Solution refractive index sensor based on high resolution total-internal-reflection heterodyne interferometry

Sensors and Actuators A 241 (2016) 190–196

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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna

Solution refractive index sensor based on high resolution total-internal-reflection heterodyne interferometry Jiun-You Lin Department of Mechatronics Engineering, National Changhua University of Education, No. 2, Shi-Da Road, Changhua City 50074, Taiwan, ROC

a r t i c l e

i n f o

Article history: Received 22 December 2015 Accepted 7 February 2016 Available online 9 February 2016 Keywords: Solution refractive index High resolution Total internal reflection Heterodyne interferometry

a b s t r a c t In this paper, a solution refractive index sensor is proposed based on a high resolution total-internalreflection (TIR) interferometry. In the proposed sensor, a half-wave plate and a quarter-wave plate that exhibit specific optic-axis azimuths are combined to form a phase shifter. When an isosceles right-angle prism whose base contacts with a tested solution is placed between the phase shifter and an analyzer with suitable transmission-axis azimuth, it shifts and increases the phase difference of the s- and ppolarization states at one TIR. The increased phase difference relates to the solution refractive index; thus it can be easily and accurately measured by evaluating the phase difference. The feasibility was demonstrated by experimental results. This method has the merits of both common-path interferometry and heterodyne interferometry. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Accurate measurements of solution refractive index (RI) are often needed in biochemical analysis and clinic monitoring. Many optical reflection techniques have been developed for measuring solution refractive index, such as Brewster angle methods [1,2], total internal reflection (TIR) interferometry [3–5], differential refractometry [6], and surface plasmon resonance (SPR) technique [7–9]. The Brewster angle method estimates the refractive index of a solution by measuring the reflectance of polarized light from a sample surface near the Brewster angle, and the system yielded a measurement resolution of nearly 10−4 RIU. In the TIR interferometry, the refractive index is inferred from the TIR phase difference between two interference signals. The method showed a detection limit of approximately 10−3 − 10−5 RIU. The differential refractometry uses a linear diode array to detect the angular distribution of the intensity of a divergent light beam reflected from the prism-sample interface. The desired refractive index is estimated by measuring the critical angle obtained from the curve of the ratio of the incident and reflected light intensities. A high resolution of better than 3 × 10−6 RIU from this method was achieved. The SPR technique determines the refractive index by measuring the SPR reflectance, phase or wavelength shifts of an associated light beam. The technique can achieve an excellent measurement resolution superior to 10−5 RIU.

E-mail address: [email protected] http://dx.doi.org/10.1016/j.sna.2016.02.020 0924-4247/© 2016 Elsevier B.V. All rights reserved.

In this paper, an optical sensor is proposed for measuring solution refractive index using high resolution TIR heterodyne interferometric technique. A linearly heterodyne light propagates through a phase shifter, consisting of a half-wave and a quarterwave plate, subsequently penetrating an isosceles right-angle prism with a solution at an angle larger than the critical angle. The light in the prism undergoes one TIR, finally traveling through an analyzer to extract the interference signal of the p- and s-polarized light. When the azimuth angles of the phase shifter wave plates are properly selected, the final phase difference exhibited by the solution refractive index of the interference signal is linked to the azimuth angle of the analyzer transmission axis. The final phase difference can be greatly enhanced by regulating the azimuth angle of the analyzer. The enhanced phase difference is easily measurable using heterodyne interferometric technique. Hence the refractive index is accurately obtainable from the data of the measured phase difference. Compared to the previous study [10], the TIR apparatus proposed here uses less number of wave plates, thereby simplifying the optical configuration and reducing the fabrication cost. The feasibility of this method was demonstrated by the experimental results, which yielded measurement sensitivity and resolution levels of approximately 104 (deg/RIU) and1.2 to 2.5 ×10−5 RIU at the measurement range of 1.332 − 1.341.

