Noncircular pupils explained

Posted 12 August 2015 by Matt Young

Several years ago, I reviewed the book Evolution's Witness: How Eyes Evolved, by Ivan Schwab. The book is downright encyclopedic, and I could not praise it highly enough. But in my review I wondered about elongated pupils, such as those of a cat, which are barely discussed the book. I remember reading somewhere that the elongated pupil could be stopped down farther than a circular pupil, but that explanation does not account for the problem that horizontal structures will be more clearly resolved than vertical structures (presuming that the pupil is elongated vertically and the eye is nearly diffraction limited). A team from Berkeley and Durham University now proposes a better explanation. Without going into detail, they find that predators that ambush their prey, like cats, typically have vertically elongated pupils. From the abstract:

Vertically elongated pupils create astigmatic depth of field such that images of vertical contours nearer or farther than the distance to which the eye is focused are sharp, whereas images of horizontal contours at different distances are blurred. This is advantageous for ambush predators to use stereopsis to estimate distances of vertical contours and defocus blur to estimate distances of horizontal contours.

One way to put it: All the blur due to defocus is in the vertical direction, so horizontal contours are blurred when defocused, whereas vertical contours are not, because the blur is parallel to the contour; see their Figure 2(A). I do not want to go into detail, but they demonstrate that ambush predators, like the cat, that prowl close to the ground benefit from having good stereo vision for vertical contours. Prey animals, like the goat, often have horizontal pupils, which supposedly facilitate wide-angle views. Curiously, their pupils remain horizontal regardless of the orientation of their heads. This paper goes a long way toward explaining why different animals have differently oriented pupils. You may see a video and a short article here and an NPR report here. The paper does not explain how, when I was an elongating pupil in fourth grade, my teacher, an ambush predator if ever there was one, managed to see through 360°.

29 Comments

Henry J · 12 August 2015

Re "The paper does not explain how, when I was an elongating pupil in fourth grade, my teacher, an ambush predator if ever there was one, managed to see through 360Â°."

Maybe it had to do with the orientation of some of the pupils in that teacher's class?

eric · 12 August 2015

One commenter on Jerry Coyne's site also pointed out that a cat's vertically elongated pupils allow it much better control over the amount of incoming light, due to the extra muscles needed to work the asymmetric opening. Their dynamic range is something like 130x, while circular pupils like in human eyes can only manage about 15x. So (a) they are much better at hunting in both extremes of illumination - extreme darkness and extremely bright light, and (b) cats don't need no stinkin' sunglasses.

Marilyn · 12 August 2015

So the shape of the pupil is also an indication of personality, and could be an indication of more than just natural selection, meaning the type of personality also plays a part in selection, for example a fox and a wolf. Birds of prey such as an Owl don't have this phenomena but they do elevate themselves high to spot their prey. Whatever other part of the anatomy is different most living things have eyes.

Mike Elzinga · 12 August 2015

Barn owls and other predators, including cats and wolves, supplement their vision with exquisite hearing ability. They can zero in on prey without being able to see them.

Henry J · 12 August 2015

Most living things are bacteria. ;)

David MacMillan · 12 August 2015

Birds of prey are not ambush predators. They have telescopic vision for spotting something a long way off and diving to get it. Also hearing, as Mike pointed out.

I was just noticing the horizontal pupils on a goat the other day and wondering why the nearby barn cat had vertical pupils. Now I know.

eric · 12 August 2015

David MacMillan said: Birds of prey are not ambush predators. They have telescopic vision for spotting something a long way off and diving to get it. Also hearing, as Mike pointed out.

To Marilyn, Mike, and Dave: there was a finding Matt didn't mention, which is that eye height above ground is also a correlative factor. Vertical slits are evidently more adaptive the closer you are to the ground. I forget why, go to Jerry Coyne's article to read up on that. In any event, raptors are actually consistent with the pattern because most raptors fly significantly higher than their prey and have circular pupils...but there is one bird with vertically-slit pupils: it skims across the water, ambushing fish.

