Eye pupil sizes (1 Viewer)

[takitam]

There's a lot of discussion about size of human eye pupil during twilight and night conditions and appropriate bins for such conditions. It is generally stated that during moderately cloudy day the pupil is about 3-4 mm big, and during night it reaches 6-9 mm. Please feel free to correct me if I'm wrong.

But what is the size of one's eye pupil during a sunny day and very sunny bright day in the middle of the summer(lets say north mediterranean climate)? I've never measured size of mine but I suppose it may be as small as 1.5-2 milimeters. Am I right?

I think it may be useful to provide such information in one thread, and if not maybe at least my curiosity will be satisfied

 

[Kevin Purcell]

The usual numbers are

2mm on a bright day
3mm in overcast
4mm at very dim twilight (owling ... end of birding)
5mm in urban/suburban dark
7mm at a good dark site

But the variation over the population is about plus or minus 1mm even more at the large sizes in older people.

A lot of people seem to overestimate the sizes.

You can measure your own (and get rid of all the variation) with a digital camera with a flash (no red eye that's what you want to measure!) and a ruler. Hold the ruler on your forehead for scale and self-shot in the light environment you want to check.

I'll post a chart later.

 

[henry link]

There is also a way to measure the size of your pupils with a binocular in front of your eyes. You need a glitter point on a sunny day (tiny reflection of the sun in a small round shiny object). Focus the binocular at infinity and look at the glitter point at some close distance like 5m. You will see a large unfocused disc. That is actually an image of your eye's pupil (or the exit pupil of the binocular if your eye's pupil is larger than the exit pupil). I'll leave it to your ingenuity to fashion some sort of adjustable paper caliper to place in front of the binocular objective. Adjust the caliper until you see both inside edges of it just barely impinging on the projected disk of your pupil in the binocular. Divide that measurement by the magnification of the binocular and the result is the size of you pupil under that particular lighting condition with a binocular in front of your eyes. This can also be done in low light with a pinhole in aluminum foil covering the lens of a flashlight.

It's surprising to me how large my pupils open when looking through a binocular in a heavily shaded area in daylight, around 5mm. In very bright sunlight my pupils constrict to barely more than 2mm when looking through binoculars.

 

[Flemingo]

I've read that when your old like me (48) your pupils don't dilate more than 4mm so using binos with exit pupils over this are a waste. Must try to measure mine sometime.

 

[bkrownd]

I've read that when your old like me (48) your pupils don't dilate more than 4mm so using binos with exit pupils over this are a waste.

Wouldn't a larger exit pupil figure also make the binoculars more forgiving of misalignment between your pupil and the optics, and therefore increasing viewing comfort?

 

[Flemingo]

Wouldn't a larger exit pupil figure also make the binoculars more forgiving of misalignment between your pupil and the optics, and therefore increasing viewing comfort?

Never really noticed this even when using compacts with exit pupils of 3mm. Just measured my pupil in dark with camera flash and it appears to be 5mm (rather rough measurement). I use mainly 8x32 (exit pupil 4mm) at present and never feel that the light gathering is poor even in dull light. Maybe I'm just not discerning enough. It's all a trade off between weight, size and light transmission.

Just re-read Kevin's post and it suggests that 4mm is normal for dusk viewing (I don't go birding in the dark) so 8x32 should be fine. Of course the bigger the objective theoretically the more resolving power you have. Not certain how important this is in practice!

 

[Kevin Purcell]

Just re-read Kevin's post and it suggests that 4mm is normal for dusk viewing (I don't go birding in the dark) so 8x32 should be fine. Of course the bigger the objective theoretically the more resolving power you have. Not certain how important this is in practice!

Bins are limited by the resolving power of the eye x the magnification. This is always much less than the diffraction limited value for the bins.

Plus bins rarely get to that level because of all the "extra" optical junk in the tube. They aren't "simple" astronomical telescopes ... the aberrations of the optical parts are the limitation.

Even the human eye suffers when the f number drops (in dark situations) reducing it's resolution to perhaps half the value in daylight. Note this is the opposite of what a naive physicist would say (one who believes the cornea and lens are perfect systems and the diffraction-limited value would increase as the aperture increases). Except at very small apertures (very bright daylight) the eye isn't diffraction limited.

