Ishikawa Oku LaboratoryUNIVERSITY OF TOKYOhttp://www.k2.t.u-tokyo.ac.jp/

Development of variable-focus lens with liquid-membrane-liquid structure and 30 mm optical aperture

Lihui Wang, Hiromasa Oku, Masatoshi Ishikawa.University of Tokyo, Japanwanglihuiamos@gmail.com

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Research Background

• Normal Lenses:

• Single lens with Variable-focus:

wikipeida.org

glasses plastic

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Related Research

• Liquid-Membrane Lens• single liquid chamber• deformable wall (1or2)• [−6.0 +7.6] diopters• optical aperture 7mm• 1ms response time

• Liquid-Liquid Lens• [-50 +50] diopters• optical aperture 3.0mm• wavefront error 80.3nm

at 109mm focal length• 2ms response time

H Oku, et al. Applied Physics Letters, 2009

H Oku, et al. Optics Express, 2004

Dynamorph Lens Driving mechanisms:pressure, electreowetting, dielectric

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Dynamorph Lens

Un-solved Problem (Lens Aperture)

• Liquid-Liquid Structure (review Dynamorph Lens)• Capillary Length:

• If D(lens aperture) < < lc(capillary length), Gravity Effect is negligible.

Interface tension: 34.8mN/mDensity water: 0.997g/cm3 capillary length=12.7mm >> 3mm (lens aperture)Density PDMS :0.975g/cm3

• What if Large Optical Aperture!• Key Point: Capillary Length Surface Tension???

okay

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Research Purpose

• Variable-Focus Liquid Lens with Large Optical Aperture • Structures of liquid lens (30mm)• Sufficient optical performance

• Theoretical analysis • Membrane Deformation• Spherical Deformation• Symmetry Deformation

• Experiment • A prototype of liquid lens with 30m aperture• Evaluate optical performance

Next slide

FollowingNext slide

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Lens Structure

• Liquid-Membrane-Liquid Structure• elastic force surface tension capillary length

Liquid-Liquid Lens• optical performance

Liquid-Membrane Lens• large aperture

Liquid

Membrane

Liquid

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Membrane Deformation 1/2

• 30mm diameter with boundary clamped elastic membrane• Silicon membrane parameters:

• 30mm aperture, 0.1mm thickness, 1.8MPa Young modulus, 0.45 Passion ratio• Assuming uniform pressure acting on one side

• uniform pressure of [1 10 20 40 60 80 100 130] Pa

-15 -10 -5 0 5 10 150

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

radial coordinate (mm)

mem

bran

e de

form

atio

n (m

m)

p=1

p=10

p=20

p=40

p=60

p=80

p=100

p=130

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Membrane Deformation 2/2

• Recall capillary length

• assuming Water and PDMS infused (referring Dynamorph Lens )

Elastic force average

liquid-membrane-liquid is a possible solution

Liquid-Membrane-Liquid vs Liquid-Membrane

Elastic force

0 20 40 60 80 100 120 1400

0.5

1

1.5

2

2.5

3

3.5

4

external pressure(Pa)

mer

idio

nal s

tres

s of

ela

stic

tity(

N/m

)

Capillary length

0 20 40 60 80 100 120 1400

20

40

60

80

100

120

140

external pressure (Pa)

capi

llary

leng

th (

mm

)

meridional of elastic forceliquid-membrane-liquid lens

0 20 40 60 80 100 120 1400

0.5

1

1.5

2

2.5

3

3.5

4

mer

idio

nal o

f ela

stic

forc

e (N

/m)liquid-membrane-liquid lens

liquid-membrane lens

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Spherical Deformation 1/2

• Comparison of 3mm variable liquid lenses

Liquid-Liquid Lens vs Liquid-Membrane-Liquid Lens• Evaluate Criteria: wavefront error Peak-to-Valley (PV)

Root-Mean-Square-Error (RMSE)

Liquid-Liquid Lens• Aperture 3mm• Liquid-Liquid interface• Wavefront error (PV, RMSE)

New Model• Aperture 3mm• Liquid-Membrane-Liquid• Wavefront error (PV, RMSE)

Data from exist paperExperiment data

Data from simulation1. Modeling 3mm silicon membrane2. Acting pre-gravity map of water-PDMS3. External pressure loaded4. 3D deformation optical path lengths5. Optical path lengths spherical surface

H Oku, et al. Applied Physics Letters, 2009

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Spherical Deformation 2/2

• Comparison of 3mm variable liquid lens

Liquid-Liquid Lens vs Liquid-Membrane-Liquid Lens

Peak-to-Valley (PV)

