h a l f b a k e r yI never imagined it would be edible.
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So, I was trying to think of how to make a contact lens
(or
any lens) which would give you an infinite depth of field.
The topic of "pinhole lenses" has already been discussed.
In
theory, a pinhole lens is great, but a greater depth of
field
is paid for by a much lower total light intensity.
Pinhole
glasses have multiple pinholes, and they work, but not
very
well.
So.
First, we're going to make a single pinhole lens.
Imagine a
small cube of transparent material (acrylic or whatever),
maybe 1mm on a side. Coat the face of it with black
paint, and then make a pinhole in the middle of the
paint.
You now have a pinhole camera (of sorts). If the back of
the cube were a screen, you would see projected on to it
a
perfect image of what the camera was looking at, albeit
very dim (also upside down, but hey, details).
However, there is no actual "screen" on the back of this
camera. Instead, the back of the camera has a slight
curvature on it, so that it acts as a micro-lens, projecting
the perfect image (which has been "focussed" by the
pinhole) onto the retina. This "micro lens" doesn't have
to
do much focussing (except for compensating for anything
that the eye's own lens does).
So far, so pointless. We are still looking at the world
through a single small pinhole, and the image (although
in
focus throughout) will be very dim.
Now, though, we make a second cube, similar to the
first
one, and we glue the two of them side by side. We also
make a micro-lens on the back of this second cube. This
micro lens is similar to the first one, except that it has a
tilt on it so that it projects the second image
superimposed
on the image from the first one.
So we now have two pinhole images, both in perfect full-
depth focus, and projected superimpositionally on the
retina.
And so we continue. By the time we've finished, we have
a
contact lens which consists of perhaps a hundred
individual
pinhole camera facets, with all 100 images projected in
alignment on the retina.
(Note: in case there's any doubt, each pinhole image
covers the full field of view, just as a "normal" pinhole
camera images the whole scene in front of it. It's not
like
pinhole glasses, where you see only a small part of the
field of view through each pinhole.)
Such a contact lens would give you an acceptably bright
image (perhaps 20% of the normal light intensity, which
would not be noticeable - a well-lit room is tens of times
dimmer than daylight) covering the whole field of view,
and with everything being simultaneously in focus.
(?) MB's slightly less famous eye experimenter
http://gorm.wordpre...ith-a-blunt-needle/
[Ling, Jul 10 2011]
MB's slightly less than successful experiment
http://i923.photobu...%20MkI/IMG_5419.jpg
[MaxwellBuchanan, Jul 10 2011]
[link]
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My initial response to the final paragraph was a grumpy "Oh yeah? Prove it." But since I have no data to the contrary, I'll restrain myself and try a nap instead. |
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It did remind me of a pair of glasses a friend of mine had in the early seventies, that did something similar but without the projections in alignment on a common spot. The image was of having compound eyes like a fly. |
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Light refracted through a glass of water or a particularly
curved windscreen on a car might play merry hell with
these, as it does with similar optics such as certain (older)
telephoto
lenses and roof-prism binocs. I don't know this for certain,
I'm just postulating. Knowing my wife's troubles with
contacts before her lasik, I might also say these should be
daytime-use only devices. |
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//It did remind me of a pair of glasses...// Yes, I
have just bought a pair out of curiosity, and they
are hopeless. They do give an uncanny depth of
field, but the pinholes are too far in front of the
eyes, and any part of the scene is viewed through
only one pinhole per eye, so it is like looking at
the world through a collander. |
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However, by converging all the full-field images
from multiple pinholes close to the cornea, I think
this effect could be eliminated. |
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Incidentally, I am not sure of the exact lens
geometry which would be needed to combine all the
pinhole images as I described, but I suspect it might
turn out to be a regular convex lens. |
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In this case, then, what we would have is basically a
regular "positive" contact lens, but with the front
face being opaque apart from multiple pinholes. |
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IMHO, light (falling on retina) from one big lens will always be more than 100 pinholes combined. Hence resulting image will always be dimmer. |
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Focal lenght of a pinhole is determined by hole diameter. Smaller the hole, smaller the focal length. Hence there will be restriction on how much smaller holes can be made. I am not sure, if it will be possible to fit 100 holes. |
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Superimposing 100 images can be trickier than using a mere convex lense. I think a simple lense may not work. |
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[Max] I think your logic is flawed here. For instance, if you replace a pupil 2 mm in diameter with a pair of pinholes 2 mm apart, the effective depth of field will be about the same, except that out-of-focus objects will now appear to be doubled, rather than blurred. As the number of pinholes increases, the result will approach a dimmer version of an image with the same depth of field as a pupil whose size is the same as the total extent of the pinhole field, rather than one the size of an individual pinhole. |
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To put it another way, your 100 images are taken from 100 vantage points, so they can only be made to coincide for a single focal plane; objects at other distances will be blurred due to parallax. [Edit] Or rather, the 100 images of objects at other distances will not coincide, due to parallax. |
