Fundamental study for measuring microflow with Michelson interferometer enhanced by external random signal

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1 Bulletin of the JSME Journal of Advanced Mechanical Design, Systes, and Manufacturing Vol.8, No.4, 2014 Fundaental study for easuring icroflow with Michelson interferoeter enhanced by external rando signal Masaki MICHIHATA*, Phong TRAN DANG*, Terutake HAYASHI* and Yasuhiro TAKAYA* *Departent of Mechanical Engineering, Osaka University 1-1 Yaadaoka, Suita, Osaka , Japan E-ail: Received 7 March 2014 Abstract We propose a easuring technique for icroflow based on the stochastic resonance phenoenon. The inute changed signal fro the icroflow hidden within the threshold of ulti-threshold iaging sensors, such as CCDs, can be reconstructed using an external rando signal. The differences in optical path length fringes of a Michelson interferoeter were enhanced by scattered light using a icro Brownian particle solution. In this paper, we investigate the required characteristics of the external rando signal nuerically and experientally. The feasibility of the proposed ethod was experientally confired. The nuber of pixels required to reconstruct the signal was saller than expected owing to internal and environental noise signals. We show that the standard deviation of the external rando signal plays an iportant role in enhancing the accuracy of the easureent. Key words: Microflow, Stochastic resonance, Interferoeter, Optical path difference, μ-tas, CCD 1. Introduction Recently, there has been significant growth of research into icrodevices that use the flow of liquid reagent in icro channels, such as lab-on-chip and icro-total analysis syste (µ-tas) devices. It is not straightforward to evaluate reactions, ixing or separation of fluids because of the scale effect and hence to understand the icroflow in these devices (Arora et al., 2010). A easureent technique for icroflow is necessary in order to clarify characteristics such as velocity, density, teperature and coposition. Micro particle iage velocietry (icro-piv) has been developed as the easureent technique for velocity distributions of icroflows (Sinton et al., 2004). However, the refractive index of the icroflow is difficult to easure, although it is effective for analyzing icroflow properties. Understanding the refractive index in icroflow helps in onitoring the aterial coposition, ixing, cheical reaction process and so on. This study eploys a light interferoeter to sense the inute change of optical path length fro the icroflow refractive index. For the visualization of a flow-field, a two-diensional iage sensor, such as a charge-coupled device (CCD) caera, is necessary. However, the dynaic range of these iage sensors is narrow. The quantization process degrades the resolution, and unwanted internal noise, such as shot or readout noise is caused. To address these probles, this study ais to establish a ethod for easuring refractive index with high sensitivity for the visualization of icroflow using external rando signals. There are several ethods to copensate the quantized data in an iage, such as dithering (Gaaitoni, 1995) and digital or low pass filters. These techniques treat the already-quantized data and hence interpolate the iages. It is not possible to restore the original signal, because the inforation between discrete signals has already been lost. The proposed ethod ais to reconstruct the original signal hidden in the sensor threshold. In any biological systes, the detection of a weak signal has been achieved using external or internal signals. This is explained by a phenoenon called stochastic resonance (Gaaitoni, 1998), in which the signals hidden within the sensor threshold can be obtained by adding an appropriate additional external signal. In order to realize this ethod, the properties of the external signal are essential, being required sae physical quantity as the original signal. This study proposes to use the scattering rando signal as the external signal to stiulate the iage of the interference fringes. A CCD caera is used Paper No

