Exit pupil and AFOV

[jetstream]

On 05/05/2020 at 11:25, miguel87 said:

Glad you cleared up the wasted light issue tho. It had been troubling me to be honest!

https://www.cloudynights.com/topic/471216-exit-pupil/

If you limit effective aperture with the eye what resolution is available? the aperture of the scope or the stopped down aperture with the eye? does this affect the f ratio of the system including the eye?

@andrew s?

Edited May 8, 2020 by jetstream

[andrew s]

Simple bit first. If the entrance pupil of the eye is smaller that the exit pupil of the telescope/eyepiece it will limit the effective aperture and hence light grasp.

The effect on resolution is more complex. You normally need quite a high magnification to see a diffraction limited image. I suspect t there is a crossover from the eye limiting the resolution to the telescope/eyepiece/seeing limiting the resolution. I don't  know exactly where this is as the exit pupil reduces and probably changes person to person.

Regards Andrew 

[miguel87]

31 minutes ago, andrew s said:

Simple bit first. If the entrance pupil of the eye is smaller that the exit pupil of the telescope/eyepiece it will limit the effective aperture and hence light grasp.

I would use the analogy I used before of a 7mm diameter circular camera sensor with the exit pupil placed perfectly on it.

Let's use the full moon as an example, taking up the centre of the resolved exit pupil image on the sensor.

If you remove the outer circumference of pixels on the sensor so that it is only 5mm in diameter (equivalent of the human pupil being smaller than the telescopes exit pupil) then the resolved image of the moon remains entirely in the centre of the sensor.

The image would not be any dimmer because the light has been focused into an image with brightness distributed non-uniformly across it (I.e. the moon is brighter than the sky around it.

So as was explained so well to me earlier, there is NO brightness loss in the part of the image that enters the eye as the exit pupil gets larger.

You have to remember the exit pupil as a little floating 2d image in the air, it is focussed already. It is not evenly spread light.

[andrew s]

Light is not focused at the exit pupil @miguel87 that's were you analogy fails. With a telescope/eyepiece the rays from a star are parallel through the exit pupil.

You need to look at some ray diagrams to really understand what is going on.

Regards Andrew 

[miguel87]

20 minutes ago, andrew s said:

Light is not focused at the exit pupil @miguel87 that's were you analogy fails. With a telescope/eyepiece the rays from a star are parallel through the exit pupil.

You need to look at some ray diagrams to really understand what is going on.

Regards Andrew 

It is focussed or else how would a DSLR sensor with no lens and no focus ability be able to take a sharp image straight from the exit pupil plane?

The whole purpose of the telescope is to bring light to focus at a point.

That point is the exit pupil.

Edited May 8, 2020 by miguel87

[andrew s]

38 minutes ago, miguel87 said:

It is focussed or else how would a DSLR sensor with no lens and no focus ability be able to take a sharp image straight from the exit pupil plane?

The whole purpose of the telescope is to bring light to focus at a point.

That point is the exit pupil.

Quit right, but the focal point is not the exit pupil. That's what you are  misunderstanding.  

The exit pupil is where the entrance pupil is imaged not the object e.g the star.

For a telescope used at prime focus ( telescope plus CCD) the exit pupil is at infinity! As the objective (as entrance pupil) can't image itself.

Your 7mm aperture is acting as a field stop.

It a complex  subject.

Regards Andrew 

Edited May 8, 2020 by andrew s

[miguel87]

10 minutes ago, andrew s said:

Quit right, but the focal point is not the exit pupil. That what you are  misunderstanding. 

Right, but we use the exit pupil to view the image. Which comes just after the focal point. Once past the focal point, the light is not uniformly distributed, it is the image of whatever we are looking at. Otherwise eyepiece projection would result in a blank, evenly lit image.

And I know you dont like my DSLR sensor analogy but it works because it literally samples a 'slice' taken through the optical cone of light after the focal point. But it shows that the light at this cross-section is not evenly distributed but forms an image. 

Edited May 8, 2020 by miguel87

[John]

Does this shed any more light on this topic (see what I did there 😞

https://www.telescope-optics.net/eyepiece1.htm

 

[miguel87]

19 minutes ago, andrew s said:

 

The exit pupil is where the entrance pupil is imaged not the object e.g the star.

