Page 235 - Optofluidics Fundamentals, Devices, and Applications

210 Cha pte r Ni ne

invariant of the left Cauchy-Green tensor and J is the determinant of
F
the deformation gradient tensor, J = det( )
J = J
el + ε 3
(1 )
th
where ε is thermal strain. Basically, J describes the volume change
th
and J is the elastic part of volume change. Note that I and I remain
el 1 2
constant under volume change.
One major improvement in membrane processing is the application
of prestretch where the membrane is in tensile stress before being bonded
to the Al ring. Prestretch of the membrane not only prevents wrinkling
at low lens power (nearly flat surface) but also greatly suppresses the
effect of gravity. In addition, adjusting the amount of prestretch allows
us to adjust the value of conic factor [43]. The effect of prestretch is simu-
lated in COMSOL. Figure 9-5a shows the simulated profile under differ-
ent fluid pressure. After COMSOL Multiphysics analysis, simulated lens
profiles are fitted to the elliptical equations. The relationship between the
conic factor and the radius of curvature is shown in Fig. 9-5b. The rapid
increase in the value of conic constant has an insignificant effect in real
applications since it happens when the lens power becomes very low.

Lens profile
1.6

1.4 11 kPa 13 kPa

1.2 9 kPa
Displacement (mm) 0.8 1 7 kPa

5 kPa
0.6
3 kPa
0.4

0.2 1 kPa

0
–2 –1.5 –1 –0.5 0 0.5 1 1.5 2
mm
FIGURE 9-5 (a) Lens profi le simulated from COMSOL Multiphysics (b) Conic
constant vs. curvature from simulation. (F. S. Tsai, S. H. Cho, W. Qiao, N. H.
Kim, and Y. H. Lo, “Miniaturized unifi ed imaging system using bio-inspired
fl uidic lens,” Proceedings of SPIE, vol 7061, 70610N, 2008.)