Why does brightness reduce when magnification increases?

[mattnedgus]

OK so just as I was writing my original and confused question I had a thought and think I might have worked it out.  I've attached a drawing to try and show what I mean and help others if they're ever as confused as I was.  I could only find sources that quoted brightness reduces four-fold for a two-fold increase in magnification, but I just couldn't wrap my head around and visualise it (too little mental exercise these days!!) -  I knew it was something to do with the area of a circle but that's about it.  Then I had a thought and made a little drawing:

• The blue circle represents what the telescope can see - for example it's maximum field of view (i.e. the most amount of sky it could ever possibly see: I worked out a theoretical 18.92 degrees for the SW200P - the second image shows how I came to this conclusion).  
• The grey object (of no particular shape) in the middle of these blue circles is the same size because as far as the telescope is concerned the sky is the same scale (the scope still "see's" the same circle of sky).  
• The red circle represents a lower power eyepiece's view and encircles a larger [field of view] area of the sky (the lower red circle show's what we'd see in the eyepiece: a smaller, brighter object)
• The green line represents a higher power eyepiece's view and encircles a narrower [field of view] area of the sky (the lower green circle show's what we'd see in the eyepiece: a larger, dimmer object)

Am I right in thinking that the higher power eyepiece takes the light from a smaller [field of view] 'circle' in the sky than the lower power, but 'blows it up' to the same size in the eyepiece for us to see, as in the lower green and red circles?  And if so is that what explains why the brightness goes down four-fold for a two-times magnification (because the light from a smaller [field of view] area is being shown at the same/similar size to the eye)?

And essentially is this right: the scope always see's the same [field of view] 'circle' of the sky but the different eyepieces pick out different sized [field of view] 'circles' of this?

Before I realised this I was under the delusional and confused impression that a smaller object in the sky might be brighter because the whole of the objective aperture could be used for that one object!!

 

[Charic]

Inverse Square Law may help?

Tricky subject, used it  when learning 35mm photography many years ago, with several flash heads! If you doubled the distance to your subject, you needed four times the output from the flash head to maintain the same brightness level.

On our 200's the scopes ability to gather light is over 800 times more than our eyes alone.
This suggests that the image should be that many times  brighter in the final image, but not always the case. Any non point source  like your galaxies, are called extended bodies,  their light is already spread out, diffuse,  and any  magnification using the telescope causes more loss of light in proportion to the level of magnification. 

[acey]

"Brightness" can mean illumination (aka apparent magnitude) or surface brightness (aka luminance). The former (illumination) can be thought of as how much light a source sheds on your eye (or any other surface), the latter (luminance) is closer to our subjective sense of how "bright" something looks. A telescope increases illumination and reduces luminance.

When a target is magnified its apparent size (angular size) is increased. The telescope doesn't take in any more light, it just spreads the rays more widely. So surface brightness is lowered and the target looks fainter. The background sky is affected in the same way.

Surface brightness is a logarithmic quantity, so we can't say that doubling the magnification will reduce surface brightness by a quarter. Also our perception is affected by target size and background brightness, so the exact effect of magnification is complicated. But the general principle is that if a target is too small it won't be seen, and if it's too faint it won't be seen, so the trick is to find a magnification range where the target is not too small or too big (and faint) to be visible.

 

 

[Ouroboros]

A bigger image contains the same amount of light spread over a larger area of the retina.  So it appears fainter. Twice the magnification reduces the brightness of the image by a factor of four. 

[Stu]

Looking at your diagrams, I think there is a fundamental misunderstanding about the ray traces in a scope. All light from astronomical sources is effectively at infinitity, even the moon, so the light rays always enter the scope as a parallel beam. The path the light takes is always the same through until the eyepiece where it is magnified to a degree depending upon the focal length of the eyepiece.

One proof of this is that a long Dewshield does not vignette the image, which it would if the situation were similar to your diagram.

As for the rest, I'm sure Acey has it covered so will defer to his answer

[mattnedgus]

I could really do with a good book to understand the theory I think!  The effect of exit pupil is my new confusion!

 

On 06/08/2016 at 14:22, Charic said:

Inverse Square Law may help?

It does thank you - there's a diagram that shows it graphically here: https://en.wikipedia.org/wiki/Inverse-square_law which helps me visualise the rule.  It's unbelievable how much I've forgotten over these last 15 years since I did an engineering degree!

 

On 06/08/2016 at 15:50, acey said:

"Brightness" can mean illumination (aka apparent magnitude) or surface brightness (aka luminance). The former (illumination) can be thought of as how much light a source sheds on your eye (or any other surface), the latter (luminance) is closer to our subjective sense of how "bright" something looks. A telescope increases illumination and reduces luminance.

Thanks acey, I wanted to try and understand illumination and luminance better and read this Illumination vs Luminance Link where the author says that illuminance is measured as light striking a surface (the incident) and luminance is measured as the light coming off the surface that has light hitting it (the reflected).  Then I got more confused and wasn't sure how that applied to your description or a telescope other than the light hitting/reflected from the objective and primary.

