lenses – Fountain Magazine

Brittlestars: Fabricating Microlenses with Perfect Geometry

Louima Cunningham — Sat, 01 Nov 2014 00:00:00 +0000

The unity underlying nature manifests itself in many different forms. Sometimes various “things” work towards accomplishing only one task while sometimes only one “thing” is utilized in many different tasks. We can already see countless examples of both phenomena with our naked eyes; however, the developing science and technology let us observe many more interesting examples in the micro and nano scale. This article aims to describe one little example of this miraculous work of art in which many things are made from one thing and to show that the more we study nature in detail the more we admire all that have been granted to us.

Brittlestars form a large group of sea animals that are similar to starfish. There are more than 2,000 species of brittlestars. However, this article will focus on two of them, Ophiocoma pumila (Figure 1a) and Ophiocoma wendtii (Figure 1b). In spite of their similar appearance, these two kinds of brittlestars have one main difference. While O. pumila is insensitive to light, O. wendtii is highly light sensitive. For example, the latter has different colors at day and night, as shown in Figure 1b, left and right respectively. More interestingly, O. wendtii can sense shadows of predators and quickly move into dark areas such as a cave or underneath a rock.

To understand the mechanisms behind the difference in light sensitivities of these two species, Joanna Aizenberg and her colleagues investigated1 the microstructure of both brittlestars’ outer skeletons with an electron microscope and came up with a striking result: The top surface of O. wendtii’s skeleton has very well ordered lens-like hemi spherical elements (Figure 1f). The cross section image of one of those hemispheres actually looks like a compound lens made up from two hemispheres with different diameters (Figure 1g). On the other hand, O. pumila’s skeleton had a typical stereom (sponge-like calcite) structure (Figure 1e). These images strongly suggest that the lenses in O. wendtii’s skeleton are responsible for the relatively high light sensitivity. However, understanding how that really happens require further investigation.

It is well-known that spherical lenses suffer from a problem called “spherical aberration,” which means that the light rays that are closer to the optical axis are focused at a different point than the ones that are away from the axis. A quick solution to this problem is to use two lenses, whose diameters have a certain ratio, back to back; this helps to correct the aberration originating from the first one with the second one. Interestingly, when Aizenberg et. al. calculated1 the optimum compound lens configuration for O. wendtii’s skeleton, which has the minimum aberration, their result matched the original lens structure perfectly (the orange outline in Figure 1e). They were also able to locate the focal point of these lenses (d = 4-7 um* below the lens) with the same method. Their further electron microscopy studies showed optically sensitive nerve bundles exactly at that location. All these results clearly show that O. wendtii’s skeleton has the perfect geometry to collect and focus light to improve its light sensitivity. However, there is one big question about these lenses: their material.

Calcite, a kind of calcium carbonate (CaCO3), is a common ingredient of the shell or the skeleton of marine organisms. Interestingly, the birefringence property of calcite makes it very unfavorable as a lens material. In a birefringent material the speed of the light depends on the direction it travels with respect to the crystallographic axes of the material. As a result, if one looks through it, they will observe a doubly refracted image (Figure 2). Being the most famous example of birefringent crystals, calcite’s refractive index is 1.64 parallel to one crystallographic axis and 1.49 in the perpendicular direction. Therefore a regular calcite lens cannot focus light on a single spot, unless it is oriented along a special crystallographic axis (c-axis to be specific), which would be along the diagonal of the prism in Figure 2.

At this point we are not surprised to learn that the optical axis of the O. wendtii’s lenses, and the c-axis of the calcite crystal that they are made of, indeed overlap. We are not surprised because we already had a strong feeling that these lenses should work. However, it is quite surprising that these little creatures can grow single crystals of calcite with a specific crystallographic orientation. As Kenneth Towe states in the context of a similar study, “This precise orientation of crystals is the big mystery of biomineralization. Organisms know how to do it; we do not yet know how they know.”3

Biomineralization, the controlled deposit of inorganic minerals by living organisms, is a very active research field attracting many scientists from various disciplines, including biology, physics, chemistry, and material science. In general, controlling crystal structures at small length scales is a very challenging task. Scientists spend millions of dollars to build state-of-the-art facilities for single crystal materials synthesis. They work in clean rooms, under an ultra high vacuum and at extremely high temperatures. On the other hand, from brittlestars to large whales, almost all living creatures have biominerals, such as bones and shells, manufactured in chemically dirty environments and at decent temperatures. Organisms are apparently equipped more efficiently than our laboratories are.

A. Ali Eren has a Ph.D. in Physics and lives in the USA. He studies physical chemistry of biological processes.

References

*1 um (micron) is one thousandth of a millimeter. Human hair is approximately 100 micron thick.

Aizenberg, Joanna, et al. “Calcitic microlenses as part of the photoreceptor system in brittlestars.” Nature 412.6849 (2001): 819-822.
ttp://jademellor.com/blog/2013/6/21/rainbow-rhombus, accessed 4/20/2014
Towe, Kenneth M. “Sea urchins as crystallographers.” Science 311.5767 (2006): 1554-1555.

Pinhole Cameras, Imaging, and The Eye

Louima Cunningham — Sat, 01 Apr 2006 00:00:00 +0000

Cameras, eyes, telescopes, microscopes are various imaging systems. In general, everyone knows that an imaging system has one or multiple lenses. Interestingly, one can also make a camera without using a lens! Such cameras are called “pinhole cameras.”¹ A pinhole camera is actually very simple to make: a box with a pinhole, that is to say, a hole that measures a millimeter or less at the center of one face (Fig. 1). 2 In Fig. 2 (a), a picture taken by a pinhole camera can be seen.³ You might wonder how such a beautiful picture can be taken using a very simple box with a pinhole, considering that thousands of dollars are spent on high-quality cameras. What is more interesting is that there is a sea creature that has a pinhole eye! A nautilus, shown in Fig. 3, has a pinhole eye.⁴ Also, some of the surveillance cameras use pinhole designs with no lenses.⁵ Understanding how a pinhole camera works is very instructive to capture the essence of imaging.

