Exit pupil and AFOV

[miguel87]

You previously said that the airy disc of a star in an 8 inch scope is around 1.4 arc seconds.

Let's use an example of my 20mm eyepiece in my 200p, a magnification of 50x, a AFOV of 50° and a TFOV of 1°.

The 1.4 arc second airy disc would fit 42.9 times across an arc minute and 2571.4 times across the diameter of the 1° TFOV.

Human monocular vision is around 120° horizontally with a resolution according to Rayleigh's criterion of 50 arc seconds (based on a 4mm pupil which is what this eyepiece provides).

This suggests the eye has 3600 'pixels' across the diameter of the eyepieces apparent 50°

These pixels are smaller than the 2571 stars we could stretch across.

So even at only 50x mag we have the ability to see the increasing size of the airy disc. And to me this seems apparent as the pin sharp small stars in my 32mm eyepiece slowly become slightly rounder as I move up through 20mm, 10mm, 6mm eyepieces until there is a very obvious round airy disc in the 3mm at 333x.

Edited May 18, 2020 by miguel87

[Ags]

On 11/05/2020 at 22:00, miguel87 said:

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.

There is no other light to cause "increased brightness". The image you see in the eye is described fully by the light in the exit pupil. So if the exit pupil is larger than they eye pupil due to low magnification, the star is dimmer.

It is astronomy 101 that you use high magnification to resolve faint stars in star clusters. This is a technique used by most observers. Who is wrong - your theory or all those observers?

[miguel87]

2 minutes ago, Ags said:

There is no other light to cause "increased brightness". The image you see in the eye is described fully by the light in the exit pupil. 

If you are correct, then why would a smaller exit pupil (I.e. higher mag) dim the image of a planet? If a 2mm and a 4mm exit pupil both fit entirely in your pupil and you are getting all of the light, then why is jupiter dimmer in a 2mm exit pupil than in a 4mm?

It is do do with light being stretched over larger areas. In a really big exit pupil, the light is being condensed to a smaller area, so any object appears smaller and brighter.

[miguel87]

14 minutes ago, Ags said:

 

It is astronomy 101 that you use high magnification to resolve faint stars in star clusters. This is a technique used by most observers. Who is wrong - your theory or all those observers?

All those observers.

Limiting magnitude is dictated by the aperture of the telescope, not the magnification being used.

The reality involves the effect of contrast and overall image brightness. So yes some dim stars are easier to see with the human eye under high mag. But they are not any brighter.

 

Edited May 18, 2020 by miguel87

[Ags]

Of course I understand that as do most other observers. But (unless you are at a very dark sky site) you will only see stars at the limiting magnitude at high magnification, and definitely not at such low magnification that exit pupil exceeds eye pupil.

M13 is easily visible at the moment. Why not look at it with an eyepiece giving a 7mm exit pupil and one giving a 1 mm exit pupil and see which resolves more stars in the cluster? I am assuming you are in an urban/suburban location.

Edited May 18, 2020 by Ags

[miguel87]

The more extended an object is, the more it appears to dim.with magnification because it's relative area increase is greater (doubling mag on orion could cause it to go from an apparent 30 degrees to 60 degrees whereas a star might go from an apparent1 arc second to 2 arc seconds). The spread of light is hugely different.

Just because stars appear to dim less does not mean that they do not dim.

Edited May 18, 2020 by miguel87

[vlaiv]

23 minutes ago, miguel87 said:

You previously said that the airy disc of a star in an 8 inch scope is around 1.4 arc seconds.

Let's use an example of my 20mm eyepiece in my 200p, a magnification of 50x, a AFOV of 50° and a TFOV of 1°.

The 1.4 arc second airy disc would fit 42.9 times across an arc minute and 2571.4 times across the diameter of the 1° TFOV.

Human monocular vision is around 120° horizontally with a resolution according to Rayleigh's criterion of 50 arc seconds (based on a 4mm pupil which is what this eyepiece provides).

