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# Aperture, light collection and f/ratio

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### #1 StuartT

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Posted 18 May 2021 - 06:12 PM

Can someone please clear up a little confusion I have?

I was always taught that light gathering power was purely a function of aperture of a scope. So a 8" scope will gather a lot more light than a 4" scope (presumably 4 x more, as it's actually about area of aperture).

But then I discovered about f/ratios and that a f/5 scope would be 'faster' (i.e. brighter) than an f/10 scope.

So now how do I factor that in?

Would an 8" scope which is f/10 still gather 4 x as much light as a 4" scope that is f/5 ?

In other words is light gathering ability only about aperture? In which case why is a f/5 4" scope faster (brighter) than a f/10 8" scope?

I'm not sure I am explaining my confusion clearly but I hope someone can see what I am getting at.

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### #2 havasman

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Posted 18 May 2021 - 06:23 PM

But then I discovered about f/ratios and that a f/5 scope would be 'faster' (i.e. brighter) than an f/10 scope.

Faster does not = brighter.

Your original concept that > aperture = > light gathering is correct.

But there is more that goes into how bright the image you see may be. Exit pupil size, for instance. That is determined by eyepiece focal length where the shorter focal length eyepiece will produce a smaller exit pupil.

Edited by havasman, 18 May 2021 - 06:24 PM.

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### #3 Redbetter

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Posted 18 May 2021 - 06:59 PM

Photography/imaging causes a lot of confusion about ratio and brightness.  Visual observing is different, so it is best to ignore imaging based discussion and explanations when trying to understand visual.  Light gathering as seen at the eyepiece is primarily about the aperture.  Lesser considerations are system light transmission after losses due to less-than-100% mirror transmission, obstructons, and glass elements in the optical path.

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### #4 Asbytec

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Posted 18 May 2021 - 07:29 PM

It's my understanding all apertures at the same focal ratio produce an image of extended objects (not stars) of equal surface brightness per unit of area - normally per arc second. The difference is the larger aperture forms a larger image because at a given focal ratio the focal length is longer. So increased light gathering is spread over a larger image obeying the inverse square law. As Red said above, this is more of a concern for imaging. As Havasman said, the exit pupil of an afocal system (with an eyepeice) governs the image surface brightness as a function of magnification.
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### #5 TOMDEY

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Posted 18 May 2021 - 08:14 PM

Well, that's partially-correct, as far as it goes.

This topic comes up often and is rarely explained correctly. The stock "right answer" that ~Light Gathering Power~ is defined by the optical aperture area of the telescope, and nothing else. The tacit implication is that this metric (times a constant) holds comparatively across all telescopes. So one would conclude that an eight-incher has four times the LGP of a four-incher. Well, that leaves out the other half of the formula. If we logically define LGP as the inherent ability of the telescope to transport photons from Object Space (aka the universal sky) to Image Space (the telescope's focal plane where is conjugated e.g. film, CCD, CMOS, retina, etc.), we must take both parametrics into account; area alone is not enough. It is therefore the combination of aperture area and available (well-corrected / unvignetted) object-space field solid angle. That is, the scalar product of A (aperture area) and Ω (omega, field solid angle). This is what we call the étendue of the telescope. étendue = AΩ.

There are some rules of thumb to follow in computing LGP. From the object-space side it is the telescope Entrance Pupil that defines area and the object-space covered field that defines solid angle. From the image-space side it is the telescope Exit Pupil that defines area and the image-space apparent field that defines solid angle. These are coupled throughout the telescope train, inside and out, by the Lagrange Invariant which is a special case of Emmy Noether's Conservation Theorem, applied to light.

One can then finesse that metric to determine the pragmatic Information Throughput of the system, by applying generally small correction factors like spectral throughput, central and other obstructions, vignetting, apodization, quantum efficiency, etc. At that point you know what portion of the information leaving object-space actually gets registered by your telescopic system. This is why ~Information Theory~ is so fundamental to all observational sciences.    Tom

Conclusion: Light Gathering Power is most logically defined by the Telescope's étendue = AΩ.

