A Liquid Lens with Liquid-Membrane-Liquid Structure Lihui Wang, Hiromasa Oku, Masatoshi Ishikawa University of Tokyo, Japan wanglihuiamos@gmail.com

Research Background Modelling Human Crystalline: Prototypes of Variable-focal Lens: Liquid-Membrane, Electrowetting, Liquid-Liquid Lens http://www.vdwoxford.org/ United States Switzerland France Dynamorph Lens Japan

Related Research Electrowetting lens 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 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.2138-49 (2004) Dynamorph Lens http://www.varioptic.com/ Hiromasa Oku and Masatoshi Ishikawa. Applied Physics, Vol.94, 221108 (2009)

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/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 Following Next slide

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

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

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

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, 221108 (2009)

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)

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

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