2 as a sensor. Our purpose is to verify the feasibility of this visualization ethod for icroflow based on stochastic resonance. This ethod would be best suited for the case in which the optical path difference fro the icroflow does not generate a steep change teporally or spatially. 2. Principle In analogue to digital conversion, inute changes in the signal are hidden in the threshold of the sensor, such as CCD. We propose a easureent principle for the interferoeter that will reconstruct the hidden inforation within ulti-threshold sensors on the basis of stochastic resonance (Michihata et al., 2013; Tran et al., 2013). The fundaental concept of the ulti-sensor detecting syste based on stochastic resonance (Collins et al., 1995) is shown in Fig. 1(a). One original signal is considered (Fig. 1(b)). An external rando signal (Fig. 1(c)) is added to the original signal before it reaches the sensors in order to stiulate the sensor (Fig. 1(d)). The external signal ust be independently rando for each sensor. The sensor digitizes the original signal together with the external rando signal (Fig. 1(e)). These discrete signals are then sued and averaged to reconstruct the original signal (Fig. 1(f)). To apply this concept, ultiple sensors are required, and these should be ulti-threshold sensors. In practice, the original signal consists of interference fringes varying in space and tie according to the icroflow. To easure the icroflow, a CCD caera is eployed as the ultiple threshold sensor array. Therefore, the original signal is not identical to the easured signal. Although different signals are incident on different sensors, several neighboring sensors are used to average the signal so that differences between the easured signal and incident signal to each sensor are iniized. This directly relates to the easureent accuracy. The larger the nuber of sensors averaged, the ore precise the easureent. The sensors are averaged spatially and teporally as shown in Fig. 2. The output of sensors, P (i,t), are averaged along with the sensor nuber, i, and tie, t, (or frae nuber) to obtain the (a) Flow of the signals (b) Original signal (c) External rando signal (d) Mixed signal (e) Quantized signal (f) Reconstructed signal (output) Fig. 1 Concept of signal detection based on the stochastic resonance 2

3 Fig. 2 Averaging of pixels on the CCD caera. Fig. 3 Scheatic diagra of the Michelson interferoeter with external rando signal. averaged output intensity P ave as follows, where a and b are the first and last sensor nuber, respectively. 3. Siulation 3.1 Siulation odel P ave = b t n i=a t=t 0, (1) First, we investigate the properties of the proposed ethod using a coputer siulation prior to experients. Our proposed syste incorporates a Michelson interferoeter, which is illustrated in Figure 3, with the easured paraeter being the change of the optical path length. A CCD caera was used as ultiple threshold sensors to easure the intensity of the interference fringes. The light bea propagates through the saple. We assue that the refractive index of the saple changes slightly and uniforly. This variation produces a change in the optical path length, resulting in changes of the intensity distribution of the interference fringes in the CCD. For siplicity, it is presued that all pixels of CCD caera receive the exact sae change in one frae. These variations of the refractive index are set equivalent to an intensity of the interference fringes saller than 1 gray level of the CCD. The interfered light is cobined with the external rando signal, which has a spatially and teporally rando intensity distribution. The ixed bea is incident to the CCD. The intensity of the ixed bea is I = I 1 + I I 1 I 2 cos( 4πdΔn /λ + φ) +δ i, (2) where I, I 1, and I 2 are the intensity of ixed bea at CCD, object bea and reference bea, respectively; φis the phase difference in the object and reference beas; λ is the wavelength of the light source; d is the thickness of the saple; Δn is the change of the refractive index of the saple; δ i is the intensity of the external rando signal; and i is the pixel nuber of the CCD. The CCD used was 8 bits, so the intensity of the interference fringes was quantized by 256 gradations. The wavelength of the light source was 633 n. In the siulation, the external rando signal was treated as a signal with white Gaussian distribution (zero ean). The standard deviation of the external rando signal was varied fro 0 to The nuber of the sensors is deterined by N pixels in the CCD. The correlation coefficient, C, was used to quantify the effect of the external rando signal, P (i,t) C = i=1 ( x i x) y i y ( ) ( x i x) 2 y i y i=1 i=1 ( ) 2, x = i=1 x i, y = i=1 y i, (3) where x i and y i are input and output data, and is the nuber of data points. A preliinary calculation shows that a change of 1 grayscale level in the CCD is equivalent to a change of in the intensity of the interference fringes, I, and also equivalent to a change of in the refractive index of the saple, Δn.. 3