J.-Y. Lin / Sensors and Actuators A 241 (2016) 190–196

191

be derived using Fresnel’s equations and Jones matrix calculation [11]:



 2 ◦

  2 −1 sin 45 + sin sin i /np ) − (n/np ) 1/2  ◦   ◦ −1 −1

−1

␦ = 2 tan

tan 45 + sin

  = tan−1 Fig. 1. The solution refractive index measurement apparatus.

ts t  s tan ˇ tp t  p

(sin i /np ) · sin 45 + sin





,

(7)

(sin i /np )

 ,

(8)

and the transmission coefficients are determined as follows: 2. Principle

tp =

2.1. Phase difference resulting from high resolution TIR apparatus ts =

Fig. 1 demonstrates the optical configuration of the high resolution TIR apparatus. For convenience, the +z axis is set in the direction of the propagation of light and the x axis is perpendicular to the plane of the paper. A linearly polarized light whose light polarization plane is properly set at an angle  p from the x axis exhibits the following Jones vector:



Ei =

cos p

1 = 45 + sin

sin i np

ts=

cos2 ˇ

Et = sinˇcosˇ

sinˇcosˇ 2

sin ˇ



2np 1 − (sini /np )



0

ts ts exp(−iı/2)

1 √ 2

1

−i 1

2





ımax = 2tan



1/2

,

(9)

,

(10)

.

(11)

,

(12)

 1/2 2



1/2

2

(np /n) − 1 2(np /n)



.

(13)

The phase-level change allows the ϕ versus  i curve to increase the linearity, extending the variation range of the phase difference ϕ. This increased linearity can enhance the uniformity of the sensitivity of the ϕ versus  i curve. Fig. 2 displays the relation between

  ×

−i

2

2 1/2

cosi + np 1 − (sini /np )

−1

0

1/2

Eqs. (6)–(12) indicates that the phase difference ϕ depends on the parameters of ,, n, np , and  i . If the values of , , n, and np are specific, the phase difference ϕ is a function of the incident angle  i . When the parameter  (determined by the value of ␤) is set toward 45◦ , the value of tan(45◦ ±) will become large, as shown in Eq. (6). Under the condition, proper selection of the parameter  can substantially increased the phase difference ϕ. In the proposed method,  is used to vary the phase level of ı/2 and is determined based on the azimuth angle of the fast axis of H1 . In this method, it is set at approximately (␲/4 − ı,max /4), where ımax denotes the maximal value of the phase difference ı and is expressed as follows [12]:

(2)

tp tp exp(−iı/2)



2

2 1/2





When  i exceeds  ic , which is the angle that makes  1 equal the critical angle  1c , the light is completely reflected at the prism/tested solution interface. The light output from the prism travels through an analyzer ANt (the transmission axis is ␤ to the x-axis) for interference. The amplitude Ei becomes Et , as follows:









.



np cos i + 1 − sin i /np

(1)



2 cos i

2np 1 − sin i /np

tp =

The light is guided to pass through a phase shifter, comprising a half-wave plate H1 (with fast axis at a /2 angle to the x-axis) and a quarter-wave plate Q1 (with fast axes at 45◦ respect to x-axis), and is subsequently incident at  i on one side of an isosceles right-angle prism P with refractive index np . The prism is mounted on a rotation stage. The hypotenuse of the prism is contacted with a tested solution of refractive index n. The light beam penetrates into the prism at an incidence angle of  1 onto the prism/solution interface. The relation between the angles  i and  1 can be determined as follows: −1





sin p

◦

2 cos i

cos i + np 1 − (sin i /np )



.



np cos i + 1 − (sin i /np )

cos sin sin

−cos



cos p sin p



 = (At1 cosp exp(i) + At2 sinp exp(i␲/2))

cosˇ



sinˇ

(3)

where the amplitudes At 1 and At 2 can be written as follows:

 At1 =

 At2 =

1/2

1 2 2 [(tp t  p cos ˇ) + (ts t  s sin ˇ) + tp t  p ts t  s sin 2ˇ · sin(2 + ı)] 2

,

(4)

,

(5)

1/2

1 2 2 [(tp t  p cos ˇ) + (ts t  s sin ˇ) − tp t  p ts t  s sin 2ˇ · sin(2 + ı)] 2

and the phase difference ϕ can be expressed as follows:  = tan−1 [− tan(45◦ − ) · tan( + ı/2 − /4)] − tan−1 [− tan(45◦ + ␴) · tan( + ␦/2 − /4)]

.

