Performance of a Micro-Optical Wall Shear Stress

Sensor Based on Whispering Gallery Mode Resonators

Tindaro Ioppolo1, Ulas K. Ayaz2, M. Volkan Ötügen3

Southern Methodist University, Dallas, TX 75275

In this paper, we discuss the dynamic performance of a novel wall shear stress

sensor concept based on whispering gallery mode (WGM) shifts of a dielectric

microsphere resonator. In the shear stress sensor model, the wall shear stress acting

on a sensing element, typically 125 m in diameter, is transmitted mechanically to

the microsphere and the transmitted force leads to shifts in the WGMs of the

microsphere. By monitoring these WGM shifts, the magnitude as well as the

direction of the wall shear stress can be measured. The measurement principle was

demonstrated in a previous paper which presented static shear stress results. The

sensor used in the present study is a dielectric microsphere made of

Polydimethylsyloxane (PDMS), and is tested for loading for dynamic measurements,

An electronic circuit is developed to track the fast moving optical resonances

(WGM) under dynamic loading.

I. Introduction

The measurement of wall shear stress still remains as a challenge in fluid mechanics. The dynamic

measurement of local wall shear stress is important both for the standpoint of basic fluid mechanics

research, and the perspective of dynamic flow control. Most of the current sensors are indirect

measurement techniques where the wall shear stress is obtained through a set of assumptions. These

include hot-wire/film-based anemometry1 or heat flux gages

2, surface acoustic wave sensors

3 and laser

based velocity sensors, the surface oil film interferometry.4,5,6 7

A number of new MEMS-based sensors

have been proposed recently (thermal8’9, floating element

10 and optical wall shear sensor

11) whose

fabrications are simple but may prove difficult to calibrate. Another type of sensors are optical MEMS

(MOEMS) sensors, whose working principle is based on laser Doppler anemometry. However promising

they are, generating sufficiently small measurement volumes for high Reynolds numbers proves to be

difficult. A direct measurement method is the floating element sensor which is based on the measurement

of the deflection of a floating beam whose top surface is flush with the wall. A number of techniques

(capacitive12

, piezoresistive13,14

, differential optical shutter, fringe moiré15

) have been developed to measure

the displacement of the floating element, and although some of them are promising, some may suffer from

electromagnetic noise interference, tunnel vibration, and undesirable flow through gaps16

.

The wall shear stress sensor discussed in this paper is based on the WGM shifts of a dielectric

microsphere. This concept was discussed in 17

, where we demonstrated the feasibility of a WGM wall shear

stress concept for the first time. The concept was demonstrated experimentally under steady flow

conditions. In this paper we carry out a further study of the sensor concept and its performance, including

its dynamic response and bandwidth. The WGM sensor provides a high dynamic range as well as temporal

and spatial resolution, further it is immune to electromagnetic interference.

The principle of the sensor can be explained as the measurement of force exerted by the flow on a

small element flush with the wall. This element passes the force to the dielectric microsphere, whose

WGM shifts are monitored to measure the force exerted on the microsphere. Such measurement of the

1 Post Doctoral Associate, Mechanical Engineering Dept., AIAA Member

2 Doctoral student, Mechanical Engineering Dept.

3 Professor and Chair, Mechanical Engineering Dept., AIAA Associate Fellow

47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition5 - 8 January 2009, Orlando, Florida

AIAA 2009-314

Copyright © 2009 by Tindaro Ioppolo. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

force principle is built on our previous studies on WGM-based force sensor concept18

, and will be

explained briefly in the following section.

II. Measurement Principle

As noted in the previous section, the measurement principle of the WGM sensor concept is based on the

mode shifts of the dielectric microsphere of about 300-950 m diameter. When the microsphere is coupled

to an exposed section of the fiber core (Fig.1), the optical resonances (called the whispering gallery modes

or WGM) are observed as sharp dips in

the transmission spectrum as shown in

Fig. 2. Provided that the refractive index

of the sphere is greater than that of the

surrounding medium, the light introduced

tangentially into the microsphere

circulates along the inside surface

through total internal reflection. After

completing a circle in the interior of the

sphere, if the light returns to its starting

point in phase, resonances are observed.

