Exit pupil and AFOV

[Stu]

1 hour ago, miguel87 said:

Seems like you havent actually been reading the posts on this topic so it's kind of hard to continue the conversation.

I have addressed all the points you make above. Even calculating more precisely the size 'in human pixels' of a star and they are much bigger than one tenth of a pixel. And the increase in size will be visible from approx 85x to the human eye, even calculating for the uneven distribution of light.

Also the graph showing the spread of light of the airy disc has already been posted and discussed.

Also already been said but the airy disc isnt something that 'becomes visible' at a certain point. The airy disc IS the telescopes image of the star produced at the focal plane, there is no other image of a star that it is able to produce. If you can see a star, that is the airy disc, just really small or bigger.

So as I said above, the point at which the human eye can detect this given various different factors is not what i am discussing.

You also say that it is not relevant to the use of telescopes. Great, I never said it was. I'm just stating that the image of the star dims with magnification as part of my understanding of how a telescope works and produces an image. I was confused at how a star was a poont source but then suddenly not a point source as any increase in size under magnification must be physically linear. I starting looking into how a telescope 'makes' an image of a star

If you saying 'it's not relevant', is saying yes it's right then that's fine. And it seems strange to tell me it's not relevant. To who is it not relevant? It is obviously relevant to me else I wouldn't be discussing it. You don't have to reply to my messages, especially if you haven't read all the previous ones.

Miguel, with the greatest respect it seems to be you that is not necessarily accepting input from very experienced members, referring to respected references who are trying to help you understand what is going on. I don’t believe continued rebuttal of accepted facts furthers the conversation.

[miguel87]

1 hour ago, Stu said:

Miguel, with the greatest respect it seems to be you that is not necessarily accepting input from very experienced members, referring to respected references who are trying to help you understand what is going on. Continued rebuttal of accepted facts doesn’t really further the conversation I don’t think.

If you can give me an example I will happily apologise. I am actually very grateful for the input.

What is actually happening is that more experienced members are being listened to and I am not. But I didnt expect anything different. People just want to tell me I'm wrong but we are discussing different topics. When I try to explain people say I am being rude.

With the exception of Vlaiv who understood what I was saying.

I am interested in how a telescope works and produces images. I was interested in the issue of stars and point sources and how the airy disc worked and how an object could be both point source and extended. 

I am not concerned with human perception.

Just the process of what the telescope does. There's nothing wrong with that.

And with all due respect, number of posts on a website has no bearing on knowledge. There is many people in the world with much better knowledge than all of is and they have zero posts on this website.

[Mr Spock]

Perhaps it's time to let the subject rest for a while. Going round in circles never achieves anything.

[Stu]

28 minutes ago, miguel87 said:

If you can give me an example I will happily apologise. I am actually very grateful for the input.

What is actually happening is that more experienced members are being listened to and I am not. But I didnt expect anything different. People just want to tell me I'm wrong but we are discussing different topics. When I try to explain people say I am being rude.

With the exception of Vlaiv who understood what I was saying.

I am interested in how a telescope works and produces images. I was interested in the issue of stars and point sources and how the airy disc worked and how an object could be both point source and extended. 

I am not concerned with human perception.

Just the process of what the telescope does. There's nothing wrong with that.

And with all due respect, number of posts on a website has no bearing on knowledge. There is many people in the world with much better knowledge than all of is and they have zero posts on this website.

I have not exhaustively read through the thread, but what I generally see is that you are challenging ideas that are accepted as fact by the vast majority, through both theory and experience. It seems a little arrogant to think that you alone have a different theory, are the only one to have considered these issues and are the one that is correct. Don has explained where your theory or calculations are incorrect a couple of times but you do not seem to want to listen.

Personally I try not to obsess over theory. I am interested in where it helps me understand what is happening with my scope, and to be able to observe in the best way but that is about my limit.

I see that fainter stars become more visible with higher magnification as the point source stays bright but the sky background dims. That happens, I see it does so that is enough for me. I’m unclear what your problem with accepting this is, but we seem to be going round in circles.

[miguel87]

52 minutes ago, Stu said:

I have not exhaustively read through the thread, but what I generally see is that you are challenging ideas that are accepted as fact by the vast majority, through both theory and experience. It seems a little arrogant to think that you alone have a different theory, are the only one to have considered these issues and are the one that is correct. Don has explained where your theory or calculations are incorrect a couple of times but you do not seem to want to listen.

