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Research Papers

Mechanics of Tunable Hemispherical Electronic Eye Camera Systems That Combine Rigid Device Elements With Soft Elastomers

[+] Author and Article Information
Chaofeng Lü

Department of Civil Engineering and
Soft Matter Research Center,
Zhejiang University,
Hangzhou 310058, China
Department of Civil and Environmental
Engineering and Mechanical Engineering,
Northwestern University,
Evanston, IL 60208

Ming Li

Department of Civil and Environmental
Engineering and Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
State Key Laboratroy of
Structural Analysis for Industrial Equipment,
Dalian University of Technology,
Dalian 116024, China

Jianliang Xiao

Department of Mechanical Engineering,
University of Colorado,
Bouldera, CO 80309
e-mail: Jianliang.Xiao@colorado.edu

Inhwa Jung

Department of Mechanical Engineering,
Kyung Hee University,
Seocheon-dong, Giheung-gu,
Yongin-si, Gyoenggi-do 446-701, Korea

Jian Wu, Keh-Chih Hwang

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
Center for Mechanics and Materials,
Tsinghua University,
Beijing 100084, China

Yonggang Huang

Department of Civil and Environmental
Engineering and Mechanical Engineering,
Northwestern University,
Evanston, IL 60208

John A. Rogers

Department of Materials
Science and Engineering,
Beckman Institute, and Materials
Research Laboratory,
University of Illinois,
Urbana, IL 61801

1Corresponding author.

Manuscript received December 19, 2012; final manuscript received February 12, 2013; accepted manuscript posted March 6, 2013; published online August 21, 2013. Assoc. Editor: Huajian Gao.

J. Appl. Mech 80(6), 061022 (Aug 21, 2013) (7 pages) Paper No: JAM-12-1565; doi: 10.1115/1.4023962 History: Received December 19, 2012; Revised February 12, 2013; Accepted March 06, 2013

A tunable hemispherical imaging system with zoom capability was recently developed by exploiting heterogeneous integration of rigid silicon photodetectors on soft, elastomeric supports, in designs that can facilitate tunable curvature for both the lens and detector. This paper reports analytical mechanics models for the soft materials aspects of the tunable lenses and detector surfaces used in such devices. The results provide analytical expressions for the strain distributions, apex heights and detector positions, and have been validated by the experiments and finite element analysis. More broadly, they represent important design tools for advanced cameras that combine hard and soft materials into nonplanar layouts with adjustable geometries.

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References

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ABAQUS, 2009Analysis User's Manual, Vl. 6.9, Dassault Systèmes, Pawtucket, RI.

Figures

Grahic Jump Location
Fig. 1

The stress–strain curve for PDMS (Sylgard 184, 10:1 mixing ratio of prepolymer and curing agent) obtained from experiments [16] and from the hyperelastic model in Eq. (2.3) with the coefficients C1 = 0.29 MPa, C2 = 0.015 MPa, and C3 = 0.019 MPa

Grahic Jump Location
Fig. 2

(a) Photograph of a camera system with a tunable lens (transparent thin PDMS membrane with tlens = 0.2 mm thickness and Rlens = 4.5 mm radius) placed above a tunable photodetector array (16 × 16 pixels mounted on a thin PDMS membrane with tsub = 0.4 mm thickness and Rsub = 8 mm diameter); (b) angled view of the photodetector surface before and after deformation; (c) schematic illustration of the deformation of the tunable lens due to water injection; (d) schematic illustration of actuating the tunable photodetector deformation via water extraction

Grahic Jump Location
Fig. 3

Distributions of strains in the meridional and circumferential directions in the tunable lens for an apex height H = 5Rlens/8 due to water injection

Grahic Jump Location
Fig. 4

Normalized apex height H/Rlens of the tunable lens versus the normalized applied pressure pRlens/(Gtlens) due to water injection, where Rlens and tlens are the radius and thickness of the lens, respectively, and G is the shear modulus. The prestrain in the lens is ε0 = 0, and −2% as in experiments [7].

Grahic Jump Location
Fig. 5

Normalized apex height H/Rsub of the tunable detector surface versus the normalized applied pressure pRsub/(Gtsub) due to water extraction, where Rsub and tsub are the radius and thickness of PDMS substrate for the detectors, respectively, and G is the shear modulus. The fill factor of detectors is f = 30% as in experiments [7]. The prestrain is ε0 = 0 and 2% in the PDMS substrate.

Grahic Jump Location
Fig. 6

Normalized apex height H/Rsub of the tunable detector surface versus the normalized applied pressure pRsub/(Gtsub) due to water extraction, where Rsub and tsub are the radius and thickness of PDMS substrate for the detectors, respectively, and G is the shear modulus. The fill factor of detectors is f = 0, 30%, and 60%. The prestrain is ε0 = 0 in the PDMS substrate.

Grahic Jump Location
Fig. 7

(a) Side view of the deformed profiles of detector surface at different stages of water extraction (apex height H = 1.2 mm and 2.4 mm). (b) Top view of the detector positions for an apex height H = 2.87 mm. The radius and thickness of PDMS substrate is Rsub = 8 mm and tsub = 0.4 mm, and the fill factor of detectors and prestrain are f = 30% and ε0 = 2%, respectively, as in experiments [7].

Grahic Jump Location
Fig. 8

The images of an array of bright circular discs, captured at the state of R = 17.8 mm, Rlens = 6.9 mm, and distance between lens and detector is 27.3 mm. (a) 3D rendering of the image on the hemispherical detector surface, (b) Planar projection of the image in (a).

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