Δαφνη Ευτυχια Αρθουρος

My circadian patterns have been randomized by this cold. I'm not sure whether I'll make it to rehearsal tonight -- if I do, maybe I should wear a mask, and I certainly won't be playing woodwinds, but it may be moot anyhow because the person I expected to ride with is having transportation difficulties of her own. I'm uncomfortable, annoyed and frequently sleepy. It's not a monster as colds go, partly because my "get over it faster" tactics, which don't seem to be making it faster, do seem to be helping with symptom-management, but it's still a nuisance.

I've found a new game: playing with the cat's pupils. Perrine was in a "want to pounce on things" mood, and I was sleepy, and I moved my hand under the blanket and she tracked the motion ... so far pretty normal person-playing-with-cat stuff ... but then I noticed that when I moved in certain ways, her pupils suddenly got Really Huge for a moment, and contracted again soon afterwards. So I sat there poking my finger out and hiding it again, watching her pupils dilate and contract and dilate and contract, and being disproportionately amused.

It did get me thinking about the phenomenon from a biological perspective though, as well. When something interesting happens in hunting mode, the pupils open up by several f-stops, which means much more light is entering the eye, which kindasorta makes sense ... unless the pupils were at the right size to be comfortable in the current environment to begin with, in which case her world would suddenly go way too bright, wouldn't it? And the reduced depth-of-field means fewer things are in focus ... or maybe that's the point, to isolate the thing that moved in her field of view from the background? Or maybe her pupils weren't at the "right" size for the amount of light in the room, but narrowed down for hunting mode to provide greater depth-of-field for motion detectin, and opened up to enough-light-to-see-clearly to examine the motion once it was detected? I'm going to have to start noting the size of her pupils in various moods and lighting conditions to establish "comfortable normal" as a function of brightness, compare that to what her eyes do in hunting/play mode, run some depth-of-field experiments on my own eyes ... and I'll still wonder whether differences between feline and human retinas, or differences in how our brians process visual stimuli, mean that the perceptual effects for her are completely different from what I calculate. Maybe cat eyes handle overbrightness better than human ones? (I've never seen a cat shake its head or look uncomfortable after a flash photograph, but I've seen plenty of humans complain about spots in front of their eyes.)

Hmm. It occurs to me that there's someone I might be able to ask for a layman's version of the feline visual system. In the meantime, does anyone here happen to know off the top of his or her head the distance from lens to retina in a cat's eye? (That is, the effective focal length of the lens of a cat's eye when focused at infinity? I think there was some dicussion of the optical properties of human eyes on the Pentax-Discuss Mailing List a year or so ago, if I can find it, and I'm not sure mammal eyes can be thought of as having a single focal length (because they change shape to focus instead of changing distance from the retina) ... if that half-remembered detail is right, there might be more math involved.

An aside about lenses and eyes: There's a bunch of stuff I understand, a bunch of stuff I don't understand yet, and a bunch of stuff I kindasortaalmost understand about lenses. This will be so basic as to be boring to a lot of people, interesting background for others, unknown but irrelevant to some, and a useful clue as to where to start educating me (or to throw corrections for the stuff I've just gotten wrong) for those who have the large quantities of clue that I desire. Go ahead and skip it if you don't want a thrown-together primer on cameras and eyes.