Personally I try not to obsess over theory. I am interested in where it helps me understand what is happening with my scope, and to be able to observe in the best way but that is about my limit.

I see that fainter stars become more visible with higher magnification as the point source stays bright but the sky background dims. That happens, I see it does so that is enough for me. I’m unclear what your problem with accepting this is, but we seem to be going round in circles.

I do accept this is what is seen with the eye. I'm really trying to explain that this is not what I am talking about but I think that is the problem. People keep repeatedly going back to how things appear to the human eye. Which is very informative but it's not the question I was asking.

I was just trying to resolve two pieces of information I had been told which conflict each other that is all.

1)a star is a point source as does not dim under magnification.

2) you can resolve a stars airy disc under high magnification.

I'm very sorry if I offended anyone I just wanted to know how the telescope manages to produce both a point source and extended object at the same time.

But people just keep talking about limiting magnitude and the human eye and telling me I am not understanding.

Vlaiv did understand and said that yes, stars are not a true point source in the telescope but appear that way until at least 85x and then it might be possible to see them dim visually.

I just took this a step further logically and thought that despite the limitations of the human eye, the image of the star must actually grow and shrink with magnification like any other object, but the size of it is so tiny that it is difficult to see.

When I make this point I am told it is irrelevant to the use of a telescope. (Not helpful).

So yes I am challenging the common held belief that stars do not dim under magnification. I have good evidence and theory to do do and even some well respected members who agree with me 

So if challenging long accepted beliefs is arrogant then fine, I am arrogant. But it also seems that I am right. Now I'm not saying that anyone else in this discussion is wrong, they are just answering a different question about what the human eye can see. And I can't seem to manage to get people to realise that is not what I am talking about.

Apologies again.

Edited May 20, 2020 by miguel87

[vlaiv]

1 minute ago, miguel87 said:

I do accept this is what is seen with the eye. I'm really trying to explain that this is not what I am talking about but I think that is the problem. People keep repeatedly going back to how things appear to the human eye. Which is very informative but it's not the question I was asking.

I was just trying to resolve two pieces of information I had been told which conflict each other that is all.

1)a star is a point source as does not dim under magnification.

2) you can resolve a stars airy disc under high magnification.

I'm very sorry if I offended anyone I just wanted to know how the telescope manages to produce both a point source and extended object at the same time.

But people just keep talking about limiting magnitude and the human eye and telling me I am not understanding.

Vlaiv did understand and said that yes, stars are not a true point source in the telescope but appear that way until at least 85x and then it might be possible to see them dim visually.

I just took this a step further logically and thought that despite the limitations of the human eye, the image of the star must actually grow and shrink with magnification like any other object, but the size of it is so tiny that it is difficult to see.

When I make this point I am told it is irrelevant to the use of a telescope. (Not helpful).

So yes I am challenging the common held belief that stars do not dim under magnification. I have good evidence and theory to do do and even some well respected members who agree with me 

So if challenging long accepted beliefs is arrogant then fine, I am arrogant. But it also seems that I am right. Now I'm not saying that anyone else in this discussion is wrong, they are just answering a different question about what the human eye can see. And I cane seem to manage to get people to realise that it not what I am talking about.

Apologies again.

There are at least two or three different meanings of star being point source.

I've mentioned this before - star is a true point source for most intents and purposes. Let's take a solar size star that is very close to earth - let's say 10 Ly.

That is 1.4e+6 km at distance of 9.461e+14.

Angular size of this object would be 2*arctan(  (diameter / 2) / distance ). We can use small angle approximation tan X = X and we can see that angle is hence diameter / distance. This is angle in radians.

Angle is 1.47976e-9 or if we convert that into arc seconds - ~ 3.0e-4" - 0.0003" of angular size.

This is star that is very close. We can see stars that are hundreds and thousands times more distant. In fact - there has been a hand full of stars that we have resolved: https://en.wikipedia.org/wiki/List_of_stars_with_resolved_images

All other remain point sources.

Then there is notion of point like source for visual observation - this is what most other participants of this thread assume.

