Optical MEMS Scanner for Bio-Medical Imaging

Shorya Awtar, David Shorya Awtar, David ReinharthReinharth, , KlintKlint Rose, Rose, WenyangWenyang Sun, Hoe Sun, Hoe PhongPhong ThamTham

Optical MEMS Scanner for Optical MEMS Scanner for BioBio--Medical ImagingMedical Imaging

Group F2Group F2

Optical Coherence Tomography

fiber

f2 + f3

f1

f2 f3 f4 OCT Images

Current OCT Probe

Design Requirements• Optical probe to scan an optical beam across tissue

– Handheld, pen-like package– Fit within 9 mm inner diameter

• Two-dimensional scan– 2-4 kHz for each direction– +/- 15 degrees optical (+/- 7.5 mechanical)

• Reflective scanner surface• 2-10 µm spot size at 1-2 mm working distance• Power: 1 mA at 50-100 volts

Typical 2D Mirror Designs

Single beam design (OMRON)

Double gimbals

Folded beams

3-D Self-assembly

• Decoupled DOFs– Cantilever beams produce

bending– Torsion bar produces

twisting

Fixed Base

Mirror

Torsion Bar

CantileverBeam

IntermediateMassCantilever

Beam

x

θ

F

F

x

θ

L

L/3 Virtual Pivot

• No mirror translation– Principle of Virtual Pivot– Valid for zero moment at

the cantilever tip

Device Concept

Bending Mode560 Hz

Torsion Mode15.5 kHz

Finite Element Based Modal Analysis

• Bending Mode Analysis

• Assume torsion bar is rigid in bending

• Generalized coordinates : x1and θ1

Mass 2 Mass 1

MIRROR

CantileverBeams

TorsionBar

m1

m2

x1

x2

θ1

L1

LC

L2

CO

2 2 1 1 1 1 11 1 1 1 1

2 222 21 1 1 1 1 1 1

1 2 1 1 1 1

( ) ( ) 2 2

[ ( ) ] ( ) 3 2 6

c c in

oc c c in

k L k L cms b s k X mL s b L s V

k L k L k L cI s b b L s mL s b L s X V

+ + = + + Θ +

+ + + Θ = + + −

System Modeling: Dynamics

4 3 211 2 1 1 1 1 1 1 1 2

2 221 1 1

1 1 1 1 1 2 1 1

21 1 1 1 1 1 11

( ) .....3

.... 3 12

3 3 6 2

c c oc

c c

c c i

LmI s mb I b s mk L L k I b b s

L k Lb k L L b k L b k s

L L k L k L cm L s b L s V

+ + + − + + − + + + Θ

= − + − +

n

First Bending Mode

Second BendingMode

System Modeling: Dynamics

• Torsion Mode Analysis

• Generalized coordinates : φ1and φ2

{ }{ }

4 3 21 2 1 4 2 3 1 2 2 1 2 3 4

2 3 4 1 4 1 2 2 2 2

( ) ( ) .....

.... ( )

t t t t t t

in

I I s I b I b s I K I K K b b s

K b b K b s K K K c V

+ + + + + ++ + + Φ =

Φ1

Φ2

System Modeling: Dynamics

• Blue: Bending Analysis– W1=553 Hz

Q1=1740– W2=4225 Hz

Q2=2700

• Red: Torsion Analysis– W3=2083 Hz

Q3=56000– W4=16.3 kHz

Q4=26190

System Modeling: MATLAB Results

16.27 kHz15.54 kHzPure Torsion of Torsion Bar7

12.63 kHzOut-of-plane Bending of Torsion Bar6

11.67 kHzIn-plane Bending of Cantilever Beams and Torsion Bar5

5623 HzIn-plane Bending of Torsion Bar4

4225 Hz3025 HzCompound Bending of Cantilever 3

2083 Hz2190 HzSimple Torsion of the Cantilevers2

553 Hz562 HzSimple Bending of Cantilevers 1

MATLAB Results

ProEResultsDescriptionVibration

Mode

FEM vs. Analytical Model

Range of Motion and Input Voltage

• Analytical Estimate (MATLAB)– Θ1/Vin is 0 dB @ 553 Hz

=> 5.7deg/V for Q=1740– Φ2/Vin is –15 dB @ 16.27 kHz

=> 1.8 deg/V for Q=26190

• FEA Estimate (Pro/Mechanica)– Apply dynamic load boundary condition– Specify a quality factor of Q=1500– 15 deg/V

• Experimental measurement of damping shall produce more accurate estimates

• Effect of air damping directly affects performance of scanning system

• A simple model was used to estimate 4 different damping coefficients of the structure

Fluid Mechanics Considerations

• Stokes’ Law ⇒ Re < 1⇒ linear relationship between force and velocity

• For our model, Re = 23.1 (> 1)

What to do?