(6)

In Eqs. (3)–(6), ı is the phase difference between the s- and ppolarizations of one TIR at the prism-solution interface; (tp , ts ) and (t p , t s ) are the transmission coefficients at the air-prism and prismair interfaces, respectively;  and  are the parameters introduced using the phase shifter and analyzer ANt , respectively. ı and  can

the phase difference ϕ and incident angle  i at an azimuth angle of ␤ when the conditions of np = 1.77862 and n = 1.332, and the calculated value  ∼ = ␲/4 − ımax /4 = 36.8◦ are substituted into Eqs. (6)–(12). For comparison, the relation of the phase difference ı versus the incident angle  i is marked as “o” in Fig. 2. The simulated results indicates that at the angles 44◦ ≤ ␤ ≤ 46◦ the phase difference ϕ exhibits sharp and large phase-difference variations around the incident angle  io at which the phase difference ϕ = 0◦ . By contrast, the curve ı indicates the condition of a small, unchangeable phase-difference variation. Additionally, Fig. 3 shows the plots of the reflection coefficients At 1 and At 2 , as exhibited in Eqs. (4) and (5). Because at the parameter  ∼ = ␲/4 − ımax /4 and the angles 44◦ ≤␤ ≤ 46◦ , the value of [(tp t p cos␤)2± (ts t s sin␤)2 ] is close to that of tp t p ts t s sin(2␤)·sin(2±ı) in the vicinity of  io , the simulation therefore demonstrates that the values of At1 are large and At 2 are small, especially at ␤=45◦ . Based on the characteristics of the distinct sharp phase-difference variation, and the dependence

192

J.-Y. Lin / Sensors and Actuators A 241 (2016) 190–196

Fig. 2. The phase difference ϕ versus the incident angle  i for 40◦ ≤␤ ≤ 50◦ .

between the phase difference ϕ and the solution refractive index n, the system can be applied for measuring the refractive index n of the contact solution with high resolution.

Although ϕ is independent of  p , It and Ir depend on  p , as indicated in Eqs. (14) and (15). To increase the contrast of It and Ir , the following condition should be applied to the measurement system: ␣ is closed to 0◦ and  p is closed to 90◦ as ␤ approaches 45◦ .

2.2. Phase difference measurement using heterodyne interferometry 3. Experimental results Fig. 4 illustrates the experimental setup for performing this measurement. A linearly polarized light passes through a half-wave plate H0 and its polarization plane is at  p with respect to the x-axis. The light passes through an electro-optic modulator (EO) driven at an angular frequency ω, and is incident on a beam splitter (BS). The BS divides the light into two parts: reflected and transmitted beams. The reflected beam proceeds through an analyzer ANr at a transmission axis ␣ to the x-axis, entering a photodetector Dr . The intensity detected by Dr can be determined based on the following Jones matrix calculation: Ir =

1 2



2

2



2(cos ˛ cos  p ) + 2(sin ˛ sin p ) + sin(2p ) sin(2˛) cos (ωt − BS ) ,

(14)

where Ir is the reference signal and ϕBS is the phase difference between the p- and s-polarizations produced by the reflection at BS. The transmitted beam passes through a phase shifter and penetrates into an isosceles right-angle prism P at  i on one side of the prism. After one TIR, the light output from the prism travels through an analyzer ANt at a transmission axis ␤ to the x-axis, and ends at a photodetector Dt . The intensity of the light detected by Dt can be determined based on Eq. (3)



2

2



It = |Et |2 = (At1 cos p ) + (At2 sin  p ) + At1 At2 sin 2p · cos(ωt +  − /2) ,

(15)

and It is the test signal. The intensities It and Ir are transmitted to a lock-in amplifier (LIA) for phase analysis, allowing the phase difference = ϕ+ϕBS − /2

(16)

to be accurately measured. The final phase difference ϕ = −ϕBS + ␲/2 is obtained from Eq. (16) as ϕBS there can be estimated with Chiu’s method [3]. As indicated from Eqs (6)-(13), the solution refractive index n can be calculated with measurement of ϕ if  i , , np and ␤ are specified.

