Erlend Langsrud:
An F/2 telescope is 25x faster than a F/10 scope will the same focal length. Key here is "same focal length" which means same object space sampling. So in that instance, the reason the F/2 telescope is faster is because it has 5x the aperture! The aperture is key in determining how much power is captured by the optical system. Look at the derivation of the camera equation by John Hayes, below. Optical power, P, captured by the system from a source of radiance L and area dA is dictated purely by the aperture of the lens and the distance. The focal length then dictates how that power is translated to image plane irradiance. A 200mm f/4 and 250 mm f/4 will provide the same irradiance on the focal plane, but for different reasons. The 200 mm f/4 focuses a larger area on the same pixel size as the 250 mm f/4, but the 250 mm captures more power from a fixed angular object area than the 200mm. A 250 mm lens will ALWAYS capture 56% more power from a given object area than a 200mm lens and this will be true regardless of f#. This gives you the ability, in post, to bin down the 250mm image to a common image scale (assuming the FOV is not lost), so you achieve a higher effective irradiance. This is the true advantage of aperture. For a given FOV and given viewing size/resolution, the larger aperture scope will always provide the better image - simply because it has captured more power from that FOV than the smaller aperture scope. And nothing you do can change that.  |
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Kay Ogetay:
There is a nifty Astronomical SNR calculator here...
https://www.mirametrics.com/sn_calculator_mvn.php
It's meant for photometry and so the SNR value it gives relates to the image of a single star against it's background (i.e. aperture photometry), but it is fun to play around with and change parameters to see what makes the biggest difference to SNR for that purpose. *Hint Hint* Bumping up the aperture is what makes the most difference!
Reading the fine prints is important. This calculation is, as it states, for "point sources". For that, we know aperture matters as John Hayes discusses this difference in the video. But in astrophotography we target extended objects. For that, f-ratio is what matters.
*Sorry for some reason I couldn't include this in the previous answer. Correct hence why I stated it is used for photometry purposes. Also, you say that for astrophotography ‘we’ are interested in extended objects. Well, you will have to speak for yourself in n that one!
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Arun H:
Erlend Langsrud:
An F/2 telescope is 25x faster than a F/10 scope will the same focal length.
Key here is "same focal length" which means same object space sampling. So in that instance, the reason the F/2 telescope is faster is because it has 5x the aperture! The aperture is key in determining how much power is captured by the optical system.
Look at the derivation of the camera equation by John Hayes, below. Optical power, P, captured by the system from a source of radiance L and area dA is dictated purely by the aperture of the lens and the distance. The focal length then dictates how that power is translated to image plane irradiance. A 200mm f/4 and 250 mm f/4 will provide the same irradiance on the focal plane, but for different reasons. The 200 mm f/4 focuses a larger area on the same pixel size as the 250 mm f/4, but the 250 mm captures more power from a fixed angular object area than the 200mm.
A 250 mm lens will ALWAYS capture 56% more power from a given object area than a 200mm lens and this will be true regardless of f#. This gives you the ability, in post, to bin down the 250mm image to a common image scale (assuming the FOV is not lost), so you achieve a higher effective irradiance. This is the true advantage of aperture. For a given FOV and given viewing size/resolution, the larger aperture scope will always provide the better image - simply because it has captured more power from that FOV than the smaller aperture scope. And nothing you do can change that.
As I explained in my reply, obviously if you hold FOV constant then increasing aperture will increase brightness. This is because a 200mm f/4 and 250mm f/4 **will not** have the same FOV! You say in your own reply that if you assume a constant focal length then of course increasing aperture increases brightness, but then go on to fall victim to the same pitfall in reasoning. You simply cannot “ignore” FOV when talking about focal ratios with different apertures. The entire reason that the focal ratio isn’t changing is because the focal length is increasing proportional to the aperture. You say yourself that irradiance is constant for systems with the same focal ratio, but then say that since the 250mm receives 56% more light it will have greater irradiance. The simple and hard truth is that systems with an equal focal ratio will reveal equally dim parts of the sky in equal time (assuming a low or zero noise camera with small pixels). As you increase aperture while holding focal ratio constant, you are receiving more photons while imaging a smaller area of sky on the same sensor area, which makes irradiance and image brightness constant. As I have already said, the only advantage of aperture is detail and sampling. Even on an ideal camera with impossibly small pixels and zero noise, the rayleigh limit is higher on a larger aperture. This allows you to extract finer detail on smaller objects, which is why we can’t just crop down a Rokinon 135mm f/2 and expect the same detail as an 8” Edge HD but 25x faster. What you will have is a 25x brighter image, but with much lower angular resolution.