Such a condition for optical resonance is

satisfied if lnR 02 , where is the

vacuum wavelength of the laser l is an integer, R0 is the sphere radius and n is the sphere refractive index

An incremental change in the index of refraction or radius of the sphere will result in a shift in the

resonance frequency, therefore, any change in the physical condition of the surrounding that induces a

change in index of refraction or radius of the microsphere can be sensed by monitoring the WGM shifts.

n

n

R

R

0

0 (1)

Here is the frequency. The observed

WGM linewidth , is related to the quality

factor, Q =/. The smaller the energy loss

inside the sphere, the higher the Q-factor;

with Q as the losses vanish. One of the

remarkable features of this measurement

concept is the very high Q factors that can

be achieved with this arrangement (Q values

of 107 or better can be achieved). Since the

position of the the WGM in the transmission

spectrum determines the value of the

measured quantity (in the present

application, force acting on the sphere) the

large Q values lead to high measurement

resolution. The distance between two consecutive resonances, the free spectral range (FSR in Fig. 2) is

given by FSR = c/(2nR0) where c is the vacuum speed of light.. While is related to the measurement

resolution, FSR may be viewed as the measurement range in the traditional interferometric sense. However,

in the present, we developed an electronic circuit for WGM resonance tracking that locks the laser

frequency to a given WGM and follows it as it moves dynamically in the transmission spectrum under

unsteady force loading. With this feature, high-frequency unsteady measurements are possible and the

dynamic range of the measurement system is not limited by the FSR. rather, the dynamic range as well as

bandwidth of the sensor is limited by the material properties of the sensor (sphere).

Scanning laser

Photodiode

Optical fiber

Figure 1: Schematic representation of WGM sensor

FSR

1 2

Figure 2: Transmission spectrum

Ph

oto

dio

de

ou

tpu

t

III. Dynamic Force Measurements

3.1. Experimental Setup

The opto-electronic setup is shown schematically in Fig. 3. Briefly a tunable distributed feedback (DFB)

laser (with 1.312 µm central wavelength and 10mW maximum power) drives the system. The DFB laser is

frequency dithered over a small bandwidth (in the order of a resonance linewidth). The laser is coupled

into a single mode optical fiber, whose output end is connected to a fast photodiode to monitor the

transmission spectrum. A section of the fiber is tapered down to a diameter of ~10 µm (by heating and

stretching the fiber). The microsphere is brought into contact with the tapered fiber section to facilitate light

coupling between fiber and resonator. The transmission

spectrum through the fiber is normalized by a reference

signal taken directly from the laser and analyzed by

using an analog circuit, designed and built in-house, to

detect and then track the WGM resonance, allowing

unsteady force measurement. Once the resonance

location is found, it is given as feedback to the laser so

that the central wavelength of the dither corresponds to

the resonance frequency. The analog signal

corresponding to the resonance location is then

digitized using 16-bit A/D converter, and recorded on a

PC. The schematic of the WGM detection-tracking

system is shown in Fig.4. The normalized signal from

the analog divider, as depicted in Fig.5-a, is given as

input to a signal conditioning circuit that offsets the

minimum of the signal so that a portion of the signal

crosses the the “zero” level, as shown in Fig. 5-b. This

signal is then fed to a zero cross detector. The output of

the zero cross detector is used as logic control for a

switch that takes the average of the electrical current of

the laser diode during the interval the signal crosses the

zero level. The laser diode current is then digitized and

converted to the corresponding laser wavelength. Thus,

given a transmission signal, the analog circuit finds the

laser wavelength corresponding to the resonance location allowing unsteady force measurements. As

Figure 4: Block diagram of the WGM

detection-tracking analog circuit Figure 3: Opto-electronic setup

I

a)

))

Zero cross

detector output

b)

I

Figure 5: normalized signal a); Zero

cross detector input output, b)

described above, the corresponding laser current value is fed to the controller to update the central

wavelength of the laser dither. This way, the laser is “locked” to the selected resonance (WGM) and

continuously follows it allowing for unsteady measurements.