To validate the approach, pure water and some glucose solutions in different weight percent were tested. A SF11 isosceles right-angle prism with np = 1.77862 was used as a TIR apparatus. The prism and the analyzer ANt were, respectively, mounted on a high-precision rotational stage (Model SGSP-120YAW, Sigma Koki) and on a precision polarizing rotation holder (Model SPH30, Sigma Koki). The angular resolutions of the rotational stage and the holder are 0.0025◦ and 0.014◦ , respectively. The 632.8 nm line from a HeNe laser modulated by an electro-optic modulator (Model 4002, New Focus) was the heterodyne polarized light. The heterodyne light generated a frequency difference of 1 kHz between p- and spolarized beams. A lock-in amplifier (LIA) (Model SR830, Stanford) with an angular resolution 0.01◦ was applied to measure the phase difference. Based on the results reported by Chen et al. [7], the temperature coefficient of refractive index of solution was inferred to be dn/dT∼ =−1.1×10−4 / ◦ C at temperature T = 15 ∼ 35 ◦ C. The result shows that a temperature variation will result in the measurement errors. To avoid the situation, the temperature in the experiment was performed at room temperature T = 28 ◦ C using a temperature controller. The error caused by temperature fluctuation can therefore be negligible. First, we estimate the value of  by measuring the phase difference ϕ under the conditions of  p = 45◦ ,  = 0◦ , and ␤ = 44◦ , and the azimuth angle of Q1 at 0◦ with regard to the x-axis. Under the operation conditions, the phase difference ϕ can be equal to the equation −ı, if the total internal reflection occurs. Then the sample was slowly rotated to identify the angle of  ic that occurred at the abrupt change of the phase difference ϕ = −ı. The angle of  ic = 6.220◦ was measured, and the refractive index n = 1.332 can be obtained based on Snell’s law. By using Eq. (13), the constant ∼ = ␲/4 − ımax /4 = 36.8◦ can also be estimated. Next, the azimuth angle of H1 was set to meet the constant value of , and the azimuth

J.-Y. Lin / Sensors and Actuators A 241 (2016) 190–196

Fig. 3. The reflection coefficients (a) At 1 and (b) At 2 at the angles 40◦ ≤ ␤ ≤ 50◦ .

193

194

J.-Y. Lin / Sensors and Actuators A 241 (2016) 190–196

Laser

H1 Q1

BS

H0

Rotation stage

Phase shifter

Heterodyne light source

ANt

P

Dt

EO n Driver

ANr Temperature controller Dr Ir

Lock-in Amp

It

PC

Fig. 4. The schematic diagram of the refractive index measurements.

Table 1 Experimental results and the corresponding reference data. Glucose concentration (g/l)

ϕ (◦ )

n (T = 28 ◦ C)

nref (T = 25 ◦ C)

0 10 20 30 40 50 60 70

34.50 25.05 15.95 4.38 −8.24 −22.60 −32.45 −40.46

1.33200 1.33331 1.33436 1.33553 1.33673 1.33876 1.33926 1.34032

1.33231 1.33349 1.33468 1.33587 1.33706 1.33825 1.33944 1.34063

4. Discussion To estimate the measurement resolution of this system, the equation ϕ is differentiated; thus, the resolution can be related as follows: nres = |

Fig. 5. Measurement results and associated theoretical line of phase difference versus the refractive index of glucose solutions.

angle of Q1 was adjusted to 45◦ . Finally, the incident angle  i = 8.3◦ and the azimuth angle ␤ = 44◦ were chosen. In addition, the azimuth angles of  p and ␣ were set as 85◦ and 5◦ respectively to increase the contrast of the signals It and Ir . Fig. 5 shows the plotted measurements and theoretical results, where “O” represents the measured data, and the solid line represents theoretical calculations by substituting the reference values nref into Eqs. (6) and (7). The reference values nref are taken from another method proposed by Yeh [13]. The measured ϕ and their associated n values of the samples are listed in Table 1. In addition, the associated reference values nref are also presented in Table 1 for comparison. As seen in Fig. 5, the measurement values differ slightly from the theoretical results, because of the experiments of the two methods being operated at different measurement temperature. However they still demonstrate the same trend in phase-difference variations.

