tan θi

This system can measure the phase difference between P- and S-polarizations by using the method of TIRHI for measuring the refractive index of a liquid. From Fig. 4, the heterodyne light source consists of a He–Ne laser, a polarizer (P), and an electro-optics modulator (EOM). The linear polarization light passing through a polarizer and an EOM will cause as a heterodyne light source with two orthogonal polarizations. And the difference frequency between them

(7)

and the total phase difference is given using φ = mδ,

(8)

where m is an integer. From Eqs. (7) and (8), the phase difference per unit length of D-type sensor is given using φ φ = . L L

(9)

From Fig. 3(c), the incident angle has a small range from θi min to 90◦ . The interference intensity is given using I(t) = lim

N→∞

N 

Ii (1 + Vi cos(2πft + φi ))

i=1

= I[1 + V cos(2πft + φ)]

(10)

Fig. 4. Block diagram of the experimental setup: P, polarizer; EOM, electro-optic modulator; H, half-wave plate; FOS, fiber optic sensor; A, analyzer; D, photodetector; FG, function generator; L: lock-in amplifier; C, computer.

M.-H. Chiu et al. / Sensors and Actuators B 101 (2004) 322–327

is decided by the modulation signal that came from a function generator (FG) [14]. This light source can be aligned its polarizations by using a half-waveplate (H) as the P- and S-polarizations corresponding to the plane of incidence of the sensing surface of the D-type FOS. The objective lenses (L1, L2) with the same numerical aperture of 0.1 are used to couple the light in and out of the FOS, respectively. Selecting a partial light with a specific angle launch out of FOS, the optical signal due to heterodyne interference can be achieved using an analyzer (A) and transformed into an electronic signal (It) by a detector (D). A lock-in Amplifier (L) was used for measuring the phase difference between the test signal (It) and reference signal (Ir). The reference signal also came from the function generator (FG) synchronously with the same frequency of the modulation signal. When the test medium on the FOS is changed, the phase difference will be changed immediately, and the phase difference variations can be recorded in real-time using a computer (C). The refractive index or concentration was achieved by substituting the δ value into Eq. (2) when the incident angle θi and n1 were known.

3. Experiments and results The experimental structure is shown in Fig. 4. The heterodyne light source had two linearly orthogonal polarizations with a 2 kHz frequency difference and a center wavelength of 632.8 nm. The fiber core of the D-type FOS with refractive index of 1.47 was about 4 mm long (L = 4 mm) and 4 ␮m high (h = 4 ␮m). The system was calibrated in air before measuring, and assumed that the refractive index of air was equal to 1. After calibration, for special incident angle, the launch angle of the partial of the beam out of the FOS was selected strictly at θi = 86.45◦ . Substituting the values of L, h, and θi into Eq. (7), the number of TIRs m was calculated about 31. The prism method had been verified the feasibility of the refractive index measurement [12], the experimental results could be looked upon as reference data. The optical path is shown in Fig. 5 and the experimental structure is also shown in Fig. 4, but FOS replaces by a right angle prism. The prism is made of SF11 with a refractive index of 1.77862,

Fig. 5. The optical path in a right angle prism.

325

Fig. 6. Phase difference comparisons between the D-type FOS and prism methods.

θ1 = 45◦ and θi = 68.426◦ for measuring variable alcohol concentrations from 10 to 90%. The measurement results of D-type FOS method were compared with the prism method to verify the correspondence between the theory and experiments. The test liquids were the same of the prism method. The results of phase differences versus alcohol concentrations of these two methods are shown in Fig. 6. It can be seen that the phase difference range for the D-type FOS with a large number of TIRs is much larger than that of the prism method. Then the sensitivity of the D-type FOS is better than the prism method. If the phase resolution measurement has a value of 0.01◦ , the concentration resolution is 0.06%. Because the phase difference is proportional to the FOS length, the sensitivity is increased if the D-type FOS length is increased. Substituting Eq. (8) into Eq. (2), the refractive indices for variable alcohol concentrations are presented in Table 1 and Fig. 7. The average refractive index resolution is about 3 × 10−5 at φ = 0.01◦ . From these results, the refractive indices between the D-type FOS and prism methods are very close. The average measurement accuracy was about ±0.002. For this reason, multiple TIRs are better than only one TIR. High sensitivity was demonstrated in the D-type FOS.

