'Fast' scopes and exposure time.

[Merlin66]

Here are three pages from "Tools of the Astronomer", p108-110.

Read these through a couple of times. The references to film should obviously now be replaced with CCD, but the message is the same.

HTH

[robbieince]

It's a popular misconception to say a shorter focal length scope pulls in more photons than a longer focal length scope of the same diameter.

Light from the sky is essentially parallel rays and so the amount of light coming in is purely limited by aperture.

It's the job of the mirror or lens to take these parallel light beams and bring them to focus. It's the size of this focal Image that decides of the scope is fast or slow.

Regards

Rob

[Jessun]

Light from the sky is essentially parallel rays and so the amount of light coming in is purely limited by aperture.

That would mean that your lens would have to be a couple of hundred thousand lightyears across to do a nice M31... ;-)

To get a 5 degree field of view the rays coming in have at the extreme a 5 degree difference in angle. To watch 10 degrees of the sky the angle widens to 10. And more light comes in to reach focus.

(A small very short F fish eye lens can collect some 180 degrees of the sky and collect well, half the light in the visible universe. Nothing parallel here. Now use the same tiny aperture to build a pocket size F10 telescope - it will only look at a tiny fraction of the sky and be very dark indeed to use...)

The parallel rays are from diagrams that I'm guessing only for convenience show parallel rays bend to reach focus. But that same lens also at least nearly brings to focus rays collected at an angle, and that's what makes them useful for photography etc. The optical errors typically gets worse towards the edges AFAIK though.

And sure; two lenses of the same aperture regardless of what focal length scope they are about to go into are stricktly speaking hit by roughly the same ammount of photons if held up next to eachother. But this includes all stray light too - light from acute angles that cannot be focused, and we're only interested in focused light. We're not talking about areas of solar panels here...

Move the focuser in and out of focus and you'll see some of this stray light in the blurr, it's all there - just not focused. Most of it has hit the inside of the tube and some will only just miss the CCD or eye piece.

Interesting discussion, and I don't mind being wrong btw if that will be the ultimate outcome :-P

/Jesper

[dph1nm]

Ah, this is our old friend the f-ratio myth again. I think the term 'fast' should be banned from telescope discussions!

Aperture determines how many photons you get - a galaxy image will be formed of the same number of photons in the same exposure time in an f2 scope or an f8 scope of the same aperture.

So if you presented both images at the same resolution they would be identical in depth!

The idea that f2 is 'faster' comes from the fact that by default the resolution is much lower than at f8 - this makes the image appear brighter because the pixels are much bigger. But remember, you could always take the f8 image, decrease the resolution, and thus produce an identical image to that from the f2 scope! So in what sense is f2 'faster'?

NigelM

[dph1nm]

Sure, on the chip a galaxy for instance appears smaller, but this means it's also brighter.

What exactly do you mean by 'brightness'?

It's total brightness will be the same (same number of photons).

It's surface brightness per square arcsecond will be the same.

It's surface brightness per square mm will have changed - so what?

NigelM

[Jessun]

NigelM I don't think it's a myth at all, I believe it to be true!

OK, fill a huge wall with light bulbs arranged to match the pixel pattern of your scope and camera. At some distance you will have one bulb in each pixel on the chip. And the chip will count the photons from one bulb per pixel.

Now change the lens in the scope to a shorter F lens; same aperture. To reach focus the chip naturally needs to travel a loooong way in the scope, and once in focus you will conclude that you are looking at a much bigger section of the wall - this is simple optics - and you'll find that each pixel now recieves the light from not one bulb but a few. You cant see it visually within the pixel if it's looking at one bulb or many but you can certainly read out the photon count, and it's counting proportionally faster per pixel.

Sure, detail is lost, no longer can you distinguish each bulb and pinpoint it by say switching it off. Whereas the first scope will have one black pixel, the second scope will have a mere drop in photon count, could be any one of a handfull of bulbs that was turned off. Something got dimmer in that region of the wall.

Saturating the chip with photons is quicker with the second scope. Go extreme and go F stupidly low and the wall of bulbs will shrink in view to the very central last pixel, but this pixel will overflow very quick indeed, and so you can image the wall lightning fast very very bright - only pin ***** small and well, useless perhaps :-)

So I'd say a short F-ratio is fast in that respect.