Mike Elzinga · 12 August 2015

eric said:
David MacMillan said: Birds of prey are not ambush predators. They have telescopic vision for spotting something a long way off and diving to get it. Also hearing, as Mike pointed out.
To Marilyn, Mike, and Dave: there was a finding Matt didn't mention, which is that eye height above ground is also a correlative factor. Vertical slits are evidently more adaptive the closer you are to the ground. I forget why, go to Jerry Coyne's article to read up on that. In any event, raptors are actually consistent with the pattern because most raptors fly significantly higher than their prey and have circular pupils...but there is one bird with vertically-slit pupils: it skims across the water, ambushing fish.

Yeah, I read the article. It is because when you are closer to the ground, the angle from your eye to the focal point on the ground determines the depth of focus along the ground. The plus-or-minus five degree angle about the line of site determines the near and far points in which things are in focus. If you are high above the ground, that distance within which objects are in focus encompasses a much larger area on the ground.

stevaroni · 12 August 2015

I've tried to explain this to people for years (it's pretty obvious if you spend your days with imaging systems like I do).

For most terrestrial animals, some kind of iris is pretty essential, since the amount of light in the environment varies widely during the day. The retina works best in narrow(ish) illumination range, and a lens and pupil large enough to gather a useful amount of light at night and in dusk would allow to much light in during the bright mid-day. The iris opens and closes to regulate the amount of light at the retina to a comfortable level.

But as any photographer will tell you, an iris has a secondary function. By "irising down" to a smaller pupil the iris limits the 'working" part of the lens to the less curved central area, where light rays get bent less passing through the lens. This improves the "depth of field", the sharpness in the part of the image that isn't at the exact plane of focus.

A circular aperture affects horizontal and vertical details equally, but if you squeeze the pupil into a vertical oval you can preferentially "spend" the available depth of field gain sharpening vertical details.

To state the obvious, sharpening vertical details makes it easier to detect horizontal motion, a significant advantage if you're a creature like a cat, whose dinner prospects depend of noticing little things scurrying through the brush.

You can also see weird pupils in sheep and goats, but on those animals the reason for the pupil seems to be to allow a greater field of view. In these animals the retina wraps around the inside of the eye for a much greater angle than our eyes, and the eyes are spaced wide on the head and don't pivot in their sockets nearly as much as ours. Sheep eyes are a fixed-array early warning radar, optimized to broadly scan as much of the horizon as possible.

Lurker111 · 13 August 2015

"The paper does not explain how, when I was an elongating pupil in fourth grade, my teacher, an ambush predator if ever there was one, managed to see through 360Â°."

Your teacher was a Twiloite, with perfect 20-20-20-20 vision.

See here:

http://trueclassics.net/2011/10/03/dont-forget-rob-thumbs-up/

W. H. Heydt · 14 August 2015

stevaroni said: I've tried to explain this to people for years (it's pretty obvious if you spend your days with imaging systems like I do). For most terrestrial animals, some kind of iris is pretty essential, since the amount of light in the environment varies widely during the day. The retina works best in narrow(ish) illumination range, and a lens and pupil large enough to gather a useful amount of light at night and in dusk would allow to much light in during the bright mid-day. The iris opens and closes to regulate the amount of light at the retina to a comfortable level.\

Okay...a bit off topic, but I've got to ask... What is the effective ISO rating of the human retina, and what is the F-stop range of the human iris?

W. H. Heydt · 14 August 2015

Lurker111 said: "The paper does not explain how, when I was an elongating pupil in fourth grade, my teacher, an ambush predator if ever there was one, managed to see through 360Â°." Your teacher was a Twiloite, with perfect 20-20-20-20 vision. See here: http://trueclassics.net/2011/10/03/dont-forget-rob-thumbs-up/

Be vewy, vewy qwiet...I'm hunting twilobites?

Mike Elzinga · 14 August 2015

W. H. Heydt said: Okay...a bit off topic, but I've got to ask... What is the effective ISO rating of the human retina, and what is the F-stop range of the human iris?