Fig. 7. Experimental results of the D-type FOS and prism methods.

326

M.-H. Chiu et al. / Sensors and Actuators B 101 (2004) 322–327

Table 1 The errors of refractive index of alcohol with variable concentrations Alcohol C (v/v) (%)

10 20 30 40 50 60 70 80 90

n2 (prism method)

1.336 1.338 1.342 1.345 1.350 1.354 1.360 1.365 1.372

n2 (FOS)

1.335 1.339 1.344 1.348 1.350 1.353 1.356 1.362 1.369

n2 = n2 (FOS) − n2 (prism)

−0.001 0.001 0.002 0.003 0.000 −0.001 −0.004 −0.003 −0.003

n2 m = ±1

m = ±2

φ = ±0.01◦

9.0 × 10−3 8.7 × 10−3 8.3 × 10−3 8.1 × 10−3 7.9 × 10−3 7.7 × 10−3 7.5 × 10−3 7.1 × 10−3 6.6 × 10−3

1.82 × 10−2 1.75 × 10−2 1.68 × 10−2 1.63 × 10−2 1.60 × 10−2 1.56 × 10−2 1.51 × 10−2 1.43 × 10−2 1.32 × 10−2

3.04 × 10−5 2.98 × 10−5 2.92 × 10−5 2.87 × 10−5 2.84 × 10−5 2.80 × 10−5 2.76 × 10−5 2.67 × 10−5 2.56 × 10−5

4. Discussion From Eqs. (2) and (8), the refractive index of n2 is a function of δ, θi , n1 , and m. The refractive index errors can be divided into three parts, the phase error (φ), the incident angle error (θi ), and the error due to the number of TIRs (m). These errors can be summed up as n =

∂n ∂n θi (m δ + m δ) + ∂φ ∂θi

(12)

where n = n2 /n1 , n1 is the refractive index of fiber core for the specific wavelength. n2 is the refractive index error for the test medium. In our experiments, the optical structure is a common-path configuration and the FOS is fixed on a stage, therefore the environmental influences could be canceled and the fluctuation of θi is zero. And the fluctuation of phase (φ) is only due to the error of lock-in amplifier that is equal to ±0.01◦ . From Table 1, the average refractive index error due to this item can be calculated at a value of ±3 × 10−5 . From Eq. (12), for estimating the value of n2 exactly, the phase errors are due only to the calculations of m and δ. Hence, the phase error φ = m δ is zero if there is no environmental influence or any pollution in the test liquid. If m = ±1 and m = ±2, the values of n2 are about of ±7.9 × 10−3 and ±1.6 × 10−2 , respectively. If the number of TIRs is estimated exactly, the errors m and δ are equal to zero. For this matter, the value of m can be calibrated in air before measuring and assume that n2 = 1.0. To sum up the minimum absolute errors of the phase and refractive index are about 0.01◦ and 3 × 10−5 , respectively. From Eq. (12), The last error item due to estimating error of θi from −0.1 to 0.1◦ for the variant alcohol concentrations is shown in Fig. 8. The maximum absolute value |n2 | is about 8 × 10−3 at θi = ±0.1◦ . We can reduced this errors, if m and θi are estimated exactly using numerical methods with respect to the known values for n1 , n2 , L and h. Therefore, from Table 1, the total refractive index error n2 comes from the lock-in amplifier phase error, n1 and θi . It has an accuracy of approximately ±0.002. Because the phase variation due to θi is larger than the others, FOS must be kept straight to prevent this error from

Fig. 8. The error of refractive index of n2 due to θi .

occurring. In another words, the FOS is very sensitive to bending. If FOS is kept straight and fixed on a holder or stage, the fluctuation of n2 is only due to the resolution of lock-in amplifier. And the average concentration and refractive index resolutions are about 0.06% and 3×10−5 , respectively, for a 4 mm long FOS. The common path heterodyne technique for measuring the phase shift difference between the P- and S-polarizations can achieve the interference fringe in real-time and it can exclude the influence of environment. The signal is more stable and easier to process than of the intensity-based system.

