Aperture Stop versus Exit Pupil Stop

Although I think I understand this, I am getting beat up, accused of being
stubborn, and probably close to being verbally abused about this elsewhere.
Since I know this never happens here, and that there will uniform agreement
on the issue, I thought I'd ask s.a.a. to join the discussion g.

We all know that an aperture stop reduces light grasp and resolution. If
you use a telescope at a very low power, or low power binoculars with large
objectives, the exit pupil can be larger than the eye, so the eye's pupil
acts as a stop. Obviously, light is lost, but what about resolution? Now I
know that when the exit pupil fills the eye's pupil, the power is too low
for you to utilize the resolution of the lens, although you have as much
light and resolution as you can possibly get at that magnification. So
let's just say "is potential resolution lost?"

Perhaps there is a better way to ask this. If you have a telescope with a 2
mm exit pupil, and you put a 1 mm stop at the exit pupil, is the resolution
halved? It would certainly seem that additional diffraction occurs from the
outer edge of the pupil or "exit pupil stop" opening - but how to you figure
out the effect of this on top of the diffraction from the telescope entrance
pupil?

Clear skies, Alan

Alan French wrote:
Although I think I understand this, I am getting beat up, accused of being
stubborn, and probably close to being verbally abused about this elsewhere.
Since I know this never happens here, and that there will uniform agreement
on the issue, I thought I'd ask s.a.a. to join the discussion g.

We all know that an aperture stop reduces light grasp and resolution. If
you use a telescope at a very low power, or low power binoculars with large
objectives, the exit pupil can be larger than the eye, so the eye's pupil
acts as a stop. Obviously, light is lost, but what about resolution? Now I
know that when the exit pupil fills the eye's pupil, the power is too low
for you to utilize the resolution of the lens, although you have as much
light and resolution as you can possibly get at that magnification. So
let's just say "is potential resolution lost?"

Perhaps there is a better way to ask this. If you have a telescope with a 2
mm exit pupil, and you put a 1 mm stop at the exit pupil, is the resolution
halved? It would certainly seem that additional diffraction occurs from the
outer edge of the pupil or "exit pupil stop" opening - but how to you figure
out the effect of this on top of the diffraction from the telescope entrance
pupil?

Hunh! Someone (whose name I won't mention yet) just asked me this same
question, probably from the same discussion. I still have the same
answer. Here it is (slightly edited for clarity):

===BEGIN QUOTE===

[question about 7x42 binoculars (yielding a 6 mm exit pupil) entering
an eye pupil of only 2 mm: does this mean the effective aperture is
42 * 2/6 = 14 mm, both in terms of light gathering *and* resolution?]

The real image formed by the objective still has the full resolution
of any 42 mm objective--an Airy disc of about 2.7 arcseconds FWHM.

However, a 2 mm eye pupil also imposes its own Airy disc on the
retinal surface--one that is 21 times larger than for the objective,
because the eye pupil is 21 times smaller than the objective. In this
case, that's 2.7 times 21, or about 57 arcseconds.

That's 57 arcseconds at the retina. That means that any detail in the
image which spans 57 arcseconds when magnified (by the 7x power of the
binoculars) will be at the limit of resolution, due to diffraction at
the eye pupil. Well, an object whose image is 57 arcseconds across
when magnified 7x must start out at 57/7 or 8.1 arcseconds. That 8.1
arcseconds is--aha!--the Airy disc size imposed by a 14 mm objective.

In fact, no matter how you adjust the numbers, the eye pupil *does*
limit the resolution you see through the eyepiece, to the same extent
that it limits light gathering (in terms of effective aperture).

This suggests that it may be possible to improve perceived resolution
during the day, by using a neutral density filter and carefully shielding
your eyes from stray light. I'm not sure how much filtering would have
to be employed--it might be too much to see anything...

=== END QUOTE ===

I hope that's helpful. Goodness knows I wouldn't want to add more fuel
to the fire. :-T

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

I think it would have to. Suppose you built a 8-inch telescope with a f.l.
of 48 inches, then equipped it with a 48 inch f.l. eyepiece. The result
would be a 1x scope with and exit pupil of 8 inches. Looking through it
would be the equivalent of looking through a plain 8 inch window...no
magnification, no increase in brightness, and no increase in resolution over
what the unaided eye would see...a definite drop in resolution from the
original aperture.