4 Fig. 4 Siulated reconstruction of the CCD signal. Fig. 5 Siulated reconstruction of the rap signal 3.2 Siulated result The possibility of reconstructing the original signal using the external rando signal was checked. The conditions of the siulation were: I 1 = I 2 = 1, d = 100 µ, and φ = 6.09 rad. Standard deviation of δ i = The axiu variation width of Δn = , which results in changes in the intensity of the interference fringes saller than the threshold of the CCD sensors. The nuber of the sensors, N, was 400. The siulated results are shown in Figure 4. As shown, the input signal, saller than the threshold of the CCDs, could be reconstructed. The correlation coefficient of this reconstructed signal was The proposed ethod was copared with noral detection by the CCD for the case of a rap function as the input signal. The thickness of the saple, d = 50 µ; the intensity of the external rando signal at that pixel, δ i = 0.006; and the axiu variation width of refractive index, Δn = 0 to Figure 5 shows the siulated result. Without the external signal, the soothly changing signal was not easured correctly. However, the output signal of the proposed ethod follows the input signal, which verifies the effectiveness of the proposed ethod. We then exained the influence of the aplitude of the external rando signal, which is controlled by the standard deviation. The standard deviation of the external rando signal was varied fro 0 to 0.01 with different nubers of sensors, N. Other paraeters were fixed: d = 100 µ, φ = 6.09 rad, and Δn = As shown in Fig. 6, the external rando signal produces the axiu of the correlation coefficient.. Considering that a standard deviation of is equivalent to 1 gray level, the standard deviation of the external rando signal ust be saller than half of 1 gray level of the CCD. With a large nuber of sensors, the correlation coefficient was close to 1 and steeply increased with the standard deviation of the external rando signal. This clearly shows that the nuber of sensors is highly iportant to iprove the sensing perforance. We also note that the correlation coefficient decreased for increased standard deviation of the external rando signal. This eans that increasing the aplitude of the external rando signal above the ideal level no longer enhances the sensor perforance. This relationship of the standard deviation with the correlation coefficient depends on the original signal. When the original signal varied greatly, the optial standard deviation becae close to half of 1 gray level. Therefore, the aplitude of the external rando signal ust be tuned depending on the conditions such as the nuber sensors in the CCD. The resolution was evaluated as follows. A step signal of a certain height was input together with the external rando signal. The output signal was evaluated if it can be distinguished into two regions before and after the additional step signal, as shown in Fig. 7, Step 1 and Step 2, respectively. The paraeter, D, is introduced to evaluate the resolution D = ( I step2 σ step2 ) ( I step1 σ step1 ), (4) where I bar and σ are the average and standard deviation of the ixed intensity output signal, respectively. When the value D is positive, the signal is considered to be distinguished. The iniu change of the refractive index at the sallest value D is considered as the resolution of the syste. In this case, d = 100 µ, and the standard deviation of the external rando signal was optiized fro 0 to 0.03 every tie. The siulated result is shown in Fig. 8. By increasing the nuber of sensors the resolution was rapidly iproved. Considering both Fig. 6 and Fig. 8, the nuber 4

5 Fig. 6 The influence of the aplitude of the external signal. Fig. 7 Scheatic of including a step signal. Fig. 8 Siulation odel for the resolution of the proposed ethod. Fig. 9 Phase differences between signals and threshold. Fig. 10 SNR for changing signal phase in the proposed odel of sensors should be larger than 100 to obtain better sensing perforance. On the other hand, a sall nuber of the sensors is required, as entioned above. This iplies that there is an optiu nuber of sensors. The perforance of the proposed ethod is deeply influenced by the phase difference between the signal and sensor thresholds (Fig. 9). Aong sub-threshold signals, a signal near the threshold (Signal 1) can be stiulated with an external rando signal of sall aplitude. A higher aplitude external rando signal is needed to stiulate the signal in the center of the upper and lower threshold region (Signal 2). Thus, the phase difference should be discussed. For this investigation, the input signal was set to be a sinusoidal wave. The response aplitude was copared with the noise aplitude of different frequencies (signal to noise ratio, SNR). Changing the phase difference, φ fro 7.1 to 7.75 rad, the axiu aplitude ratio was as shown in Fig. 10. As anticipated, higher SNR was obtained for the signal near the threshold and the lowest for signals near the center of the threshold region. This nonlinear perforance should be noted as an iportant property of the proposed ethod. 4. Experient 4.1 Experiental setup A scheatic of the experient setup for testing the feasibility of the proposed concept is shown in Fig. 11. It is a 5