To start with, there's a "lens", which may be (usually is) made of more than one piece of glass -- the simplest lenses, which have major problems for photography, are a single piece of glass (like on the 1939 box camera I borrowed from anniemal) but modern camera lenses have multiple "elements" (pieces of glass) glued together into "groups". A handheld maginfying glass is a single-element lens. And as I understand it, so is a mammalian eye. For a camera lens (and a magnifying glass), there's a focal length which denotes the distance between the ... I think it's called a "node"? ... of the lens and the film plane at which objects infinitely far away will be in focus. If I understand right, for a single-element lens, this "node" is the lens itself, but more complex lens systems can have it inside the lens or somewhere behind the rear element of the lens. Most camera lenses focus closer than infinity by moving farther away from the film. The entire lens -- front element, rear element, any internal elements -- moves together as a unit. But there are some camera lenses (frequently zooms, but I don't think this design is limited to zoom lenses) which focus by moving internal lens elements instead of the entire lens, so something inside is moving relative to the front and back of the lens. So the "node" is moving even though the rear element of the lens is staying the same distance from the film the whole time. Zoom lenses pretty much have to use this trick, I think, because they're rearranging their internal elements to change focal length but have to remain focussed at the same distance as they do so. (A lens that changes focal length but does not automagically compensate to stay in focus as it does so is call "varifocal", but as I understand it, to be called "zoom", the lens has to retain focus as it zooms, at least to withing whatever tolerances the marketing department and the consumers can agree are reasonable.) Other odd optical magic that makes "focal length" not just mean "distance from film to lens" are things like telephoto and reverse-telephoto designs. Since my ancient 400mm lens is nearly half a meter long, it's not a "telephoto" lens; it's just a long lens. But a more expensive (and more modern) 400mm lens might only be 150mm long physically -- it's optically longer than its physical length. Obviously the rear element of that lens is not 400mm from the film, but that mysterious "node" (gee, I hope I'm using the right term) must be that far away! So the "node" must be in front of the lens. Hmm. Earlier I wrote that the node could be behind the lens; I guess it can go both ways. And as I understand it, if you want a 17mm lens and you can't get closer than 28mm from the film because the camera's mirror (assume an SLR for the moment) is in the way, you need a "reverse telephoto" that has the "node" behind the lens. So right here in this paragraph you can see how much I know and don't know about lenses.

Now the way depth-of-field works is that only objects at one precise distance are truly exactly in focus, but objects slightly closer or farther away are "close enough to being in focus" that we don't perceive the difference. Given an infinite-resolution sensor, we could magnify the image far enough to see that wee blurring on objects 9999mm and 10001mm away when we had the lens focussed at exactly 10.000m, but in practice we're limited by a) the size of the film grain, and b) perceptual limits at "normal" viewing distances. (That is, even if the blur is wide enough to be measurable on real-world film, it doesn't matter if it's too small to notice on an 8x10 print at arm's length or a poster viewed from the middle of the room.) We measure how out-of-focus something is with a concept called the "circle of confusion" (which I've always thought would be a great name for a band). Given an infinitely small object -- a point -- we should get an infinitely small spot on the film. If it's out of focus, we'll get a disc on the film instead of a point. That disc is the circle of confusion. If the circle of confusion is too small to notice or to care about, the object might as well be in focus. I suppose we could say that the object is in focus to an engineer even though it's not in focus to a mathemagician, and I'm not sure what the physicist would say.

"Depth of field" (or, if you're Kodak, "depth of focus") refers to the distance between the closest and furthest objects that are "practically in focus" (i.e. have circles of confusion too small to care about). Now technically this is subjective, because different people can have different ideas about how sharp is sharp enough -- how small the circle of confusion has to be -- but in practice there's enough general agreement based on "normal viewing distance" for prints and slides, that we've got tables and calculators and spreadsheets and funny markings on our lenses that people don't argue about all that much. (Some folks quietly fudge the calculations in a more conservative direction, but I haven't seen flamage about it, or even much serious discussion. We've got a couple centuries of "most photographers know what's good enough" momentum going.) Now here's the thing about depth of field ("DOF") and pupils: a smaller aperture -- opening through which light passes -- of the lens, the smaller the circles of confusion. And therefore the large the DOF. On a lens with no iris, the aperture is the width of the lens, but most camera lenses (other than box cameras and instamatics) have adjustable apertures so that we can choose whether to isolate a subject by throwing the background out of focus (large aperture) or keep all of a scene in focus (small aperture) -- the tradeoff being that for a single light-level and film-speed, we have to compensate for aperture with shutter speed. (Note that DOF is relative to distance -- the same aperture will produce a narrower DOF at 10cm than it does at 10m. This is part of what makes "macro" photography so tricky -- it's hard to get the body and legs of the same 2mm-wide spider in focus.) We can even use a trick to make a "usually in focus" camera, using the "hyperfocal distance" of a lens -- for a given focal length and aperture (and film size; I think the "commonly accepted" numbers are different for 8x10, 4x5, 6x7, 6x4.5, 35mm, APS, and 110), there's a distance you can focus the lens to where everything from some distance away to infinity is all "in focus". So for a box camera or an instamatic or one of those single-use cameras, the manufacturer has chosen a focal length, aperture, and focus distance such that the lens is focussed at the "hyperfocal distance", and the user never has to focus. You can't take pictures very close up with a fixed-focus camera, but everything from (what the manufacturer thinks of as) "normal snapshot distance" to the horizon is all in focus without fancy electronics and motors and without the user having to do anything.