This suggests the eye has 3600 'pixels' across the diameter of the eyepieces apparent 50°

These pixels are smaller than the 2571 stars we could stretch across.

So even at only 50x mag we have the ability to see the increasing size of the airy disc. And to me this seems apparent as the pin sharp small stars in my 32mm eyepiece slowly become slightly rounder as I move up through 20mm, 10mm, 6mm eyepieces until there is a very obvious round airy disc in the 3mm at 333x.

First - let's examine airy disk profile:

I've marked with red markers size of airy disk and also with yellow markers - points where most of the light of airy disk is concentrated - this contributes to actual amount of light.

If you want to be very specific about how much light you want to include - you can do gaussian approximation of airy disk function and then use exact radius depending on amount of light you want contained within.

Let's say for sake of argument -  that half of the diameter carries the bulk of light from airy disk pattern.

That is 0.7".

You don't need to do above calculation - it is enough to know that resolving power of human eye is 1 minute of arc. You need x85 magnification to have significant section of airy disk become 1 arc minute.

I've already written this above.

Focal length of human eye is about 20mm (source: http://labman.phys.utk.edu/phys222core/modules/m8/human_eye.html )

Rod cell is about 2-3um in diameter (source: https://en.wikipedia.org/wiki/Rod_cell and https://www.ncbi.nlm.nih.gov/pubmed/1427131 )

Which means that sampling rate of human eye is about half minute of arc and in turn that gives about 1 minute of arc resolution.

In order for main portion of airy disk to be significantly spread over rods - it needs to be about 1.5 arc minutes in diameter - that way we can roughly say it will be spread over 9 instead of 4 cells.

It will be dimmer by 9/4 in linear light = x2.25

That is when you switch from x85 power to x130 power in 8" scope. Let's see what magnitude difference that makes. -2.5 * log(2.25) = 0.88 magnitudes of difference.

If one had two scopes next to each other - one having eyepiece with x50 and one having eyepiece with x130 magnification - and switched between them - they should be able to see the dimming of the star by almost a magnitude due to spreading of light from star.

If you however use a single scope and switch the eyepiece - chances of spotting the difference are slim to none - since contrast of whole view sill be altered and we remember relative brightness differences much more than absolute brightness.

 

[miguel87]

20 minutes ago, Ags said:

 

M13 is easily visible at the moment. Why not look at it with an eyepiece giving a 7mm exit pupil and one giving a 1 mm exit pupil and see which resolves more stars in the cluster? I am assuming you are in an urban/suburban location.

I am in a rural location but o dont know why that matters. And you are now talking about an extended object which is different to an individual star.

[miguel87]

15 minutes ago, vlaiv said:

 

If one had two scopes next to each other - one having eyepiece with x50 and one having eyepiece with x130 magnification - and switched between them - they should be able to see the dimming of the star by almost a magnitude due to spreading of light from star.

If you however use a single scope and switch the eyepiece - chances of spotting the difference are slim to none - since contrast of whole view sill be altered and we remember relative brightness differences much more than absolute brightness.

 

I agree completely. As I said before the subjective process of viewing is very complex and involves a lot of factors.

But the fact remains that a star dims under magnification. The effect may be very difficult to see visually.

Even under modest magnification despite claims that it would have to be extreme.

Edited May 18, 2020 by miguel87

[Ags]

35 minutes ago, miguel87 said:

I am in a rural location but o dont know why that matters. And you are now talking about an extended object which is different to an individual star.

Rural location matters because that determines how bright your sky background is. The contrast technique people are talking about on this thread works by attenuating the sky background but as yours is already dark I don't know if you will see the effect.

M13 is a star cluster - I am talking about reolving the individual stars in M13, which is possible for scopes of 4 inches aperture and up, roughly. Technically, the greater magnification will attenuate the fuzzy glow of M13 itself, so I will stick my neck out and say that you should resolve more stars at high mag in M13 from your location.