That's an interesting question that has actually been explored. It is similar to the issue that comes up when trying to equate CCD and diode array imaging systems to film. One of the major differences between film and the eye has also become a design feature in CCD and diode array imagers; that of "anti-blooming" technology which allows an array of diodes or a CCD array to encompass a much larger dynamic range in sensitivity within the same image frame without the charge from a pixel spilling over into adjacent pixels. The eye and imaging arrays with anti-blooming technology respond by suppressing sensitivity as the intensity of light on the retina or array increases. This "feature" is also a characteristic of the ears of many animals as well as sound-detecting technology. There is an interesting little experiment most people can do - it depends on the age of the eye - to illustrate that suppression of light intensity. Shut off an overhead light and immediately plunge your vision in complete darkness. You will need a light that shuts off very rapidly, such as an LED or bright compact fluorescent bulb, and you will need to be looking away from the light when you shut it off. In the very brief instant after the light has been shut off, you will experience a "flash" in your vision as the room goes into complete darkness. That is the suppression mechanism "discharging" to give the illusion of a bright flash just after the overhead light has gone out.

W. H. Heydt · 14 August 2015

Mike Elzinga said:
W. H. Heydt said: Okay...a bit off topic, but I've got to ask... What is the effective ISO rating of the human retina, and what is the F-stop range of the human iris?
That's an interesting question that has actually been explored. It is similar to the issue that comes up when trying to equate CCD and diode array imaging systems to film. One of the major differences between film and the eye has also become a design feature in CCD and diode array imagers; that of "anti-blooming" technology which allows an array of diodes or a CCD array to encompass a much larger dynamic range in sensitivity within the same image frame without the charge from a pixel spilling over into adjacent pixels. The eye and imaging arrays with anti-blooming technology respond by suppressing sensitivity as the intensity of light on the retina or array increases. This "feature" is also a characteristic of the ears of many animals as well as sound-detecting technology. There is an interesting little experiment most people can do - it depends on the age of the eye - to illustrate that suppression of light intensity. Shut off an overhead light and immediately plunge your vision in complete darkness. You will need a light that shuts off very rapidly, such as an LED or bright compact fluorescent bulb, and you will need to be looking away from the light when you shut it off. In the very brief instant after the light has been shut off, you will experience a "flash" in your vision as the room goes into complete darkness. That is the suppression mechanism "discharging" to give the illusion of a bright flash just after the overhead light has gone out.

Interesting...my "take away" is that modern electronic imaging mimics some tricks that Nature came up with to handle extremes of light. Which suggests--even if the rods/cones system didn't--that the effective "speed" of the retina is variable, so I should ask about range, rather than a value, and expect two ranges, one for each receptor type. Anybody got any numbers? (I asked my opthamologist about this once and got a blank look. I don't think she understood the film and camera side of the comparison.)

Mike Elzinga · 14 August 2015

W. H. Heydt said: Anybody got any numbers? (I asked my opthamologist about this once and got a blank look. I don't think she understood the film and camera side of the comparison.)

It is considerably more complicated than that; and different fields of photonics have built up traditions and standards that apply to those particular fields. In the case of colorimetry, one speaks of the luminosity functions, or luminous efficiency functions; both photopic and scotopic. In the case of CCD imaging systems and some infrared imaging systems, there is quantum efficiency given in terms of the number of electrons per photon. This, in turn, depends on the photon energy and the amount of scattering and/or absorption of photons that occur within the overlying materials covering the photodiode. All of these systems depend on wavelength - photon energy - and ultimately boil down to how big a system-sensing voltage pulse is generated by a photon. Some sensors - e.g., photomultipliers and channeltrons - use a cascading process in which an electron knocked loose from a photosensitive material is accelerated in an electric field and made to collide with the same material knocking loose even more electrons in a multiple cascading effect that results in thousands to millions of electrons being generated by a single photon. The ISO of film actually comes down to the average number of silver halide molecules that are affected by an incoming photon. Atomic bonds are changed in the silver halide crystals that then make the halide "susceptible" to being "fixed" by the developer which takes away the halide atom and leaves the pure silver. I am not aware of any recent attempts to attribute an ISO number to the eye; the eye system is just too complicated for a single such number. Colorinetry demands a far more complex description of the response of the eye to light of varying wavelength. There are entire IEEE and CIE (International Commission on Illumination) industrial standards that are used to match up various color-producing devices and printing with the response of the human eye.