"Alan French" wrote in message
...
Although I think I understand this, I am getting beat up, accused of being
stubborn, and probably close to being verbally abused about this
elsewhere.
Since I know this never happens here, and that there will uniform
agreement
on the issue, I thought I'd ask s.a.a. to join the discussion g.

We all know that an aperture stop reduces light grasp and resolution. If
you use a telescope at a very low power, or low power binoculars with
large
objectives, the exit pupil can be larger than the eye, so the eye's pupil
acts as a stop. Obviously, light is lost, but what about resolution? Now
I
know that when the exit pupil fills the eye's pupil, the power is too low
for you to utilize the resolution of the lens, although you have as much
light and resolution as you can possibly get at that magnification. So
let's just say "is potential resolution lost?"

Perhaps there is a better way to ask this. If you have a telescope with a
2
mm exit pupil, and you put a 1 mm stop at the exit pupil, is the
resolution
halved? It would certainly seem that additional diffraction occurs from
the
outer edge of the pupil or "exit pupil stop" opening - but how to you
figure
out the effect of this on top of the diffraction from the telescope
entrance
pupil?

Clear skies, Alan

Alan, et al,
Here's a different take on it.

Brightness is brightness and when the exit pupil is bigger than the eye, the
image gets dimmer. The interesting part is resolution. Consider that there's
really two things going on.
1) A telescope (large) aperture is forming an image at the focal plane with
all the resolution it's capable of at any point in time.
2) An eyepiece is magnifying that image and an observer is seeing the
magnified image at whatever resolution it's pupil and retinal acuity permit.

Now, at low power, the eyepiece does not magnifying the image enough for the
resolution at the focal plane to matter; the eye's the limiting factor. So
at very low power, once the exit pupil exceeds the dilated eye, the
resolution in the perceived image stays the same as if the exit pupil just
filled it.

As Brian said: "...no matter how you adjust the numbers, the eye pupil
*does*
limit the resolution you see through the eyepiece..."

Put another way, until you magnify the focal plane image enough to see the
telescope Airy disk, the eye's the limit. Given that you don't see the
scope's Airy disk until the exit pupil's 1mm or less, the scope isn't the
limiting factor until you're way inside the eye's optimum 2-2.5mm.

My $0.02,

Have fun,
Frank

"Alan French" wrote in message
...
Although I think I understand this, I am getting beat up, accused of being
stubborn, and probably close to being verbally abused about this
elsewhere.
Since I know this never happens here, and that there will uniform
agreement
on the issue, I thought I'd ask s.a.a. to join the discussion g.

We all know that an aperture stop reduces light grasp and resolution. If
you use a telescope at a very low power, or low power binoculars with
large
objectives, the exit pupil can be larger than the eye, so the eye's pupil
acts as a stop. Obviously, light is lost, but what about resolution? Now
I
know that when the exit pupil fills the eye's pupil, the power is too low
for you to utilize the resolution of the lens, although you have as much
light and resolution as you can possibly get at that magnification. So
let's just say "is potential resolution lost?"

Perhaps there is a better way to ask this. If you have a telescope with a
2
mm exit pupil, and you put a 1 mm stop at the exit pupil, is the
resolution
halved? It would certainly seem that additional diffraction occurs from
the
outer edge of the pupil or "exit pupil stop" opening - but how to you
figure
out the effect of this on top of the diffraction from the telescope
entrance
pupil?

Clear skies, Alan

"Frank Bov" wrote in message
...
[SNIP]
Now, at low power, the eyepiece does not magnifying the image enough for
the
resolution at the focal plane to matter; the eye's the limiting factor. So
at very low power, once the exit pupil exceeds the dilated eye, the
resolution in the perceived image stays the same as if the exit pupil just
filled it. [SNIP]

Frank,

Yes, that's one reason the debate I'm in elsewhere is so strange. Folks
want to believe they are utilizing the full resolution of a pair of 8x42
binoculars on a bright sunny day, yet 8 power is not enough magnification to
use the resolution of even a much smaller lens.

Clear skies, Alan

Very interesting!

Here's another tidbit: Because of uncorrected aberrations, the resolution of
the lens of the eye is maximum at 2 mm pupil diameter and falls off with
larger or smaller pupils.

