Page 253 - Optofluidics Fundamentals, Devices, and Applications

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When the mold is overfilled with fluid to produce a convex profile,
plano-concave lenses can be molded. After one lens is molded, the
liquid-filled mold can be tuned to another shape.
The roughness of the surface of the molded lens is measured using
an optical interferometer (Veeco NT 1100). The root-mean-square
(RMS) surface roughness of the molded PDMS lenses is less than
6 nm. The surface quality is comparable to commercial lenses and
adequate for most optical systems although more demanding optical
systems may require an RMS roughness of less than 2 nm [75].
As discussed earlier, radius of curvature alone is not sufficient to
describe the profile of the molded lenses. The lens profile can be more
precisely represented by an aspherical function [Eq. (9-1)]. In order to
fabricate aspherical lenses of designed profiles using the liquid-filled
mold, both the curvature and the conic factor need to be precisely
controlled. A simple calculation shows that the surface profile of an
infinitely thin elastic membrane under fluidic pressure is parabolic,
corresponding to a conic factor of −1 [79]. However, in reality, the
elastic membrane has a finite thickness and shows nonlinear hyper-
elastic behavior. Figure 9-23 shows that a wide range of conic factors
can be obtained from different process and material parameters, such
as membrane thickness and amount of prestretch, suggesting that a
large family of focus-fixed aspherical lenses can be produced from a
tunable liquid-filled mold.
Figure 9-23 represents various combinations of curvature and
conic factor of the liquid-filled tunable mold [80]. Different extents of
prestretch, for example, result in various combinations of conic fac-
tors and curvatures. In this specific case, only positive conic factors
are obtained. Negative conic factors can be obtained with different
process parameters since the conic factor approaches −1 (e.g.,
parabola) for infinitely thin elastic membrane [79]. Sophisticated
membrane processing techniques other than thickness and prestretch
offer possibilities for even more complicated lens profiles. These tech-
niques include varying elastic constants and membrane thickness
along the radial axis.

9-4-2 Summary
We have discussed a new way of fabricating aspherical polymer
lenses using tunable liquid-filled molds. The surface roughness of the
molded lenses is less than 6 nm, which is adequate for most optical
systems. The curvature and the conic factor, two key parameters to
define an aspherical lens, can be controlled by changing process
parameters such as the applied pressure, the percentage of prestretch,
the membrane thickness, and the mechanical constants of the
membrane. This unique capability enables us to prototype an optical
system in a cost-effective and time-efficient manner.