What is interesting with aperture on the other hand is when looking at how each bulb behaves - or each star. Sure a bigger lens will be hit by more photons from each bulb, as they spread their light evenly in all directions, so a bulb sends out photons at different angles to hit the full lens and the lens focuses these photons nicely. Just changing to a bigger lens though for the same F-ratio means it is now looking at fewer bulbs (simple field of view calculation), so the total photon count remains the same - as does the percieved speed. You merely get more photons from each bulb but collected but from a smaller patch of the wall - and this evens out any aperture change.

Counting photons, think of each bulb on its own - aperture good, the whole wall - F-ratio good. There is no conflict in this.

/Jesper

[Jessun]

only pin ***** small

How clever of me...

[Ags]

I think we are introducing too many variables - aperture, f ratio, chip size etc.

I don't think we are all talking about the same thing.

If you say that a faster scope puts more photons on a given chip, that is true assuming the entire field is illuminated.

But if you take a pitch black sky and a little galaxy, a scope with larger aperture will put more photons from that galaxy onto the chip.

The difference is that the slower scope makes a larger image of the galaxy relative to the amount of light it has captured, so less light falls on each pixel, even though the total number of pixels getting galaxy photons is greater.

[Jessun]

I think we are introducing too many variables - aperture, f ratio, chip size etc.

That's why this subject is confusing. Above I at least tried to keep it simple to start with, one chip, one aperture, just a lens change. The scope gets longer or shorter just out of necessity to reach focus with a particular lens/mirror.

If you say that a faster scope puts more photons on a given chip, that is true assuming the entire field is illuminated.

Yes that's true.

But if you take a pitch black sky and a little galaxy, a scope with larger aperture will put more photons from that galaxy onto the chip.

Yes naturally, it's going towards the pin point case or single bulb above. How much light is collected from each bulb. The ones that are in view that is. Bulbs out of view due to "zooming" are lost photons... It's just hard to explain that this evens out for the same f-ratio as aperture changes. Two same length exposures look equally good from two scopes with the same f-ratio but different aperture.

The difference is that the slower scope makes a larger image of the galaxy relative to the amount of light it has captured, so less light falls on each pixel, even though the total number of pixels getting galaxy photons is greater.

Well, I think we fully agree, we just perhaps express it differently to suit our struggling minds :-)

It's really helpful to play with a FOV calculator, and change the values around, one at a time perhaps haha.

/Jesper

[ollypenrice]

Precisely wrong ;-). The faster one is looking at more sky, at a wider field of view so draws more photons from that bigger region. And this wider field picture of the fast scope is still crammed into the same image chip, so each pixel is bombarded with photons from more sky and thus the resulting picture gets bright quicker.

Sure, on the chip a galaxy for instance appears smaller, but this means it's also brighter.

/Jesper[/quote

How does the objective know what the focal ratio behind it is? It doesn't. An aperture of X collects Y photons and focal ratio does not affect that at all. An aperture of 2X collects 4Y photons and an aperture of 4X collects a gleeful 16Y photons.

Now, what do we do with those photons? Do we make a bright widefield image or zoom in on only a part of it and make a dimmer close-up? This is what your point addresses. At a fixed aperture the close up is achieved by increasing the focal length. However, photons collected is proportional only to aperture.

In discussing this topic I find it best to treat F ratio as a secondary effect, which it is. The primary players are aperture and focal langth.

Take 2 scopes of a metre FL. They will take the same picture as each other. One has twice the aperture, so four times the area of objective, so it collects four times as many photons and takes a quarter as long to get the same result. Dead easy.

Olly

[Jessun]

How does the objective know what the focal ratio behind it is? It doesn't

It does indeed; it can work it out by pondering over its own curvature right there on the factory table. Or to be more precise its narrow acceptable focal length range...

An aperture of X collects Y photons and focal ratio does not affect that at all. An aperture of 2X collects 4Y photons and an aperture of 4X collects a gleeful 16Y photons.

Yup, true for each lighs source but the f-ratio determines the FOV and thus how many light sorces you bring in focus.

The primary players are aperture and focal langth

All three kinda linked as in a triangle, you tweak one the other two have to budge.

/Jesper

[Jessun]

Take 2 scopes of a metre FL. They will take the same picture as each other. One has twice the aperture, so four times the area of objective, so it collects four times as many photons and takes a quarter as long to get the same result. Dead easy.