3.2. Dynamic Force Measurement

The experimental setup is shown in Fig. 6. The force is exerted on the microsphere using two stainless

steel pads that compress the microsphere

along the polar direction. (The polar

direction is that normal to the plane of light

circulation in the sphere). As shown in Fig

6, one of the pads is driven by a

piezoelectric actuator. The motion of the

piezoelectric actuator, in turn, is driven by

a power amplifier that is controlled by a

function generator. This way it is possible

to control the amplitude and frequency of

the motion of the piezoelectric actuator.

The input voltage to the piezoelectric-

actuator is recorded together with the

WGM shift by using a DAQ card. A series

of experiments were carried out in order to

investigate the WGM shift due to the

applied dynamic force for a range of frequencies.

The sensor used for these preliminary experiments

is PDMS (60:1) with a diameter of about 900m.

Figures 7, 8 and 9 show the input voltage of the

piezoelectric actuator and the corresponding

WGM shifts for three different frequencies. A

phase shift between the piezo actuator signal and

the WGM shift is seen in all three cases. This shift

is essentially due to viscous energy dissipation in

the sphere as it deforms. If we assume that there is

no time delay between the piezo actuator signal

and the actuator’s actual motion, the phase delay

between this signal and the WGM shift signal can

be used to estimate the energy dissipation in the

sphere sensor. Our near future goal is to carry out

Figure 6: Unsteady force measurement setup

-6

-4

-2

0

2

4

6

8

10

0.0 0.4 0.8 1.2 1.6 2.0

Time, ms

d

, p

m

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Vo

lta

ge, V

WG M

P iezo

Figure 9: Comparison of WGM shift to

piezo-electric actuator’s input voltage at 1

kHz.

-10

-5

0

5

10

15

20

0 2 4 6 8 10 12 14 16 18 20

Time, ms

d

, p

m

-0.5-0.4-0.3-0.2-0.10.00.10.20.30.40.5

Vo

lta

ge, V

WG M

P iezo

Figure 8: Comparison of WGM shift to

piezo-electric actuator’s input voltage at

100 Hz.

-5

0

5

10

15

20

25

0 50 100 150 200

Time, ms

d

, p

m

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

Vo

lta

ge, V

WG M

P iezo Input

Figure 7: Comparison of WGM shift to piezo-

electric actuator’s input voltage at 10 Hz.

a series of measurements similar to those shown in Figs 7, 8 and 9 to quantify the energy dissipation at

different frequencies in order to determine the mechanical quality factor of the sensor and the frequency

response characteristics of the sensor.For this, an appropriate spring-mass model of the sensor system must

be used. Such a model is shown in Fig. 11 corresponding to the wall shear stress sensor design depicted in

Fig 10.

IV. Conclusion

The dynamic performance of a

whispering gallery mode-based shear

stress sensor has been investigated. In

the experiments, a 900 m diameter

Polydimethylsyloxane (PDMS) sphere

was used. A sinusoidal load was

applied to the sphere uniaxially using a

piezoelectric actuator with frequencies

up to 1 kHz. An electronic circuit was

also developed and incorporated into

the measurement system to track the

dynamic, fast moving optical

resonances (WGM) under dynamic

loading The WGM shifts closely

followed the sinusoidal input signal to

the piezoelectric actuator. A small phase shift was observed between the actuator signal and the WGM

shift. This shift is attributed to the viscous energy dissipation in the sphere as it deforms..

Figure 10: Schematic of shear stress sensor a) Cross sectional, b) side view

Sensing Element

Contact Point

Polymeric Foundation

Microsphere sensor

Tapered Optical Fiber

Sensing Element

Contact Point

Polymeric Foundation

Microsphere sensor

Tapered Optical Fiber

a) b)

Figure 11: Modeling of the sensor

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Based on Whispering Gallery Mode Resonators", 46th AIAA Aerospace Sciences Meeting and Exhibit, 8-

11 January 2008 Reno Nevada. 18

T. Ioppolo T., M. Kozhevnikov, M. V. Ötügen, V. Sheverev. “Performance of a Whispering Gallery

Mode Resonator-Based Micro-Optical Force Sensor”, 45th

AIAA Aerospace Sciences Meeting and Exhibit,

8-11 January 2007 Reno Nevada.