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### #6 KBHornblower

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Posted 18 May 2021 - 08:20 PM

It's my understanding all apertures at the same focal ratio produce an image of extended objects (not stars) of equal surface brightness per unit of area - normally per arc second. The difference is the larger aperture forms a larger image because at a given focal ratio the focal length is longer. So increased light gathering is spread over a larger image obeying the inverse square law. As Red said above, this is more of a concern for imaging. As Havasman said, the exit pupil of an afocal system (with an eyepeice) governs the image surface brightness as a function of magnification.

My bold.  As I understand it, Havasman did not say that the exit pupil governs the image surface brightness.  He said that the exit pupil size is determined by the focal length of the eyepiece for any given objective.  At the risk of sounding pedantic I will repeat my assertion that the exit pupil size does not govern the brightness.  The exit pupil size and the surface brightness are concurrently governed by the optical geometry, making a handy correlation.

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### #7 Redbetter

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Posted 18 May 2021 - 09:06 PM

Exit pupil size and surface brightness directly correlate.   Not sure why this is so hard to understand.

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### #8 Asbytec

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Posted 19 May 2021 - 01:19 AM

Tom, thank you for the most concise explaination of etendue I've seen

KB, I must have forgotten what Havasman actually said by the time I wrote my reply. I must have inferred a little.
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### #9 Tony Flanders

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Posted 19 May 2021 - 05:48 AM

Conclusion: Light Gathering Power is most logically defined by the Telescope's étendue = AΩ.

I think it depends on your goal. Etendue is indeed the most important metric for telescopes designed to do wide-field sky surveys using photographic plates or electronic sensors. Examples of telescopes designed for maximum étendue would be the 48-inch Samuel Oschin Schmidt camera on Mount Palomar and the forthcoming Large Scale Synoptic Telescope (LSST).

The closest equivalent in visual observing is sky sweeping -- browsing large swaths of sky either for fun and individual edification or for finding new comets.

But if your goal is to observe maximum detail in individual objects that fit entirely inside the field of view, then what you care about is aperture, and aperture alone.

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### #10 kathyastro

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Posted 19 May 2021 - 06:39 AM

It depends whether you are talking about visual observing or imaging.  The optical systems for the two activities are different and they therefore behave differently.

For visual observing, aperture matters.  Any two scopes of a given aperture, when compared at the same magnification, will produce visual images of equal brightness.  Aperture and magnification are the only variables.  Focal length (and therefore focal ratio) does not matter for brightness.

For imaging, only focal ratio matters.  Any two scopes of a given focal ratio will produce images of equal brightness when compared using the same sensor.  Focal length and aperture do not matter independently.  Only their ratio matters.

Since we are on the "no astrophotography" forum, I assume you are talking about visual observing, so aperture is what matters to you.

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### #11 spereira

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Posted 19 May 2021 - 07:23 AM

Moving to Equipment.

smp

### #12 Star Geezer

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Posted 19 May 2021 - 09:00 AM

For imaging, only focal ratio matters.  Any two scopes of a given focal ratio will produce images of equal brightness when compared using the same sensor.  Focal length and aperture do not matter independently.  Only their ratio matters.

It seems the same would be true for the same focal length eyepiece. That cannot be right, can it?

An 8” f/4 would ideally gather 4 times more light than a 4” f/4 at equal magnification, but with the same eyepiece would have double the magnification.

How much of a dimming effect does magnification produce?

### #13 Jon Isaacs

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Posted 19 May 2021 - 09:20 AM

It seems the same would be true for the same focal length eyepiece. That cannot be right, can it?

An 8” f/4 would ideally gather 4 times more light than a 4” f/4 at equal magnification, but with the same eyepiece would have double the magnification.

How much of a dimming effect does magnification produce?

Doubling the magnification means the light is spread out over twice the diameter or 4 times the area.  The image brightness is dimmed by a factor of 4. You have 4 times as much light so the net result is they're the same brightness.

This is how I think about it:

A visual telescope is an afocal system, it's a objective and an eyepiece. Ignoring transmission losses:

- The brightness of a star, because it's a point, only depends on the aperture.

