The Trilobite Eye

May 3, 2013

The eye is such a complex structure that many people have trouble with the idea that Nature could have created eyes through evolution. That's not such a problem when you consider that the fully-formed mammalian eyes we see today were not created ex novo; rather, they are the end point in a long chain of smaller steps.

As an experimentalist, I see a parallel between the evolutionary development of the eye and the differences between my string and sealing wax (nowadays, duct tape and five-minute epoxy) prototypes and the final commercial products based on them.

Charles Darwin highlighted the eye as something seemingly difficult to explain by evolution. However, he then reasoned that "...numerous gradations from a simple and imperfect eye to one complex and perfect can be shown to exist, each grade being useful to its possessor..." would do the trick.[1] I'm reminded of the ancient proverb, as listed by Erasmus in his Adages, "In the land of the blind, the one-eyed man is king."[2]

Animal eyes have lenses formed from the protein, crystallin, an apt name for such a transparent material. The now extinct trilobites (Animalia, Arthropoda, Trilobitomorpha, Trilobita), which encompassed ten orders of species, are a remarkable exception. Trilobite eyes were made from the inorganic material, calcite. A recent arXiv posting by Vernon L. Williams discusses the optical properties of calcite and their affect on lens performance.[3]

Trilobite fossil of the genus Hoplolichoides. Ordovician trilobite fossils are numerous in the Ordovician clay of quarries around Saint Petersburg, Russia, where this specimen was recovered. (Photo by Ghedoghedo, via Wikimedia Commons.)

Radioactive trilobites make an appearance in the original Godzilla film (1954, Ishiro Honda, Director).[4] Trilobites were a remarkably successful species, flourishing in the oceans for 270 million years from 520-250 million years ago. Calcium is abundant in ocean water, so calcite crystal, which is chemically calcium carbonate, was a ready choice as a lens material, as it was for the trilobite exoskeleton.

A calcite crystal of the Iceland Spar variety. Hexagonal crystals often have such a rhomboid habit. (Photograph by Parent Géry, via Wikimedia Commons.)

Trilobite eyes were compound eyes constructed much like insect eyes, as an array of closely-packed hexagonal facets. For trilobites, the material for these facets was optically-clear calcite, an hexagonal crystal, the "c-axis" of which was oriented with the axis of incoming light rays. Although calcite is optically transparent, it has one other optical property. It's birefringent.

Non-polarized light entering a birefringent crystal is split into two beams, one of which (the "ordinary" beam) follows the usual refraction laws, with the other ("extraordinary" beam) going off at a different angle. These beams are actually a split of the polarization of the entry beam, a phenomenon much beloved by early optical physicists, who used this effect of calcite in Nicol and Glan-Thompson prisms to polarize light.

Seeing Double Photograph showing how the double refraction of calcite will split an image in two. A calcite crystal was placed over some text. (Via Wikimedia Commons.)

This splitting of the beams arises from the different refractive indices of calcite for the two polarizations. For 600 nm light, roughly in the middle of the visible range, calcite has an ordinary index n_o of 1.486, and an extraordinary index n_e of 1.660. These different indices cause the beam paths to diverge when the incident beam is not along the optical axis (c-axis).

This divergence isn't a problem at small angles, but it causes a fuzzy image for calcite lenses when there's a wide field of view. For trilobites, this meant that they had good forward vision, but they had poor peripheral vision, probably mitigated by the compound nature of the lens (see graph). If your object is just to eat things in front of you and avoid large predators moving towards you from any direction, this probably wasn't too much of a problem.

Focal depth error as a function of angle, measured from the optical axis, for a typical calcite lens. The source data for this plot are from ref. 3. (Graph of data from Table I of ref. 3, rendered using Gnumeric.)[3]

Transparent calcite is just one form for calcite crystals, and there are many opaque forms. One interesting chemical property of calcite is its retrograde solubility. Nearly every water-soluble crystal dissolves faster in hot water. Calcite is less soluble in water as the temperature increases; and, no, trilobites didn't have their eyes dissolve in their ocean environment, since it was a high pH solution (basic).

References:

1. Charles Darwin, "On The Origin Of Species. Or The Preservation Of Favoured Races In The Struggle For Life," Sixth Edition, 1859, via Project Gutenberg.
2. Erasmus quotes the proverb as, "In regione caecorum, rex est luscus" (Adages III, iv). I prefer the simpler, "Inter caecos, luscus rex."
3. Vernon L.Williams, "Evolution and the Calcite Eye Lens," arXiv Preprint Server, April 3, 2013.
4. Godzilla, Ishiro Honda, Director, 1954, on the Internet Movie Database.