Ishikawa Oku Laboratory UNIVERSITY OF TOKYO A Liquid Lens with Liquid- Membrane-Liquid Structure Lihui Wang, Hiromasa Oku,

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

A Liquid Lens with Liquid-Membrane-Liquid Structure

Lihui Wang, Hiromasa Oku, Masatoshi IshikawaUniversity of Tokyo, [email protected]

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

Switzerland

Research Background

• Modelling Human Crystalline:

• Prototypes of Variable-focal Lens:• Liquid-Membrane, Electrowetting, Liquid-Liquid Lens

http://www.vdwoxford.org/

FranceUnited StatesDynamorph Lens Japan


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

http://www.varioptic.com/

Hiromasa Oku and Masatoshi Ishikawa. Applied Physics, Vol.94, 221108 (2009)

H Oku, K Hashimoto, and M Ishikawa. Optics Express, Vol.12, No.10, pp.2138-49 (2004)

• Electrowetting lens• [-5 +15] diopters• optical aperture 2.5mm• wavefront error 50nm• auto-focusing for 30fps

Dynamorph Lens


Dynamorph Lens

Un-solved Problem (Aperture)

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

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

Interface tension: 34.8mN/m

Density 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

Florian Schneider, et al. Optics Express, Vol.17, No.14, pp.11813-21 (2009) Horizontal Vertical


Research Purpose

• Variable-Focal Liquid Lens with Large Optical Aperture • Enlarge optical aperture of liquid lens (30mm)• Sufficient optical performance

• Theoretical analysis of interface deformation• Membrane Deformation• Spherical Deformation• Symmetry Deformation

Next slide

FollowingNext slide


Proposed Structure

• Liquid-Membrane-Liquid Structure• 0.1mm thickness silicon membrane inserted• available optical aperture 30mm• elastic force take place of surface tension

Liquid-Liquid Lens

Liquid-Membrane Lens

Liquid

Membrane

Liquid

O1 O2 O3 O4 O5 O6

N2(window)N1(air)

N3(liquid 1) N4(membrane) N5(liquid 2) N6(window) N7(air)

Refraction

Position

window liquid 1 membrane liquid 2 window

front

SandwichStructure


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

bra

ne d

efo

rmation(m

m)

p=1

p=10

p=20

p=40

p=60

p=80

p=100

p=130

H. HenckyZ. Math. Phy. 63, 311–317 (1915).


Membrane Deformation 2/2

• Recall capillary length

• assuming Water and PDMS infused (referring Dynamorph Lens )• re-calculate the capillary length

• capillary length > 3*30mm(aperture) is required

Elastic force average

elastic membrane is a possible solution

Liquid-Membrane-Liquid vs Liquid-Membrane

Capillary length (Water-air assumed)

0 20 40 60 80 100 120 1400

2

4

6

8

10

12

14

16

18

20

external pressure(Pa)

theo

retic

al c

apill

ary

leng

th(m

m)

Elastic force

0 20 40 60 80 100 120 1400

0.5

1

1.5

2

2.5

3

3.5

4


mer

idio

nal s

tres

s of

ela

stic

tity(

N/m

)

Capillary length (Water-PDMS assumed)

0 20 40 60 80 100 120 1400

20

40

60

80

100

120

140


theo

retic

al c

apill

ary

leng

th(m

m)


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 length5. Optical path length spherical surface

Hiromasa Oku and Masatoshi Ishikawa. Applied Physics, Vol.94, 221108 (2009)


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 2400

100

200

300

400

500

600comparing with PV and RMSE

focal length(mm)

com

paris

on r

esul

t(nm

)

l-l pv

l-l rmselml pv

lml rmse


Symmetry Deformation 1/2

• External pressure elastic force capillary length• value of elastic force is depended on external pressure.• gradually increasing

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

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

• infused liquids– Water and PDMS liquid

• meshing the membrane into 1425 elements• large deformation under [0 6 20 120]Pa


Symmetry Deformation 2/2

External pressure 0Pa External pressure 6Pa

External pressure 20Pa External pressure 120Pa

0 20 40 60 80 100 120-0.5

0

0.5

1

1.5

2

2.5

3x 10

-3 distance and external pressure

external uniform pressure(Pa)

poin

t of

max

imum

def

orm

atio

n to

cen

ter(

m)

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


Conclusion and Future Work

• Variable-Focal Liquid Lens with Large Optical Aperture • Liquid-Membrane-Liquid Lens with 30mm aperture • optical performance theoretically

• Membrane Deformation• Spherical Deformation• Symmetry Deformation

• Future Work• available liquid pairs. silicon membrane PDMS liquid .

Convex Concave

Liquid Density Refractive

Sugar Water 1.20 1.4112

Glycerin 1.25 1.4732

SantoLight5267 1.26 1.6737

Liquid Pairs Candidates

Lens power: ―[-4.1 +4.3] diopters ― [-245.5 +230.2]mm focal length


Sincerely appreciate for your time.

Documents

Ishikawa Oku Laboratory UNIVERSITY OF TOKYO A Liquid Lens with Liquid- Membrane-Liquid Structure Lihui Wang, Hiromasa Oku,