 

In a telescopic system the entrance pupil is just the aperture of the instrument where light enters. Therefore not relevant to the properties of the exit pupil in this case.

I know it is very complicated an I'm sure you have more experience than myself but...

Unless I can understand how a cross section of the light cone taken by a DSLR chip shows the full detail of the image, without the image apparently being present there?

In this instance, what is focussing the image?

[miguel87]

12 minutes ago, John said:

Does this shed any more light on this topic (see what I did there 😞

https://www.telescope-optics.net/eyepiece1.htm

 

An interesting read, thanks.

"The image formed by the telescope objective is real, and can be observed directly"

So at the point of the field stop of an eyepiece, the eyepiece 'selects' a portion of the image (a real observable image with non-uniform brightness) to work with. It passes through various optics and produces an exit pupil.

The converging cone is made parallel (collimated into pencils), therefore at infinity (the paths would never converge).

If the image that the eyepiece is working with is 'real' and 'directly observable' AND a camera sensor can be placed in the light path to sample the photons and create an image. I dont understand how brightness can be uniform?

There surely must be a real image at the exit pupil.

[andrew s]

9 minutes ago, miguel87 said:

Right, but we use the exit pupil to view the image. Which comes just after the focal point. Once past the focal point, the light is not uniformly distributed, it is the image of whatever we are looking at. Otherwise eyepiece projection would result in a blank, evenly lit image.

And I know you dont like my DSLR sensor analogy but it works because it literally samples a 'slice' taken through the optical cone of light after the focal point. But it shows that the light at this cross-section is not evenly distributed but forms an image. 

 

We don't use the exit pupil to view the image. The image from an eyepiece is at infinity ! We align the exit pupil of the telescope/eyepiece with the eyes entrance pupil and the cornea and lens then focus the light on the retina.

With eyepiece projection ths eyepiece is reposition to form an image and the exit pupil will shift but it will not be at the focal point. It will be close as the objective focal length is much longer the thst of the eyepiece. 

Light is not evenly distributed  at the focal point if it were there would be no image!

The definition of the exit pupil is "The image of the entrance pupil formed by the optics of the system in question. " it is completely  relevant.

One more time. At prime focus the objective forms an image on the DSLR sensor which is at the focal point/plane. Telescopes are normally designed so the the objective is the entrance pupil. The exit pupil will then be at infinity.

What limits the field of view is called a field stop. It could be the edge of the sensor, baffles in the telescope tube or the dew shield or your 7mm hole. As you say it just limits the field not the intensity across the field.

In some cases you get vignetting where other elements than the objective are limiting  the aperture as you go off axis.

Regards Andrew 

[andrew s]

4 minutes ago, miguel87 said:

An interesting read, thanks.

"The image formed by the telescope objective is real, and can be observed directly"

So at the point of the field stop of an eyepiece, the eyepiece 'selects' a portion of the image (a real observable image with non-uniform brightness) to work with. It passes through various optics and produces an exit pupil.

The converging cone is made parallel (collimated into pencils), therefore at infinity (the paths would never converge).

If the image that the eyepiece is working with is 'real' and 'directly observable' AND a camera sensor can be placed in the light path to sample the photons and create an image. I dont understand how brightness can be uniform?

There surely must be a real image at the exit pupil.

I think you have the basic idea but you continue to misunderstood what the exit pupil is.

As the exit  pupil is an image of the objective/aperture stop formed by the eyepiece,  all the light that goes through the objective goes through the exit pupil and as at the objective the light rays from a star are parallel.  There is no real image your eye forms the real image.

A camera at prime focus is at the focal point the exit pupil is at infinity.

Regards Andrew 

[miguel87]

The exit pupil is not far from prime focus, and as you see with a camera or lens, as you move away from prime focus the sharp points spread out and become halos with details of the primary. But even when a long way out of focus, the light across the whole image is not uniform. You can easily get a sense bright areas and dark areas because every light source across the image will turn into it's own little halo, but stay in location. So even out of focus, the image is not uniformly bright.

If the exit pupil at the lens of the human eye was like a perfectly uniform white piece of paper then there is nothing to bring into focus. There has to be information there for the eye to interpret, just like the out of focus view we see in an eyepiece before we move the lens to sit right at the focus point.