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I don't know how you can say it any better…….
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August Norman:
You simply cannot “ignore” FOV when talking about focal ratios with different apertures. The entire reason that the focal ratio isn’t changing is because the focal length is increasing proportional to the aperture. You say yourself that irradiance is constant for systems with the same focal ratio, but then say that since the 250mm receives 56% more light it will have greater irradiance. Suggest going back and re-reading what I wrote because you have completely misunderstood my post and point. As an example, I never claimed "that since the 250mm receives 56% more light it will have greater irradiance.". Please take the trouble to read what I wrote and don't attribute to me things I didn't write. The math and my post is there for all to see. I am not confused about it at all. If you can disprove with math the following statement I made, I certainly would be curious because I am always curious about new physics. "For a given FOV and given viewing size/resolution, the larger aperture scope will always provide the better image - simply because it has captured more power from that FOV than the smaller aperture scope. And nothing you do can change that." |
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The issue is in the very first sentence, “for a given FOV”. FOV is not given, it is a function of focal length which itself is given by focal ratio when you increase the aperture. It is physically impossible to maintain the same FOV without changing to a larger sensor (but at that point the extra irradiance is due to the additional sensor area). You cannot hold field of view constant while changing focal length, it’s just not congruent with reality. A great example of this is a small refractor vs a RASA, you’ve got a 60mm f/6 refractor, 360mm focal length, and a 200mm f/2 RASA, 400mm focal length. Their focal lengths are nearly the same, but obviously f/2 is faster than f/6. This is an example of holding field of view constant while increasing aperture, and whaddya know, it changes the focal ratio. It is impossible to change either focal length, aperture, or focal ratio without affecting another. If you hold focal ratio constant and change the aperture, you’re also changing focal length. Hold focal length constant and change the aperture, you’re also changing focal ratio. Hold the aperture constant and change focal length, that changes focal ratio. What you’re essentially saying when you say “for a given FOV” is “Change aperture, but don’t change focal length, and then also don’t change focal ratio”. It is mathematically incoherent. These physical quantities are directly mathematically related and you cannot change one in isolation.
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August Norman:
The issue is in the very first sentence, “for a given FOV”. FOV is not given, OK... I understand. Let me clarify. Yes, for a given sensor area, the smaller focal length scope will always provide a larger FOV. That is not in dispute. But there are many, many instances where two scopes of different apertures can capture a desired FOV. We do not always utilize the full FOV afforded by our scopes. A good example would be M51 and its immediate surroundings. Or perhaps something like the Owl Nebula. Both fields would fit within the sensor area of either a 200 mm f/4 or a 250 mm f/4 using a 2600MM Pro camera. To achieve the same viewing size, you would crop the 200 mm f/4 image more. The effective irradiance achieved on the final image scale will be greater with the 250mm f/4 than the 200mm f/4. This is a pretty common use case for those that image dim PNs or galaxies. Hence the italics around the statement: "For a given FOV and given viewing size/resolution, the larger aperture scope will always provide the better image - simply because it has captured more power from that FOV than the smaller aperture scope. And nothing you do can change that. "If the FOV you desire cannot be achieved with a given scope/camera combination, then it is not a basis for comparison. The above only holds when the FOV you desire can fit in your recording system. The reason this is important is because of the question the OP asked: Can larger aperture offset a slower scope vs a faster scope?Assuming the FOV he desires can be captured by both scopes either using a common or different recording system, the larger aperture scope will have the advantage.
