Impossible dim-light vision?

I have been puzzling for some time over the claims of many websites of how many times the eyes of various nocturnal animals are more sensitive to dim light than the human eye because, when I plug in the figures they give into the physical equations, the numbers don't add up and I don't see how you could make those figures add up without breaking the known laws of physics!
What I hope here is for somebody to either tell me exactly where in my mathematical calculations or assumptions I have gone wrong or confirm that all of those website claims are wildly wrong!!!

For any given particular aperture area of an eye (usually this equates with the pupil area -but I will keep referring it to the 'aperture' here to emphasize the physical rather than the biological aspects of it ) , there must be a fundamental physical limit to how sensitive the eye can be to dim light. That is because light is made of discrete particles called photons and, for a given amount of intensity of light, at any given moment of time, there would not an infinite but rather a finite average number of photons that just happen to be heading exactly towards the aperture of the eye and thus only a finite maximum average number of photons can be entering through the aperture of the eye each second that can then all be detected by the retina. This puts an absolute theoretical upper limit to the sensitivity of dim light of the eye defined by, given the aperture area, the proportion of photons which just happen to be heading towards the aperture that would both enter that aperture, reach the retina, be absorbed by the retina and be detected by the retina.
For example, if there is only one such photon heading towards the aperture per second, then the absolute theoretical upper limit to the sensitivity of that very dim light would be an average one photon detected per second and that cannot be improved on without increasing the aperture area.

Now, I have deduced from the info on a website (specifically, this one: http://www.schoolphysics.co.uk/age16-19/Medical%20physics/text/Eye_/index.html
“...In dim light 5% of the light energy falling on the eye is reflected by the cornea, 35% goes through the cornea and is absorbed by the black pigment on the inner surface of the choroids, 50% is absorbed by the lens and humours, and the final 10% is absorbed by the rods. ...” ) that the human eye, given its typical maximum aperture area, once it has been adapted for dim light by being in darkness for more than half an hour, has about 10% of the theoretical absolute maximum sensitivity of light. This is because, out of all the photons heading towards the aperture area, about 10% are absorbed by the rod cells and I am assuming here that the the proportion that are absorbed by the rod cells that are actually detected by them is close to 100% .

This above means that NO EYE, no matter how good in dim light, providing its aperture is never much more than that of a human eye and assuming the wavelengths it can detect are not much different either, can be much more than 10 times more sensitive to dim light than the human eye.

Now, the problem here that I perceive is this: according to many websites, there are many examples of nocturnal animals with eyes that obviously couldn't have an aperture area much greater that that of the human eye and yet, according to these same websites, their eyes have vastly greater than 10 times greater sensitivity to dim light!!!!
Example:

http://en.wikipedia.org/wiki/Gecko
“....Nocturnal species have excellent night vision; their eyes are 350 times more sensitive to light than the human eye ...”

-well, according to my calculations, for it to be 350 times more sensitive to light than the human eye, The gecko's eye aperture would have to be at least 35 times greater (actually, it MUST be greater than this! ) which means its diameter would be almost 6 times greater in dim light than that of a humans in dim light! I don't think any gecko eye pupil can be that large!

And another example:
http://www.chegg.com/homework-help/questions-and-answers/owls-large-sensitive-eyes-good-night-vision-assume-thatthe-pupil-owl-s-eye-diameter-85-mm--q239098

“...Owls have large, sensitive eyes for good night vision. Assume thatthe pupil of an owl's eye can have a diameter of 8.5 mm (as compared with a maximum diameter ofabout 7.0 mm for humans). In addition, the owl's eye is about 100times more sensitive to light of low intensity than a human eye,allowing owls to detect light ...”

-but, again, even taking account of that greater aperture size (of owl eyes in this case ), I cannot make the numbers add up!



Anyone?

Take into account that cats have a reflective surface behind their retinas to improve their chances of catching light. The properties of the lens and humours may be more conducive to light transfer. A factor of 5 or so isn't unrealistic. They have different densities of rods and cones. The brain does a lot of signal processing, and will fill in for the cat where there's poor data.

On the other hand 350x sounds too much; did Wikipedia give a reliable source for the 350x greater light sensitivity for a gecko?

Which part of the eye are we talking about?

Humans have almost no rods in the centre of the eye where we have our
colour vision focused.

Which means in very low light levels you can only really see stuff out of the
corner of your eye.

This is very evident when doing astronomy, as looking through a telescope
you have to look at stars out of the corner of your eye or they mysteriously
disappear.