 

[falcondude]

What will be the theoretical resolution of a given binocular, assuming no abberation or defect at all?

 

[ThoLa]

What will be the theoretical resolution of a given binocular, assuming no abberation or defect at all?

See here:
http://www.akoehler.de/
Click: "Auflösungsvermögen"

 

[Surveyor]

Go to Wikipedia and search Dawes Limit and/or Rayleigh Criterion.

A good general starting place is 116 / Aperture (mm)=Arc Seconds. There are more detailed structures that define the relationship to wavelength, etc. but for general use the above is close enough.

I typically use 1.25 Dawes as being good for binos, this is a very rough approximation based on the fact that .80~.82 Strehl is considered diffraction limited. After about 1.5 Dawes, I will look for the cause of the aberrations.

Example: A 42 mm objective would have a Dawes limit of 2.8 Arc Seconds (116/42) so I would think anything up to 3.5 arc seconds would be very good in a low powered bino, 4 arc seconds is common even in very expensive glass. At above 5 arc seconds you may start noticing some degradation in the view, depending on your visual acuity.

Hope this helps.

Best,
Ron

 

[Kevin Purcell]

What will be the theoretical resolution of a given binocular, assuming no abberation or defect at all?

http://en.wikipedia.org/wiki/Diffraction_limited

d= lamda / 2 sin(alpha)

or

alpha = arcsin( lamda / 2 d)

alpha = diffraction limited resolution
lamda = wavelength of light
d = diameter of a limiting stop (i.e. the telescope objective in this case).

alpha = arcsin( lamda / (2 d))

For a 40mm binocular aperture in yellow (575nm) light

alpha = arcsin( 575nm / (2 *40mm) )
= arcsin( 575e-9 / 80e-3 )
= 0.0004118 degree
= 1.48 arc seconds

It's interesting how close bins come to this (e.g. the Chinese ED are a bit worse than half the diffraction resolution).

For the human eye in with a 2.5mm pupil the diffraction limit is 16 times worse at 24 arc seconds but the actual resolution of the eye is rather worse than that (usually said to be around 60 arcseconds in this form or twice that in line-pairs-per-mm).

First determined by Abbe (one of the many things he did including the Abbe and Abbe-Konig prism)

For more on diffraction see

http://en.wikipedia.org/wiki/Diffraction

 

[Kevin Purcell]

Go to Wikipedia and search Dawes Limit and/or Rayleigh Criterion.

A good general starting place is 116 / Aperture (mm)=Arc Seconds of diffraction spot. There are more detailed structures that define the relationship to wavelength, etc. but for general use the above is close enough.

http://en.wikipedia.org/wiki/Rayleigh_criterion

The Raleigh Criterion seems to be an emprical forumal and differs from the Abbe limit by a factor of two. Any idea why? Perhaps the Bessel function 1.22 for measuring the ring around the Airy disc?

Also what wavelength of light is the Rayleigh Criterion applied to? Red? 562 nm for the Dawes Limit. That would account for some of it.

Example: A 42 mm objective would have a Dawes limit of 2.8 Arc Seconds (116/42) so I would think anything up to 3.5 arc seconds would be very good in a low powered bino, 4 arc seconds is common even in very expensive glass. At above 5 arc seconds you may start noticing some degradation in the view, depending on your visual acuity.

I always find it interesting to not that the spec for the US Militaries bins (the 7x50 M22 and 7x28 M24 is 9 arc seconds though I suspect the bins all do rather exceed that.

 

[falcondude]

Ron and Kevin P, thanks a lot for the wiki links. So a larger glasses, say 50mm, should have an upper hand on resolution? Can we tell with human eyes?

 

[Kevin Purcell]

Ron and Kevin P, thanks a lot for the wiki links. So a larger glasses, say 50mm, should have an upper hand on resolution? Can we tell with human eyes?

No. Not for real binoculars.

The resolution is human eye's acuity / magnification.

This is not near the diffraction limit until you get to much higher magnifications than binoculars have.

 

[henry link]

My experience with measuring the resolution of binoculars closely matches Ron's. A good result raises a nice green flag for axial sharpness and a mediocre or bad result needs to be investigated with a star-test. My loose criteria are:

130/D or better means you have lucked into an excellent specimen of a good design.