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Arun H:
August Norman:
The issue is in the very first sentence, “for a given FOV”. FOV is not given,
OK... I understand. Let me clarify. Yes, for a given sensor area, the smaller focal length scope will always provide a larger FOV. That is not in dispute.
But there are many, many instances where two scopes of different apertures can capture a desired FOV. We do not always utilize the full FOV afforded by our scopes. A good example would be M51 and its immediate surroundings. Or perhaps something like the Owl Nebula. Both fields would fit within the sensor area of either a 200 mm f/4 or a 250 mm f/4 using a 2600MM Pro camera. To achieve the same viewing size, you would crop the 200 mm f/4 image more. The effective irradiance achieved on the final image scale will be greater with the 250mm f/4 than the 200mm f/4. This is a pretty common use case for those that image dim PNs or galaxies. I mentioned this in my previous reply on why we can’t just crop down an f/2 telephoto lens, but I suppose I’ll repeat it. Yes, the larger aperture will be better, but NOT because it is brighter, only because it is more detailed. When you crop the larger data, you are losing resolution but you are not losing brightness. The irradiance per photosite is the exact same for every system with the same focal ratio, and all that a larger aperture affords you is additional detail. This is useful for small distant galaxies and such, but a small refractor of the same focal ratio will have the same brightness when pointed at that region of sky as a 1m imaging newtonian would. The difference is, the newtonian has a greater angular resolution and sampling. The effective irradiance would be the exact same, because it is quantized by the photosites and not continuous. When you crop in, you simply lose resolution and will have less detail than the larger aperture. The reason you can get more detail in the same brightness is because the higher sampling rate is accompanied by an increase in aperture. Each pixel sees less and less sky, but more and more photons are coming from the point in the sky (relatively speaking). This also breaks down a little bit for exceptionally dim objects with a photon flux of only one or two photons per minute, as at that point the aperture doesn’t really change how much light is received. In simple terms: Short focal length and small aperture means very few photons per unit area but sampling a large portion of sky per pixel, long focal length large aperture means lots and lots of photons, but sampling a very small portion of sky per pixel. It balances out exactly.
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OK… I think I am pretty much done here.
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August Norman:
Yes, the larger aperture will be better, but NOT because it is brighter, only because it is more detailed. While what you say is true, if you are viewing a given smaller object (like the Owl Nebula) on your screen at the same magnification (arcsec/pixel), the Owl Nebula from the larger aperture scope will have better S/N regardless of the focal ratio. It will also, as you say, have more detail. If you view them both at native resolution (assume same camera), yes faster focal ratio = brighter. But if you view them at equal magnification, aperture will always win (again, assuming you have exposed long enough to overcome read noise in the slower scope)
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Rick Krejci:
August Norman:
Yes, the larger aperture will be better, but NOT because it is brighter, only because it is more detailed.
While what you say is true, if you are viewing a given smaller object (like the Owl Nebula) on your screen at the same magnification (arcsec/pixel), the Owl Nebula from the larger aperture scope will have better S/N regardless of the focal ratio. It will also, as you say, have more detail. If you view them both at native resolution (assume same camera), yes faster focal ratio = brighter. But if you view them at equal magnification, aperture will always win (again, assuming you have exposed long enough to overcome read noise in the slower scope) Well that’s just the thing, they won’t have equal magnification. Longer focal length means greater magnification (fewer arcseconds per pixel) and as I have hopefully established, focal length will increase proportional to aperture. You can’t hold magnification constant for the same reason you can’t hold FOV constant, in fact they’re both the result of the exact same mechanism. If you’re talking about binning, it’s essentially a moot point. We may as well get into the pros and cons of different pixel sizes. And of course, if you mean to compare say a 100mm f/10 to a 200mm f/5, what you’re doing is holding focal length constant while increasing aperture, which will brighten the image as well as providing more detail.
