Exit pupil and AFOV

[miguel87]

13 minutes ago, Ags said:

If I have an F4 scope and I use a 40mm plossl, the exit pupil will be 10 mm. This means most of the light from the star will not fit in your eye pupil. So the star will be fainter than if I had used a 4 mm eyepiece giving a 1 mm exit pupil. This only applies to point sources, extended object do get fainter at smaller exit pupils and reach a maximum brightness at exit pupil = eye pupil.

Even tho the star is a point source, it still reflects of every part of the primary mirror/lens, and because the exit pupil is an image of the primary, the larger the exit pupil, the brighter the star will be.

Even if the exit pupil is 10mm, you will still get 5mm+ into your pupil. Brighter than 1mm.

It might appear relatively brighter because the background sky will be much dimmer at 1mm. But if you measured the brightness of the star point it will be dimmer in a 1mm exit pupil than a 2, 3, 4 etc

Edited May 11, 2020 by miguel87

[Ags]

I think what you are not getting is that there is exactly the same amount of light in the 10 mm and 1 mm exit pupil. That's because the 40 mm eyepiece is ten times further from the focal plane of the telescope (compared to the 4 mm eyepiece) so the same amount of light is simply ten times more spread out, resulting in a bigger exit pupil.

Edited May 11, 2020 by Ags

[miguel87]

9 minutes ago, Ags said:

I think what you are not getting is that there is exactly the same amount of light in the 10 mm and 1 mm exit pupil. That's because the 40 mm eyepiece is ten times further from the focal plane of the telescope so the same amount of light is simply ten times more spread out.

But the field stop on the shorter FL eyepiece would not intercept the whole cone of light, it selects a smaller area evidenced by the smaller TFOV. So it isnt the same amount of light.

Also remember that a star doesnt exactly behave like a true point source of light. It's best resolution in a telescope is the airy disc. The size of the disk depends the optics being used and resolution.

Edited May 11, 2020 by miguel87

[Ags]

At the focal plane (where the field stop is ideally) the light from the star is focussed to a point. If that point is inside the field stop (no matter how big the field stop is), 100% of the light of the star goes on to the eye lens. For example, given the same scope a star will be the same brightness in a 3.5 mm Ethos with a massive field stop or a 3.5 mm planetary eyepiece with a tiny field stop. The ethos let's through more light with it's bigger field stop, but it does so by showing more stars not by making individual stars brighter.

Edited May 11, 2020 by Ags

[miguel87]

4 minutes ago, Ags said:

At the focal plane (where the field stop is ideally) the light from the star is focussed to a point. If that point is inside the field stop (no matter how big the field stop is), 100% of the light of the star goes on to the eye lens. For example, given the same scope a star will be the same brightness in a 3.5 mm Ethos with a massive field stop or a 3.5 mm planetary eyepiece with a tiny field stop. The ethos let's through more light with it's bigger field stop, but it does so by showing more stars not by making individual stars brighter.

The percentage of the light lost around the pupil when the exit pupil is too big, is balanced out by the increased brightness of reduced magnification.

The only way to better a bigger exit pupil on a certain telescope is to decrease magnification. And as a result, brightness increases.

So yes, some light is lost around the eye, but I image is brighter anyway so nothing is dimmed.

[Ags]

29 minutes ago, miguel87 said:

Also remember that a star doesnt exactly behave like a true point source of light.

Yes, at high magnifications the point source approximation breaks down. But it holds true for most of the magnification range.

[miguel87]

2 minutes ago, Ags said:

Yes, at high magnifications the point source approximation breaks down. But it holds true for most of the magnification range.

I wonder at what magnification a star starts to dim? I always ask to many questions and then never understand the answers 😂

[Don Pensack]

On 11/05/2020 at 11:35, John said:

I guess this may or may not be related to all this but I find that using high magnification (very high sometimes) and obviously very small exit pupils helps me pick dim point sources out, eg: super novae, quasars, faint planetary moons etc. These don't seem to be as apparent at lower magnifications.