 

On 06/08/2016 at 15:50, acey said:

The telescope doesn't take in any more light, it just spreads the rays more widely

acey, I think this is key (but then I get confused with Exit Pupil )  - this is what I was trying to show with those red and green circles: that when a higher power EP is used, it takes a smaller portion of the sky and makes it up to the same size.  The reason I get confused with Exit Pupil is because the exit pupil also reduces with increased power and so fewer 'cones' in the eye are receiving input - which must also have an effect on the apparent brightness?

 

On 06/08/2016 at 16:28, Ouroboros said:

A bigger image contains the same amount of light spread over a larger area of the retina.  So it appears fainter. Twice the magnification reduces the brightness of the image by a factor of four. 

But doesn't the image change in size with the exit pupil also? 

 

On 06/08/2016 at 16:57, Stu said:

Looking at your diagrams, I think there is a fundamental misunderstanding about the ray traces in a scope. All light from astronomical sources is effectively at infinitity, even the moon, so the light rays always enter the scope as a parallel beam.

I think so too - when I drew that I was trying to understand the maximum field of view the scope could ever possibly see.  I still think light from the wide angle I drew light would enter the scope and hit the parabolic primary, but because of the parabolic shape most of the light from extreme angles would be reflected at angles that would hit the sides of the scope rather than be focused onto the secondary.

 

[mattnedgus]

In case it helps anybody in the future who finds this post, I found this link that made some real (intuitive vs academic) sense to me:  https://www.astronomics.com/eyepiece-exit-pupils_t.aspx

It links the exit pupil size with the brightness of extended objects, rather than using magnification as a reason only.

So now as I understand it, for a given scope f ratio: if the magnification is doubled, the exit pupil diameter is halved and it's area is 1/4 of the size.

This feels easier to understand than when I was trying to consider the field of view of the eyepiece!  Hopefully it's the correct way of looking at it!

[Ouroboros]

Matnedgus - that link explains it quite well doesn't it. Good the way it explains the difference in how brightness behaves for a point source like a star and an extended source like a galaxy. I've noticed this particularly when looking at faint nebulas and how much fainter they become at higher magnifications until they can become almost impossible to see. I think we are all saying things in slightly different ways too. 

[Louis D]

On ‎8‎/‎6‎/‎2016 at 08:22, Charic said:

On our 200's the scopes ability to gather light is over 800 times more than our eyes alone.
This suggests that the image should be that many times  brighter in the final image, but not always the case.

Interestingly, unless you use an electronic image intensifying eyepiece, the image at the eyepiece will never be brighter than the image to the unaided eye.  It will just able to be magnified to be easier to see.  Think about it, the full moon at 800 times brighter would practically blind you because its as bright as asphalt at noon on a sunny day at the equator.  Clearly, it's not 800 times brighter no matter how low a power you may try to use.  That's why it's so difficult to see large, diffuse objects like Barnard's Loop.  Nobody noticed it until astrophotography came around to integrate the light flux over time.  Ironically, small, faint nebula are easier to see in a telescope than large, equally faint nebula.  After having looked through a Gen3 light intensifying tube at a recent star party, I'm seriously considering dropping the several large to pick one up just to be able to easily see nebulae in realtime.

[Charic]

16 hours ago, Louis D said:

 Clearly, it's not 800 times brighter no matter.........

It is brighter but not 800  times brighter, '800 times more capable' could have been a better description?
If I had omitted the word  'ALWAYS' it would have been a little less ambiguous!
 

 

[Louis D]

18 minutes ago, Charic said:

It is brighter but not 800  times brighter, '800 times more capable' could have been a better description?
If I had omitted the word  'ALWAYS' it would have been a little less ambiguous!
 

 

Here's a good explanation of the subject of image brightness.  You're right about point sources, and I'm right about extended light sources.

 

[Charic]

Thanks,  were  actually reading from the same hymn sheet there, the first sentence, third paragraph, was the reference I  associated with! we'll get there....

[Louis D]

What's also interesting is that with a big enough telescope and the right imaging techniques, the largest, closest "point" sources become extended objects.  There's even a list of them.  This stuff fascinates me.  Someday, maybe we'll see someone waving back at us.

[mattnedgus]

On 09/08/2016 at 19:39, Ouroboros said:

Matnedgus - that link explains it quite well doesn't it. Good the way it explains the difference in how brightness behaves for a point source like a star and an extended source like a galaxy. I've noticed this particularly when looking at faint nebulas and how much fainter they become at higher magnifications until they can become almost impossible to see. I think we are all saying things in slightly different ways too. 

I think you could be right.  From the internet searches I did there seemed to be many ways of saying the same thing which made finding something 'sound' (that I could understand!) feel like trying to run on treacle.

 

On 10/08/2016 at 21:21, Louis D said:

What's also interesting is that with a big enough telescope and the right imaging techniques, the largest, closest "point" sources become extended objects.  There's even a list of them.  This stuff fascinates me.  Someday, maybe we'll see someone waving back at us.

From KIC 8462852 perhaps? 

That's an interesting link!  (Unfortunately I can't open the other to Starizona yet - looks like they're down for maintenance!)