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August Norman:
Well that’s just the thing, they won’t have equal magnification Do you always present every image at 100% native resolution? Sometime we resample, particularly for very long focal lengths where are are severely over-sampled, you often down-sample to make it look sharper and cleaner. If you have a presentation size and FOV in mind for a given object, the image from the larger aperture scope that still meets the presentation size and FOV will have better S/N for that presentation size, be it a print or viewing on a screen. You'll be wasting all that FOV from the smaller wider scope and cropping or sometimes up-sampling. Completely different situation for extended objects where you need the entire FOV from the smaller scope. Different tools for different situations. Trying not to get in between people talking past each other here.
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Magnification is a meaningless concept in focal imagery and I'd be vary of presenting arguments on "perceived" qualities.
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Clayton Ostler:
Am I wasting money on buying a bigger aperture scope if it is slower than my faster/smaller aperture scope? No you're not; it's generally a good investment.
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Kay Ogetay:
Steeve Body:
Well from personal experience, running tak FSQ 106 f3.6 and the 135mm lense samyang at f2.8 as a dual rig, the FSQ capture way more light than the samyang at f2.8… the samyang is I think 65mm… so aperture seems in this case to make a really big difference…
That doesn't sound right Steeve. I'm pretty sure that's what you get, but not because of the aperture. Those are two very distinct optics. Samyang doesn't give the same performance at F2.8 that Tak does give at F3.6, not to mention your pixelscale differs. It's very clear that one gets better SNR for extended objects if the F ratio is lower, not just theoretically but fair comparisons also show this. But if you are targeting faint point sources like stars, then you need aperture --hence why we have large aperture scopes for research. But we also have Dragonfly array-like ultra-fast systems for extended objects with low surface brightness.
*Actually it is quite straightforward to see how effective f-ratio increases SNR --and why it matters. Take the same two telescopes and make an array, the effective ratio is sqrt(2) times lower. But what you basically get is x2 the exposure time. It is the equivalent of exposing two times more, or you can have two of the same telescopes. Everyone agrees that two times the exposure time would give you sqrt(2) increase in SNR, but for some reason, F-ratio is still a discussion. In fact that's why they are both ~sqrt(N), because they are essentially equivalent. It's a known fact in science, hence we design things according to that.
It all depends on what you need. Both low f ratio and higher aperture for high focal length are great. It is the purpose and how you do it that matters. Hey Ogetay, Yes, on paper a lower f-ratio should collect more light per unit area on extended objects. But in real world use, why is the FSQ106 at f/3.6 consistently outperforms the Samyang at f/2.8 in the observation I have made on the same object (horsehead, orion etc...)? The images were taken at the same time with the same amount of integration time... I understand it is different pixel scale... but even with that before doing this experiment I was certain that the samyang would yield better results on faint nebulosity than the FSQ.... I'm not seeing that.... Here is what I'm seeing  |
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It looks to me like there would be a lot less arguing here if some of you guys would go watch (and understand) this presentation: https://www.youtube.com/watch?v=HiJoqQp1qFI.--particularly starting at slide #28. None of this stuff is the least bit controversial once you understand a little bit about radiometry. John
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The point both Rick and I are trying to make is shown below. - In the case of the 200 mm f/4 vs 250 mm f/4, when you use two images at native or captured resolution with a common camera, you are using equal sampling in image space. This gives the same sampling in image space. In this case, the signal is just (F2/F1)^2=1.
- But if you bin the 250 mm f/4's image (and crop the 200 mm f/4's image) to a common FOV and common resolution, you are using equal sampling in object space, which gives case 2 - S1/S2=(D1/D2)^2 -> the signal per new pixel size is 56% greater with the 250mm.
This is entirely expected from the left hand side of the first point in John's camera equation  The power captured from a fixed area dA of object only depends on aperture (for a given distance). In the second case, each pixel is representing the same object area, so the ratio of signals can only depend on the lens diameter.  |
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Hey Ogetay,
Yes, on paper a lower f-ratio should collect more light per unit area on extended objects. But in real world use, why is the FSQ106 at f/3.6 consistently outperforms the Samyang at f/2.8 in the observation I have made on the same object (horsehead, orion etc...)?