6 Fig. 11 Experiental setup Fig. 12 Size distribution of particles Table 1 Fig. 13 CCD iage of the scattered light. The iage brightness has been increased to aid the reader Standard deviation of the scattered light Laser power [µw] Standard deviation [gray level at 8-bit] Spatial Teporal Michelson interferoeter based syste, which consists of the Michelson interferoeter as the original signal and the scattered light as the external rando signal. The light was ixed at bea splitter 2. Two different lasers are used as a light source to avoid the interference between the original signal and the external signal. The laser diode (λ = 532 n) for the interference fringes and the He-Ne laser (λ = n) for the scattered light are eployed. The laser power was adjustable using the variable neutral density filters (filter 1 and filter 2 in Fig. 11). Fine positioning of irror 1 was controlled by a piezo-stage. A CCD caera (8-bits, 30,000 pixels) was used as the ulti threshold sensors. The pixel size of the CCD is 6 µ 6 µ. To reduce the environental effect (teperature fluctuation and air turbulence), the whole the optical syste was accoodated in a heat-isolated box. To test the proposed principle, instead of a icroflow saple, irror 1 was tilted to provide the change of the optical path length, causing the interference fringes on the CCD. Scattered light was used as the external rando signal, derived fro a icro Brownian particles solution prepared by silica particles and alcohol solvent. For the stochastic resonance, the external signal ust be rando for tie and for 6

7 each single pixel (Collins et al., 1995). Dynaic light scattering has been previously confired to provide an appropriate scattering length (Tran et al., 2013). The average size of the silica particles was 400 n (see Fig. 12). The concentration of the particles in the solution was 8.0 g/l. 4.2 Randoness of external signal Figure 13 shows the iage of the scattered light taken by the CCD, which shows the external signal is spatially randoly distributed over whole sensor array of the CCD. The iages were taken for 100 fraes with the frae rate of 5 fps. The laser power was varied fro 62 µw to 816 µw. The pixels were evaluated to calculate the standard deviation of the intensity for 400 pixels (20 pixels 20 pixels) for each iage. The teporal property was evaluated by calculating the standard deviation of the intensity of a randoly chosen fixed pixel across each of the 100 fraes. The results are shown in Table 1. The standard deviation changes with the laser power as expected. Thus, the standard deviation of the external rando signal can be tuned by the laser power. However, if the laser power of the scattered light were high, the intensity of the ixed light (original signal and external signal) incident onto the CCD is doinated by the external rando signal. Therefore, the laser power should be set as sall as possible not to influence the original signal. 4.3 Measureent of interference fringe with the external rando signal Feasibility of the proposed ethod Feasibility of the proposed ethod was experientally confired. An 8-bit CCD was used as reference to check the perforance of the signal reconstruction. The 8-bit-signal was converted into a 4-bit-signal and this 4-bit-signal was applied as the pseudo-original signal to test the perforance of the proposed ethod. The 16 gray levels at 8-bits was shrunk to 1 gray level at 4-bit. Mirror 1 was slightly tilted to induce interference fringes on the CCD as shown in Fig. 14. The optical path length of the easured saple was not varied teporally in this case. The iage was taken for 100 fraes in series at a frae rate of 5 fps. The standard deviation of the external rando signal was set to 6 gray levels at 8-bits, which is 0.38 gray levels at 4 bit, and the laser power was set to 250 µw. The intensity of interference fringes with the external rando signal was copared to the intensity without the external rando signal. Figures 15 and 16 show that results of one intensity profile of the interference fringes (A to B in Fig. 14) without and with the external rando signal, respectively. In this case a single pixel was averaged over the 100 fraes. Black and red plots indicate the 8-bit and 4-bit data, respectively. Figure 15(a) shows the averaging ethod itself has a significant effect to interpolate the profile, however, there are still quantized signals found in Fig. 15(b). On the contrary, Fig. 16 shows that the external rando signal could enhance to obtain the hidden data. It was possible to reconstruct a saller change than the 1 gray level at 4-bit (see Fig. 16(b)). We note that the intensity profile of 4-bit is lower than one of 8-bit as seen in both Fig. 15 and Fig. 16. This is because the conversion process (8-bit into 4-bit) produces a half-bit bias in the intensity profiles. These results clearly show the effect of the external rando signal to reconstruct the hidden data Pixel averaging effect As entioned above, the nuber of pixels at one frae to average should be as sall as possible when considering Fig. 14 Representative iage of interference fringe with the external rando signal 7

