Focal length and Focal ratio - test my sanity

[rogerg (Roger)]

Ok, I need a sanity check...

I'm convinced I understand focal length & focal ratio correctly but often people just don't believe me, largely due to the mentality that "bigger scope gives brighter image". I have had this debate with many amateur astronomers over the years. So, here goes and please tell me if I'm wrong...

I am talking photographic only - not visual.

Take a 8" SCT:
- focal length: 2000mm
- focal ratio: f/10

Take a 12" SCT:
- focal length: 3048mm
- focal ratio: f/10

If the same star were photographed in both, with all other things being equal (same camera, same viewing conditions, etc) then the same star would appear the same brightness (pixel brightness values would be the same) between the two scopes for the same star photographed. The magnification/resolution/field-of-view would be different (the 12" would show a smaller FOV due to the longer focal length) but the same star would in fact have the same pixel brightness. This is because they are both F/10.

Then, let's add a reducer to the 8":

Take a 8" SCT @ F/4:
- focal length: 800mm
- focal ratio: f/4

Take a 12" SCT:
- focal length: 3048mm
- focal ratio: f/10

Now in the above case, the same star photographed in both will have a higher pixel brightness in the 8" because the focal ratio is F/4 vs the F/10 of the 12". So, even though the 12" is a "bigger scope" if the resolution of 800mm is sufficient to identify the given star the 8" at F/4 will actually provide a brighter image of the given star.

If I'm wrong, then my whole understanding of my camera lenses and telescopes is potentially wrong and I should give up photography right now

But... just checking?!???

Thanks,
Roger.

[multiweb (Marc)]

Originally Posted by rogerg

Take a 8" SCT:
- focal length: 2000mm
- focal ratio: f/10

Take a 12" SCT:
- focal length: 3048mm
- focal ratio: f/10

If the same star were photographed in both, with all other things being equal (same camera, same viewing conditions, etc) then the same star would appear the same brightness (pixel brightness values would be the same) between the two scopes for the same star photographed.

My understanding is that the star would be brighter in the larger aperture scope (12" SCT) for the same F/ratio. But because the FL is greater in the 12" at F/10 the image scale (using the same camera) decreases dramatically and that's a difference in signal per pixel because star light is spread over multiple wells on the CCD rather than less so your CCD is in essence less sensitive and you get a darker picture although more light makes it in with the 12".

Originally Posted by rogerg

Then, let's add a reducer to the 8":

Take a 8" SCT @ F/4:
- focal length: 800mm
- focal ratio: f/4

Take a 12" SCT:
- focal length: 3048mm
- focal ratio: f/10

Now in the above case, the same star photographed in both will have a higher pixel brightness in the 8" because the focal ratio is F/4 vs the F/10 of the 12". So, even though the 12" is a "bigger scope" if the resolution of 800mm is sufficient to identify the given star the 8" at F/4 will actually provide a brighter image of the given star.

Yes the F/4 will be faster. It won't collect more light than the 12" but at 800mm FL you've more than doubled your image scale so you focus more star light into single wells and get a brighter picture.

When it comes to star light I've always understood the rain analogy. If it's raining down and you hold a bucket next to a glass for 1 min then aperture wins. Always.

That's pretty much it (I think). Maybe some one can chime in and confirm (or not)

[Terry B]

The focal ratio is less important for stars than for extended objects.
For the same exposure the 12" scope at f10 will show dimmer stars than the 8" scope at f10. For bright stars it makes less difference as they spread over more pixels.
If this wasn't the case there would be no point to the large professional scopes

[rogerg (Roger)]

Originally Posted by Terry B

The focal ratio is less important for stars than for extended objects.
For the same exposure the 12" scope at f10 will show dimmer stars than the 8" scope at f10. For bright stars it makes less difference as they spread over more pixels.
If this wasn't the case there would be no point to the large professional scopes

Well surely the point of a larger scope is you have higher resolution at a reasonable focal ratio - you have that longer focal length but at something useable rather than F/32 or such.

If a 12" at F/10 were to record brighter stars than a 8" at F/10 then why does a 200mm F/2.8 lens record brighter stars than a 200m F/4?
... edit, let me correct that to a better comparison where I'm not mixing aperture and focal length:
If a 12" at F/10 were to record brighter stars than a 8" at F/10 then why does a 60mm (aperture) lens @ F/2.8 record brighter stars than a 60m (aperture) lens @ F/4?
... edit(2) ... hmm, ok ... may have to answer my own question here. The lens would stop down the aperture, hence changing it from 60mm to something smaller (50mm say)

I'm going to have to think about this some more

[multiweb (Marc)]

Originally Posted by rogerg

Well surely the point of a larger scope is you have higher resolution at a reasonable focal ratio - you have that longer focal length but at something useable rather than F/32 or such.