The images were taken at the same time with the same amount of integration time... I understand it is different pixel scale... but even with that before doing this experiment I was certain that the samyang would yield better results on faint nebulosity than the FSQ.... I'm not seeing that....
Here is what I'm seeing When you register and present the objects as you have here - so you have the same FOV and same resolution for the object area of interest as seen on screen - you are effectively using equal sampling in object space. This should and does result in the scope with larger aperture (the FSQ) showing the better image, exactly as predicted.
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Arun H:
Erlend Langsrud:
An F/2 telescope is 25x faster than a F/10 scope will the same focal length.
Key here is "same focal length" which means same object space sampling. So in that instance, the reason the F/2 telescope is faster is because it has 5x the aperture! The aperture is key in determining how much power is captured by the optical system.
Look at the derivation of the camera equation by John Hayes, below. Optical power, P, captured by the system from a source of radiance L and area dA is dictated purely by the aperture of the lens and the distance. The focal length then dictates how that power is translated to image plane irradiance. A 200mm f/4 and 250 mm f/4 will provide the same irradiance on the focal plane, but for different reasons. The 200 mm f/4 focuses a larger area on the same pixel size as the 250 mm f/4, but the 250 mm captures more power from a fixed angular object area than the 200mm.
A 250 mm lens will ALWAYS capture 56% more power from a given object area than a 200mm lens and this will be true regardless of f#. This gives you the ability, in post, to bin down the 250mm image to a common image scale (assuming the FOV is not lost), so you achieve a higher effective irradiance. This is the true advantage of aperture. For a given FOV and given viewing size/resolution, the larger aperture scope will always provide the better image - simply because it has captured more power from that FOV than the smaller aperture scope. And nothing you do can change that.
I don't think we disagree at all. Do we? I was about to go into formulas, but decided to just write the two simple statements which, in my opinion, says it all.
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Arun H:
Hey Ogetay,
Yes, on paper a lower f-ratio should collect more light per unit area on extended objects. But in real world use, why is the FSQ106 at f/3.6 consistently outperforms the Samyang at f/2.8 in the observation I have made on the same object (horsehead, orion etc...)?
The images were taken at the same time with the same amount of integration time... I understand it is different pixel scale... but even with that before doing this experiment I was certain that the samyang would yield better results on faint nebulosity than the FSQ.... I'm not seeing that....
Here is what I'm seeing
When you register and present the objects as you have here - so you have the same FOV and same resolution for the object area of interest as seen on screen - you are effectively using equal sampling in object space. This should and does result in the scope with larger aperture (the FSQ) showing the better image, exactly as predicted. it looks exactly the same without the 135mm being star aligned to the FSQ. here I'm just trying to make the comparison easier
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Erlend Langsrud:
I don't think we disagree at all. Do we?
I was about to go into formulas, but decided to just write the two simple statements which, in my opinion, says it all. We don't disagree. But I don't think it directly answers the question the OP posted, and probably neither do any of the other answers, including mine. That's probably why 20% of people still are not sure and there is still confusion, so here is a simple Yes/No answer. The OP asked: Can larger aperture offset a slower scope vs a faster scope?The answer is: Yes, it can. Provided you use large enough pixels with the larger aperture scope (natively or through binning/resampling) .You would have to ensure that the FOV you desire is captured in your sensor area, but if it is, then appropriate choice of pixel size will result in the larger aperture scope outperforming the small scope even if the small scope has lower f#, for the same presented image. The details of why this works I cannot explain any better than John has already explained in his video and I will not try.
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Steeve Body:
Kay Ogetay:
Steeve Body:
Well from personal experience, running tak FSQ 106 f3.6 and the 135mm lense samyang at f2.8 as a dual rig, the FSQ capture way more light than the samyang at f2.8… the samyang is I think 65mm… so aperture seems in this case to make a really big difference…
That doesn't sound right Steeve. I'm pretty sure that's what you get, but not because of the aperture. Those are two very distinct optics. Samyang doesn't give the same performance at F2.8 that Tak does give at F3.6, not to mention your pixelscale differs. It's very clear that one gets better SNR for extended objects if the F ratio is lower, not just theoretically but fair comparisons also show this. But if you are targeting faint point sources like stars, then you need aperture --hence why we have large aperture scopes for research. But we also have Dragonfly array-like ultra-fast systems for extended objects with low surface brightness.