140-150/D means probably no problem, but no bragging rights either.

160-180/D means something is certainly wrong, but it may be harmless in normal use. A star-test will reveal what the problem is. I'm not happy to see an expensive binocular do no better than this.

200/D or worse means something is seriously wrong, but even this might not be very visible in most situations if the problem is mostly confined to the outside third of the objective as is often the case with pinching and astigmatism.

I would add that small aperture binoculars tend to do better than large ones. I've come to expect resolution closer to perfect from 30mm binoculars compared to 50mm binoculars, so I hold small binoculars to a higher standard. I should also add that the right and left barrels are quite independent. I don't think I've ever seen exactly the same performance in both.

 

[Surveyor]

http://en.wikipedia.org/wiki/Rayleigh_criterion

The Raleigh Criterion seems to be an emprical forumal and differs from the Abbe limit by a factor of two. Any idea why? Perhaps the Bessel function 1.22 for measuring the ring around the Airy disc?

Also what wavelength of light is the Rayleigh Criterion applied to? Red? 562 nm for the Dawes Limit. That would account for some of it.



I always find it interesting to not that the spec for the US Militaries bins (the 7x50 M22 and 7x28 M24 is 9 arc seconds though I suspect the bins all do rather exceed that.

Sorry Kevin, I just saw your post.

It has been quiet some time since I visited Dawes and Rayleigh and I am not going to right now. The following is what I remember (and for me, that is never to be relied upon). The Rayleigh criterion is set up for splitting double stars or measuring the power in the gap. Rayleigh uses two Airy disks, the center of the second star at the end of the Radius of the Airy disk of the first, or two exact size Airy disks separated by their radius. From memory, the 1.22 is a constant added to correct for the change from a slit or rectangle to a circular pattern, I do not remember the derivation of the constant.

The Dawes Limits were set up by empirical observations of double stars with various size apertures and compiling data of the doubles resolved. In general, it is about 85% of the Rayleigh figures.

Since both terms are for seperation of figures, I deem them to be more applicable to lines pairs test instead of line or point resolution.

As to the visual acuity, I guess I have a somewhat different impression than you. I think that the image will show improvement down to about half of the visual acuity (maybe line or point resolution, I have no explanation). Somewhere on the forum there was a discussion far back that I believe Henry or Kimmo had shown empirical data that supported that notion, but I have been unable to find it, or just not remembering it correctly.

If all was limited by visual acuity, why would so many say the Chinese ED’s are sharper than about all they compared them to, surely all of them were not worse than their visual acuity/power.

Just my opinion, that and $1.50 may get you a cup of coffee.

Have a good day.

Ron

 

[ronh]

Hooray for binoculars that resolve three or more times better than the eye. Beyond the ability to tell two closely separated objects apart (resolution), I believe there lies a realm of finer detail that determines how sharp the image looks.

People measure what is easy to measure. Nobody measures contrast, the other great cause of image greatness or mediocrity.

Which all, combined with an additional $.85, will get you a shot of espresso dumped in to boot.

BUT HENRY, considering your statement about the high resolution of small binoculars. You probably test compacts at full aperture, which would be reasonable considering their small exit pupils. But would they beat a large bino at the same effective aperture?
RonH

 

[Kevin Purcell]

Well, contrast is really just transmission (assuming no scatter between the elements to raise the "black level", which is less a big if than it used to be). And people do measure and worry about it.

Of course with my favorite topic, stray light and veiling glare, we know this not to be the case in real life. It's still the place were the top bins hold the lead. But the lead is smaller.

Modern bins, ya gotta love 'em

(And of course I've drifted off the original topic) so here's that graph of average pupil size against luminance. I don't have a cite for this as it came of cloudynights. The other has the cite in the image.

View attachment pupil size chart - Brown et al published the following chart of pupil size by age based on three res



Hmmm it only has one chart ...

 

[Surveyor]

I think I am going to side with RonH on this one. I think that people may be mixing contrast, as pertains to resolution and MTF with saturation, or level intensity, which is a function of transmission. I have been guilty of that myself, and still do so occasionally. Some of this confusion is learned from the old CRT TV days. Do a Google search for contrast and brightness controls for CRT’s. They are actually labeled awkwardly and do not control what they claim to.