Or is that something different at work ?

 

That is making the detail large enough for the eye to see.  It's a fine line: dimmer with magnification, but larger and easier to see.  There is a "eutectic" point somewhere in there that yields the best visibility.  That usually requires experimentation.

[Don Pensack]

On 11/05/2020 at 12:19, miguel87 said:

Even tho the star is a point source, it still reflects of every part of the primary mirror/lens, and because the exit pupil is an image of the primary, the larger the exit pupil, the brighter the star will be.

Even if the exit pupil is 10mm, you will still get 5mm+ into your pupil. Brighter than 1mm.

It might appear relatively brighter because the background sky will be much dimmer at 1mm. But if you measured the brightness of the star point it will be dimmer in a 1mm exit pupil than a 2, 3, 4 etc

Nope.  The star image's brightness represents the entire primary.  When you use a higher power, you stop down the field size of the eyepiece, but every point on the telescope's focal plane is STILL illuminated by the entire primary.  You aren't reducing the brightness of the star point.  That's why the faintest stars are always visible at high power, not low.  Yes, there is an increase in contrast, but that increase in contrast would not occur if the star images dimmed with magnification.

[miguel87]

44 minutes ago, Don Pensack said:

 

 

Edited May 15, 2020 by miguel87

[vlaiv]

10 minutes ago, miguel87 said:

The star does not function as a true point source.

It actually is - "true point source" with respect to resolving power of any telescope that we have. In fact maybe for telescope the seize of solar system it would not be point source.

This does not mean that star will be point like in a telescope - telescope optics can't resolve something past airy disk sizes - and airy disk size depends on aperture size.

It also depends on seeing - in poor seeing threshold star will fade out of view quicker - because combined airy disk of telescope and seeing aberrations spread light too much.

 

 

[miguel87]

1 minute ago, vlaiv said:

 

This does not mean that star will be point like in a telescope - telescope optics can't resolve something past airy disk sizes - and airy disk size depends on aperture size.

 

 

Agreed. So anything that has its light source spread over an area will dim as that spread increases?

[vlaiv]

1 minute ago, miguel87 said:

Agreed. So anything that has its light source spread over an area will dim as that spread increases?

I have to be very careful here as there are different answers depending on context.

If you increase magnification for anything that has surface - surface brightness with respect to apparent angular size will decrease. On the other hand - surface brightness with respect to actual angular size will not change.

What does this mean?

Take sky for example - we have sky that has certain brightness - like mag21 - which means magnitude 21 per arc second squared brightness. Increase magnification - it will look darker. Measure it, regardless of magnification or pixel scale - you will always get mag21 per arc second squared.

So in absolute terms - brightness does not change. In relative terms it does change - if you spread light over more receptors (eye cone cells or camera pixels) - same amount of brightness gets registered by more receptors - each receptors gets less photons - in that sense - each receptor registers lower signal - but total number of photons remains the same.

Makes sense?

[miguel87]

9 minutes ago, vlaiv said:

I have to be very careful here as there are different answers depending on context.

If you increase magnification for anything that has surface - surface brightness with respect to apparent angular size will decrease. On the other hand - surface brightness with respect to actual angular size will not change.

What does this mean?

Take sky for example - we have sky that has certain brightness - like mag21 - which means magnitude 21 per arc second squared brightness. Increase magnification - it will look darker. Measure it, regardless of magnification or pixel scale - you will always get mag21 per arc second squared.

So in absolute terms - brightness does not change. In relative terms it does change - if you spread light over more receptors (eye cone cells or camera pixels) - same amount of brightness gets registered by more receptors - each receptors gets less photons - in that sense - each receptor registers lower signal - but total number of photons remains the same.

Makes sense?

Yeah I get that, obviously  I'm not gonna actually change the brightness of the object.

But we all agree that planets are dimmer under higher magnification, because that same amount of light is spread out.