*Actually it is quite straightforward to see how effective f-ratio increases SNR --and why it matters. Take the same two telescopes and make an array, the effective ratio is sqrt(2) times lower. But what you basically get is x2 the exposure time. It is the equivalent of exposing two times more, or you can have two of the same telescopes. Everyone agrees that two times the exposure time would give you sqrt(2) increase in SNR, but for some reason, F-ratio is still a discussion. In fact that's why they are both ~sqrt(N), because they are essentially equivalent. It's a known fact in science, hence we design things according to that.
It all depends on what you need. Both low f ratio and higher aperture for high focal length are great. It is the purpose and how you do it that matters.
Hey Ogetay,
Yes, on paper a lower f-ratio should collect more light per unit area on extended objects. But in real world use, why is the FSQ106 at f/3.6 consistently outperforms the Samyang at f/2.8 in the observation I have made on the same object (horsehead, orion etc...)?
The images were taken at the same time with the same amount of integration time... I understand it is different pixel scale... but even with that before doing this experiment I was certain that the samyang would yield better results on faint nebulosity than the FSQ.... I'm not seeing that....
Here is what I'm seeing Steve, 1) Comparing stretched images isn't how you compare signals. You have to look at the actual ADU values for pixels that are looking at the same points in object space. 2) You have to use identical cameras with identical pixel size and responsivity. 3) You have to take into account the throughput of the optical system. That includes the transmission factors for each surface. It's important to understand that it is totally possible to have a very fast objective that has a lot of elements with poor coatings producing a lower signal than a slower system with fewer components that have very high performance coatings. This is one reason that the Dragonfly systems focus on getting lenses with the highest possible transmission. The equations that I provided in my presentation allow for differences in transmission factors. John
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Ok, I will try to make my two cents on this one. I've noticed almost everyone responding about technical questions about the telescope/camera/f.ratio etc. But reality lies in the physics and particulairly in the photometry which is the only doninant and only factor in our case. Sice we are using sensors that doesn't have the "reciprocity failure or Swartzchild effect" we can assume we are collecting energy in a linear way (and this is the only reason we can make statistics and math on multiple and even different exoposure to increment the SNR). First of all you have to think in angles of sky that You are sampling on a single "pixel". Having two systems that have different focal lenght but the same sensor (reguardless the FOV) is not a valid example to take into consideration. You MUST refer to the same ANGLE of sky sampled per pixel. This means that on a telescope whith shorter focal lenght You will have a greater angle of sky sampled at pixel level, for doing a "real" comparison You should have a longher focal lenght scope coupled with a bigger pixel in order to accomplish the same sampling angle of sky for doing any comparison. In fact tha photometry of an angle of considered sky contain more energy that a smaller angle of the same source, conseguently there are less photons to be captured in time. Photometry in fact is the measured flux of photons on a given angle in time. Having a "fast" f ratio nowdays is a wrong statment in terms, it is much better to say a wide field scope. The f ratio "fastness" is in fact a myth deriving from the old emulsion in which the reciprocity failure was a real problem. With modern sensors that uses the photoelectric effect is no more true in fact, since they are linear in acquiring the datas up until they're maximum capacity of contain a charge, is not important at all the time You need to fill the well. In old days we had to deal with density of a 3d media such as the emulsion, nowdays we work with a bidimensional matrix which is not affected by time of acquisition. We must stop thinking We are taking "pictures" and start thinking We are making measurements instead. Our intent is to measure