And finally there is telescopic image of point source - this is Airy pattern / disk - that depends on telescope aperture (size) and also depends on how good optics of telescope is - (shape). Two different sized scopes will show different star image (size and shape - but shape changes are very small and often difficult to notice even on very high magnifications).

Finally - there is atmosphere that arguably has the greatest impact on star shapes in telescope.

To recap:

- Star is point source due to vast distances involved

- Star is "extended" source in telescope due to airy pattern and atmospheric influence

- that behaves for the most part to most observers as point source again because of the way eye and camera sensors work

 

[miguel87]

Thanks Vlaiv, that explains in more detail what I was trying to understand.

The thing that struck me was that when looking in the telescope you are not viewing the actual star. But the image created by the telescope, I just couldn't get my head around how this could be a point source with no measurable physical dimensions when it existed only inches in front of my face!

I totally understand that the disc the scope produces is tiny and any changes in size and brightness may not be perceptible to us at all. I was just interested in what the telescope was actually doing with the light.

Sorry for bringing you into this again @vlaiv 😂 you were just the only person who seemed to understand what I was getting at.

I now have an understanding and perhaps most people think it is wrong. Perhaps it IS wrong. But I don't want to cause trouble so I will stop where I am.

✌

Edited May 20, 2020 by miguel87

[Stu]

45 minutes ago, miguel87 said:

I do accept this is what is seen with the eye. I'm really trying to explain that this is not what I am talking about but I think that is the problem. People keep repeatedly going back to how things appear to the human eye. Which is very informative but it's not the question I was asking.

I was just trying to resolve two pieces of information I had been told which conflict each other that is all.

1)a star is a point source as does not dim under magnification.

2) you can resolve a stars airy disc under high magnification.

I'm very sorry if I offended anyone I just wanted to know how the telescope manages to produce both a point source and extended object at the same time.

But people just keep talking about limiting magnitude and the human eye and telling me I am not understanding.

Vlaiv did understand and said that yes, stars are not a true point source in the telescope but appear that way until at least 85x and then it might be possible to see them dim visually.

I just took this a step further logically and thought that despite the limitations of the human eye, the image of the star must actually grow and shrink with magnification like any other object, but the size of it is so tiny that it is difficult to see.

When I make this point I am told it is irrelevant to the use of a telescope. (Not helpful).

So yes I am challenging the common held belief that stars do not dim under magnification. I have good evidence and theory to do do and even some well respected members who agree with me 

So if challenging long accepted beliefs is arrogant then fine, I am arrogant. But it also seems that I am right. Now I'm not saying that anyone else in this discussion is wrong, they are just answering a different question about what the human eye can see. And I can't seem to manage to get people to realise that is not what I am talking about.

Apologies again.

To attempt to summarise...

You accept that stars behave as point sources and don’t dim up until the point that the airy disk is resolved - correct?

You accept that up until this point, fainter stars will become visible because the extended object that is the sky background dims, but the star doesn’t - correct?

Once the airy disk is resolved, you are saying that increasing magnification increases its size so that it must start to dim at the same rate that the sky background is dimming - is that what you are saying? So from this point on no more stars would become visible? Is that what you are saying?

Nothing I’ve read refers to this effect,  and the fact that fainter stars have smaller apparent spurious airy disks means that they will likely resolve at higher powers, so increasing power will continue to show more stars beyond the point where the brighter stars resolve.

Is this what you are talking about?

What is it that people are not understanding?

I do not know whether spurious disks decrease in surface brightness as they are magnified more; intuitively I think yes but don’t know.

[vlaiv]

9 minutes ago, Stu said:

Once the airy disk is resolved, you are saying that increasing magnification increases its size so that it must start to dim at the same rate that the sky background is dimming - is that what you are saying? So from this point on no more stars would become visible? Is that what you are saying?

Nothing I’ve read refers to this effect,  and the fact that fainter stars have smaller apparent spurious airy disks means that they will likely resolve at higher powers, so increasing power will continue to show more stars beyond the point where the brighter stars resolve.

I have couple notes on this one - just random points that ought to be taken into account when taking about such phenomena:

- all stars form equal airy disk (this is not strictly true as stars have different spectra and there is dependence of airy disk size on wavelength - but we can say that they are equal for purpose of discussion) as it is property of the telescope not of the star.