If you increase mag enough on a star then you will resolve the airy disc. It will not remain a point of light because you are not examining the star itself. You are imaging the image created at the focal plane. 

The image on the focal plane is a disc, it has dimensions and therefore the image of it in an eyepiece will dim as it is spread out under higher mag.

If the image of the star at the focal plane was an actual physical point then fine. This would need literally perfect optics. But it isnt, not even close really.

Edited May 15, 2020 by miguel87

[vlaiv]

4 minutes ago, miguel87 said:

Yeah I get that, obviously  I'm not gonna actually change the brightness of the object.

But we all agree that planets are dimmer under higher magnification, because that same amount of light is spread out.

If you increase mag enough on a star then you will resolve the airy disc. It will not remain a point of light because you are not examining the star itself. You are imaging the image created at the focal plane. 

The image on the focal plane is a disc, it has dimensions and therefore the image of it in an eyepiece will dim as it is spread out under higher mag.

If the image of the star at the focal plane was an actual physical point then fine. But it isnt, not even close really.

I just jumped in this discussion again and I'm not quite sure what is being discussed, but star is point like for quite a large span of magnifications.

If you want to get somewhat more technical - most people resolve at about 1 minute of arc. Airy disk size for 8" scope is 1.28" - we can say that most of light is concentrated under half of that so about let's say 0.7". We need about x85 magnifi8cation to get into region of 1 arc minute. To start resolving airy disk - you need couple times that. This is why people say - do star testing with x200 or x300 mag.

Even at these magnifications - airy disk is still not large enough for eye to see significant dimming. Eye does not work linearly - having half of the light will not make something as half as bright to our eye - this is one of the reasons we have magnitude system that is logarithmic in nature. It is also reason why most people don't notice vignetting up to 50% visually.

Yes, you will see star dim when you crank up magnification - but you need to use crazy powers to see it clearly.

[miguel87]

4 minutes ago, vlaiv said:

I just jumped in this discussion again and I'm not quite sure what is being discussed, but star is point like for quite a large span of magnifications.

If you want to get somewhat more technical - most people resolve at about 1 minute of arc. Airy disk size for 8" scope is 1.28" - we can say that most of light is concentrated under half of that so about let's say 0.7". We need about x85 magnifi8cation to get into region of 1 arc minute. To start resolving airy disk - you need couple times that. This is why people say - 

Yes, you will see star dim when you crank up magnification - but you need to use crazy powers to see it clearly.

This is all I was saying, that it will dim with magnification.

I know it's not huge because they are such ti y objects.

Having said that, the brightness of Vega last night in my 32mm and 6mm was very noticeably different.

 

[Don Pensack]

21 minutes ago, miguel87 said:

This is all I was saying, that it will dim with magnification.

I know it's not huge because they are such ti y objects.

Having said that, the brightness of Vega last night in my 32mm and 6mm was very noticeably different.

 

That could have been the eyepieces in question.  Assuming your scope is f/5, I would guess a 1mm exit pupil (5mm eyepiece) would be about the minimum for the Airy Disc to present a noticeable size.

At 6mm, you should not have detected any decrease in brightness of Vega.  The overall field brightness would be dimmer, but Vega?  I would suspect your 6mm eyepiece may have a significantly lower transmission than the 32mm.

[miguel87]

11 minutes ago, Don Pensack said:

That could have been the eyepieces in question.  Assuming your scope is f/5, I would guess a 1mm exit pupil (5mm eyepiece) would be about the minimum for the Airy Disc to present a noticeable size.

At 6mm, you should not have detected any decrease in brightness of Vega.  The overall field brightness would be dimmer, but Vega?  I would suspect your 6mm eyepiece may have a significantly lower transmission.

Nope. The 6mm has less glass and is much more expensive so I doubt it.

Also you dont just suddenly get to a certain magnification and boom, from a tiny dot to an airy disc. Its grows and shrinks with magnification (obviously you need high mag to see this).

