Relationship of Aperture to Image Brightness

[Littleguy80]

Does increasing aperture, increase the image brightness for a fixed exit pupil? My feeling is that the image brightness remains constant through the fixed exit pupil and the change comes in image scale, which increases. If image scale is fixed then exit pupil increases with increased aperture and a brighter image is observed. Would be interested to hear people’s thoughts on whether my understanding is correct or not.

This comes from a discussion on how aperture masks work and whether they lead to a reduction in the amount of light entering the telescope. Intuitively, it seems like the answer must be yes though I’ve been told this may not be correct. 

[vlaiv]

Depends on a target. There are two different types of targets - extended targets and point sources.

Any target is point source provided it is sensed by more than one receptor. This holds for both visual and imaging - if target is spread over single pixel or single "visual cell" (here it could actually be few real cells - not sure how this works in combination with brain). In simple terms - point source is a star that has not been resolved into airy disk.

Everything else is extended source.

Extended source keeps the same brightness if you increase aperture but keep exit pupil the same. In order to understand why - one just needs to see condition to keep the same exit pupil with increasing aperture. Exit pupil is image of aperture and its size is size of aperture divided with magnification. If we increase aperture, to keep the exit pupil constant, we need to increase magnification by the same amount.

If we have 100mm scope and 1mm exit pupil, this means that we are at x100 magnification. If we increase aperture to 200mm, in order to keep 1mm exit pupil, we need to change magnification to x200.

This change in magnification means that light on sensor (eye or camera sensor) is spread around more, and in fact - it is now on 4 times larger surface (if we increased aperture and magnification by x2). Surface of aperture changed by factor of x4 and also area that light gets spread over increased x4 - brightness per unit sensor area remains the same. We see same brightness and sensor captures same number of photons per each pixel.

With point sources - it does not get spread and it stays "in the same place", since image is not resolved. With point source brightness is increased by increase of aperture - up to moment when point source gets resolved and is no longer point source.

[cloudsweeper]

Neil - for extended objects, Surface Brightness (brightness per unit area) depends on the Exit Pupil squared, and apparent magnitude is the integral over that area.  The key point is that SB itself is not enough - magnification also comes into play.  Now, as aperture increases, you get more mag for a given SB.

At this point, some people believe that the resulting increased brightness is a perception issue, while others (myself included) think that it is because the SB is integrated over a larger area.  I exchanged mails with Randy Culp over this matter, and he concurred.

Think of it like this.  A 10-LED torch is brighter than a 1-LED version, but they have the same SB.

It is an interesting - and contentious - issue!

(For a point source, things are different - brightness depends only on aperture.)

Observation, equipment, theory - what a great pastime this is!

Doug.

[andrew s]

In the eye several rods can be hard wired together so in effect on eye hardware  binning 👀

Regards Andrew 

Edited October 16, 2020 by andrew s

[Littleguy80]

1 hour ago, cloudsweeper said:

Think of it like this.  A 10-LED torch is brighter than a 1-LED version, but they have the same SB.

Thanks Doug. Let me see if I#'m understanding it correctly. The surface brightness of each LED is the same but the cumulative effect leads to a bright torch. I guess this is where we get light acting as wave. The 10 LEDs add up to increase the amplitude of the light wave? The translation to the scope idea is that increasing aperture is like adding extra LEDs to the image because.....the resolution is increased?

I think I get the idea with stars being point sources as you and Vlav both explained. 

[Littleguy80]

16 minutes ago, andrew s said:

In the eye several rods can be hard wired together so in effect on eye hardware  binning 👀

Regards Andrew 

Thanks Andrew. Would that make a difference with the change in aperture? Wouldn't the eye's sensitivity be a constant, taking out things like dark adaption of course.

[andrew s]

9 minutes ago, Littleguy80 said:

Thanks Andrew. Would that make a difference with the change in aperture? Wouldn't the eye's sensitivity be a constant, taking out things like dark adaption of course.

I think that's true. However, it means a "point source" can be somewhat spread out and still be act as a point source as far as the eye is concerned. 

The eye brain system is very non linear as well as the  basic logarithmic sensitivity to steady light it can be adaptive in low light in complex ways. 

Regards Andrew 

Edited October 16, 2020 by andrew s

[andrew s]

10 hours ago, Littleguy80 said:

This comes from a discussion on how aperture masks work and whether they lead to a reduction in the amount of light entering the telescope. Intuitively, it seems like the answer must be yes though I’ve been told this may not be correct. 

Aperture masks clearly lead to a reduction in light entering the telescope.  That's what a mask is. What else it does depends on its design and other environmental conditions.