- at threshold levels of vision, human vision does not quite behave like smooth function - we can say that it is non linear (in fact, it is always non linear in our sensation but this is not what it is meant here - it is non linear in physical response) - hence spreading equally objects of certain brightness will result in change in contrast between them - this is why (together with other factors - like how well we perceive contrast depending on object size) we have magnification that shows particular galaxy the best under given conditions - it darkens background the most and galaxy the least - hence creating best contrast.

- we have to observe profile of Airy pattern - it is not flat / uniform - it is rather pointy - and while we can at certain magnification resolve whole disk - with faint stars, parts of airy profile that are bright enough to trigger response might not be resolved and are still point like - this graph can probably explain it better:

If we don't see the rest of the airy disk - above top of the peak will not be resolved - even if full disk is.

[Stu]

16 minutes ago, vlaiv said:

I have couple notes on this one - just random points that ought to be taken into account when taking about such phenomena:

- all stars form equal airy disk (this is not strictly true as stars have different spectra and there is dependence of airy disk size on wavelength - but we can say that they are equal for purpose of discussion) as it is property of the telescope not of the star.

- at threshold levels of vision, human vision does not quite behave like smooth function - we can say that it is non linear (in fact, it is always non linear in our sensation but this is not what it is meant here - it is non linear in physical response) - hence spreading equally objects of certain brightness will result in change in contrast between them - this is why (together with other factors - like how well we perceive contrast depending on object size) we have magnification that shows particular galaxy the best under given conditions - it darkens background the most and galaxy the least - hence creating best contrast.

- we have to observe profile of Airy pattern - it is not flat / uniform - it is rather pointy - and while we can at certain magnification resolve whole disk - with faint stars, parts of airy profile that are bright enough to trigger response might not be resolved and are still point like - this graph can probably explain it better:

If we don't see the rest of the airy disk - above top of the peak will not be resolved - even if full disk is.

Thanks Vlaiv. Yes, that’s why I referred to the spurious disk rather than the airy disk as I believe this is the visible portion of the airy disk, and will vary according to brightness as you’ve shown.

[andrew s]

Not only is the eye on linear it is non uniform. In addition the angle of incidence effect the response of the rods (and cones). Averted vision, blind spot and all that. For more details see the pdf I linked to above.

Regards Andrew 

[miguel87]

55 minutes ago, Stu said:

 

 

Edited May 20, 2020 by miguel87

[Ags]

How can you talk about how "bright" something is without talking about how you are measuring it? If you are not measuring it (either with an eye or a camera) it doesn't make a difference...

[vlaiv]

2 minutes ago, miguel87 said:

The physical properties of the airy disc under different magnifications.

You don't really need different magnification as it does not change properties of airy disk unless in relation to something else.

Magnification on its own is scale factor - unit conversion - call it what you will - and has absolutely no impact on airy disk unless it is in relation to something else. We use term magnification to signify that is in relation to human vision. We also use term sampling rate to signify that it is in relation to camera sensor.

In fact - magnification and sampling rate are two slightly different concepts - first is about angular sizes - magnification specifies ratio of angular sizes of things, while sampling rate is related to projection - ratio of angular size to length or pixel size (which represents unit length) - in linear space.

[miguel87]

7 minutes ago, Ags said:

How can you talk about how "bright" something is without talking about how you are measuring it? If you are not measuring it (either with an eye or a camera) it doesn't make a difference...

An object has a objective luminance, a level of electromagnetic radiation in the visible spectrum, even if nothing observes it.

These values can be calculated even if they are not measured.

Same as a tree makes a sound when it falls even if nobody hears it.

Edited May 20, 2020 by miguel87

[miguel87]

Or if it makes more sense I could say how it would appear using a hypothetical perfect camera with pixels less than half the size of photons.

Edited May 20, 2020 by miguel87

[andrew s]

Just to complicate matter even more. How relevant is the Airy disk at limiting magnitude.

Clark in "Visual astronomy of the deep sky" says you need 50 to 150 photons of green light over several seconds to detect a star unaided. If it is a similar limit for the aided eye then just how well defined will the Airy disk be? Most will be concentrated in the central peak but it is not as clear cut as @vlaiv diagram with just the peak showing.