- The "surface brightness" of an extended object is the intensity of image, light per unit area.

This depends on the area of the exit pupil, that beam of light that enters the eye.

The exit pupil is equal to the aperture divided by the magnification.

A 200 mm scope at 100x provides a 2mm exit pupil, a 100 mm scope at 50x provides a 2mm exit pupil.

The intensity of a particular nebula will be identical in both scopes but it will be twice the diameter,  4 times the area in the larger scope.

For an afocal device, focal ratio only matters in that it's indirectly involved in choosing the eyepiece.

A 200mm F/10 scope requires a 20 mm eyepiece to achieve a 2mm exit pupil, a 200mm F/5 scope requires a 10 mm eyepiece.

Jon

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### #14 TOMDEY

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Posted 19 May 2021 - 09:26 AM

Tony, kathy, --- yes to that 'cept imagery and visual are fundamentally identical. The only difference between film/CCDCMOS and the retina the nature of the transducer. The only difference between the information processing and storage is the computer/brain. They both equally rank as "measurement event" detection machines with the power to condense quantum possibility into reality. At that point, the wave function collapses and information about the environment is realized.

Notice that we most often implicit that the ~telescope~ is just and only the front objective half e.g. Newt, Cass, Fractor, etc. And that the camera or eyepiece+eye are something that gets added later. But that's kinda in the weeds or trees vs forest. On the most fundamental level the telescope is the entire machine that communicates the outside world into detection and storage via the imaging light coming from objects in the environment. And étendue defines the size of that photon funnel, information throughput capacity --- Light Gathering Power.    Tom

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### #15 Star Geezer

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Posted 19 May 2021 - 10:30 AM

It was the discrepancies with my math and what is being said and the area of the field of view that lead to my confusion. So, it would be the same for a given eyepiece and the only real distinction between visual and photographic astronomy would be exposure.

Just as I thought.

### #16 Asbytec

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Posted 19 May 2021 - 03:25 PM

At the risk of sounding pedantic I will repeat my assertion that the exit pupil size does not govern the brightness.  The exit pupil size and the surface brightness are concurrently governed by the optical geometry, making a handy correlation.

I remember you discussing this, but it was a little over my head. I understood from Glenn LeDrew the exit pupil is, "the final arbiter of surface brightness". The optical geometry I believe is the solid cone both Tom and Glenn discussed.

Edited by Asbytec, 19 May 2021 - 03:27 PM.

### #17 Dave Mitsky

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Posted 19 May 2021 - 03:41 PM

Did someone mention étendue?

what is a HET (High Etendue Telescope)?

Imagine a water pipe. Etendue is the total amount of water flowing through the pipe. How can we get more water? Well, we can enlarge the pipe allowing more water to flow through and we can turn the valve on more to increase the flow of water. Enlarging the pipe is equivalent to increasing the apparent field of view while turning on the value more is equivalent to increasing aperture. Etendue is the amount of light flowing through the field of view into the eye.

https://bbastrodesigns.com/HET.html

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### #18 kathyastro

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Posted 19 May 2021 - 04:17 PM

So, it would be the same for a given eyepiece and the only real distinction between visual and photographic astronomy would be exposure.

The distinction between visual and photographic astronomy is that, for the vast majority of photographic astronomy, an eyepiece is not used.  If you are going to duplicate the optical system of visual astronomy for imaging, by using the afocal method, then yes, the differences are exposure and sensitivity.  But for most imaging, the differences are much more significant than that, because the optical system is totally different.

### #19 Star Geezer

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Posted 19 May 2021 - 05:49 PM

Even prime focal photography would not the differences be mostly due to the camera itself. For prime focal photography wouldn’t you want a fast or slow scope for the same reason visually you would want a short or long focal length scope?

### #20 kathyastro

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Posted 19 May 2021 - 06:07 PM

Even prime focal photography would not the differences be mostly due to the camera itself. For prime focal photography wouldn’t you want a fast or slow scope for the same reason visually you would want a short or long focal length scope?