 

Just because the light has been collimated and parallel does not mean it is uniformly bright.

And it is at infinity because the target is at infinity! Not a property of the exit pupil but dependent on the target. If you were looking at a person and not a star it would not be at infinity.

There is an image at an exit pupil! You can see it for yourself floating in the air upside down with a pair of binoculars on a sunny day.

Edited May 8, 2020 by miguel87

[andrew s]

@miguel87 the top blue diagram shows exactly what I have been saying. Note the rays going through the exit pupil (those of the same colour) are parallel they are not going to a focus. This is very obvious for the lines that miss the eye in the lower part of the diagram.

The focus of the lens for the rays shown is at infinity a long way from the field stop. The final focus is of course on the retina.

There would have to be a lens to the left of the one in the diagram if it were drawn for an object other than at the focal point of the lens shown. That, of course, is how a telescope/eyepiece works. The telescope forms a real image and this is where the eyepiece focus is put to deliver parallel  light to the eye. Normally this is where the field stop is placed.  The exit pupil is as in the diagram.

Where do you think the prime focus is on the diagram? 

I can't  see the lower diagram clearly enough to comment.

Regards Andrew 

PS the curved bule line is not the focus of the lens shown.  It ,ooks like it is drawn as if the where a small entrance pupil, not shown, to the left which limits the width of the ray bundles shown. It is where you would place a field stop.

Edited May 8, 2020 by andrew s

[miguel87]

Images of stars behave differently. A star is essentially a point source of light so no amount of magnification will produce an extended image. (On the assumption of perfect optics and seeing!) Therefore, the brightness of an image of a star depends on the diameter of the object glass or mirror, but not on the magnification. Thus, a high magnification eyepiece will not dim stars but can dim extended objects such as light pollution, and can be useful in increasing the contrast between stars and the background sky.

 

that is copied from Orwell astronomy society. If brightness was uniform then increased mag would not improve sky contrast

[Stu]

9 hours ago, jetstream said:

https://www.cloudynights.com/topic/471216-exit-pupil/

If you limit effective aperture with the eye what resolution is available? the aperture of the scope or the stopped down aperture with the eye? does this affect the f ratio of the system including the eye?

@andrew s?

I’ve always wondered that too!

[andrew s]

4 minutes ago, miguel87 said:

Images of stars behave differently. A star is essentially a point source of light so no amount of magnification will produce an extended image. (On the assumption of perfect optics and seeing!) Therefore, the brightness of an image of a star depends on the diameter of the object glass or mirror, but not on the magnification. Thus, a high magnification eyepiece will not dim stars but can dim extended objects such as light pollution, and can be useful in increasing the contrast between stars and the background sky.

 

that is copied from Orwell astronomy society. If brightness was uniform then increased mag would not improve sky contrast

I don't  disagree with this as stated up to the point you can resolve the Airy disk. If you continue to magnify further the disk will appear bigger and dimmer.

Regards Andrew 

[Stu]

Just now, andrew s said:

I don't  disagree with this as stated up to the point you can resolve the Airy disk. If you continue to magnify further the disk will appear bigger and dimmer.

Regards Andrew 

Doesn’t contrast improve because the sky background is dimmed by increasing magnification, effectively the same as an extended object?

[miguel87]

1 minute ago, Stu said:

Doesn’t contrast improve because the sky background is dimmed by increasing magnification, effectively the same as an extended object?

Yes exactly. But a more compact point source like star will not be dimmed (if the exit pupil airy disc has the brightness of the star spread across it's entire area, then reducing its size would dim the star too) the star is not represented in all areas of the exit pupil.

[andrew s]

1 minute ago, miguel87 said:

Yes exactly. But a more compact point source like star will not be dimmed (if the exit pupil airy disc has the brightness of the star spread across it's entire area, then reducing its size would dim the star too) the star is not represented in all areas of the exit pupil.

Look at your  blue diagram. Take the yellow rays as being from an on axis star. They will have uniformly filled the telescope objective and will uniformly fill the exit pupil of the telescope/eyepiece. 

I don't  know what you mean by the "exit pupil Airy disk" the exit pupil and the Air disk are two different things. 