It can reduce the aperture to below the "seeing" to change the image from blurring to dancing!

Apodising masks can change the diffraction pattern. 

They increase the focal ratio for H alpha solar work etc.

Regards Andrew 

[jetstream]

3 hours ago, andrew s said:

Aperture masks clearly lead to a reduction in light entering the telescope.

Does this equate to a dimmer image of the moon using a mask at the same exit pupil?

My 24" is blinding on the moon, the 15" is tolerable.

[andrew s]

1 minute ago, jetstream said:

Does this equate to a dimmer image of the moon using a mask at the same exit pupil?

My 24" is blinding on the moon, the 15" is tolerable.

If you using the same eyepiece the exit pupil will be different. If the exit pupil is the same the magnification must be different.

I think, that at the same exit pupil the smaller aperture i.e. with mask will be dimmer. 

Regards Andrew 

 

 

[Waddensky]

10 minutes ago, jetstream said:

Does this equate to a dimmer image of the moon using a mask at the same exit pupil?

The mask reduces the exit pupil. If you mask the aperture and want to keep the exit pupil the same by reducing the magnification, the image of the Moon has the same surface brightness, only smaller.

Edited October 16, 2020 by Waddensky

[jetstream]

1 minute ago, andrew s said:

I think, that at the same exit pupil the smaller aperture i.e. with mask will be dimmer. 

Yes, I've played with this extensively, mags exit pupils whatever. I was told by big dob builders, owners and optician to use an ND filter on the moon. It will literally leave a blind spot for quite a while.

I like binoviewers in these big scopes as the beamsplitter halves the light, to each eye.

[andrew s]

3 minutes ago, Waddensky said:

The mask reduces the exit pupil. If you mask the aperture and want to keep the exit pupil the same by reducing the magnification, the image of the Moon has the same surface brightness, only smaller.

Yes, your correct I was think of the illumination at the exit pupil not the final image

Regards  Andrew 

[jetstream]

3 minutes ago, Waddensky said:

The mask reduces the exit pupil. If you mask the aperture and want to keep the exit pupil the same by reducing the magnification, the image of the Moon has the same surface brightness, only smaller.

Will a larger aperture scope pack more light into the exit pupil regardless of magnification?

[andrew s]

The exit pupil is the image of the objective formed by the eyepiece.  Neglecting light loss in the optics all the light from the objective goes through the exit pupil.

The bigger the objective the more light through the exit pupil.

Regards Andrew 

[jetstream]

From Gerd Neumann's website

"Since enough light must be available to make use of the OIII filter it is best to use this filter with apertures of more than 6" (150mm). Smaller instruments do not gather enough light for meaningful and satisfying astronomical work. However, please note: Many experienced Deep Sky observers, with apertures of more than 10" (250mm), prefer using the OIII filter instead of the more versatile UHC filter. Due to the high optical quality of the Astronomik OIII filter substrate you will see the same needle-sharp stars as you would from your regular telescope."

This suggests to me that yes the aperture does contribute to the total amount of light- and continues right through the eyepiece.

As a note these filters do work in smaller apertures.

Edited October 16, 2020 by jetstream

[vlaiv]

1 minute ago, jetstream said:

From Gerd Neumann's website

"Since enough light must be available to make use of the OIII filter it is best to use this filter with apertures of more than 6" (150mm). Smaller instruments do not gather enough light for meaningful and satisfying astronomical work. However, please note: Many experienced Deep Sky observers, with apertures of more than 10" (250mm), prefer using the OIII filter instead of the more versatile UHC filter. Due to the high optical quality of the Astronomik OIII filter substrate you will see the same needle-sharp stars as you would from your regular telescope."

This suggests to me that yes the aperture does contribute to the total amount of light- and continues right through the eyepiece.

As a note these filters do work in smaller apertures.

This reminds me of another "well established truth" - F/ratio of the scope determines how fast one will acquire an image.

Both lack crucial piece of information. In this case it is magnification used.

4" of aperture can create same surface brightness of projection on retina as 8" by using suitable magnification (in the case of f/ratio it is the sampling rate or pixel size).

[jetstream]

1 minute ago, vlaiv said:

This reminds me of another "well established truth" - F/ratio of the scope determines how fast one will acquire an image.

Both lack crucial piece of information. In this case it is magnification used.

4" of aperture can create same surface brightness of projection on retina as 8" by using suitable magnification (in the case of f/ratio it is the sampling rate or pixel size).

Why does my 24" give a brighter image of the Veil using an OIII than my 15". 24" f4.1/PCII for f4.7, 15" native f4.8. Using either the 21E or 20mm APM.