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Yes, the image will definitely still be dimmer than
normal, but very large changes in light intensity
are not that noticeable (hence my point that light
intensity outdoors is much much higher than in a
well-lit room). Of course some of this is
compensated for by the eye's iris, but not much;
most of the compensation is perceptual. |
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Focal length: smaller holes give greater depth of
field, until you hit a diffraction limit. I'm not sure
what size hole would be optimal. |
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Superimposing 100 images: well, a regular lens
(including that in the healthy eye) does exactly
this and more; it is effectively superimposing an
infinite number of images (ie, from light rays
hitting all parts of the lens). Hence my suggestion
that the geometry to superimpose 100 individual
images may indeed just be a regular lens. |
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I think you misunderstand me. Not only will the image be dimmer, but the depth of field will be no better than that of a single opening whose diameter is the same as the total size of the field of pinholes. |
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[spidermother] I was replying to [VJW]'s anno (you
were
writing yours while I was replying). |
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Your point about depth of field is interesting and
probably
right... but there's got to be some edge.
Basically, a
pinhole trades brightness for depth of field, and
there
ought to be a way to capitalize on that. We can
handle
some loss of brightness without really missing it.
But, I
take your point that I may not have the right
geometry
here. |
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At a cruder level, those of us with lousy eyes
(near- and
far-sighted) already use the pinhole effect:
focussing
errors are much less severe in very bright light,
but only
because the iris contracts. The effect is a sort of
pseudo-
pinhole, where only the central part of the lens
(which
does less refraction, and where refractive errors
are lower)
is used. |
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But in the end, this argument converges with the
"pinhole
contacts" idea that was discussed elsewhere. |
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I'm going to go and play with contact lenses and
acrylic
paint. |
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(More generally, I've been thinking about ways to
use photonic materials to create an infinite depth
of field, and this idea seemed the simplest and
crudest.) |
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Just tattoo your eyes. Duh! |
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I took optics was several decades ago, but isn't the
whole depth of field issue a result of spherical lens
grinding? (A compromise as parabolic grinding is so
hard.) So can't you solve the issue by using parabolic
mirrors, parabolic lenses or spherical lenses doped to
alter radial refractive index to mimic parabolic lenses?
The later should be easy as radial doped glass is what
is used to create single mode fiber-optic cable. |
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No, depth of field is simply a consequence of aperture size. You are thinking of spherical aberration. |
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What [spidermother] said. You can have a perfect
lens (at least in theory) which will focus parallel
incoming rays of light (as from a distant source) at
a certain point. However, if the incoming rays of
light are diverging (as from a close source), the
will be focussed further back (ie, the near object
will be out of focus in the original plane). |
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Conversely, if you make a stronger lens to bring
the diverging rays into focus, it will over-refract
the parallel rays, so the distant object is out of
focus. |
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Yes, to be perfectly focussed at all distances, all of the light has to pass through a single point. A pinhole is a good approximation of that point. Two or more pinholes is not. |
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Perhaps if there were some way of increasing the amount of light through (head-mounted floodlights?), or increasing the sensitivity of the receptors (drugs? Fitting babies with these pinhole devices at birth so they develop with extra sensitivity?), then monopinholeous contact lenses may be plausible. |
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Hang on. I'm not sure I agree with that. |
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I make a good, old-fashioned pinhole camera with
a very small pinhole. I take a photo. |
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I make another identical camera, and take an
identical photo. Both photos will be fully in focus
(at least, both will be very sharp) at all depths. |
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I then superimpose those two images. Is the
result less sharp than the original? Technically,
this is no different from taking a single exposure
for twice as long, if the image superimposition is
accurate. |
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In practice, of course, there is the matter of
superimposing all the pinhole images. However,
as I mentioned earlier, this is no different from
what a regular lens does (superimposing light rays
which originate from a single point but enter the
lens at different points). |
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What counts, though, is that a lens which will
superimpose these images will work for all focal
lengths. |
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But I am not convinced by my own argument, and
it does seem elegant that two pinholes would give
a resolution similar to a single larger pinhole. |
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So, help me out here. Why does superimposing
two identical images result in a blurrier image
and, if it does, why is this different from a single
