Shorya Awtar, David Shorya Awtar, David Reinharth Reinharth , , Klint Klint Rose, Rose, Wenyang Wenyang Sun, Hoe Sun, Hoe Phong Phong Tham Tham Optical MEMS Scanner for Optical MEMS Scanner for Bio Bio - - Medical Imaging Medical Imaging Group F2 Group F2
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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