1. A Liquid Lens with Liquid-Membrane-Liquid Structure
Lihui Wang, Hiromasa Oku, Masatoshi Ishikawa
University of Tokyo, Japan

2. Research Background Modelling Human Crystalline:
Prototypes of Variable-focal Lens:
Liquid-Membrane, Electrowetting, Liquid-Liquid Lens
United States
Switzerland
France
Dynamorph Lens
Japan

3. Related Research Electrowetting lens Liquid-Membrane Lens
single liquid chamber
deformable wall (1or2)
[− ] diopters
optical aperture 7mm
1ms response time
Liquid-Liquid Lens
[ ] diopters
optical aperture 3.0mm
wavefront error 80.3nm
at 109mm focal length
2ms response time
Electrowetting lens
[-5 +15] diopters
optical aperture 2.5mm
wavefront error 50nm
auto-focusing for 30fps
H Oku, K Hashimoto, and M Ishikawa. Optics Express, Vol.12, No.10, pp (2004)
Dynamorph Lens
Hiromasa Oku and Masatoshi Ishikawa. Applied Physics, Vol.94, (2009)

4. Un-solved Problem (Aperture)
Dynamorph Lens
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/cm 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 (2009)
Horizontal
Vertical

5. 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
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Following
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6. Proposed Structure Liquid-Membrane-Liquid Structure Liquid-Liquid Lens
Liquid-Membrane Lens
Liquid
Membrane
Liquid-Membrane-Liquid Structure
0.1mm thickness silicon membrane inserted
available optical aperture 30mm
elastic force take place of surface tension
Sandwich
Structure 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
front

7. 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 [ ] Pa
H. HenckyZ. Math. Phy. 63, 311–317 (1915).

8. Membrane Deformation 2/2
Elastic force average
Recall capillary length
assuming Water and PDMS infused (referring Dynamorph Lens )
re-calculate the capillary length
capillary length > 3*30mm(aperture) is required
Capillary length (Water-air assumed)
Elastic force
Capillary length (Water-PDMS assumed)
elastic membrane is a possible solution
Liquid-Membrane-Liquid vs Liquid-Membrane

9. 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 paper
Experiment data
Data from simulation
Modeling 3mm silicon membrane
Acting pre-gravity map of water-PDMS
External pressure loaded
3D deformation optical path length
Optical path length  spherical surface
Hiromasa Oku and Masatoshi Ishikawa. Applied Physics, Vol.94, (2009)

10. Spherical Deformation 2/2
Comparison of 3mm variable liquid lens
Liquid-Liquid Lens vs Liquid-Membrane-Liquid Lens
shows smaller wavefront error
Peak-to-Valley (PV)
Root-Mean-Square-Error (RMSE)

11. 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 [ ]Pa

12. Symmetry Deformation 2/2
External pressure 0Pa
External pressure 6Pa
External pressure 20Pa
External pressure 120Pa
Symmetry Deformation
external pressure >>26Pa
point of maximum deformation
moves to center step by step

13. 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
Liquid Pairs Candidates
Convex
Concave
Liquid
Density
Refractive
Sugar Water
1.20
1.4112
Glycerin
1.25
1.4732
SantoLight5267
1.26
1.6737
Lens power: ―[ ] diopters
― [ ]mm focal length

14. Sincerely appreciate for your time.