Page 233 - Optofluidics Fundamentals, Devices, and Applications

208 Cha pte r Ni ne

9-1-3 Fluidic Lens Fabrication
The process to fabricate a membrane-based bio-inspired fluidic lens
can be divided into tsections: (1) membrane fabrication and (2) fluid
chamber fabrication. To fabricate the membrane, we first mix, degas,
and spin-coat prepolymer polydimethylsiloxane (PDMS) onto a
chlorotrimethylsilane-coated silicon wafer. The purpose of chlo-
rotrimethylsilane treatment is to avoid PDMS/Si cross-links that
cause difficulties in separating PDMS from the Si handle wafer. The
PDMS-coated wafer is kept in a 65°C oven for 40 min to cure the
PDMS. The fully cured PDMS membrane, having a typical thick-
ness of 50 to 200 μm is then separated from the Si handle wafer and
mounted onto a precision-machined aluminum ring. The donut-
shaped aluminum ring has the flatness, circularity, and concentric-
ity that meet the requirements for an optical system. The permanent
bonding of the PDMS membrane and the Al ring is performed
immediately after the UV-ozone surface treatment. This membrane/
aluminum ring is then bonded or clamped onto the lens chamber. In
the final step, the lens chamber is vacuum-filled with optical fluid.
More information on the fluidic lens fabrication process can be
found in several references [27,35–39].

9-1-4 Lens Profile Analysis
Although a lens is usually characterized by its focal length or radius
of curvature, high-quality imaging systems cannot be designed
without the accurate knowledge of the detailed lens profile when
the lens is not perfectly spherical. When the surface of a lens is not
spherical, aspheric terms have to be added in the mathematical
representation of the lens profile. The most frequently used math-
ematical model for aspherical lenses is the elliptical equation. Two
parameters, curvature and conic constant, are needed to uniquely
define an elliptical equation. Curvature is the reciprocal of the
radius at the vertex of the lens and conic constant specifies the
nature of the elliptical equation, being elliptical, parabolic, or
hyperbolic. Equation (9-1) is the general expression of an elliptical
equation:

cr ⋅ 2
z = (9-1)
−
22
1 + 1 ( k + 1) c r
where c = radius of curvature at the vertex of the lens
r = distance from the center of the lens
k = conic constant.
When the conic constant (k) is zero, the equation describes a
spherical lens. When k = −1, the shape is a parabola. When k > 0, the