[vlaiv]

3 minutes ago, jetstream said:

Why does my 24" give a brighter image of the Veil using an OIII than my 15". 24" f4.1/PCII for f4.7, 15" native f4.8. Using either the 21E or 20mm APM.

Both scopes are operating at f/4.7 - F/4.8, right?

Should give the roughly the same brightness.

Are you using binoviewer in 24" and not in 15". Viewing something with both eyes can make it appear brighter although each eye gets only 50% of the light.

[jetstream]

6 minutes ago, vlaiv said:

Both scopes are operating at f/4.7 - F/4.8, right?

Should give the roughly the same brightness.

Are you using binoviewer in 24" and not in 15". Viewing something with both eyes can make it appear brighter although each eye gets only 50% of the light.

No, just mono. Yes f4.7 and f4.8. Same optician, very smooth mirrors. The 24" specs out better on test stand than the 15" but the 15" is better in practise, the 24" can suffer minor intermittent astig from bouncing it across the gravel ie mirror cell stuff.

 

[cloudsweeper]

For a given focal ratio and eyepiece, the exit pupil will be the same, so the Surface Brightness will also be the same.  

For the same focal ratio but bigger aperture, the objective focal length must increase, i.e. mag must increase.  And this means that the integrated brightness increases - the same SB over a larger image.

Doug.

[Waddensky]

That's the reason larger telescopes enable you to see dimmer objects. The surface brightness never changes, but with the same exit pupil the larger scope has a higher magnification, and large objects are more easily detected than small objects with the same surface brightness.

[scarp15]

7 hours ago, cloudsweeper said:

For a given focal ratio and eyepiece, the exit pupil will be the same, so the Surface Brightness will also be the same.  

For the same focal ratio but bigger aperture, the objective focal length must increase, i.e. mag must increase.  And this means that the integrated brightness increases - the same SB over a larger image.

Doug.

 

7 hours ago, Waddensky said:

That's the reason larger telescopes enable you to see dimmer objects. The surface brightness never changes, but with the same exit pupil the larger scope has a higher magnification, and large objects are more easily detected than small objects with the same surface brightness.

Conversely, some objects respond more decisively with smaller aperture, fast focal ratio and very large exit pupil, when applied in the optium dark transparent sky conditions. Such an example would be Barnard's Loop; very large; 3000 light years across, emission nebula of very low surface brightness. Employing a large 6mm + exit pupil, offset by the contrast of a H-beta filter, encompassing a wide field of view may enable an observation. Larger aperture does not really gain anything at least in my own comparison between a 14" and 3.5" scope at similar exit pupil. Equally the IFN, Integrated Flux Nebula; can also, in optimum conditions be determined through moderate aperture at large exit pupil, fast focal ratio, not certain that larger aperture at the same exit pupil will gian anything related to the particular nature of this observation.

[cloudsweeper]

9 hours ago, scarp15 said:

 

Conversely, some objects respond more decisively with smaller aperture, fast focal ratio and very large exit pupil, when applied in the optium dark transparent sky conditions. Such an example would be Barnard's Loop; very large; 3000 light years across, emission nebula of very low surface brightness. Employing a large 6mm + exit pupil, offset by the contrast of a H-beta filter, encompassing a wide field of view may enable an observation. Larger aperture does not really gain anything at least in my own comparison between a 14" and 3.5" scope at similar exit pupil. Equally the IFN, Integrated Flux Nebula; can also, in optimum conditions be determined through moderate aperture at large exit pupil, fast focal ratio, not certain that larger aperture at the same exit pupil will gian anything related to the particular nature of this observation.

Yes, good point Iain!  Under dark skies, a high exit pupil can render a brighter image (SB proportional to exit pupil squared, regardless of aperture).  

Doug.

[Stu]

10 hours ago, scarp15 said:

 

Conversely, some objects respond more decisively with smaller aperture, fast focal ratio and very large exit pupil, when applied in the optium dark transparent sky conditions. Such an example would be Barnard's Loop; very large; 3000 light years across, emission nebula of very low surface brightness. Employing a large 6mm + exit pupil, offset by the contrast of a H-beta filter, encompassing a wide field of view may enable an observation. Larger aperture does not really gain anything at least in my own comparison between a 14" and 3.5" scope at similar exit pupil. Equally the IFN, Integrated Flux Nebula; can also, in optimum conditions be determined through moderate aperture at large exit pupil, fast focal ratio, not certain that larger aperture at the same exit pupil will gian anything related to the particular nature of this observation.

Yes, I guess the framing element of a very  widefield helps here. The eye detects contrast, and if the object is filling the whole field you don’t see it at all!