EDIT: So if we are talking about how good their vision is in the centre of the
eye which is crucial for really focusing on stuff then it could easily be more than
10 times improvement.
Our eyesight at night is mainly peripheral vision object avoidance.

EDIT2: Hmmm... I suspect that some detail is missing from your calulations.
You are looking at only the rods... where gecko's have night time colour vision.

This is the abstract for the paper cited for the 350 times claim...

The nocturnal helmet gecko, Tarentola chazaliae, discriminates colors in dim moonlight when humans are color blind. The sensitivity of the helmet gecko eye has been calculated to be 350 times higher than human cone vision at the color vision threshold. The optics and the large cones of the gecko are important reasons why they can use color vision at low light intensities. Using photorefractometry and an adapted laboratory Hartmann–Shack wavefront sensor of high resolution, we also show that the optical system of the helmet gecko has distinct concentric zones of different refractive powers, a so-called multifocal optical system. The intraspecific variation is large but in most of the individuals studied the zones differed by 15 diopters. This is of the same magnitude as needed to focus light of the wavelength range to which gecko photoreceptors are most sensitive. We compare the optical system of the helmet gecko to that of the diurnal day gecko, Phelsuma madagascariensis grandis. The optical system of the day gecko shows no signs of distinct concentric zones and is thereby monofocal. ...

I would need to see the whole thing to be able to comment on the calculation... But that's behind a paywall.

Originally posted by googlefudge
Which part of the eye are we talking about?

Humans have almost no rods in the centre of the eye where we have our
colour vision focused.

Which means in very low light levels you can only really see stuff out of the
corner of your eye.

This is very evident when doing astronomy, as looking through a telescope
you have to look at stars out of o see the whole thing to be able to comment on the calculation... But that's behind a paywall.

Which part of the eye are we talking about?

I assume the retina as a whole?

The sensitivity of the helmet gecko eye has been calculated to be 350 times higher than human cone vision at the color vision threshold.

Oh right, so THAT is where they got that “350” number from!!!! That would make a lot more sense. It was highly misleading of them to say:

“....Nocturnal species have excellent night vision; their eyes are 350 times more sensitive to light than the human eye ...”

-without saying this is COLOUR vision they are talking about and NOT merely dim-light vision! (which surely is the natural thing to assume I think ).
So there should be no contradiction of my calculation that their dim-light vision (ignoring colour discrimination) could not be greater than about 10 times ours at most AND their COLOUR vision threshold being more than 350 than ours -because those are two independent attributes.


BUT, I happen to know nocturnal owls are colour blind so the:
http://www.chegg.com/homework-help/questions-and-answers/owls-large-sensitive-eyes-good-night-vision-assume-thatthe-pupil-owl-s-eye-diameter-85-mm--q239098

“...Owls have large, sensitive eyes for good night vision. Assume thatthe pupil of an owl's eye can have a diameter of 8.5 mm (as compared with a maximum diameter ofabout 7.0 mm for humans). In addition, the owl's eye is about 100times more sensitive to light of low intensity than a human eye,allowing owls to detect light ...”

-still doesn't add up!
But that happens to look like a very unreliable source (they've even made obvious edit errors in that link that include space-characters missing) so; -anyone? -I should just assume that 100 figure IS wildly wrong in this case?
-The problem is that I am getting similar wild figures for owls from other websites and I have yet to find one that gives a figure for owls that is plausible according to my estimates i.e. within the range of mathematically and physically allowed values. For example:

http://soarinhawk.weebly.com/what-is-a-raptor.html
“...The eyes of owls are at least 35 to as much as 100 times more sensitive to dim light as the eyes of humans....”

-even the lower 35 figure is still way too high (by about 3 fold ) according to my calculations and should be physically impossible! -anyone?

Originally posted by humy
BUT, I happen to know nocturnal owls are colour blind so the:
http://www.chegg.com/homework-help/questions-and-answers/owls-large-sensitive-eyes-good-night-vision-assume-thatthe-pupil-owl-s-eye-diameter-85-mm--q239098

Wikipedia seems to agree with you about owls, this is what they had to say in the vision sub-section (referring to a peer reviewed paper):

While it is commonly believed that owls have such great nocturnal vision due to their large (and thus very light-gathering) eyes and pupils and/or extremely sensitive rod receptors, the true cause for their ability to see in the night is due to neural mechanisms which mediate the extraction of spatial information gathered from the retinal image throughout the nocturnal luminance range. These mechanisms are only able to function due to the large sized retinal image.

so chegg.com seems to be wrong on this.