Matt Young · 15 August 2015

The eye can see over an intensity range of 1 million or so. The pupil diameter typically varies from perhaps 1 mm or a bit less to 6 mm, so a factor of 40.

Interesting but ultimately futile attempt to get at the ISO number of the retina here. They claim that the "sensitivity" of the retina is 600 times more at night than during the day, which seems awfully low to me, considering that 600 times 40 is nowhere near 1 million. I do not know offhand whether the integration time is longer for scotopic (dark-adapted) vision (I'll bet Mike Elzinga does).

But the article illustrates the difficulty of comparing the eye to a camera.

Matt Young · 15 August 2015

The ISO of film actually comes down to the average number of silver halide molecules that are affected by an incoming photon.

Silver halide grains, no?

stevaroni · 15 August 2015

Matt Young said:
The ISO of film actually comes down to the average number of silver halide molecules that are affected by an incoming photon.
Silver halide grains, no?

No, if I recall correctly the silver halide molecules form very small crystals of a few molecules. An incoming photon of sufficient energy causes a change in a small region of the crystal sub-structure moving (again, IIRC) 4 molecules into a different crystalline arrangement. This region, and billions like it, become the "latent image", imprinted onto the film but at the moment unobservable. When the film is placed in developer these tiny spots become the seed crystals from which the grains of metallic silver will grow.

Mike Elzinga · 15 August 2015

Matt Young said:
The ISO of film actually comes down to the average number of silver halide molecules that are affected by an incoming photon.
Silver halide grains, no?

I think that "grain size" is the term commonly used. The grains are irregular, dendritic polycrystals of silver halide molecules. If the grains are larger, the film is more sensitive (more silver halide molecules per grain), but the resulting image is also "grainier" (how's that for two different uses of the same word?). Smaller grains mean less sensitive film (fewer molecules per grain) but the film has higher resolution (less grainy).

I do not know offhand whether the integration time is longer for scotopic (dark-adapted) vision (Iâll bet Mike Elzinga does).

Completely dark-adapted vision is quite quick to respond to tiny light flashes; very likely close to being single-photon response. I remember discovering this as a kid when I ordered an "Atomic Bomb Ring" from a cereal box cover. Some of the doped plastic used in particle detection in physics produces flashes that the completely dark-adapted eye can see. In fact, that "Atomic Bomb Ring" used some of the early scintillating plastic. When using dark-adapted vision, it is best not to use the fovea; direct your central focus slightly away from the target of vision. However, even the central part of the vision involving the cones is quite quick to respond. Another little experiment that is fun to do is to go into a dark closet and allow the eyes to completely dark adapt. Then pull a piece of Scotch tape or a sticky label slowly off a plastic surface. You can see fairly bright flashes of light of different colors - depending on the "stickiness" of the tape - at the junction of the tape and the plastic surface. You will probably need to get your eye quite close to the junction between the tape and the plastic. Some of those colors are in the green; which suggests that the bonds being broken are out there in the 2 eV range; and that is also the most sensitive part of the response curve of the eye.

Matt Young · 15 August 2015

I agree that 4 or so photons are needed to "render developable" a single silver halide grain. But those grains are a micrometer or so in diameter. See the nice pictures here. As a general rule, bigger grains lead to faster (more sensitive) films, but it is still 4 photons per grain, not per molecule.

Matt Young · 15 August 2015

(howâs that for two different uses of the same word?)

Photographic scientists use graininess and granularity as 2 distinct concepts, but never mind. The undeveloped silver halide grains are not irregular, but the developed silver image is.