Missed this one, yes of course Olly, spot on, but notice f-ratio halved on one of them. The small F-ratio one is faster for the same patch of sky! That brings us to the point of the "myth" that F ratio can translate to speed. Looking at that number alone on any scope will tell you what kind of exposure time you'd expect to use with one of your trusty ATIKs. For field of view you may need a pen and paper. Well I sure do!

You know this inside and out Olly I am sure. Different approaches again,

/Jesper

[Moonshane]

I'm just gonna look through my newt.......my brain aches!

[ollypenrice]

The dreaded F ratio myth arises when you start talking about different pictures as if they were the same picture. A widefield picture with a galaxy in it is not the same as a close up of just the galaxy. So I try to insist upon talking about the same picture (ie I want to fix the focal length.) If you fix the focal length and then consider two apertures, large and small, it would be plain nuts not to call the large one fast and the small one slow. Equally it would be nuts, at a fixed aperture, to say 'I will shorten my focal length, so speeding up my F ratio, so I can get the same result faster.' All you'll get is a smaller galaxy. Blow it up on the screen and it will get dimmer (and more blurred).

Whether anyone ever really believed in the F ratio myth is an interesting question. I think it's a straw man, quite honestly. Did anyone ever really think that by shooting at a quarter of the image scale for a quarter of the time that they'd get the same result? I doubt it.

Olly

[Jessun]

Hmm... figured I'd throw in another thought.

What's interesting and quite different about F number is that is has no unit. It just describes a relationship of two other real numbers, and as such it is transferable between lenses to compare their optical power - what has been asked of a lens to do at the drawing table. Is it very curved and refracting a lot? Or rather flat? The answer is hidden in the universal F-number. For scopes that is...

I for one believe that two F8 scopes regardless of size will fill the same chip with the same ammount of photons in the same time. Two F5 copes will match eachother but will fill that same chip with the same number of photons faster.

It works well for me to get to grips with this trinity that is aperture/focal length/the relationship between the two.

This is not at all a shot at "result" as such. No one thinks you get the same "result" on the screen faster with a fast scope. I am merely counting total ammount of photons coming in from anywhere in space, landing anywhere on the chip. Going to the bottom with the very expression FAST. A messy blurr can be rather fast indeed!

I think Olly that we actually agree on the nuts and bolts here given a white board and a few pens, we just have a different take on that triangle.

/Jesper

[CanesVenatici]

Hmmm,

Must admit I am still reading around trying to understand all this, but there is plenty of material around arguing that what Olly called the 'F ratio myth' is just that, and that the reason a 'fast', smaller aperture scope is usually preferred for imaging has a lot more to do with other factors. For example, those pages that Merlin posted up state that such a scope will record fewer feint stars and make the star images less dominant in the image. A small refractor will also suffer less of off-axis aberrations.

This page appears to contain some pretty authoritative information:

Aperture, f-ratios, myths, etc. | Ask Craig | Stark Labs

If we keep the aperture constant and change the f-ratio by somehow scaling the focal length (reducing or extending it), we’re not changing the total number of photons hitting our detector from a given DSO. As Stan Moore and others have pointed out on pages like the one dedicated to the “f-ratio Myth”, it is the aperture alone that determines how many photons we gather from a DSO. If you imagine your scope to be a bucket, catching photons streaming across space, it should be obvious that the bigger a bucket you have, the more photons you get. Period. No ifs, ands, or buts as it were.

This same page also notes that:

Running at a larger f-ratio for a given aperture means that you are spreading the light over more pixels. Thus, each pixel is getting less light and so the signal hitting that pixel is less. Some aspects of the noise (e.g., read noise) will be constant (not scale with the intensity of the signal the way shot noise does). Thus as the signal gets very faint, it gets closer and closer to the read noise.

This seems to directly relate to what I suggested about a 'faster' scope effectively magnifying / 'spreading out' the image less than a slow scope. Even here the advantage of a faster scope is due to the way the less magnified image reduces the number of pixels used to capture the object, so allowing the signal to stand out better from the background noise, including that produced by the detector chip itself. Nothing to do with a 'faster' scope magically capturing more photons than a slower scope of the same aperture!

Er, I think!

[CanesVenatici]

P.s. It also seems that, from a visual observing perspective, that a 'fast' scope will NOT give a brighter image than a 'slow' scope, assuming that eyepieces are chosen that give the same exit pupil diameter for each scope.