Originally posted by DeepThought
Wikipedia seems to agree with you about owls, this is what they had to say in the vision sub-section (referring to a peer reviewed paper):

While it is commonly believed that owls have such great nocturnal vision due to their large (and thus very light-gathering) eyes and pupils and/or extremely sensitive rod receptors, the true cause for their abil ...[text shortened]... function due to the large sized retinal image.

so chegg.com seems to be wrong on this.

That makes sense.

I remember talking to a lecturer at university who was talking about installing a
multimillion dollar CCD camera on to a major telescope (upgrading from film/plate
photography to digital) a few years earlier.
This CCD was something like 1.1 Mega-pixels.

And then contrasting that multimillion dollar 1 Mega-pixel CCD with the multi-mega-pixel
CCD's you could now (at the time) get in a £50 camera or phone.


While the mobile phone camera has many more pixels, it wont produce nearly as good
an image as it's much much smaller than the one fitted to the telescope. (as well as
lower quality resulting in more noise)
The awesome optics of the telescope obviously help... But the CCD size plays a big part.
Even within ordinary cameras, the better quality ones have physically larger CCD's as
opposed to ones with higher pixel counts.

So it could well be the case that a creature adapted for night vision with highly light
sensitive light detectors right in the centre of their vision (unlike us) and with the
image spread over a larger surface (by perhaps having a much narrower field of
vision?) would have much superior vision at night, possibly up to 350? times as
good as ours... without actually being 350 times more light sensitive than us.

To be 350 times as light sensitive over all (as opposed to in the centre of the retina)
at 80% light capture you would need an iris radius of the order of 23mm (diameter 46mm).
Which is probably much larger than any land animal or bird... but is smaller than giant squid
which can clock in at 90mm pupil.
https://en.wikipedia.org/wiki/Giant_squid

Originally posted by humy
“...In dim light 5% of the light energy falling on the eye is reflected by the cornea, 35% goes through the cornea and is absorbed by the black pigment on the inner surface of the choroids, 50% is absorbed by the lens and humours, and the final 10% is absorbed by the rods. ...” )

Is this 10% of all light entering the eye reaching the rods, or 10% of all light heading towards a rod? What percentage of the surface of the retina has rods? Other poster say that retinas have different rod densities, so maybe that is a factor.
I am not sure if this is what googlefudge was saying, but focus might be very important. If you stick a zoom lens on a camera, I believe it collects more light from a given place in the scene. So if your night vision is looking at a 180 degree view in front of you, and an owl only looks at a 10 degree cone in front of it, it may see better in that cone. I believe hawk have very good long distance vision in a small cone of vision.

Originally posted by twhitehead
Is this 10% of all light entering the eye reaching the rods, or 10% of all light heading towards a rod? What percentage of the surface of the retina has rods? Other poster say that retinas have different rod densities, so maybe that is a factor.
I am not sure if this is what googlefudge was saying, but focus might be very important. If you stick a zoom l ...[text shortened]... tter in that cone. I believe hawk have very good long distance vision in a small cone of vision.

Is this 10% of all light entering the eye reaching the rods, or 10% of all light heading towards a rod?

10% of all light heading towards the pupil reaching the rods.

What percentage of the surface of the retina has rods?

Not sure but I assume most of it.

Originally posted by DeepThought
Wikipedia seems to agree with you about owls, this is what they had to say in the vision sub-section (referring to a peer reviewed paper):

While it is commonly believed that owls have such great nocturnal vision due to their large (and thus very light-gathering) eyes and pupils and/or extremely sensitive rod receptors, the true cause for their abil ...[text shortened]... function due to the large sized retinal image.

so chegg.com seems to be wrong on this.

if chegg.com is wrong on this then so too must every one of the many websites that I have looked at!
Perhaps this is a widespread scientific myth that has been propagated about owl sensitivity to dim light which is grossly exaggerate and perhaps owls only have about ~5 times greater sensitivity to dim light compared with humans? (which would be a vastly more realistic figure than the 100 fold figure usually quoted! ) . If so, I am appalled by the propagation and acceptance of such misinformation!

Originally posted by humy

What percentage of the surface of the retina has rods?

Not sure but I assume most of it.

In the area with cones, each cone only detects one colour range. So for a given colour of light, only one third of the retina can detect it.

http://en.wikipedia.org/wiki/Absolute_threshold
Interesting.
Some parts of the eye have more rods, so they clearly do not have full coverage throughout.
It only takes one photon to stimulate a rod.
It takes 9 rods to see a photon each to tell the brain something is happening.