Resolving power is directly linked to aperture and optics' quality but I think it is independent from light gathering capabilities.

Originally Posted by rogerg

If a 12" at F/10 were to record brighter stars than a 8" at F/10 then why does a 60mm (aperture) lens @ F/2.8 record brighter stars than a 60m (aperture) lens @ F/4?

I don't think you can compare it like this. On one side you're modifying FL as well as aperture and on the other side you're modifying only FL. 12" will always gather more light than 8". A 60mm lens at F/2.8 is faster than the same lens at F/4 because in the latter you've decreased the image scale on your sensor.

To recap you want more light in get more aperture. You want more fine details. Match your camera pixel size and scope FL to get a better image scale. Regardless of aperture.

[rogerg (Roger)]

Originally Posted by multiweb

To recap you want more light in get more aperture. ....

Well, I still don't think that's the full story... would it not be more correct to say: "you want more light in get more aperture (for the given focal length)" ?

If you have an 8" at 200mm focal length, as you say it is putting the light across a smaller area hence intensifying the light per pixel hence brighter image.
If you have an 8" at 2000mm focal length, the light is spread out more, so you will not get as bright an image.

An 8" at 200mm is F/1, and 8" at 2000mm is F/10.

Right?

[tempestwizz (Brian)]

If you are talking about extended objects, ie anything but stars, the most of the above logic holds true.
Stars however are different, since depite their apparen brightness and size, they are truly only pinpoints of light of different brightness. In this case F ratio has no affect, only aperture.
Why does your F2.8 produce apparently brighter stars than when at F4.. because of another optical function, and which your eye pays part to as well. Its PDF, point dispersion function. As bright pinpoints of light pass through any different medium, glass or eyeball, they tend to be scattered, and appear bigger than they actually are. The scattering is proportional to brightness.
An 8" F4 optical system will record a higher nebula: star brightness than an 8" F10. In both cases though, the star brightness should be pretty much the same. ( Notwithstanding the difference in field of view).

Took me quite a while to get that concept into my tiny brain, as it goes against conventional photographic theory.

HTH

BC

[bird (Anthony Wesley)]

as said above, the rules are different for extended objects (like planets) where the light spreads out over a larger area as you increarse focal length, vs stars (or any point source) where the light is always a point source no matter what the focal length.

Generally speaking the focal ratio will give you the image brightness, but I think this only applies to extended objects.

Likewise focal length gives you image size, but again only applies to extended objects, ie you can see that a star is always a point source no matter what the focal length (within reason!).

cheers, Bird

[multiweb (Marc)]

Originally Posted by rogerg

Well, I still don't think that's the full story... would it not be more correct to say: "you want more light in get more aperture (for the given focal length)" ?

Well of course the visible FOV recorded on your sensor real estate for a given image scale will be a function of aperture and FL. If you modify one independently from the other you'll modify your FOV. But aperture wins still for a given FOV, which really is what we're talking about when we're taking a picture of a DSO. We frame it and we make sure everything "fits in".

Let's take a concrete example.

Scope 1: 5" newtonian F/5 - 650mm FL

Scope 2: 11" SCT F/1.8 - 504mm FL (give or take depending on mirror position at focus)

Both these system will give a similar image scale between 2.8 and 2.9asp respectively. Scope 2 resolving power is better because of larger aperture and Scope 2 light gathering power is also better because of larger aperture.

At the end of the day I'm still covering 2.9 x 1.8 degrees of sky regardless with both scopes at a very similar image scale. So from the CCD perpective the same photons are coming in but loads more of them for the same unit of time. Now you'll say yeah but if I make the C11 slower to F/5 to match the newt then the image will be darker. Yes but I'm only looking at maybe only 1 x 0.8 degrees of sky?

[bmitchell82 (Brendan)]

very interesting.

I guess i can only add with my own observations.

a magnifiying glass and a small ant

holding the mag glass away, the light is dispersed over a area. the light hasn't changed

as you come to focus it gets brighter till the rays fry said poor ant to its demize

Im guessing and I stress im no professor nor boffin, that if the same light is spread out over more area the intensity of the light is less.