Just because a binocular will transmit 95% of 630 nm light does not mean the view contains that much light at that point (intensity or saturation). A view might contain only 2% light at, say, 500 nm and increase to 90% light intensity at 550 nm (again saturation) but the optics may only have enough resolution to display a blur of the average light color every 2, 5 or 10 nm depending on the resolvable angular width of the optics and the linear dimensions of the color transition. Resolution and contrast pertain to spatial relationship, or simply, how one space compares to other spaces of similar dimensions, 3 arc seconds or whatever size is the smallest to detect changes.

A very quick Google search turned up this simple explanation, a couple of paragraphs under the first picture, sum up nicely.

http://www.luminous-landscape.com/tutorials/understanding-series/understanding-mtf.shtml

I am no expert on light or color and know that even the experts have trouble with the terms and definitions of the science. This just represents my personal, naïve, understanding of these terms.

Best to all.
Ron

 

[Kevin Purcell]

I think I am going to side with RonH on this one. I think that people may be mixing contrast, as pertains to resolution and MTF with saturation, or level intensity, which is a function of transmission. I have been guilty of that myself, and still do so occasionally. Some of this confusion is learned from the old CRT TV days. Do a Google search for contrast and brightness controls for CRT’s. They are actually labeled awkwardly and do not control what they claim to.

I do actually understand the difference in both cases

On a TV the "contrast" control sets the maximum white level (or more correctly the gain of a video amp which sets the maximum output level for a given input). The "brightness" control sets the black level (i.e the offset which just sets a black level signal to black on the display.

There are parallels in the optics world too.

Transmission == "contrast" control == setting the maximum white level (how bright can the image be).

Scatter == "brightness" control == setting the minimum black level (because scatter brightens the blacks)

The "true" contrast is really related to transmission/scatter (which is were veiling glare becomes apparent in a reduction of contrast in high light levels). But for a constant scatter it scales as transmission (which was my point above).

I really have to start a thread on Vubravitch's paper on bin design that ronh pointed us to: he points out that in daylight the bin's "efficiency" depends on only two things: the magnification and the transmission. Exit pupil, objective diameter and may other factors don't matter (so long as EP > eye's entrance pupil). Of course in real life how much bigger the EP is matters for other reasons but not in this ability to identify targets.

I think transmission is in general an under-rated factor by birders but good transmission at a reasonable price is easier to get today than ever before.

In all of these cases I'm assuming a "large" target so you are close to the zero of the MTF plot (i.e. at the highest values). Again for birders I can think of some cases (say a grating-like or a dotted or speckled or vermiculous pattern on a bird's plumage) which would move along the MTF curve and you'd start to see reduced contrast effects for high spatial frequency targets.

Just because a binocular will transmit 95% of 630 nm light does not mean the view contains that much light at that point (intensity or saturation). A view might contain only 2% light at, say, 500 nm and increase to 90% light intensity at 550 nm (again saturation) but the optics may only have enough resolution to display a blur of the average light color every 2, 5 or 10 nm depending on the resolvable angular width of the optics and the linear dimensions of the color transition. Resolution and contrast pertain to spatial relationship, or simply, how one space compares to other spaces of similar dimensions, 3 arc seconds or whatever size is the smallest to detect changes.

I think you misunderstand MTF and maybe are confusing spatial frequency with changing wavelength (frequency) of the light. That's not the case. The MTF doesn't imply any sort of wavelength resolution. These systems are linear and don't mix different colors. There is no binning into 2nm boxes. The MTF (which you usually measure at one wavelength though you can change to another value) says nothing about the change in MTF with wavelength which should change in a predictable manner though it may get worse in real life with multilayer coatings that aren't flat in frequency response. That would change the amplitude of the MTF. The width of the MTF should change with wavelength too.

The spatial resolution of a bin will vary by a factor of two over the visible spectrum. We just make a convenient fiction to quote a value (usually in the green about in the middle). It'll be 1.4 time higher at the red end and 0.7 time lower at the blue end. As theire all below the acuity of the eye it makes not difference to the user.