the photometry of a given angle with as much precision possible and everything that is not part of that exact measurement is the NOISE. In digital in fact, everything that is uncertain becouse of the limits of precision in the measurement we have, is the NOISE. Talking about SNR means only that, what is certain Vs. what is uncertain. The professionals talks about "confidence grade" I.E. a confidence grade of 3 means that the acquired measure is almost 3 times bigger than the uncertain measurement. We so have to underestand what kind of error (NOISE) we are going to have during a measurement and they are indeed of various kind. To us simple photographers we havo to think about the one that is by far the most relevant one and is part of the many that are in the category of SHOT NOISE and is indeed the SKY NOISE. The sky noise is mostly due to light pollution, scattering, seeing etc and is not under our control but, we are lucky enough to say that is a RANDOM noise so it accumulates in a non linear fashion. Consider the reality and not the tech data, where do You think there is more sky noise, in a 1 degrre field or in a 5 degree field? It is very intuitive to say that in a 5 degree angle there is much more sky noise that in the 1 degree field. Considered this imagine you have a system that sample 1 degree per pixel with an f3 system and a f8 system, in a shot of 30" on which one You think You acquire more noise? Now think at the signal You want to measure on the same angle that has a "fixed" photon flux of 1000 photons per second, how many photons will You acquire in a 30" exposure with the same system with no errors? You could be tempted to say 1000*30 is 30000! But no it is not true becouse the distribution of photons is not linear! The flux is constant but the distribution is POISSON and so You will have one exposure that could be 28000 and the next could be 32000 on the same pixel. This means that a "faster f ratio system" acquires the data "faster" about the linear flux BUT the same is true for the SKY NOISE so the final SNR is the same! We are not trying to increase the signal but the SNR so, on the same considered angle of sky measured, the only thing that can increase that SNR in the same amount of exposure time is related to the cahance of capturing that fixed flux and the only way to do so is to have a large collecting area. A fast f ratio system is indeed faster at acquiring that flux ONLY on a considered angle that is equal to 0 but, since we are not able to consider an angle=0 there is no advantage in having a faster filling the pits system reguard the SNR respect to a "slower" one. I repeat that this is true only on an equal considered angle sampled since, changing that angle, will also change the photometry (the total energy present) of that angle of sky. Think at a small planetary nebula that is 10 mag in 4" of arc and a huge 1 degree galaxy that also is 10 mag, which one is easier to get a good SNR using the same system? You will for shure have a clear image of the nebula since the total energy is emitted in a smaller angle while the galaxy enit the same energy on a much greater angle so, having a sample rate of I.e. 1"/pix We will have much more energy per pixel in the nebula than in the galaxy synce the magnitude is represented as a 0degree angle and is the same for both subjects. I realize I've already written a small bible here…  In conclusion, on a linear acquisition device such has a CCD or CMOS, f ratio will not change the SNR on a giveng angle sampled that must be equal in both system, the only thing that will improve SNR on the same angle is the chance to acquire more photon flux and is the collecting area of the system. Hope this helps to clarify and not confuse more… Sorry for the many typo errors You will find…
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Giovanni Paglioli:
Ok, I will try to make my two cents on this one. I've noticed almost everyone responding about technical questions about the telescope/camera/f.ratio etc. But reality lies in the physics and particulairly in the photometry which is the only doninant and only factor in our case. Sice we are using sensors that doesn't have the "reciprocity failure or Swartzchild effect" we can assume we are collecting energy in a linear way (and this is the only reason we can make statistics and math on multiple and even different exoposure to increment the SNR).