8 Fig. 15 (a) (b) Intensity profile (A to B) of the interference fringe without the external rando signal Fig. 16 (a) (b) Intensity profile (A to B) of the interference fringe with the external rando signal Table 2 Conditions for averaging pixels Spatial pixel Teporal pixel Total nuber of pixels Case 1 1 (1 1) 100 fraes 100 Case 2 4 (2 2) 25 fraes 100 Case 3 9 (3 3) 11 fraes 99 Fig. 17 Interference fringes with three different averaging 8

9 the accuracy of reconstruction. The results shown in Figs. 15 and 16 were teporally averaged, which decreases the teporal resolution. Therefore, the intensities of the pixels are averaged both spatially and teporally, as shown in Fig. 2. The nuber of pixels is fixed to 100. Three different averaging ethods are copared as suarized in Table 2, and the resultant intensity profiles are shown in Fig. 17. There is no rearkable difference because the nuber of pixels used was alost the sae in each case. However, we note that case 3 (red line in Fig. 17) exhibits a flatter profile. This is because spatial averaging by 3 3 pixels is the effect of a low pass filter. However, the teporal resolution is 10 ties greater owing to the low frae nubers required. Therefore, if we sacrifice spatial resolution, the nuber of pixels to average in the spatial doain for any one frae should be increased Influence of the nuber of frae to average Our siulation study found that the nuber of fraes to average is iportant to the perforance of the proposed ethod, as shown in Figs. 6 and 8. To increase the accuracy of the easureent, the nuber of the fraes should be increased. However, the higher nuber of fraes akes the easureent resolution worse. We investigate the influence of the nuber of the frae experientally. At fixed spatial averaging (set to 1 1); the teporal averaging was varied by averaging over different nubers of fraes. Figure 18(a) shows the results for the whole profile and Fig. 18 (b) and (c) show the detailed parts. Surprisingly, even averaging 5 fraes works as shown in Fig. 18(b) where the intensity distribution by averaging 5 fraes is well agreed with others (50 fraes and 100 fraes). However, if carefully looking at Fig. 18(c), the averaging 5 fraes has errors and the signal is still quantized. Averaging over 50 and 100 fraes shows only a very slight difference fro each other. Therefore, the optiu nuber of fraes to average lies between 5 to 50 fraes. (b) (a) Fig. 18 Interference fringe with different teporal averaging (c) Fig. 19 Experiental result to copare averaging effect in teporal and spatial doain 9