5. Conclusion A D-type FOS, used as a refractometer based on TIRHI was presented in this study. This device is very sensitive to refractive index measurements for liquids. The average concentration and refractive index resolutions for this FOS, at 4 mm long, were 0.06% and 3 × 10−5 , respectively. Although it has high resolution, but due to the errors of n1 and

M.-H. Chiu et al. / Sensors and Actuators B 101 (2004) 322–327

θi , the accuracy of n2 referring to the results of the prism method is only at ±0.002. Its small size has a large number of TIRs, and the phase shift is very larger than of only one TIR. Furthermore, it just only needs little liquid for testing. This method has the other merits, such as, simple, high stability and resolution, and real-time measurement.

Acknowledgements This study was supported in part by the National Science Council in Taiwan under contract no. NSC 91-2622-E150-022-CC3.

327

[8] A. Asset, S. Sandgren, H. Ahlfeldt, B. Sahlgren, R. Stubbe, G. Edwall, Fiber optical Bragg grating refractometer, Fiber Integr. Opt. 17 (1998) 51–62. [9] Y.L. Lo, H.Y. Lai, W.C. Wang, Developing stable optical fiber refractometers using PMDI with two-parallel Fabry-Perots, Sens. Actuators B, Chem. 62 (2000) 49–54. [10] M. Shribak, Polarimetric optical fiber refractometer, Appl. Opt. 40 (2001) 2670–2674. [11] M. Born, E. Wolf, Principles of Optics, seventh ed., Combridge, UK, 1999, pp. 48–52. [12] M.H. Chiu, J.Y. Lee, D.C. Su, Refractive-index measurement based on the effects of total internal reflection and the uses of heterodyne interferometry, Appl. Opt. 36 (1997) 2936–2939. [13] D.C. Su, J.Y. Lee, M.H. Chiu, New type of liquid refractometer, Opt. Eng. 37 (1998) 2795–2797. [14] D.C. Su, M.H. Chiu, C.D. Chen, Simple two-frequency laser, Prec. Eng. 18 (1996) 161–163.

References Biographies [1] A. Suhadolnik, A. Babnik, J. Možina, Optical fiber reflection refractometer, Sens. Actuators B, Chem. 29 (1995) 428–432. [2] A.L. Chaudhari, A.D. Shaligram, Multi-wavelength optical fiber liquid refractometry based on intensity modulation, Sens. Actuators A 100 (2002) 160–164. [3] I.K. Ilev, Fiber-optic autocollimation refractometer, Opt. Commun. 15 (1995) 513–516. [4] F. Meriaudeau, A. Wig, A. Passian, T. Downey, M. Buncick, T.L. Ferrell, Gold island fiber optic sensor for refractive index sensing, Sens. Actuators B, Chem. 69 (2000) 51–57. ˇ [5] R. Slav´ık, J. Homola, J. Ctyroký, Miniaturization of optic surface plasmon resonance sensor, Sens. Actuators B, Chem. 51 (1998) 311– 315. ˇ [6] R. Slav´ık, J. Homola, J. Ctyroký, Single-mode optical fiber surface plasmon resonance sensor, Sens. Actuators B, Chem. 54 (1999) 74– 79. [7] R. Falciai, A.G. Mignani, A. Vannini, Long period gratings as solution concentration sensors, Sens. Actuators B, Chem. 74 (2001) 74–77.

Ming-Hung Chiu received the MS and PhD degree from the Institute of Electro-Optical Engineering, National Chiao Tung University, Taiwan in 1994 and 1997, respectively. He joined the faculty of the Department of Electro-Optics Engineering at National Huwei Institute of Technology in 2001. His current research interests are in the areas of optical metrology, optical information processing, fiber optic sensor and smart structure. Hsiharng Yang is an associate professor in the Institute of Precision Engineering at National Chung Hsing University in Taiwan. He received his Doctor of Engineering degree from Louisiana Tech University (LaTech), USA in 1998. He served as a research assistant in the Institute for Micromanufacturing at LaTech. His research field focuses on the development of micro-electro-mechanical system (MEMS) and MOEMS products. Shao-Nan Hsu received the MS degree from the Institute of Precision Engineering at National Chung Hsing University, Taiwan in 2003. His current research interests are in optical metrology and fiber optic sensor.