Completely dark-adapted vision is quite quick to respond to tiny light flashes; very likely close to being single-photon response.

Yes, when you were a kid, you probably had something close to single-photon response; alas, not any longer. But that does not answer my question, which refers to the decay time of the response -- that is what would determine the exposure time or "shutter speed" for a diffuse object (I think).

Mike Elzinga · 15 August 2015

Matt Young said: Yes, when you were a kid, you probably had something close to single-photon response; alas, not any longer. But that does not answer my question, which refers to the decay time of the response -- that is what would determine the exposure time or "shutter speed" for a diffuse object (I think).

Ah; you used "integration time," a term that has a couple of different meanings in various fields. In signal detecting and processing it often refers to a summation process in which a signal or image is built up over time to enhance the signal or image and reduce noise. But, yes, it also refers to the decay or "latency" period before which a system can then respond to another input. I don't know what that is for the human eye. And, yes, my old eyes are, sadly, quite different from my younger eyes. But I can still do some of those experiments. I don't get the results as consistently as I used to. I also am still suffering from swelling due to a "branch retinal vein occlusion" in one of my eyes. Getting old sucks.

phhht · 15 August 2015

Mike Elzinga said: Getting old sucks.

Indeed. Have you noticed the utter absence of any godly miracles to cure age?

TomS · 15 August 2015

phhht said:
Mike Elzinga said: Getting old sucks.
Indeed. Have you noticed the utter absence of any godly miracles to cure age?

How about curing Alzheimer's disease? There surely are many family members who pay attention to faith healers.

Mike Elzinga · 15 August 2015

phhht said:
Mike Elzinga said: Getting old sucks.
Indeed. Have you noticed the utter absence of any godly miracles to cure age?

Heh! It must be that "genetic entropy" crap.

Matt Young · 15 August 2015

But, yes, it also refers to the decay or âlatencyâ period before which a system can then respond to another input. I donât know what that is for the human eye.

I was thinking of the decay time and assuming that the decay time was roughly the frame rate and therefore the exposure time. If we knew the exposure time, the F-number (easy!), and the illuminance, then we cd deduce the ISO speed, at least for that illuminance. But now that you mention latency period, I think maybe I should have thought the flicker frequency, which must be around 30 Hz. Yes, my optometrist often bawls me out for comparing the eye too closely to an optical instrument.

Getting old sucks.

What H.L. Mencken said. What Maurice Chevalier supposedly said, though I had always thought it was Maugham.

Mike Elzinga · 15 August 2015

Matt Young said: What H.L. Mencken said. What Maurice Chevalier supposedly said, though I had always thought it was Maugham.

:-) Well, I hope I'm doing it right. I keep making progress on classical guitar - and I can even compose and transcribe music for the guitar - something I never had time for when I was working. I get regular exercise, keep working on all sorts of things that challenge the brain (still the math/physics nerd), mow the lawn, travel, and generally keep busy. I don't put up with the hassle of fixing my car any more - I let the dealership handle it. And I stay off ladders - my wife doesn't allow me on the roof.

shebardigan · 16 August 2015

My new favorite "getting older" visual phenomenon is idiopathic preretinal macular fibrosis ("cellophane disease"). Really puts an end to your amateur astronomy fun.

The eye surgeon said "There are procedures we can perform for this; it our clinical group's policy not to perform them unless we see at least a 50% chance that you will not be worse off than before. It will have to get a lot worse before we would consider that."

Mike Elzinga · 16 August 2015

shebardigan said: My new favorite "getting older" visual phenomenon is idiopathic preretinal macular fibrosis ("cellophane disease"). Really puts an end to your amateur astronomy fun. The eye surgeon said "There are procedures we can perform for this; it our clinical group's policy not to perform them unless we see at least a 50% chance that you will not be worse off than before. It will have to get a lot worse before we would consider that."

They told me, "Cheer up; things could be worse." So I cheered up; and sure enough things got worse.