Work in the transition region (10 < Re < 1000)Messy calculationsFluidic FEM analysis

Make simplifying assumptions and work with Stokes’ Law

System Modeling: Damping

Working With Stokes’ Law

• Assuming Stokes’ Law for Re > 1 results in huge underestimation of actual damping present in system

• Solution: Use the constant value calculated from Stokes’ Law and multiply it by a factor of 10

Compensates for underestimationtakes into account material damping inherent in system

System Modeling: Damping

Translational Damping in Bending (b1)

• Assuming Stokes’ Law:

⇒

⇒ b1 = 4.8×10-6 Ns/m

1 1DF C wV bVη= =

1 1Db C wη=

System Modeling: Damping

Rotational Damping in Bending (b2)

• Assume that force F acting on m1 as it rotates is constant

• Moment, M1, acting on m1 about CG of the structure due to F is:

( )1 max1 2b l q p

Mθ

ω−

⇒ =

pFpFp q

=+ q

FqFp q

=+

Fp Fq

System Modeling: Damping

• Next, we find M2 acting on m2due to bending of the beams

• Pressure, P :

• Differential force, dF :

• Then M2 of entire mass m2about O is:

21

2mm wVb

wFP ==

xdxw

bdFm

ωθmax1=

221 max22 1 max0

1212

mw

mm

bM x dx b wwθ ω θ ω= =∫

• Moment of entire structure about its CG:

⇒

⇒ b2 = 1.68×10-12 Nsm

( )( )21 max1 2 26

12 mbM M M l q p w bθ ω ω = + = − + =

( )( )21 max2 6

12 mbb l q p wθ

= − +

System Modeling: Damping

Rotational Damping in Torsion (b3 and b4)

• Consider m1. We know that F = CDηw1V

• Pressure, P :

• Differential force, dF :

• Moment of the entire mass m1 about centerline:

⇒

⇒ b3 = 6.12×10-13 Nsm b4 = 1.65×10-14 Nsm

1

1

D DC wV C VPw b bη η

= =

xdxCdF D ωηθmax=

∫ === 20 3

31max

2max

1

1212

w

DD bwCdxxCM ωωηθωηθ

31max3 12

1 wCb Dηθ= 3max4 12

1mD wCb ηθ=

System Modeling: Damping

Deflection Due to Gravity

• Deflection: x = mg/k1 = 0.183 µm

Modeling: Static Deflection

Dynamic Deformation of Mirror [1]

• Dimensions of scanning mirror optimized to satisfy Rayleigh Limit.

• Rayleigh Limit allows a peak-to-valley surface deformation, δ, of λ/4.⇒ δ < 212.5 nm

• δ for our mirror: 212.1 nm

( )( ) 5

2

22

221183.0

−

=l

Etf θπνρδ

[1] R.A. Conant, J.T. Nee, K.Y. Lau and R.S. Muller, “A Flat High-Frequency Scanning Micromirror”, Hilton Head 2000 Conference, Hilton Head, South Carolina, June 4-8, 2000.

Modeling: Mirror Deformation

δ

• Maximum bending stress, σmax = 2.73 MPa

• Maximum shear stress, τmax = 611 MPa

• Yield strength of silicon: 2,800 – 6,800 MPa

⇒ Fatigue by cyclical bending and torsion is not a concern

Safety Factor of 2

Modeling: Fatigue Failure

• Electromagnetic:Provides relatively large forces and has high repeatabilityBut poor in high-frequency operationsExternal coils needed to produce magnetic field

• Electrostatic:Versatile and simpleBut inherent problem of electrostatic instability (i.e. pull-in voltage)Problem of non-linearity – crosstalk is too large to achieve independent control of the angles