∂n |SD , ∂

(17)

where nres is the measurement resolution and ϕSD the measurement standard deviation (SD). In the system, the standard deviation (SD) was calculated from eight measurement data for each concentration sample. According to the calculated results, the maximum and the minimum SD values were found to be approximately 0.21◦ and 0.10◦ . Substituting the values of ϕSD ∼ = 0.21◦ and 0.10◦ , and the experimental results into Eq. (17), the resolution nres between 1.2 × 10−5 and 2.5 × 10−5 RIU can be obtained. In addition, the sensitivity S of this system is defined as follows: S=|

∂ |, ∂n

(18)

Based on the results shown in Fig. 5, the sensitivity was calculated to be S∼ =104 (deg/RIU). Although the measurement resolution and sensitivity can be further improved at the azimuth angle ␤ = 45◦ , both the intensity and the contrast of the test signal decrease rapidly. To avoid these conditions, ␤ = 44◦ was chosen in the experiment. However, at the fixed angle ␤, the RI sensitivity and RI resolution can still be improved by regulating the  value without reducing the intensity and the contrast of the test signal. Fig. 6 shows that at ␤ = 44◦ regu-

J.-Y. Lin / Sensors and Actuators A 241 (2016) 190–196

Fig. 6. The phase difference ϕ (␲/2 − ı,max /2) ≤ ≤(␲/4 − ı,max /8).

versus

the

incident

angle

i

for

Fig. 8. The reflection coefficient (␲/4 − ı,max /2) ≤ ≤(␲/4 − ı,max /8).

195

At 2

versus

the

incident

angle

i

for

reflected light is greatly enhanced to result in high measurement sensitivity and resolution, as the wave plates and the analyzer in the interferometer under appropriate conditions. We measured some glucose solutions in different weight percent with a measurement resolution and sensitivity of 1.2 to 2.5 × 10−5 RIU and 104 (deg/RIU), respectively, at a measurable range of 1.332–1.341. This method has advantages of both common-path configuration and heterodyne phase measurement. Acknowledgment The authors would like to thank the Ministry of Science and Technology, R. O. C, for financially supporting this research under Contract No. 102-2221-E-018-021. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.sna.2016.02.020. Fig. 7. The phase difference ϕ versus the refractive (␲/4 − ı,max /2) ≤ ≤(␲/4 − ı,max /8) at a specific incident angle  i .

index

n

for

lating the  value significantly changes the slope of the ϕ versus  i curve, thereby leading to the variation in the RI sensitivity, RI resolution, and the measurable range. Fig. 7 demonstrates the phase difference ϕ versus the refractive index n for the various parameters  at a specific incident angle  i . Clearly, at the parameter (␲/4 − ı,max /3) ≤ ≤(␲/4 − ı,max /8), the system suitably detects a minute RI variation owing to its high sensitivity and narrow measurement range. Conversely, it can be applied for measuring a large RI difference at the parameter (␲/4 − ı,max /2) ≤  ≤ (␲/4 − ı,max /3). Fig. 8 also reveals that at (␲/4 − ımax /2) ≤  ≤ (␲/4 − ımax /8) all the reflection coefficients At 2 are almost equal (At2 ∼ =0.02 ∼ 0.03) in the measurable range. It means that at a fixed angle ␤ the intensity and the contrast of the test signal can be maintained nearly constant under the different values of . 5. Conclusion In this paper, we have designed a highly sensitive total-internalreflection sensor for measuring the refractive index of a solution. The phase difference between s- and p- polarizations of totally

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Biography Jiun-You Lin received his MS degree from the Institute of Electro-Optical Engineering of National Chiao Tung University, Taiwan, in 2000 and his Ph.D. degree from the

Institute of Electro-Optical Engineering of National Chiao Tung University, Taiwan, in 2004. He joined the faculty of National Changhua University of Education in 2005, where he is currently an associate professor with the department of Mechatronics Engineering. His current research activities are in optical metrology and optical sensor.