10 The reason why averaging 5 fraes still works is considered to be the existence of internal and environental noise signal. In the easureent syste, there is always the shot and read out noise in the CCD, which was about 2 gray levels at 8-bit in our setup. Environental fluctuations such as vibration, teperature fluctuation, air turbulence are further noise sources. All environental and internal noise induces about 10 gray levels peak to peak. These signals ay serve as the rando signal, so the total external rando signal can be larger than expected. These environental and internal noise signals are also the reason why siple averaging is able to interpolate the profile, as shown in Fig Influence of the standard deviation of the external signal As shown in Fig. 6, the standard deviation of the external rando signal is iportant to enhance the easureent accuracy. Also as expected, at the sae standard deviation, the easureent resolution is different in ters of the phase lag to the sensor threshold. It is not easy to change only the standard deviation experientally (the intensity of the scattered light is also changed). Therefore in this case, the standard deviation of the external rando signal was fixed and the threshold was changed. That is, 8-bit-signal was converted into 3-bit and 4-bit signals for coparison. The easureent conditions were the sae as the previous investigation above. The standard deviation of the external rando signal was set to 6 gray levels at 8-bits, which is 0.38 gray levels at 4 bit and 0.19 gray levels at 3 bit. Spatial and teporal averaging were 1 1 and 100 fraes, respectively. The result is shown in Fig. 19. The intensity profile of the 3-bit is still quantized at any parts. This is because the standard deviation of the external rando signal is too sall to stiulate the original signal. This iplies that accuracy depends on the standard deviation of the external rando signal. Therefore this has to be optiized against the height of the threshold of the sensor used. 5. Conclusion We proposed a easuring technique for icroflow by eploying a Michelson interferoeter enhanced by an external rando signal. The inute changed signal hidden in threshold of the ulti-threshold sensor can be reconstructed by adding the external rando signal to the original signal. Our findings are suarized as follows. 1) We experientally proved that the external rando signal could enhance the perforance of the easureent. 2) The nuber of pixels to average is saller than expected in the siulation study because internal and environental noise is incorporated into the external rando signals. Therefore, the reconstruction of the signal could be achieved with less than 50 pixels. 3) The standard deviation of the external rando signal plays an iportant role in iproving the accuracy of the easureent. Hence, it is iportant to optiize the relation between the standard deviation of the external rando signal and the height of the threshold of the sensor. As a ulti-threshold sensor, 8-bit CCD was used in this paper. This ethod is expected to be applicable other sensors with appropriate external rando signal. References Arora, A., Sione, G., Salieb-Beugelaar, G. B., Ki, J. T. and Manz, A., Latest developents in icro total analysis systes, Anal. Che., Vol. 82, No. 12 (2010) pp Benzi, R., Sutera, A. and Vulpiani, A., The echanis of stochastic resonance, J. Phys. A: Math. Gen., Vol.14 (1981), pp.l453-l457. Collins, J. J., Chow, C. C., and Ihoff, T. T., Stochastic resonance without tuning, Nature, Vol.376, No.20 (1995) pp Gaaitoni, L., Stochastic resonance and the dithering effect in threshold physical systes, Phys. Rev. E, Vol.52, No.5 (1995), pp Gaaitoni, L., Hänggi, P., Jung, P. and Marchesoni, F., Stochastic resonance, Rev. Mod. Phys. Vol.70 (1998) pp Michihata, M, Tran Dang, P., Hayashi, T. and Takaya, Y., Fundaental investigation for Stochastic etrology with ulti-sensors for icro-syste technology: In case of optical path length, Proc. 21 st photonics in easureent, 10

11 (2013) (Published in CD). Sinton, D., Microscale flow visualization, Microfluid. Nanofluid., Vol.1, Issue 1 (2004) pp2-21. Tran Dang, P., Michihata, M., Hayashi, T. and Takaya, Y., Enhanceent of sensing resolution for inute refractive index change of icro flow by light interferoeter using stochastic resonance, Proc. the 7th international conference on leading edge anufacturing in 21st century (2013) pp [DOI: /jads.2014jads0049 ] 11