Regards Andrew 

[vlaiv]

1 minute ago, miguel87 said:

Or if it makes more sense I could say how it would appear using a hypothetical perfect camera with pixels less than half the size of photons.

No need to use that - use a bit of wave mechanics to describe what is going on - it is fairly "easy" to understand it.

It is very similar in nature to double slit experiment - different paths come together at certain places and phase of the light makes it either reinforce itself or destructive interference happens.

A bit of math will tell you that you need to integrate over aperture and very soon you'll see that what you derived is actually Fourier transform of aperture. Now you have a tool to examine Airy patterns of different types of aperture (obstructed, with spider support, hexagonal, square, ....).

If you go further - you'll also notice that another Fourier transform of particular Airy pattern gives you MTF - this is how airy pattern affects image produced by aperture. This will explain why there is maximum resolving power of a telescope and why unobstructed aperture gives better contrast for visual.

There is field of optics called Fourier optics that deals with all of this.

https://en.wikipedia.org/wiki/Fourier_optics

[andrew s]

8 minutes ago, miguel87 said:

Or if it makes more sense I could say how it would appear using a hypothetical perfect camera with pixels less than half the size of photons.

Might be better to discuss a perfect continuous detector. The size of a photon is a whole new can of worms, even if it has a well defined meaning at all.

Regards Andrew 

[andrew s]

5 minutes ago, vlaiv said:

No need to use that - use a bit of wave mechanics to describe what is going on - it is fairly "easy" to understand it.

It is very similar in nature to double slit experiment - different paths come together at certain places and phase of the light makes it either reinforce itself or destructive interference happens.

A bit of math will tell you that you need to integrate over aperture and very soon you'll see that what you derived is actually Fourier transform of aperture. Now you have a tool to examine Airy patterns of different types of aperture (obstructed, with spider support, hexagonal, square, ....).

If you go further - you'll also notice that another Fourier transform of particular Airy pattern gives you MTF - this is how airy pattern affects image produced by aperture. This will explain why there is maximum resolving power of a telescope and why unobstructed aperture gives better contrast for visual.

There is field of optics called Fourier optics that deals with all of this.

https://en.wikipedia.org/wiki/Fourier_optics

I fully agree provided you have enough illumination. The interference pattern builds up one detection at a time. You need enough detections for the pattern to appear.  

At the limit of detection is this true?

Regards Andrew 

[vlaiv]

Just now, andrew s said:

I fully agree provided you have enough illumination. The interference pattern builds up one detection at a time. You need enough detections for the pattern to appear.  

At the limit of detection is this true?

Regards Andrew 

I think that it is - we only need to substitute notion of intensity of light with notion of probability of photon detection in specific area (and then integrate over that area).

[andrew s]

1 minute ago, vlaiv said:

I think that it is - we only need to substitute notion of intensity of light with notion of probability of photon detection in specific area (and then integrate over that area).

Yes, but the eye/brain only integrates over a few second. Is 50 to 150 hits enough to define the 2D Airy disk that well. I think not. We will just "see" an unresolved  somewhat localised source on the edge of visibility.

Clearly, this needs some controlled experiments rather than more theoretical speculation!

Regards Andrew 

[vlaiv]

3 minutes ago, andrew s said:

Yes, but the eye/brain only integrates over a few second. Is 50 to 150 hits enough to define the 2D Airy disk that well. I think not. We will just "see" an unresolved  somewhat localised source on the edge of visibility.

Clearly, this needs some controlled experiments rather than more theoretical speculation!

Regards Andrew 

I'm not even certain about 50 to 150 part - threshold of detection is about 7 photons (5-9 in some sources).

Since we are talking about eye/brain system - we need to take into account image build up and filters that our brain use (like noise suppression filter - we never seem to see photon noise at those levels and it should be obvious).

[Ags]

But if we are talking about an airy disk / diffraction pattern, we should stick to treating the photons as waves right?

 

Edited May 20, 2020 by Ags

[andrew s]

3 minutes ago, vlaiv said:

I'm not even certain about 50 to 150 part - threshold of detection is about 7 photons (5-9 in some sources).

Since we are talking about eye/brain system - we need to take into account image build up and filters that our brain use (like noise suppression filter - we never seem to see photon noise at those levels and it should be obvious).

I agree, it is much  ore complex than just truncation the top of an Airy disk.

Regards Andrew