Ok, have to add my 2 cents:

The telescope forms an image that is 'diffraction limited' with respect
to the focal plane of the telescope.

The eye forms an image that is 'diffraction limited' with respect to its
focal plane.

Eg: a pair of 10x50 binoculars. Airy disc is about 2 Arcseconds of the
true field. given a 50 degree apparent field, the Airy disc is about 20
arcseconds of the apparent field. For the eyeball, in the daytime, with
a 2mm pupil and 25mm focal length, the eye's ariy disc is about 56
arcseconds of the apparent field, so the eye is the limiting factor. At
night, when the eye's pupil is 6mm accross, the eye's Airy disc is 18
arcseconds of the apparent field, so the telescope is now the limiting
factor.

for an 4" f/10 refractor, at 100x, the airy disc is about 113 arcseconds
of the apparent field. the eye's airy disc is 18 and 56 arcseconds
respectively at daytime and nighttime, so the telescope is always the
limiting factor.

did I get it right ?

Eric.


Alan French wrote:
"Frank Bov" wrote in message
...

[SNIP]
Now, at low power, the eyepiece does not magnifying the image enough for

the

resolution at the focal plane to matter; the eye's the limiting factor. So
at very low power, once the exit pupil exceeds the dilated eye, the
resolution in the perceived image stays the same as if the exit pupil just
filled it. [SNIP]


Frank,

Yes, that's one reason the debate I'm in elsewhere is so strange. Folks
want to believe they are utilizing the full resolution of a pair of 8x42
binoculars on a bright sunny day, yet 8 power is not enough magnification to
use the resolution of even a much smaller lens.

Clear skies, Alan

Zane wrote:
It's a little hard to apply this in a general fashion. The reason
being that the PSF on the retina is actually worse for pupil sizes
larger than about 2.5 mm instead of better, as would be the case for a
diffraction limited sensor. IOW, the eye is not diffraction limited
at pupil sizes above this, with the _absolute_ resolution getting
worse with increasing aperture, and not simply as a ratio of the
diffraction limit.

I think you're right. The reason I didn't get into that (other than
that I didn't appreciate it in full) is that as far as I could tell,
the aberrations of the eye could only make things worse with respect
to the resolution possible with a 42 mm objective--not better.

I still maintain that the best resolution one can achieve with a 7x42
pair of binoculars with a 2 mm eye pupil is no better than what one
could get with that eye pupil and a 14 mm objective *at some specific
magnification*, which depends on that particular observer.

However, I agree that the maximum resolution achievable with the same
instrument with a 6 mm eye pupil is not the full resolution of the
42 mm objective, but is instead quite a bit less, because of eye
aberrations. It's the reason why I put a stop in the middle of my
telescope when I built a singlet refractor as a kid, isn't it?

Isn't Stiles-Crawford for rods a fairly weak effect? If the eye pupil
is 6 mm, chances are it's pretty dark out, and Stiles-Crawford might
not be that significant.

Brian Tung
The Astronomy Corner at http://astro.isi.edu/
Unofficial C5+ Home Page at http://astro.isi.edu/c5plus/
The PleiadAtlas Home Page at http://astro.isi.edu/pleiadatlas/
My Own Personal FAQ (SAA) at http://astro.isi.edu/reference/faq.txt

Hunh! Someone (whose name I won't mention yet) just asked me this same
question, probably from the same discussion.

Just to note, that someone was me. This discussion is happening on the
Astromart birding optics without photos forum.

Alan, with some "help" from me has tried to explain this time and time again
but without success.

I think a pointer to S.A.A. is the next step.

jon

"Brian Tung" wrote in message
...
[SNIP]
However, I agree that the maximum resolution achievable with the same
instrument with a 6 mm eye pupil is not the full resolution of the
42 mm objective, but is instead quite a bit less, because of eye
aberrations. It's the reason why I put a stop in the middle of my
telescope when I built a singlet refractor as a kid, isn't it?
[SNIP]

Brian,

Doesn't this assume that the optical system is diffraction limited, which I
suspect may not be the case for binoculars. They are not made for high
power viewing, generally, and it requires time and money to make diffraction
limited optical systems.

Clear skies, Alan