In order to get a sharp image, ideally one point on the image (film) should receive light rays from only one point on the object. In practice, this ideal case can not be achieved in case of a large pinhole. If we have a large pinhole, as seen in Fig. 4, the light rays emerging from one point on the object reaches multiple points on the film. Also, multiple points on the object can arrive at a single point on the film. The result of both cases is a blurry image. For a small pinhole, however, there are light rays emerging from a point on the object in all directions, and only a very small amount of light is received on the film. To produce a decent image on the film, the exposure time needs to be very long, especially when a very small pinhole is used. Of course, we can make the pinhole a little larger to capture more light. But, wait! This would make the image blurry. Therefore, for pinhole photography, the size of the pinhole sets the quality of the image and the minimum exposure time. Also, we can take the picture of a still object, but a moving object cannot be captured easily by a pinhole camera due to the long exposure time. One important question is: Can we make reduce the size of the pinhole size to increase the quality of the image? Well, physics says: “No!” Fig. 5 shows a comparison of the images of a filament taken by a pinhole camera.⁶ As the size of the pinhole gets smaller and smaller, the effects of the diffraction phenomenon are more and more pronounced, and the image becomes blurry again. We also notice that the image is barely formed with a very small pinhole, indicating that very little light is received.

How can we gather more light and still make the image sharp? Can we achieve this with just the pinhole? Apparently not. That is why we mention lenses when talking about any imaging system. This is what a lens basically does. A lens gathers more light, and still preserves the one-to-one correspondence between the points on the object and those on the image. So, a lens is very useful for imaging. Most cameras have one or multiple lenses. Our eyes have lenses. We should remember, though, a pinhole camera takes a picture, but the compromise is the exposure time. Now, we see that a lens solves the exposure time problem, but is there a price to pay? To answer this question, let’s take a look at once again Fig. 2, where we see two pictures, one taken by a pinhole camera, and the other one by a lens camera. Look at the pictures carefully, and try to understand the difference before proceeding. As you probably observed, in the pinhole camera image everything in the picture is in sharp focus, from the close-by plants to the far distant beacon, and the clouds in the sky. However, in the lens camera image, only the closest daisy is in focus, and the other daisies, only a few meters away, are blurry. Indeed, we lose the depth of field in our images when using a lens camera. Depth of field can be defined as “The distance between the nearest and farthest points that appear in acceptably sharp focus in an image.” This is actually something we live with everyday. Try to focus your eyes on a mountain far away; the objects that are very close will not be in focus anymore. So, our eyes, consisting of lenses, also have limited depth of field. A nautilus eye, on the other hand, has an infinite depth of field, as it has a pinhole eye. Therefore, the price paid for gathering more light with a lens is that not everything will be in focus.

We can understand why lens cameras have a limited depth of field while a pinhole camera has nearly infinite depth of field if we consider the focusing mechanism of a lens. Given a pre-determined film position, a lens can only form sharp images of an object at a certain distance from the lens. Other points that are farther from or closer than same section of the object will be out of focus. However, if the size of the object is not large, we usually do not notice this effect. When we want to take pictures of close-by objects, then this effect is clearly seen, as Fig. 2 (b) shows.

Actually, we can correct this problem. The image of the farther points of the object forms at a farther point on the film. So, multiple light rays coming from one point will end up on the film. If we place an aperture next to the lens, then we can block some of these light rays. If we make the size of the aperture sufficiently small, we can get a sharp image of the farther point. Our original question about the lenses can be posed once again at this point: By using the aperture we make the image sharper, but what do we lose? Of course, since we block some of the light rays, we lose the light-gathering ability of the lens. Now, if we make the aperture size smaller and smaller, we finally reach the pinhole, and an almost infinite depth of field!

Our eyes also use similar mechanism of placing an aperture. The amount of light allowed to enter each eye is controlled by the iris, a circular diaphragm that opens wide at low light levels and closes to protect the pupil (the aperture) and retina (light detector of the eye) at very high levels of illumination. As illumination changes, the diameter of the pupil (positioned in front of the crystalline lens) reflexively varies between a size of about 2 to 8 millimeters. When illumination is very bright, the pupil narrows and light rays from the side are excluded from the optical pathway.⁷ The result is a sharper image on the retina. A very narrow pupil (approximately 2 millimeters) produces diffraction artifacts that spread the image of a point source on the retina, similar to the image of the filament captured by a very tiny pinhole (Fig. 5)

In conclusion, a pinhole camera is a very instructive tool for learning about imaging concepts. A pinhole camera has an infinite depth of field and the ability to produce sharp images regardless of the distance of the objects. This comes with a price, though: the small size of the pinhole limits the amount of light received by the film, so long exposure times are needed. A lens helps to gather more light, but compromises the depth of field. These concepts are used in imaging technologies, and can be found in the eyes of living organisms.

Notes

E. Hecht, Optics, 2nd edition, pp. 199. Addison-Wesley Publishing Co.
http://images.encarta.msn.com/xrefmedia/aencmed/targets/illus/ilt/T045986A.gif.
http://www.kosara.net/gallery/.
http://www.eyedesignbook.com/.
http://www.spylife.com/pinholecam.html.
http://www.umiacs.umd.edu/~ramani/cmsc426/Lecture3.pdf
http://www.olympusmicro.com/primer/lightandcolor/humanvisionintro.html.