exposure of twice the length? |
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[EDIT - don't forget, we're not talking about two
pinholes forming a single image; we have two
pinholes forming independent images which are
then aligned. I agree that a single pinhole camera
with two pinholes will be a mess.] |
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[Note: I am just waiting for the paint to dry on a
pair of contacts. So, if I do not make any further
annotations, please contact me by braille.] |
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Two identical images can be superimposed, but two images taken from slightly different positions can't. If you line up the foreground, the background will be slightly out, and vice versa. |
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//In theory, a pinhole lens is great// |
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Not so much. They always give blurrier picture compared to simple lense. Photos have a dreamy look; Borders are always darker compared to center, unlike simple lens. |
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Superimposing : If you draw the ray diagram, I think it will be clearer. For a lense, these will 100 point sources, very close to the lense. I think it will be a mess. Also, output from the lense will be near parellel rays since, these 100 pinholes will be quite close to focal point of the lense. |
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Another approach would be to muck about with the
chemistry of your retina to make it much more
sensitive to light. Then, a pinhole opening would
give you the infinite depth of field you're after and
be bright enough. A mechanical approach could be
tried too - cats have a reflective layer behind their
retinas, so that light passes through the light-
sensitive cells twice. How hard would it be to insert
a reflective layer behind the human retina? |
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Now, a 3D retina might allow independance from the lens... |
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Hmmm. Well, after some extensive research at
the MaxCo. Optical Laboratory (involving some old
contacts, acrylic spray paint, and sophisticated
pinhole-making technology), I have to report poor
results on the pinhole front. |
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Aside from the problem that contacts slide around
on the cornea, it seems that diffraction becomes
a major problem when the (single) pinhole is small
enough to give a good image. |
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This doesn't entirely explain why the normal pupil,
when constricted by bright light, doesn't give
diffractive problems, but perhaps this is because
(a) it's still larger than my pinholes and (b) it's
closer to the lens (?). |
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The quest continues. Meanwhile, [-]. |
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[MB]... any relations to Isaac Newton? Link. |
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Oddly, he's great^n cousin. We're not in touch,
however. |
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(Painting contacts is easy; the acrylic paint is only
on the outer surface and, once thoroughly dried, is
stable and non-irritating. Photo of MkI in link.) |
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Good God...looks like something out of Terminator. Or
perhaps more fittingly: Half a hangover. |
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I tried wearing two such contacts. However, when I
disovered that I was trying to take photos using the
TV remote, I reverted to one. |
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what [spidermother]'s been saying. Yes, each pinhole image is crystal clear *but* they're not all the same image, so they wont superimpose. Blurryness is just a lot of crystal-clear superimposed images that aren't fully keyed. |
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e.g.
An artificial eye has a pupil of aperture 10mm. Incoming light-rays can enter anywhere between point Point A is at 0mm (on the left) and point B is 10mm (on the right) this pupil forms the "waist" of a cone of light. Point the eye at an equilateral triangle 10m away. Draw a line from one corner of the equilateral triangle through Point A until the ray hits the cornea. Now do the same, but through Point B. The two points hit the cornea at some distance apart. This distance is a measure of how blurry the resultant image is going to be. |
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Now repeat the process with a pinhole camera projecting one image over Point A, and another one Projecting another (crystal clear) image over Point B. Both images are clearly resolved, but by the time they are projected back onto the cornea - they don't overlap anymore. |
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Creating a lens to bend the two pinhole projections back into a single resolvable image is doing exactly what a pair of spectacles does - only in discrete, compound fashion, rather than over a continuum. The question is, does that help? |
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// Creating a lens to bend the two pinhole
projections back into a single resolvable image is
doing exactly what a pair of spectacles does - only
in discrete, compound fashion, rather than over a
continuum. The question is, does that help?// |
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Yes, it should. It's relatively easy to create a
normal contact lens which does this for a single
focal length, not for all focal lengths
simultaneously. I was hoping that, because each
pinhole image has infinite (or at least good) depth
of field, a single lens could converge them all to
give a unified full-depth image. |
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However, my experiments to date suggest that
diffraction is the real killer (I think someone
mentioned this up there). |
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I'm now seriously thinking about how to make a
contact lens with autofocus, or at least manually-
settable focus. I may post this as another idea. |
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