This is a fundamental thing when using telescopes, as i belive that understanding such as this allows us to use our equipment better.

Thanks roger for the thread!

[rogerg (Roger)]

Originally Posted by multiweb

Now you'll say yeah but if I make the C11 slower to F/5 to match the newt then the image will be darker. Yes but I'm only looking at maybe only 1 x 0.8 degrees of sky?

agreed, but, fact is, once you take the [edit]SCT to F/5 it's no better than the [edit]newtonian in terms of exposure time. Sure, it's lookng at a smaller part of the sky, but the objects that are common within the two FOV's are surely going to end up with the same pixel brightness given the sam exposure time? Because they're at the same focal ratio.

... except Bird says not the case for stars because they're point sources? ....

But I don't understand how a single point source of a star can be treated differently to a 1 billion point sources (a galaxy)?

I think I'm going to have to think about this again tomorrow when I'm not so tired

[bird (Anthony Wesley)]

Ok, so here's the other side of the argument :-)

As you increase the magnification, the airy disk gets larger (assuming a non-infinite mirror diameter). So the same amount of light is spread out over more area and it gets dimmer.

Imagine taking this to an extreme where the airy disk as captured on the ccd was 20 pixels across - each individual pixel is now a lot dimmer than before.

This only becomes apparent when the magnification reaches a point so that the airy disk is larger than the pixel size of the camera of course...

cheers, Bird

[Blue Skies (Jacquie)]

Er, can I butt in here? I'm kind of the cause of Roger's headache and while I can see people trying very hard to be helpful it's getting a bit off track of what we really want to know.

We really want to know about star brightnesses, not nebulae. We're not trying to photograph deep sky objects, it's all to do with an upcoming Pluto occultation event on 4th June. The target star is around mag 15, and the argument is whether an 8" is enough aperture to pick up this star using a focal reducer and my gstar camera. On one hand I've been told it's ok, on the other that I should try to get to a bigger scope.

I do understand that the wider field and faster f/ratio will lead to the stars being more pinpoint and hence brighter - but will they still be bright enough in this case?

(I do have an ulterior motive to all this, I'd love to know how to work out what combo of scope - f/ratio-camera etc is needed for certain magnitude limits in this kind of situation. Yeah, I know, I should be asking davegee, but Roger has started this thread first, so why not try...)

[Kal (Andrew)]

Jacquie - I think the main point to consider in your application is airy disk size. All telescopes (within reason) will see stars as pinpoints of light, but those pinpoints will have the light spread out within the airy disk (and diffraction rings) at the focal plane. You want to have your optics grab the light from the star and contain it within 4 pixels. If the airy disk is too small, you will have all the light fall within 1 pixel which isn't enough, if you have the airy disk too large you will capture it on up to 9, or 16, or 25 pixels, which is too much.

In truth you need to take into consideration other things aside from the telescope optics - you need to factor in the pixel size of the camera, and seeing conditions.

Edit: Some more info of what I am trying to explain here

[AstroJunk (Jonathan)]

F ratio is to all intents and purposes irrelevant in this conversation – it is simply the mathematical ratio of focal length / aperture. It’s a useful measure in some equations, but not here.

There are only 2 factors that are useful: Focal length, which determines image scale and Aperture which determines the number of photons available to play with.

A telescope with a focal length of 1000mm with an aperture of 250mm will give a brighter image that one of focal length 1000mm and an aperture of 150mm. End of. It only gets complicated when you start to compare different apertures and focal lengths. Luckily for us, if you double the aperture you quadruple the photon count which more than offsets the usual corresponding increase in focal length. That’s why aperture rules!
It is also true that if you reduce the focal length, the resultant image will be brighter too. This is true for stars also. Stars are not quite point sources on Earth due to that astronomically annoying thing called an atmosphere. If we were out in space, the average star would be a mere 1 milli-arc second across, but down here they are fuzzied out to a thousand times that.

So, for Jacquie, the focal reducer will make a positive difference not just in terms of brightness of star but also in the likelihood of increasing the number of comparison stars on the same frame which will come in useful later. For the Pluto event, bigger is better, but you can certainly get meaningful results with an 8”.

[White Rabbit]

Interesting discussion, and something I've thought about a fair bit.

I think it all boils down to the inverse square law http://en.wikipedia.org/wiki/Inverse-square_law.

Correct me if I'm wrong here but if you decrease the focal length to 800 F4 you may gather light faster but you spread it out over a wider surface (image scale). So the the inverse square law comes into play and diminishes your returns by a factor of 4.