Edited May 18, 2020 by Ags

[miguel87]

8 minutes ago, Ags said:

Rural location matters because that determines how bright your sky background is. The contrast technique people are talking about on this thread works by attenuating the sky background but as yours is already dark I don't know if you will see the effect.

M13 is a star cluster - I am talking about reolving the individual stars in M13, which is possible for scopes of 4 inches aperture and up, roughly. Technically, the greater magnification will attenuate the fuzzy glow of M13 itself, so I will stick my neck out and say that you should resolve more stars at high mag in M13 from your location.

I'm not sure it 'resolves' any better under high mag but details such as individual stars will be easier to see as they will be spaced further apart and the glow of the core will be dimmed.

Think about a planet, details within Jupiter's belts or the cassini division in Saturn's rings is easier under higher mag even though these both dim appreciably under higher mag. Seeing individual small details, such as a single star within a globular cluster are easier with some magnification.

I am not disputing any of that. This whole discussion is just me saying;

"Stars dim under magnification"

Many people dont think they do, at all, and believe they function as an actual point source in a telescope.

The truth is they appear to dim less than some other objects and the dimming can be hard to detect due to contrast. But they grow in size and dim just like any other object.

Edited May 18, 2020 by miguel87

[John]

1 hour ago, miguel87 said:

....Think about a planet, details within Jupiter's belts or the cassini division in Saturn's rings is easier under higher mag even though these both dim appreciably under higher mag. Seeing individual small details, such as a single star within a globular cluster are easier with some magnification...

.

Just a small point but, visually, details within Jupiters belts tend to get better defined when you back off the magnification rather than increase it. I think this is because they are low contrast features rather than the high contrast of, say, the Cassini Division.

Probably not really relevant to the overall topic though.

 

 

[miguel87]

12 minutes ago, John said:

Just a small point but, visually, details within Jupiters belts tend to get better defined when you back off the magnification rather than increase it. I think this is because they are low contrast features rather than the high contrast of, say, the Cassini Division.

Probably not really relevant to the overall topic though.

 

 

Maybe not too relevant but still interesting. I love to learn anything that I didnt know already!

I am missing a nice high-in-the-sky planet at the moment 🙁

[Stu]

13 minutes ago, John said:

Just a small point but, visually, details within Jupiters belts tend to get better defined when you back off the magnification rather than increase it. I think this is because they are low contrast features rather than the high contrast of, say, the Cassini Division.

Probably not really relevant to the overall topic though.

 

 

I think it is relevant John, and guess it relates to the contrast of extended objects Varying with magnification.

[faulksy]

and mars loves lots of power, as you know john. especially like it did around 5 years ago 😛

[Don Pensack]

Sorry, the logic is poor.

If stars behave like extended objects and dim with magnification, it is the case that they must have a surface brightness across the spurious disc of X amount.

The background sky surface brightness is, let's say, Y.  So the contrast is X/Y (we'll ignore the fact that X is really X+Y).  As we increase the magnification, the ratio between X and Y cannot change.

So contrast between the star and the sky cannot change with increased magnification.  If you have a faint star sitting by itself, you should be able to see it at low power

just as you can see it at high power.  But you can't.  No one can.  There is not enough contrast to do so.

So you have to argue that, somehow, the contrast between star and sky must change with increased magnification.  That is illogical, since if the star acts like an extended object, the contrast cannot change.

Yet, we have the experience of thousands of observers over hundreds of years that faint stars do become more visible with magnification.

This can ONLY be true, logically, if stars do not behave like extended objects in a telescope.

Here is Schaefer's paper on limiting magnitudes in a telescope.

http://adsbit.harvard.edu/cgi-bin/nph-iarticle_query?bibcode=1990PASP..102..212S&db_key=AST&page_ind=0&plate_select=NO&data_type=GIF&type=SCREEN_GIF

And a comment about the article by Nils Olof Carlin:

http://web.telia.com/~u41105032/visual/Schaefer.htm

and a limiting magnitude calculator based on Schaefer's work:

http://www.cruxis.com/scope/limitingmagnitude.htm

Note how the limit goes deeper with increasing magnification.