Either way. It is not a true point source at the focal plane. Because the mirros/lenses just arent that accurate.

And the airy disc depends on the size of the aperture. So as you zoom in or out, the disc gets larger or smaller, hence dimmer or brighter.

 

Edited May 15, 2020 by miguel87

[miguel87]

Vlaiv was able to give the size of the airy disc for a given aperture. This is in arc seconds (0.7 for 8inch scope if I remember), so objectively not a point source.

You could do the maths of the TFOV of any eyepiece divided by the airy disc diameter to figure out it's apparent angular size in the eyepiece.

You could in theory then roughly estimate its surface brightness which would decrease with greater apparent angular size.

Edited May 15, 2020 by miguel87

[Don Pensack]

4 hours ago, miguel87 said:

Nope. The 6mm has less glass and is much more expensive so I doubt it.

Also you don't just suddenly get to a certain magnification and boom, from a tiny dot to an airy disc. Its grows and shrinks with magnification (obviously you need high mag to see this).

Either way. It is not a true point source at the focal plane. Because the mirrors/lenses just aren't that accurate.

And the airy disc depends on the size of the aperture. So as you zoom in or out, the disc gets larger or smaller, hence dimmer or brighter.

 

OK.  We know the size of the Airy disc in a scope isn't relevant because then we'd all use only short f/ratio scopes, where the Airy disc is smaller.

But, the scale of the focal plane is smaller also.  At the same magnification, the Airy disc is aperture-dependent, not f/ratio dependent.

In general, the Airy Disc becomes resolved as an extended object in scopes at around 25x/inch (200x in an 8" scope), or 1x/mm or an eyepiece focal length that equals the f/ratio.

This is assuming 20/20 vision normally, but very high contrasts might allow us to see the spurious disc at lower magnifications.

Viewing Vega might be an example of high contrast, so I'll grant the Airy disc might be visible in the 6mm eyepiece.

At whatever magnification the Airy Disc becomes an extended object, you have to exceed that before the surface brightness dims with increasing magnification.

With stars, though, this occurs are really high magnifications.  Slightly exceeding the magnification where the Airy Disc becomes visible (or the spurious disc in the center of the Airy Disc more accurately) will not noticeably dim the star.

You would have to greatly exceed the 1x/mm magnification to appreciably dim a bright star like Vega.

To make it noticeably dimmer would require MUCH higher magnifications than a 6mm eyepiece would yield, as Vlaiv said in his post.

So I don't buy that the reason you saw it dimmer had anything to do with the size of the Airy disc.  There is likely something else at work, here.

 

Edited May 15, 2020 by Don Pensack

[miguel87]

9 hours ago, Don Pensack said:

 

At whatever magnification the Airy Disc becomes an extended object, you have to exceed that before the surface brightness dims with increasing magnification.

 

It is always an extended object, just a small one.

As soon as the primary has focussed the star at the focal plane it has become a non point source. Due to the airy disc, diffraction of light and any aberrations present. The image of the star on the focal plane is not a point source. Not at any magnification.

The book I have linked states that a point source is not physically realizable.   https://books.google.co.uk/books?id=8P4gBQAAQBAJ&pg=PA74&lpg=PA74&dq=a+star+is+not+a+true+point+source&source=bl&ots=CZj7YUxKkF&sig=ACfU3U1CbyTW-qgS33AQTjSEyACGEcYUQw&hl=en&sa=X&ved=2ahUKEwil2LP-67fpAhX2TxUIHSvTC9AQ6AEwAHoECAEQAQ#v=onepage&q=a star is not a true point source&f=false

Yes, it is a small object so even doubling its radius by doubling magnification will move it from about 0.7 arc seconds to 1.4. So still tiny. But the dimming process as with any other objects is still taking place.

The light source remains the same so it has to dim, there is no way around that unless you argue that...

1.) it is indeed a true point source at the focal plane.