Or do I have that completely wrong.

Sandy

[Terry B]

Originally Posted by Blue Skies

Er, can I butt in here? I'm kind of the cause of Roger's headache and while I can see people trying very hard to be helpful it's getting a bit off track of what we really want to know.

We really want to know about star brightnesses, not nebulae. We're not trying to photograph deep sky objects, it's all to do with an upcoming Pluto occultation event on 4th June. The target star is around mag 15, and the argument is whether an 8" is enough aperture to pick up this star using a focal reducer and my gstar camera. On one hand I've been told it's ok, on the other that I should try to get to a bigger scope.

I do understand that the wider field and faster f/ratio will lead to the stars being more pinpoint and hence brighter - but will they still be bright enough in this case?

(I do have an ulterior motive to all this, I'd love to know how to work out what combo of scope - f/ratio-camera etc is needed for certain magnitude limits in this kind of situation. Yeah, I know, I should be asking davegee, but Roger has started this thread first, so why not try...)

I do lots of photometry which is a similar problem to what you have. Using my 200mm scope I can certainly take good measurements of a 15 mag star using my ST10XME but to get a S/N ration above 100-1 I would need an exposure of 60secs through a V filter. Unfiltered I could probably get by with 20 secs.
For the occultation you really only need to be able to detect the object reliably so a SN of 10-1 would probably suffice. I don't know how sensitive the G star camera is but it wouldn't be hard to experiment on a 15 mag star and see what exposure length you need to reliably detect the star. My feeling is that you would be pushing it with the 8" scope and need a few seconds of exposure to detect the star. This might not be quick enough for an ocultation timing.
A larger scope will collect more photons. For this purpose the f ratio is irrelevant. Binning the pixels on the camera will have the same effect as reducing the f ratio and is easier to achieve.

[rogerg (Roger)]

... sorry, just have to laugh at this mess I've created

I hope this isn't getting beyond the point where we're going to land up with one concise conclusion

Originally Posted by bird

As you increase the magnification, the airy disk gets larger (assuming a non-infinite mirror diameter). So the same amount of light is spread out over more area and it gets dimmer.

Agreed - this is where the focal ratio (so the focal length with respect to the aperture) is increasing and so the airy disk gets larger.

Originally Posted by Blue Skies

Er, can I butt in here? I'm kind of the cause of Roger's headache

Sort of, but not entirely I have had this debate with Dave (local, not DaveGee etc) and others in the past, so hence after something conclusive rather than leading people up the garden path

Originally Posted by AstroJunk

F ratio is to all intents and purposes irrelevant in this conversation

You say that, but then you say "It is also true that if you reduce the focal length, the resultant image will be brighter too.". That is exactly focal ratio - you are decreasing the focal length with respect to the aperture, you are decreasing the focal ratio and so brightening the image

And, in our case we are talking two apertures:

12" SCT @ F/7.5 vs
8" SCT @ F/4 (or there abouts - using f/3.3 reducer)

so, sorry... it "has got complicated"

... and yes, we plan to test this, but adverse weather conditions is going to prevent that for about a week.

Originally Posted by White Rabbit

Interesting discussion, and something I've thought about a fair bit.

I think it all boils down to the inverse square law http://en.wikipedia.org/wiki/Inverse-square_law.

Correct me if I'm wrong here but if you decrease the focal length to 800 F4 you may gather light faster but you spread it out over a wider surface (image scale). So the the inverse square law comes into play and diminishes your returns by a factor of 4.

Or do I have that completely wrong.

Sandy

err, sorry, I think you're wrong I think you've got it around the wrong way - F/4 will spread the light over a smaller area than F/10 and so smaller image scale and brighter image.

[Blue Skies (Jacquie)]

Hmmm, definitely need to test this, I think it's the only way we'll know for sure. Roger, I'll contact you off-forum to arrange a date.

To everyone else -

[mithrandir (Andrew)]

Originally Posted by Blue Skies

... We're not trying to photograph deep sky objects, it's all to do with an upcoming Pluto occultation event on 4th June. The target star is around mag 15, and the argument is whether an 8" is enough aperture to pick up this star using a focal reducer and my gstar camera. On one hand I've been told it's ok, on the other that I should try to get to a bigger scope.

You might want to check on http://occsec.wellington.net.nz/plan.../pluto2010.htm because you may be outside the track.

I've tried CdC and Stellarium an their plots both look like Hobart might see it but Sydney and Perth are much closer to the edge.