Bi-convex aspheric optical lenses Abhijit Chandra Roy, Mridul Yadav, Anubhav Khanna and Animangsu Ghatak*
Abhijit Chandra Roy, Animangsu Ghatak, Mridul Yadav: Department of Chemical Engineering, Center for Environmental Science and Engineering, Indian Institute of Technology Kanpur, 208016 (India) Anubhav Khanna: Department of Chemical Engineering, Manipal Institute of Technology, Manipal, 576104, Karnataka India [*] Prof. A. Ghatak corresponding-author, E-mail:
[email protected]
Abstract: Aspheric optical lenses are important for variety of optical applications, but are difficult to fabricate in conventional top-down processes. Here we have presented a bottom-up approach involving controlled spreading of a thermally crosslinkable polymeric liquid dispensed on specially prepared substrates for making aspheric bi-convex lenses. In particular, the substrate is a solid film with a tiny hole drilled on it through which liquid can flow in and out from top to bottom side of the substrate. In addition, the two surfaces of the substrate are made to have similar or different wettability so that combined effect of gravity and surface wettability determine the distribution of liquid between its two sides. The substrate is maintained at an elevated temperature, so that the liquid spread on its surfaces, but only to a limited extent because of rapid crosslinking at the vicinity of the moving front. This process leads to bi-convex, hyperboloids and prolate spheroids, which yield aberration free images with optical resolution that far exceeds that generated by conventional microscope objectives.
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Introduction: Trilobite is a sea creature that existed 600 to 245 million years ago and became extinct before the first Dinoseraus came to earth.1 These crustaceans with exo-skeletons are known to have one of the most advanced visual systems as it comprised of compound eyes like many modern day insects; but unlike others, the lenses of its eyes were made of rigid yet transparent calcite crystals2 (which allowed it to remain preserved in fossils). While non-deformability didn’t allow minute adjustment of focal length of these lenses, this shortcoming was overcome by natural selection of an unusual but unique shape of the lens.3 Mathematicians René Descartes and Huygens had shown in 1637 and 1690 respectively that there exist only two particular shapes of a bi-convex optical lens,4 which allows light rays from a point source to be focused to a single point on the optical axis without spherical aberration. Analysis of fossilized eyes of Trilobite show that these two unique shapes were already attained in nature hundreds of million years ago.
Yet, attaining these complex shapes with spatially varying curvature is non-trivial in conventional top-down methods that involves forming, grinding and polishing the surface of a rigid material like quartz or glass or molding against a preformed surface.5-8 Such multistep methods are expensive, require skilled workman-ship, a stringent control of temperature and humidity and suffer from high failure rate. In contrast, bottom-up methods can allow fabrication in inexpensive routes via selforganization driven by physical forces. Several bottom-up processes were adopted for preparing aspheric lenses e.g. buckling instability of a thin solid film induced by wetting,9 arrested spreading of a crosslinkable sessile drop on a substrate,10 crosslinking of a pendant liquid drop,11-13 electrochemical actuation of liquid drop,14 forming doublet lens using fluidically aligned glass bead,15 pneumatic and electric field mediated tuning of asphericity of optofluidic lens,16-20 Selforganization has been used also for preparing templates for such lenses or lens arrays: for example, controlled condensation of water droplet on polymeric films21, hygroscopic liquid drop growing at 2
humid atmosphere22, instability of ultrathin polymeric films,23 all of which occur on a flat substrate. These processes yield plano-cylindrical or plano-convex lenses useful for variety of planar microsystems, but are not amenable for making bi-convex Cartesian ovals that characterize the shapes of those of the trilobites. A simple yet robust process is nevertheless required for making such lenses, as a single aspheric lens has the potential of replacing large number of optical components conventionally used in many optical and opto-mechanical devices to achieve the desired performance.24 In this context, we have presented here a process involveing two competing effects: flow of a crosslinkable polymeric liquid driven by surface tension and gravity and flow arrest by crosslinking of the polymer at an elevated temperature. The polymer flows down a tiny hole drilled on a thin solid film and distributes unequally on either side of it, resulting finally in bi-convex lenses with shapes similar to that of the trilobites. We have shown that these unique shapes can be manipulated by controlling the diameter of the hole and the temperature of the substrate. We have generated also differential wettability on either side of the substrate to further tune the distribution of liquid and rate and extent of spreading of the liquid at the respective surfaces, thereby manipulating the lens shapes. These effects finally result in optical lenses that lead to large optical magnification with minimal spherical aberration and high optical resolution.
Experimental: Materials:Polydimethylsiloxane (PDMS) (Sylgard 184, and Sylgard 184 procured from Dow Corning, USA) Charcoal powder local market, was used for preparing the substrate and lenses. 1H,1H,2H,2H-Perfluorooctanttrichlorosilane (FC) was purchased from Sigma Aldrich (USA). A digitally controlled motorized dispenser procured from Holmarc, India was used to release droplets of PDMS from syringe needles. A hot plate procured from CAT, Germany was used to uniformly
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heat the substrate. Oleophobic PDMS surface was prepared by coating it with self assembled monolayer of FC molecules by following established protocols25.
Sample
preparation:
Figure
1(a)
depicts
the
schematic
of
the
method.
A
thin
poly(dimethylsiloxane) (PDMS) sheet of thickness hs 0.15 1.0 mm was used as substrate. A hole of diameter d 0.8 2.0 mm was punctured into it to form a capillary. The substrate was freely supported on a metallic (brass/steel) annular plate of internal diameter D 7 30 mm such that the substrate hole was axially aligned with the annular support. Optical profilometry of such a substrate at the vicinity of the hole (Supporting information Figure S1) suggested negligible vertical deflection (
