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Droplet Lens

May 7, 2014

Nearly every physicist has constructed a pinhole camera in their youth. It's one experiment that requires no monetary outlay, since paper and mother's sewing pins are always at hand. This device, also called a camera obscura, was supposedly known to the Greek philosopher Aristotle (384 BC-322 BC). Pinhole diffraction is described in Book XV, chapter 6, of his "Problems," which may have been authored instead by his followers.

In the Problems, Aristotle expounds on how the image of the Sun, projected through the rectangular holes of a wicker basket, still maintains its circular shape in the image projected onto the ground. The Problems is not among the books typically studied by students of Aristotle, but it discusses many interesting questions.

One such question is "Why do all men, barbarians and Greeks alike, count up to 10 and not up to any other number...?"(Problems, Book XV, chap. 3)[1] Aristotle would have a low opinion of our binary-counting ways; viz.,
One race among the Thracians alone of all men count in fours, because their memory, like that of children, cannot extend farther and they do not use a large number of anything." (Problems, Book XV, chap. 3)[1]
pinhole cameraThe simplest type of pinhole camera will invert the image.

(Illustration by the author, using GIMP.)

Just a little more expensive than a pinhole is the ball lens, usually made in ball mills, and typically used for focusing light into optical fibers. Ball lenses also offer magnification, but they produce an imperfect image because of spherical aberration, as shown in the figure. The flawed mirror of the Hubble Space Telescope is one lesson in the fact that surface figuring is very important in optics.

spherical_aberrationAn example of spherical aberration. This is how a square grid looks when a ball lens is placed on it.

Central objects are reasonably imaged, as was the case for the original Hubble Space Telescope mirror.

(Illustration by the author, using Inkscape.)

Now that cellphone cameras have become ubiquitous, lenses have appeared for increasing the camera magnification to produce an inexpensive microscopes. One example of these is the Micro Phone lens, created via a kickstarter campaign to turn a cellphone into a 150X microscope. This fifteen dollar lens still requires an adequate light source for imaging.

A cellphone microscope lens may never be as inexpensive as a pinhole, but how low in cost can we go? Are there processes, other than casting in precision molds, by which highly magnifying lenses can be made? That's the problem tackled by scientists and engineers at the Australian National University (Canberra, Australia), and they've reported on their research in an open access paper in a recent issue of Biomedical Optics Express.

Historically, lenses were expensive to produce, since they were made by polishing flat, or near-net-shape, glass pieces into the required shape with high surface finish. More modern methods mold epoxy gels and use a subsequent thermal reflow process to make lenses.[2-3] The approach taken by the Australian research team is to hang and cure droplets of the transparent elastomer, polydimethylsiloxane, to prepare solid lenses of varying focal lengths.[3]

Says study coauthor, W. M. (Steve) Lee, "What I did was to systematically fine-tune the curvature that's formed by a simple droplet with the help of gravity, and without any molds."[3] Although it's been known for quite a while that such hanging droplets assume a lens-like shape, no one attempted to tune the process to the extent done by the Australian team.[3] This approach can possibly produce small, high quality lenses for about a penny each.[2]

In the process, a drop of polydimethylsiloxane is placed on a glass microscope slide. This is baked at 70°C to create a base, another drop is added, and the slide turned over to allow gravity to pull the material into a parabolic shape. After this is baked, additional drops can be added to produce an optimal shape.[3] In this manner, focal lengths as short as 2 mm were produced, and these are useful in collimating light from a light-emitting diode (LED) into an optical fiber.[2] These short focal length lenses could also image microscopic structures down to around 4 μm with 160X magnification.[2]

Droplet lenses
Left, a single droplet lens suspended on a fingertip. Right, ANU researcher Steve Lee holding a microscope slide with droplet lenses. (Images by Stuart Hay.)[3]

The Australian research team was able to create a low-cost digital dermatoscope of 60X magnification from a camera-equipped smartphone. The two dollar device was able to image microscopic skin structures, such as sweat pores.[2] A traditional dermatoscope costs about $500. The device can also be used by farmers to identify field pests.[3]

Cellphone dermascopeA Nexus 4 smartphone converted into a dermatoscope with the addition of a droplet lens, two light-emitting diodes as a light source, and a watch battery.

(Image by Stuart Hay, modified to include labels.)[3]

One application for such a low cost microscope is for classroom education.[3] The size limit for such lenses is presently about a half inch in diameter, but the research team is refining its process with a goal of high performance two-inch lenses.[3] As the authors state in the abstract of their paper,
"Our hanging droplet lens fabrication technique heralds a new paradigm in the manufacture of low cost, high performance optical lenses for the masses."[2]

Figure caption
The left image was taken with a penny droplet lens. The right image was taken with a $300 microscope lens. (Image: OSA/Biomedical Optics Express.)[3]

References:

  1. Aristotle, Problemata, Translated by E.S. Forster, from vol. 7 of The Works of Aristotle, W.D. Ross and J.A. Smith, Eds., Oxford Clarendon Press, 1927.
  2. W. M. Lee, A. Upadhya, P. J. Reece and Tri Giang Phan, "Fabricating low cost and high performance elastomer lenses using hanging droplets," Biomedical Optics Express, vol. 5, no. 5 (May, 1, 2014), pp. 1626-1635. Open Access PDF Article, here.
  3. Bake Your Own Droplet Lens, OSA Press Release, April 24, 2014.

Permanent Link to this article

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