I don't think it worth me continuing this exchange as we are clearly not understanding each other. 

Regards Andrew 

[vlaiv]

Very interesting point about resolution.

I wondered that often in another context - secondary mirror on folded design scopes - like Mak. How does it impact resolution.

For human eye, we can do the math. In fact, I've seen math done and it matches well with experience. Resolution of human eye is about 1 arc minute. If you take size of photo receptor cells and their density and do airy disk from regular eye pupil of 5mm - you get the same number - resolution should be 1 arc minute. This means that we have diffraction limited eyesight

 

[andrew s]

12 minutes ago, Stu said:

Doesn’t contrast improve because the sky background is dimmed by increasing magnification, effectively the same as an extended object?

I thought I had responded but it has gone  missing. 

Yes. We normally view at a magnification where the Airy disc is not resolved and so the star image is as if it were from a point source. 

Regards Andrew 

[jetstream]

22 minutes ago, andrew s said:

the top blue diagram shows exactly what I have been saying.

This has always puzzled me Andrew- thanks for clearing things up. From my completely unscientific observations I can say that stars can be made to disappear with too high a mag, whether because of seeing or other things. There seems to be a sweet spot mag wise for them.

Can I ask one more question Andrew, slightly off topic?

How much object information is in one unit of light- packet, photon or whatever? When I place my hand over part of my scope the image is still there as itself but suffers more diffraction- I think lol!

[jetstream]

10 minutes ago, vlaiv said:

Very interesting point about resolution.

I wondered that often in another context - secondary mirror on folded design scopes - like Mak. How does it impact resolution.

For human eye, we can do the math. In fact, I've seen math done and it matches well with experience. Resolution of human eye is about 1 arc minute. If you take size of photo receptor cells and their density and do airy disk from regular eye pupil of 5mm - you get the same number - resolution should be 1 arc minute. This means that we have diffraction limited eyesight

 

"Understanding Resolution and Contrast

Two points it is important to understand is the resolution a telescope can provide, and how the contrast of the objects we are imaging affects is related to what can be recorded. Its often seen quoted in the Dawes or Rayleigh criterion for a given aperture. Dawes criterion refers to the separation of double stars of equal brightness in unobstructed apertures. The value can given given by the following simple formula:

115/Aperture (mm.) For example, a 254mm aperture telescope has a dawes limit of 0.45" arc seconds. The dawes limit is really of little use the Planetary observer, as it applies to stellar images. Planetary detail behaves quite differently, and the resolution that can be achieved is directly related to the contrast of the objects we are looking at. A great example that can be used from modern images is Saturn's very fine Encke division in ring A. The narrow gap has an actual width of just 325km - which converts to an apparent angular width at the ring ansae of just 0.05" arc seconds - well below the Dawes criterion of even at 50cm telescope. In `fact, the division can be recorded in a 20cm telescope under excellent seeing, exceeding the Dawes limit by a factor of 11 times!. How is this possible?.

As mentioned above, contrast of the features we are looking at is critical to how fine the detail is that we can record. The Planets are extended objects, and the Dawes or Rayleigh criterion does not apply here as these limits refers to point sources of equal brightness on a black background. In fact it is possible for the limit to be exceeded anywhere up to around ten times on the Moon and Planets depending on the contrast of the detail being observed/imaged."

From Peach.

Whats your thoughts about telescope resolution in this context?

Edited May 8, 2020 by jetstream

[andrew s]

2 minutes ago, vlaiv said:

Very interesting point about resolution.

I wondered that often in another context - secondary mirror on folded design scopes - like Mak. How does it impact resolution.

For human eye, we can do the math. In fact, I've seen math done and it matches well with experience. Resolution of human eye is about 1 arc minute. If you take size of photo receptor cells and their density and do airy disk from regular eye pupil of 5mm - you get the same number - resolution should be 1 arc minute. This means that we have diffraction limited eyesight

 

If the secondary  mirror is properly sized it should not impact the resolution if you ignore any aberrations. 

One of my final exam question was " at what distance can you resolve the headlights of a car". That was it. I did two calculations. One as you indicate assuming the rods and cones size limited it and the other assuming the size of the iris did. Can't  recall which  was smallest.

I am sure it would be the cells with an astronomical telescopes. Regards Andrew