The thing is, since the eyes of mammals (uh, basically vertebrates in general plus the cephalopods, actually, I keep thinking "mammals" because I'm only paying attention to humans and cats at the moment) have lenses that don't move in and out like a camera lens, but change focus by changing thickness instead, I can't just do the math for a camera lens of known focal length. The lens of the eye (if I understand correctly) changes focal length instead of distance, so if the "registration distance" (distance from lens to retina / distance from lens to film) is, say, a couple of centimeters, then the eye would have to have a focal length of a couple of centimeters when looking at the horizon. But when looking at something closer, it would have to have a shorter focal length, as though it were (I don't know the math yet, so until I get around to looking it up I'll pull numbers out of my hat) say, a 15mm lens ... That is, a 20mm lens 20mm from the retina would be focussed at infinity, and a 15mm lens 15mm from the retina would be focused at infinity, but a 15mm lens 20mm from the retina would be focussed somewhere closer than infinity. So, since the lens is always the same distance from the retina, it's changing focal length to focus. I could, of course, calculate effective focal lengths for focussing at different distances once I look up the registration distance of a cat's eye and the focus-extension formulas; it's just extra math, not really harder math, I think.

So if the retina were a sheet of film or a typical digital-camera sensor, and the brain did nothing but print the image, I could simply run the numbers (once I had good starting values) and figure out what ought to be in focus and what ought to be blurry based on where Perrine's looking and the size of her pupils, assuming I can get her to sit still long enough for me to measure any of this. But the retina is not a CCD array or a sheet of film (though it has some similarities to a digican sensor) -- different parts of it have different resolution, colour information is gathered differently in different areas, and so on. And the brain isn't just forming a straight rendering of the image from the retina -- we pay attention to stuff on the periphary very differently than we do to the stuff in the center of our field of view, stochastic motion is used to fill in the blind spot and to compensate for sensor saturation, and a lot of filling-in-the-gaps is going in (before we even get to the brain-issues regarding stereo vision!). And there's a bunch of stuff like edge-detection and motion-detection going on that I'm not sure whether it's happening in the brain, the retina, the optic nerve, or where. And even for studying the behaviour of my own eyes, it's difficult to ascertain how much something is out of focus when my brain really, really wants to "fix" anything I pay attention to. Not impossible, but more effort. Add in the fact that I don't know how much of this brain/retina stuff is different for cats, or in what ways, and you can see that I'm not going to solve this problem with mathematics alone. But I hope to garner a few clues.

I'm not sure I want to figure out what to plug into a search engine to find the information I need about the feline visual system right now, or that I have the attention span to wade through the results looking for the pages I can actually understand with my lack-of-background in neurology (and I've got more urgent things to do when I feel alert enough anyhow), but it'll remain an interesting back-burner question for a while. (Explanations and URLs cheerfully accepted though. If someone has a pointer to a page that addresses exactly this phenomenon, that'd be cool-and-a-half.) Right now I think it's time for Yet Another Mug Of Decaf Earl Grey, and then I'll fall asleep watching television shows from the end of October that I'm just getting around to.

Hmm. I wonder whether I should revisit that long tangent about lenses sometime when I'm alert and focussed and better able to organize my thoughts, and put it elsewhere on the web. Then again, it's probably already been done several places by people who actually know more about the subject.

EDIT: I just read this back after I posted it and realized I am such a geek.