Or

2.) It does not increase in size with magnification. (Which is impossible unless the focal plane image contains a point source)

Edited May 16, 2020 by miguel87

[miguel87]

9 hours ago, Don Pensack said:

OK.  We know the size of the Airy disc in a scope isn't relevant because then we'd all use only short f/ratio scopes, where the Airy disc is smaller.

 

You are proving my point here; yes the airy disc is smaller in a faster scope precisely because the image created at the focal plane is on a smaller scale (less mag).

So we have evidence here that the size of the best focussed star image in a telescope gets bigger with magnification.

Why else would the airy disc be bigger on longer f/ratios?

If it behaved like a point source f/ratio would not affect it's image.

Edited May 16, 2020 by miguel87

[Don Pensack]

But to the eye, it is a point source up to about a size of 1'.

Another way to say that is that the star image may expand, but if it still occupies only 1 pixel, the camera isn't going to see it dim.

The eye has to begin to resolve the Airy disc with a visible size before magnification treats it as an extended object.

Were that not true, we would see the faintest stars at low power, which is not the case.  We see the faintest stars at high powers.

And contrast with the sky will continue to improve even above that magnification because the star's image will be ever brighter to the eye in comparison to the sky.

So, obviously, the dimming of the sky does not match the dimming of the star.  Ergo, stars do not behave as extended objects in a telescope.

 

Edited May 18, 2020 by Don Pensack

[miguel87]

9 hours ago, Don Pensack said:

But to the eye, 

 

As soon as you have said that, we are unable to discuss anything objectively. The eye is subjective, non linear and individual. We cant have an objective discussion about how thing appear "to the eye" because there are too many factors.

Also you say that "the eye needs to resolve the airy disc with a visible size before magnification treats it as an extended object"

Well, of course we are talking about visible stars! We dont know or care if the ones that aren't visible are brightening or dimming. And if you are talking about there not being a visible 'airy disc' at low mag? Then what do you think we are seeing at low mag? The airy disc is the only image of the star that the telescope has, just smaller or bigger versions. Yes there might be a size at which the human eye cannot see it as a disc, but that doesnt mean it isn't. It also doesnt mean that is isnt getting brighter or dimmer.

Also the telescope does what the telescope does based on physics. It would treat a star the same even if there was no eye looking through the telescope. Magnification plays by certain rules. Yes our subjective experiences vary but that is a totally different conversation. The moon appears bigger closer to the horizon but it isn't. If you say the stars don't 'appear' to dim with magnification then I will take your word for it. The physical truth is that they do.

Edited May 18, 2020 by miguel87

[vlaiv]

5 minutes ago, miguel87 said:

As soon as you have said that, we are unable to discuss anything objectively. The eye is subjective, non linear and individual. We cant have an objective discussion about how thing appear "to the eye" because there are too many factors.

Also you say that "the eye needs to resolve the airy disc with a visible size before magnification treats it as an extended object"

Well, of course we are talking about visible stars! We dont know or care if the ones that aren't visible are brightening or dimming.

Also this is not true, the telescope does what the telescope does based on physics. It would treat a star the same even if there was no eye looking through the telescope. Magnification plays by certain rules. Yes our subjective experiences vary but that is a totally different conversation. The moon appears bigger closer to the horizon but it isn't. If you say the stars don't 'appear' to dim with magnification then I will take your word for it. The physical truth is that they do.

Eye is also a detector like a sensor - and it behaves very similar in some aspects - one is star being resolved.

Above given analogy with sensor is valid - as long as one pixel is covering the star - star will not dim as all photons from that star will be captured in the same "bucket" - total number of photons does not change.

Similarly - eye has light sensing cells - and as long as star light is hitting one (or in reality few - you can't perfectly align to one cell in most cases) - it will detect all the light and sensation of brightness won't change.

This is also thing of physics - light comes in photons and and you can't subdivide it infinitely because of that.