The point of the links is to note that there is ample work to show that contrast increases with magnification.  THIS CAN ONLY BE TRUE IF THE SKY ACTS LIKE AN EXTENDED OBJECT AND STARS DO NOT.

My earlier point that stars do not behave like extended objects until the eye resolves the spurious disc is a possible compromise position.

Edited May 19, 2020 by Don Pensack

[miguel87]

1 hour ago, Don Pensack said:

 

The point of the links is to note that there is ample work to show that contrast increases with magnification.  THIS CAN ONLY BE TRUE IF THE SKY ACTS LIKE AN EXTENDED OBJECT AND STARS DO NOT.

Not true.

All degrees given are apparent through an eyepiece not degrees of the celestial sphere.

Imagine an object (A) of 10degrees squared surface area has a total brightness of 10. (0.1 brightness per degree squared)

Another object (B) of 0.1degrees squared size and total brightness of 100. (10'000 brightness per degree sqaured).

There is a difference in surface brightness of 9'999.9 per degree squared between the two objects in the FOV.

Now magnify 10x

Object A is now 100degrees squared (0.001 brightness per degree squared) a reduction of 0.099 per square degree.

Object B is now 1 degree squared (100 brightness per degree squared) a reduction of 9'900 per square degree.

The difference in surface brightness is now 99.999

Much less difference.

So contrast can change between two extended objects at different magnifications

Even if one object did not change in size or brightness as you suggest, the surface brightness of the other object still changes.

so either way, if a star functions as a point source or not, contrast will still change.

Edited May 19, 2020 by miguel87

[andrew s]

I came across this pdf https://www.brayebrookobservatory.org/BrayObsWebSite/BOOKS/EVOLUTIONofEYEPIECES.pdf that tells you more that you might want to know about the history of eyepieces. However, it has an appendix on " Apparent luminance of telescopic image" which is well worth a read. It includes a consideration of the angle of incidence of the ray on the rods and cones of the eye something not yet discussed here!

And I thought quantum optics was a stretch and classical optics straight forward. Silly me. 

Regards Andrew

[miguel87]

1 minute ago, andrew s said:

I came across this pdf https://www.brayebrookobservatory.org/BrayObsWebSite/BOOKS/EVOLUTIONofEYEPIECES.pdf that tells you more that you might want to know about the history of eyepieces. However, it has an appendix on " Apparent luminance of telescopic image" which is well worth a read. It includes a consideration of the angle of incidence of the ray on the rods and cones of the eye something not yet discussed here!

And I thought quantum optics was a stretch and classical optics straight forward. Silly me. 

Regards Andrew

Haha, if only things were simple!

Thanks for sharing I will definitely have a read 👍

[Don Pensack]

You are arguing that the contrast between two extended objects changes with magnification.

This is contrary to everything I've ever read or studied in school about optics..

In the case of your two extended objects, multiplying by 10 lowers the surface brightness of each equally to 1/100 of its former surface brightness.

If the ratio were originally 100,000:1 (your first example) the final example is still 100,000:1(your second example).

Contrast is a ratio, not the amount of difference.

Yes, taking 2:1 in size, a difference of 1, and doubling, yields 4:2, a difference of 2, but this is not how contrast is measured.

And all the discussions of the eye I have seen or run across describe the eye as a contrast-sensing device, and they are describing contrast as a ratio of dark to light, not a simple arithmetical difference.

And that the eye's contrast threshold lowers with decreasing brightness, from about 1.02 in daylight, to 1.20 or more with fully scotopic vision.  In your example, the difference in surface brightness is lessening with magnification, which implies that we would require larger differences between brightnesses at high powers than we do at lower powers.  Yet, the opposite appears to be true.