• Thermal:Inherent limitations for long-term use – at high temperatures, silicon loses its nearly perfect linear-elastic propertiesLarge power consumption

• Piezoelectric:Very rapid response to alternating voltage input required to drive the MEMS structure at its higher resonant frequency of 15.5 kHzAlso highly repeatable and very reliable for MEMS applications

Actuation Schemes

PZT Actuation: Base Deflection

)sin( 21 VKLVKtotal +=δ

0 2 4 6 8 10 12 14 16 18 200

1

2

3

4

5

6

7

Voltage (V)

Tip Deflection (um)

δ

Piezo

Silicon Beam

Actuated Piezo

Tip

defle

ctio

n

• Voltage causes piezo to constrict– Electrical to mechanical

coupling

• Traction between piezo and beam causes bending

• Deflection vs. voltage should be linear

K1=20.5 K2=1.85e-4

Voltage

L

Fabrication: Backside Processing

• SOI wafer substrate– Defines thickness for front-

side features– Provides etch stop for

backside DRIE

DRIE on SOI DRIE on Si

MassStructure

Fabrication: Frontside Processing

Stiffener

PZT,Electrodes, and Insulating layer

Insulating layer,Electrodes, and

Bond pads

Reflective coating

Fabrication: PZT Details

• Sol-gel deposition– Two step annealing for texture

• Etched in two step process– 10 HN4F:1HF and 2HCl:H2O

• Poled at elevated temperature with applied voltage– Increases effective d33

Device Packaging

• Packaged in a molded plastic “seat”

• Inset patterned into package aligns device

• Gap below mirror to allow for deflection

• Secured with epoxy• Contact pads wire

bonded to lead frame

Optical Design Requirements

• Optics designed to achieve a small light spot at the working distance for probing tissue

• Design for optics should interface with the two-dimensional scanning MEMS device– Probe pen diameter < 15 mm, length ~ 150 mm– Spot size between 2-10 µm– Working distance of approximately 2 mm

Fiber

Pigtail Collimator

Achromatic Lenses

Probe Pen Package

Optics Analysis

Analysis method: Gaussian Beam modeling and ABCD matrix calculation

Waist of the beam from the collimator is w0=0.2mm, divergence half angle is

2

201

2 1'

1

+==

wl

ff

R πλ

θθ

-

-301.4mm

1801.0526.0

==π

R

( ) mmlθwffw 526.0

1

2 =+=i

wj

Rq81.7+277.311

2 =−=πλ

.2.0 0=θ

)()(1

)(1

2 zj

zRzq πωλ

−=

[ ][ ]DCq

BAqqin

inout +

+=

5mm20mm f1+f2=46mm 5mmFiber

12mm

L1 L2 L3

10mm

Optics Analysis

6 mm

0.27 mm 2.6 mm

6 mm

0.53 mm 5.2 mm

Spot at Lens 1 Spot at Lens 2

Working distance d=2.013mm Spot size 2.02um

Ray tracing when beam tilted:

L1 L2 L3

Optics Simulation

• Simulation Software – Code V– spot size & dispersion curve

Spot size at working distance

Aberration analysis

Mechanical Design

• Final design is about the size of a dry-erase marker

Front CapMain Tube Mirror Housing

Rear Cap

Mechanical Assembly

ElectricalInput

OpticalInput

Package Alignment

Device Calibration/Optical Alignment

Front Cap, Main Tube

14mm 11mm

16mm

• Front cap and main tube each have threaded sections to secure lenses

Optical Calibration

Scanning (MEMS) Mirror Mount

Fixed Mirror Mount Mirror Alignment Screws

Mirror Mounts

Fixed Mirror

ScanningMirror

Electronic Connections

Holes for Alignment Screws

Rear Cap

Set Screw to Align Collimator with Fixed Mirror

Optical Fiber,Collimator

Electrical Input

• Rear cap provides strain relief for the incoming optical fiber and electrical wire

Conclusions

• Probe size– OD: 16mm, ID: 11mm, Length: 90mm

• Scanning Mirror– Scan frequencies: 550Hz & 15.5 kHz– Scan angles: +/- 10 deg (mechanical)

• Aluminum scanner surface• Spot size: 2.02 µm, Working distance: 2mm• Power Requirement: 20 Volts, <1mA