[Jessun]

I agree with all of the above. Different way again to write things.

But the f-ratio can be used to compare all telescopes in how fast they saturate a chip, or indeed a pixel on that chip. It also tells us how far the optics is pushed, gives a hint of how accurate collimation and focus has to be etc. It's a useful number in many ways.

And again a fast scope will produce an image of a DSO faster - saturating the pixels actually containing the DSO - the penalty being lost resolution. And the loss of resolution is substantial.

Keep the same eye piece and between two scopes with same F-ratio and I still argue that the they will be the same it terms of light regardless of the resulting FOV.

/Jesper

[Jessun]

And if I did not agree I would be the one having to rethink, certainly not Mr Stark.

/Jesper

[ollypenrice]

P.s. It also seems that, from a visual observing perspective, that a 'fast' scope will NOT give a brighter image than a 'slow' scope, assuming that eyepieces are chosen that give the same exit pupil diameter for each scope.

Yes, in visual observing you are interested in effective focal ratio (scope and EP combined) and in whether or not the exit pupil of a given combination will fit into your eye! How you arrive at a given effective focal ratio/exit pupil (in terms of jiggling EP/scope combinations) does not matter in principle. In practice it will cost you more to make up a system of quality 'x' if you go for a fast scope. Slow optics are easier to make, dramatically so in the case of refractors.

Olly

[dph1nm]

Whether anyone ever really believed in the F ratio myth is an interesting question. I think it's a straw man, quite honestly. Did anyone ever really think that by shooting at a quarter of the image scale for a quarter of the time that they'd get the same result? I doubt it.

Unfortunately, yes - I have even seen people, when discussing the this f-ratio question, claim that professionals use 8m telescopes just to increase the resolution, not to go deeper, because its only 'f-ratio that matters not aperture'.

NigelM

[dph1nm]

From my point of view what matters for speed is the aperture of the scope and the final scale you display the image at in term of arcseconds per resolution element. This may or may not be the same as the pixel scale of your detector, because you can bin-up images either in hardware or software. So all of these scope-camera combinations would give the identical image of a galaxy in the same exposure time

8" f16 20um pixels

8" f8 10um pixels

8" f4 5um pixels

8" f2 2.5um pixels

8" f16 5um pixels binned 4x4

8" f8 5um pixels binned 2x2

You could not get the same image in the same time with ANY 4" scope.

NigelM

[Jessun]

NigelM,

Unfortunately, yes - I have even seen people, when discussing the this f-ratio question, claim that professionals use 8m telescopes just to increase the resolution, not to go deeper, because its only 'f-ratio that matters not aperture'.

This is not a sign of believing in a "myth", it's a display of lack of understanding of f-ratio.

I think everytime you come across something in formulas that has no unit it deserves special attention, constants too for that matter like pi. No one would call pi a myth really. Mach number in aviation is one close to my field of work, it has no unit and does not tell you at all how fast you are flying - it gives you a relationship and if you understand this relationship you can immediately draw conclusions from a Mach number, it tells you something vital.

Another simple one can be the ratio between tire wall and width of the tire. It's a variable without unit but just looking at that number for any sized wheel you can determine how good will it be for going round a tight corner. The big tire is an a big car and the small on a small car; it still gives you that hunch how it will perform cornering. Transferable information.

Stupid examples perhaps but still similar in how widely used they are for their particular field of application.

F-ratio is that gem for optics - at least very simple optics as we are dealing with. Might be plenty more advanced stuff, it's not important for us though.

8" f16 20um pixels

8" f8 10um pixels

8" f4 5um pixels

8" f2 2.5um pixels

8" f16 5um pixels binned 4x4

8" f8 5um pixels binned 2x2

I don' doubt that one bit.

You could not get the same image in the same time with ANY 4" scope.

Not sure what you mean by image here. Size, saturation FOV?

Anyways, lets take some more images! You have two scopes, an F10 and F5. Lets have them both with the same aperture (Not that it matters actually - I'll return to that...)

Take the F10 an put your camera in there, do a nice long exposure of Strawman galaxy that fits neatly around the centre of your image and put it on your computer screen.

