Optics of the Neural Superposition Eye

- Drosophila melanogaster -

 

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Kuno Kirschfeld was the first to identify the subcategory of apposition compound eyes known as the ‘neural superposition eye’ [1](1976) . This is the eye type of two winged flies and several crustaceans. It is unique because each ommatidia has an array of rhabdom instead of a single one. This array matches the hexagonal layout of the ommatidia. After the light energy is converted into a synaptic signal a complex neural network links signals from corresponding fields of view [Figure 1]. This is a very efficient method of increasing the photon capture. This may also improve singal to noise ratio and is more effective for motion sensing.

Project Outline:

For this project I focused on the optical design of the fruit fly eye. The layout of apposition compound eyes is goverened by simple paraxial optics. Using the available microscopy tools, I gathered qualitative data on the eye. By combining physical measurements and the theory, I generated a computer model in a lens design software program.

Provided below are images of the basic layout, and individual structures of the eye, along with a brief explanation and some necessary theory. Finally, a first order design is provided as a computer model.

Figure 1

 

 

:IMAGES and MEASUREMENTS:

For exterior images, flies were prepared in glutaraldehyde with an ethanol rinse and then critically point dried. Charging was a big problem and the flies were coated with a thick layer of gold (100-200 angstroms). A microtome was used to gather cross sections of interior structures. Flies were embeded in an epoxy after drying. Unfortunately, attempts to disect flies that weren't CPD were unsuccessful. As you will observe, effects of the CPD process destroyed and distorted much of the interior structure, but made for some interesting pics.

Electron flight simulations of gold coated biological material: (left to right: Acc. voltage 3kV scale: .5um; Acc. voltage 5kV scale 1um; Acc. voltage 10kV scale 2.5um)

 

- - - ((( Try mouseover on images to see examples of how measurements were taken, or other suprises. ))) - - -

Spatial Resolution:

The size of compound eyes, both how large and how small, is limited by diffraction. The receiver limits how small a compound eye can be. It can't be smaller than a receiver that is optimal for gathering light in the visible spectrum. Resolution limits how large a compound eye can be. Compound eyes have poor spatial resolution compared to simple eyes, the type humans have, but they make up for it by saving space and increasing the field of view. You don't find large compound eyes because larger creatures require greater spatial resolution, and for compound eyes size increases exponentially with spatial resolution. [2]. Here I have determined spatial resolution (ommatidial angle) by measuring the curvature of the whole eye and the number of elements that subtend the arc. Note that the curvature increases drastically at the edges of the eye. This means the fly has decreased spatial resolution in its periferal vision, similar to humans.

(for small angles)

Phi, inter ommatidial angle; D, lens aperture; R, eye radius

 

 

Lens Dimensions:

The dimensions of the lens facets were measured to determine the full aperture of an individual system. This along with the lens power (or focal length) will determine the numerical aperature of the system, and define the eye's resolution.

d, diffraction limited spot size; lamda, wavelength; F/#, effective focal length(f) divided by full aperture(D)

 

 

 

Lens Curvature:

The curvatures of the corneal lens are measured to determine the power and focal length of the system. The front surface is robust and probably a fairly acurate measurement; however the drying and disection of the corneal array has most likely distorted the curvature of the rear surface. Observe the layers of proteins in the cross section. They probably deflated like a balloon during the drying procedure and that is why they separated easily from the interior eye. The corneal front surface is the most important, as it is the most powerful optic in the system. It has the steepest curvature and light bends more at the air-lens interface then it will at the lens-cone interface.

Thin lens: P, power; f, focal length, C, curvature; n1, refractive index of lens; n2, refractive index of air or surrounding media

 

 

 

Lens surface structure:

Here are some images that make current technology look like it is just catching up to mother nature -- a biological anti-reflection coating. Not as defined as those found on species of moths [3], but it shows its usefulness in nature. The small bumps (~200nm) on the surface of each lens are smaller than the wavelengths of visible light, therefore they act as a thin layer of varying refractive index. Abrupt changes in refractive index cause reflections which this layer helps to avoid. The small cracks in the right image are from multiple layers of gold coating. A thinner coating might allow an accurate meaurement of the height of the bumps.