First of all you have to think in angles of sky that You are sampling on a single "pixel". Having two systems that have different focal lenght but the same sensor (reguardless the FOV) is not a valid example to take into consideration. You MUST refer to the same ANGLE of sky sampled per pixel. This means that on a telescope whith shorter focal lenght You will have a greater angle of sky sampled at pixel level, for doing a "real" comparison You should have a longher focal lenght scope coupled with a bigger pixel in order to accomplish the same sampling angle of sky for doing any comparison. In fact tha photometry of an angle of considered sky contain more energy that a smaller angle of the same source, conseguently there are less photons to be captured in time. Photometry in fact is the measured flux of photons on a given angle in time. Having a "fast" f ratio nowdays is a wrong statment in terms, it is much better to say a wide field scope. The f ratio "fastness" is in fact a myth deriving from the old emulsion in which the reciprocity failure was a real problem. With modern sensors that uses the photoelectric effect is no more true in fact, since they are linear in acquiring the datas up until they're maximum capacity of contain a charge, is not important at all the time You need to fill the well. In old days we had to deal with density of a 3d media such as the emulsion, nowdays we work with a bidimensional matrix which is not affected by time of acquisition. We must stop thinking We are taking "pictures" and start thinking We are making measurements instead. Our intent is to measure the photometry of a given angle with as much precision possible and everything that is not part of that exact measurement is the NOISE. In digital in fact, everything that is uncertain becouse of the limits of precision in the measurement we have, is the NOISE. Talking about SNR means only that, what is certain Vs. what is uncertain. The professionals talks about "confidence grade" I.E. a confidence grade of 3 means that the acquired measure is almost 3 times bigger than the uncertain measurement. We so have to underestand what kind of error (NOISE) we are going to have during a measurement and they are indeed of various kind. To us simple photographers we havo to think about the one that is by far the most relevant one and is part of the many that are in the category of SHOT NOISE and is indeed the SKY NOISE. The sky noise is mostly due to light pollution, scattering, seeing etc and is not under our control but, we are lucky enough to say that is a RANDOM noise so it accumulates in a non linear fashion. Consider the reality and not the tech data, where do You think there is more sky noise, in a 1 degrre field or in a 5 degree field? It is very intuitive to say that in a 5 degree angle there is much more sky noise that in the 1 degree field. Considered this imagine you have a system that sample 1 degree per pixel with an f3 system and a f8 system, in a shot of 30" on which one You think You acquire more noise? Now think at the signal You want to measure on the same angle that has a "fixed" photon flux of 1000 photons per second, how many photons will You acquire in a 30" exposure with the same system with no errors? You could be tempted to say 1000*30 is 30000! But no it is not true becouse the distribution of photons is not linear! The flux is constant but the distribution is POISSON and so You will have one exposure that could be 28000 and the next could be 32000 on the same pixel. This means that a "faster f ratio system" acquires the data "faster" about the linear flux BUT the same is true for the SKY NOISE so the final SNR is the same! We are not trying to increase the signal but the SNR so, on the same considered angle of sky measured, the only thing that can increase that SNR in the same amount of exposure time is related to the cahance of capturing that fixed flux and the only way to do so is to have a large collecting area. A fast f ratio system is indeed faster at acquiring that flux ONLY on a considered angle that is equal to 0 but, since we are not able to consider an angle=0 there is no advantage in having a faster filling the pits system reguard the SNR respect to a "slower" one. I repeat that this is true only on an equal considered angle sampled since, changing that angle, will also change the photometry (the total energy present) of that angle of sky. Think at a small planetary nebula that is 10 mag in 4" of arc and a huge 1 degree galaxy that also is 10 mag, which one is easier to get a good SNR using the same system? You will for shure have a clear image of the nebula since the total energy is emitted in a smaller angle while the galaxy enit the same energy on a much greater angle so, having a sample rate of I.e. 1"/pix We will have much more energy per pixel in the nebula than in the galaxy synce the magnitude is represented as a 0degree angle and is the same for both subjects. I realize I've already written a small bible here... 
In conclusion, on a linear acquisition device such has a CCD or CMOS, f ratio will not change the SNR on a giveng angle sampled that must be equal in both system, the only thing that will improve SNR on the same angle is the chance to acquire more photon flux and is the collecting area of the system.
Hope this helps to clarify and not confuse more... Sorry for the many typo errors You will find... a few paragraphs would have helped too ;-)
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I was not reading this entire thread of responses but I would suggest the initializer of this question to first study here: https://telescope-optics.netThe question is irrelevant because it suggests to compare apples with grapes. Do also keep in mind that there is a huge difference between resolution-limited optics and diffraction-limited optics.
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