Root-Mean-Square-Error (RMSE)

shows smaller wavefront error

40 60 80 100 120 140 160 180 200 220 240100

200

300

400

500

600

focal length (mm)

PV

val

ue (

nm)

liquid membrane pvliquid membrane liquid pv

40 60 80 100 120 140 160 180 200 220 24020

40

60

80

100

120

140

160

focal length (mm)

RM

SE

val

ue (

nm)

liquid membrane rmseliquid membrane liquid rmse

liquid-liquid lensliquid-membrane-liquid lens

liquid-liquid lensliquid-membrane-liquid lens

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Symmetry Deformation 1/2

• External pressure elastic force capillary length• elastic force relays on external pressure loaded.• gradually increasing

• Conform by Finite Element Simulation (ANSYS)• membrane parameters:

– 30mm aperture, 0.1mm thickness, boundary clamped– 1.8MPa Young modulus, 0.45 Passion ratio

• infused liquid pair– Water and PDMS liquid

• meshing the membrane into 1425 elements• large deformation under [0 ~ 120]Pa

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Symmetry Deformation 2/2

• External Pressure : 0Pa 5Pa 8Pa 10Pa 20Pa … …1

MN

MX

X

Y

Z

0

.476E-04.953E-04

.143E-03.191E-03

.238E-03.286E-03

.334E-03.381E-03

.429E-03

JAN 15 201314:28:37

NODAL SOLUTION

STEP=1SUB =300TIME=60UZ (AVG)RSYS=0DMX =.429E-03SMX =.429E-03

1

MN

MXX

Y

Z

0

.667E-04.133E-03

.200E-03.267E-03

.333E-03.400E-03

.467E-03.534E-03

.600E-03

JAN 15 201315:54:35

NODAL SOLUTION

STEP=1SUB =300TIME=60UZ (AVG)RSYS=0DMX =.600E-03SMX =.600E-03

1

MN

MXX

Y

Z

0

.711E-04.142E-03

.213E-03.284E-03

.355E-03.427E-03

.498E-03.569E-03

.640E-03

JAN 15 201316:07:17

NODAL SOLUTION

STEP=1SUB =300TIME=60UZ (AVG)RSYS=0DMX =.640E-03SMX =.640E-03

1

MN

MX X

Y

Z

0

.751E-04.150E-03

.225E-03.300E-03

.375E-03.450E-03

.525E-03.600E-03

.675E-03

JAN 15 201316:38:56

NODAL SOLUTION

STEP=1SUB =300TIME=60UZ (AVG)RSYS=0DMX =.675E-03SMX =.675E-03

1

MNMX X

Y

Z

0

.905E-04.181E-03

.272E-03.362E-03

.453E-03.543E-03

.634E-03.724E-03

.815E-03

JAN 15 201317:30:17

NODAL SOLUTION

STEP=1SUB =300TIME=60UZ (AVG)RSYS=0DMX =.815E-03SMX =.815E-03

0 20 40 60 80 100 1200.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

external pressure (Pa)

dist

ance

(m

m)

Symmetry Deformation• external pressure >>26Pa• point of maximum deformation moves to center step by step

Water: 0.997g/cm3

PDMS: 0.975g/cm3

----------------------------------

0.022g/cm3

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Experiment 1/2

• Prototype• Liquid-Membrane-Liquid Lens

• with 30mm aperture

Liquid Density Refractive

Glycerin 1.25 1.4732

SantoLight5267 1.26 1.6737

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Experiment 2/2

• Optical performance• USAF1951 Chart• Resolution at f=150 mm• System magnified 2X

System magnified 2X

Vertical bar(Group4, Element2)

Horizontal bar(Group4, Element1)

Horizontal Vertical 8.975 lp/mm 8.000 lp/mm

Comparing with 11.6 lp/mm spherical interface(ZEMAX)

Light USAF1951 Liquid Lens Imager

1.5f window

liquid 1 liquid 2

window membrane 3f

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Conclusion and Future Work

• Variable-Focal Liquid Lens with Large Optical Aperture • Liquid-Membrane-Liquid Lens with 30mm aperture • Calculation & Simulation Feasibility• Experiments Prototype & Resolution

• Future Work• Available liquid pairs.• Application ???

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Acknowledgement

• Co-authors & Supervisors:• Dr. Hiromasa Oku, • Prof. Masatoshi Ishikawa.

Ishikawa Oku Laboratory 　　 http://www.k2.t.u-tokyo.ac.jp/

Sincerely appreciate for your time.