 

 

 

Rhabdomere:

Here are cross sectional images of the rhabdomere array. Although the cell structure is heavily damaged, and very brittle, it was posible to break the strucutes down the middle, exposing the dimensions of the rhabdom. These light guide structures operate similar to fiber optics, but are even smaller to accomadate the visible spectrum instead of the IR. The corneal lens and crystalline cone focus light onto the tips of the rhabdomere. The index of the center region is higher than the surrounding cell, so the light gets trapped in the rhabdom and travels down the long tube, getting converted into a neural signal. The dimensions gathered here are also adequate to determine the size of the image plane. This will be important because it will need to match the image size.

 

 

 

The Missing Pieces...

These images are evidence of many failed attempts to study the crystalline cone and other cross sectional images of the internal eye. The image on the left appears to be a slice through the cones, but there are no identifiying characteristics to take decent measurements. The center picture shows how the cones either shriveled up in the drying process or possibly detatched from the cell structure during disection. The image on the right shows how the inner eye would fall apart even under the glass blade of the microtome. The layer of corneal lenses is very durable and difficult for the blade to cut through. It would often give way, separating from the epoxy and collapsing into the interior of the eye. Part of the problem is that the interior eye was not being reinforced properly. I learned too late that the glutaraldehyde does not penetrate the exterior of the eye or the exoskeleton well and that the eye should be disected (removed) from the head before preperation. Which is not a simple procedure to implement in the scope of this project.

 

 

 

Modeling the Fly Eye:

Fortunately, I was able to gather enough information to generate an effective model of a neural superposition ommatidium. Because of constraints imposed by the theory, knowing how the light enters the system, and what the image plane needs to look like, the general design of the interior can be calculated. The length of the cone can be determined by locating the focal point of the corneal lens. This is where the rhabdomere array will start.

The system lined up suprisingly well considering I had no physical measurements of the crystalline cone. However, the off axis rays focused a little too high, hitting the outer rim of the off axis rhabdom, even losing one of the rays. This suggests that the focal length is too long in this model, and that there is additional power not currently accounted for in the model. That power could come from two probable sources. The surface between the cone and the corneal lens could be incorrect due to lack of physical data, or, more likely, there could be a gradient index in the crystalline cone. Gradient index lenses occur naturally in many of nature's eye, including humans and many species of insects and crustaceans.[2,4]

In a true system wave optics would be required to model the fiber optic structures and the diffraction limited spot size at the image plane (start of the rhabdomere array). However an internally refracting light guide is an adequate substitute.

*** The images above are examples of how values were gathered. Each of the values used for the model are averaged from 4-8 measurements on at least two different flies (excluding some parts of the crystaline cone and rhabdom). ***

Designing Artificial Compound Eyes:

By studying the natural compound eye we can learn the usefulness of such a system, and the trick that nature allready uses. Here are some examples of how the computer model generated in this project can be adapted to create an artificial system. I am working on these models to create an optical system with applications in today's world. An artificial compound lens array could be used for motion detection, robotic navigation (optical flow), range finding, telecommunications or several other uses.

 

 

References:

[1] Kirschfeld, The resolution of lens and compound eyes, In Neural principles in vision, pp 354-370, Springer Berlin (1976)

[2] M.F. Land, D-E Nilsson, Animal Eyes, Oxford University Press, (c) 2002

[3] http://www.display-optics.com/pdf/moth-eye.PDF, Reflexite Corporation, Avon CT, Pub 1999, Rev 5. (c) 2002

[4] E. W. Marchand, Gradient Index Optics, Academic Press, New York, p. 89 (1978).


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