Now take the same camera and put it in your F5 scope, do the same exposure, and Strawman galaxy is much smaller but will be way to bright! Do half the exposure; still too bright, do a bit less than half (can't from the top of my head remember the exact formula) but hey there it is now showing a similar nice exposure as the previous image on your computer screen.

OK, put the second image next to the first, do that fancy Windows7 throw of one picture left and one right. Now zoom in on the small one so it grows to the same size as the big Strawman.

They are both same size and your F10 Stramwan looks marvellous with all the intricqte detail, whilst F5 strawman looks really pixellated, blocky and reveals less detail.

Leave them on the screen and take a few steps back, then a few more... At some point, maybe 10 or 15 meters away (You're in the kitchen now...) the resolution of your eyes come into play and you hit max and beyond. Now looking back at the two Strawman galaxies you cannot tell one from the other. They are identical to your struggling eyes. Yet you know for a fact one of the images was taken using less than half the exposure time! It was taken in a Fast scope. Short F-ratio equals fast image - the myth is finally punctured. Strawman is real and doing fine! And you've come full circle with any resolution questions too.

Back at the computer screen the sacrifice is all too obvious, no detail, can't do big print etc of F5 Strawman but the principle of fast should become clear. Then you think about binning... isn't that just a version of what you just did, sacrifice one parameter to gain another! Clump more photons into one pixel by optics, or leave the optics and make pixels into one bigger is two sides of the same penny. Well someone did think about this and binned the first time! Then perhaps bin R and G and B to gain speed and then L to give back some of the lost detail...

This is just an example how you can throw all parameters around, it's all linked of course, and matching combinations as you mentioned NigelM are endless really.

Pixels are confusing and for f-ratio perhaps add no insight as I tried to bring in previous posts, I failed a bit there. So lets get rid of them. A telescope brings photons to focus on a focal plane - typically a somewhat bent imaginary plane back in the focuser tube. What you put there is not important to understand F-ratio. Put a piece of paper, an eypiece, an old 35mm film, or your lucky penny, there are your photons nicely brought to focus.

The beauty of F-ratio is that if you use the penny for instance, put it in your little F5 scope it will be hit by x ammout of photons per second. Move it around the centre and it looses illumination. Only one and a bit could perhaps get illuminated. Now go to the local massive super 3 metre telescope downtown and stick your penny to the focal plane, a quick glance on a plate on the scope reveals F5; and could you count them again you'll find that the penny collects x ammount of photons again per second. The same x! These telescopes have something in common! The F-number, no unit, is the same and MEANS something and it means just this! The telescopes speed at which it collects photons to a specified area on the focal plane; Same CCD in both or your lucky penny!

This is not perhaps crucial to understand but it's quite an Aha! when the penny drops. Right up there with the first clue how a GE mount works etc. It's good and useful as a reference between scopes.

Finally you shout but what about APERTURE! Three metres of it you said! Come on! More light surely than the measly one you used for Strawman galaxy!

Well it's all there. All you need is a bag of many more pennies, and you put them next to eachother like a honeycomb on the focal plane, tens of them in wider and wider circles. They are all illuminated! They are all in focus, they all receive the same ammount of photons as your lucky penny, and they form what could be turned into a really big high resolution image should you so wish. Aperture shows why it's really the king in collecting photons. Just not photons per second per area unit on the focal plane - the one really interesting thing about your exposure time for whatever device you use to image. That key is held by the F-number. That is all it does, but it's cool enough to be stamped on every telescope.

/Jesper

[ismangil]

Yes, in visual observing you are interested in effective focal ratio (scope and EP combined) and in whether or not the exit pupil of a given combination will fit into your eye! How you arrive at a given effective focal ratio/exit pupil (in terms of jiggling EP/scope combinations) does not matter in principle. In practice it will cost you more to make up a system of quality 'x' if you go for a fast scope. Slow optics are easier to make, dramatically so in the case of refractors.

Olly

For visual, on another thread, the issue of 'contrast' and how it relates to human eye is discussed. And how magnification affects contrast.

Best not to go there for now :-)

[Black Knight]

I've only been a member here for a year and a half, but I've seen this discussion come up often in that time, and I'm still not sure I really understand it. After each discussion I think I've finally "got it". And then after a few days I go and forget it! I feel like Homer Simpson - every time I learn something new I have to forget something else to make room in my head!

Please can we have a good simple explanation so I can staple it to my forehead?