This is not about camera response.  It is about how much light falls on the sensor area.  What the camera does with it is a subject for a different thread.

There are many reasons for someone to choose a particular scope for imaging.  Focal length is one.  Focal ratio is another.  Focal length controls the image scale.  Focal ratio controls the sensor illumination.

For visual observing, focal ratio (i.e. fast or slow) does not mean a whole lot.  It might affect eyepiece selection, but it does not affect image brightness.  That is determined by aperture and magnification.

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### #21 teashea

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Posted 19 May 2021 - 06:23 PM

Can someone please clear up a little confusion I have?

I was always taught that light gathering power was purely a function of aperture of a scope. So a 8" scope will gather a lot more light than a 4" scope (presumably 4 x more, as it's actually about area of aperture).

But then I discovered about f/ratios and that a f/5 scope would be 'faster' (i.e. brighter) than an f/10 scope.

So now how do I factor that in?

Would an 8" scope which is f/10 still gather 4 x as much light as a 4" scope that is f/5 ?

In other words is light gathering ability only about aperture? In which case why is a f/5 4" scope faster (brighter) than a f/10 8" scope?

I'm not sure I am explaining my confusion clearly but I hope someone can see what I am getting at.

You are correct, provided that if it is a mirror telescope, the central obstruction size and the reflectivity of the mirror are the same.  Some mirrors are a little more reflective than others.

### #22 Jon Isaacs

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Posted 19 May 2021 - 06:41 PM

For visual observing, focal ratio (i.e. fast or slow) does not mean a whole lot.  It might affect eyepiece selection, but it does not affect image brightness.  That is determined by aperture and magnification.

The effect of a faster focal ratio is second order, shorter, increased aberrations, eyepiece availability.

In a 10 inch F/5, the 31mm Nagler provides a 1.93° field at 40x with a 6.2 mm exit pupil.

To match that with a 10 inch F/10, you'd need a 62 mm Nagler.. they dont make eyepieces like that.

Jon

### #23 KBHornblower

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Posted 19 May 2021 - 07:00 PM

I remember you discussing this, but it was a little over my head. I understood from Glenn LeDrew the exit pupil is, "the final arbiter of surface brightness". The optical geometry I believe is the solid cone both Tom and Glenn discussed.

My misgiving about statements such as "the exit pupil of an afocal system (with an eyepeice) governs the image surface brightness" and "the exit pupil is the final arbiter of surface brightness" is that they could mislead a novice into thinking that the smaller exit pupil at higher magnification is the physical cause of the reduced surface brightness of the image on the retina.  That is not so.  The surface brightness is reduced because the same amount of light is spread out over a larger area by the stronger eyepiece.  The exit pupil is smaller because the eyepiece is intercepting the diverging rays closer to the prime focus.  There is no attenuation happening at the exit pupil.  This does not negate the hard correlation of exit pupil size and image brightness.

Just bear with me.  I can be an old curmudgeon on such points of physics, having once been a would-be physicist.

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### #24 Star Geezer

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Posted 19 May 2021 - 07:46 PM

Focal length controls the image scale.  Focal ratio controls the sensor illumination.

Thanks you, kathyastro; for your attempt to get through my thick head. In my mind your statement above could be interchanged with; Focal length controls the magnification.  Focal ratio controls the image brightness; for the same fixed focal length eyepiece.

Edited by Star Geezer, 19 May 2021 - 07:49 PM.

### #25 Asbytec

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Posted 19 May 2021 - 08:20 PM

...they could mislead a novice into thinking that the smaller exit pupil at higher magnification is the physical cause of the reduced surface brightness of the image on the retina.

There is no attenuation happening at the exit pupil.

No worries. I'm an economist. You think phiysicists have a hard time understanding the world?

It's my understanding you're right, except the image is dimmer because the exit pupil changes the geometry on the eye. From around f/3 to something slower with a smaller exit pupil and same focal length. That's what I understood Glenn to say about it.

Edited by Asbytec, 19 May 2021 - 08:28 PM.

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