Post on 03-Jan-2016
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, Japanwanglihuiamos@gmail.com
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
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
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
Ishikawa Oku Laboratory http://www.k2.t.u-tokyo.ac.jp/
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
Ishikawa Oku Laboratory http://www.k2.t.u-tokyo.ac.jp/
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
Ishikawa Oku Laboratory http://www.k2.t.u-tokyo.ac.jp/
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
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
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).
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 )• 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
external pressure(Pa)
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
external pressure(Pa)
theo
retic
al c
apill
ary
leng
th(m
m)
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 length5. Optical path length spherical surface
Hiromasa Oku and Masatoshi Ishikawa. Applied Physics, Vol.94, 221108 (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 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
Ishikawa Oku Laboratory http://www.k2.t.u-tokyo.ac.jp/
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
Ishikawa Oku Laboratory http://www.k2.t.u-tokyo.ac.jp/
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
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 • 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
Ishikawa Oku Laboratory http://www.k2.t.u-tokyo.ac.jp/
Sincerely appreciate for your time.