Yes, contrast will change between a star and the background with magnification, but it is because one acts like an extended object and the other one doesn't.

 

 

[miguel87]

13 minutes ago, Don Pensack said:

 

And all the discussions of the eye I have seen or run across describe the eye as a contrast-sensing device, and they are describing contrast as a ratio of dark to light, not a simple arithmetical difference.

 

The measurable difference in brightness changes.

Also I am not claiming to know much about contrast or limiting magnitude. All I am saying is that a star dims under magnification.

We already discussed the point at which this should be noticeable. My maths made it about 50x mag and Vlaiv (much more trustworthy!) has info to suggest about 85x mag.

Going back to basics we know the star looks bigger under high mag because the airy disc takes up more of the apparent FOV at say 200x than the star does at 30x mag.

How can an object with a fixed brightness not have its brightness spread out as it gets bigger?

[miguel87]

Also if you are arguing that the eye doesnt perceive this change in brightness then that is a different point.

You could write an accurate scientific description of why my mobile screen appears brighter at 1am in the morning than 2 in the afternoon. I'm sure this includes, contrast, eye adaptation and many other factors. But the fact remains that the screen is NOT brighter.

Equally you can explain why the stars do not appear to dim under magnification: human eye resolution, contrast etc. I am arguing that even though this may be the case, there is still a separate truth about whether the image of the star produced by the telescope actually, physically does dim.

Edited May 19, 2020 by miguel87

[Stu]

Not sure where this is all going. All I know is that generally increasing magnification shows more stars. The Mel Bartels visibility calculator and references included below it may be of some use. No mention is made of treating stars as extended objects, but this comment seems pertinent.

‘Limiting magnitude is noted for 7mm exit pupil to 2mm exit pupils. Limiting magnitude improves as the exit pupil is made smaller (magnification is increased). There is no improvement beyond 1.5-2mm exit pupil because the background has become too dim to interfere. The magnitude is lowered if the sky background brightness is brighter than 21.5 (dark skies).’
 

For more, see http://adsabs.harvard.edu/full/1947PASP...59..253B, Nils Olof Carlin: on Schaefer's Telescopic limiting Magnitudes and my Visual Astronomy page.

http://www.bbastrodesigns.com/VisualDetectionCalculator.htm

[Don Pensack]

3 hours ago, miguel87 said:

Equally you can explain why the stars do not appear to dim under magnification: human eye resolution, contrast etc. I am arguing that even though this may be the case, there is still a separate truth about whether the image of the star produced by the telescope actually, physically does dim.

But that is simply not relevant to the use of telescopes.  If a star occupies 1/10 of one pixel and is magnified 10x, it still occupies 1 pixel.  Hence, all its light falls on one pixel.

In both cases, the star appears to be equally bright.  It is not until magnification increases the size of the spurious disc to a visible size that from that point on the object dims with increasing magnification.

Hence, contrast will improve right up to that point and stay the same from that point on.

It's rational to argue that brighter stars appear to have larger spurious discs, because more of the light in the center of the Airy disc is above the visibility threshold.  The Airy disc is actually the same size as a faint star, but a lot less of the spurious disc is visible.  Therefore, the point at which the star image begins to dim with increasing magnification because it is visibly an extended object will differ for bright stars than it does for dim stars.  There are stars that stay points to the eye all the way to the maximum magnification because of that.  So the books that discuss a 1mm exit pupil as the point where the Airy disc becomes an extended object to the eye are not taking the apparent size of the spurious disc into account.

Here is a cross section of the Airy disc pattern.  The Airy disc is from the first minimum on one side to the first minimum on the other.  The horizontal line is the threshold of visibility.  It slides upward when stars get fainter, reducing the width of the spurious disc in the center and increasing the apparent gap to the first ring.

 

Edited May 19, 2020 by Don Pensack

[miguel87]

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.

Edited May 20, 2020 by miguel87