Focal length and Focal ratio - test my sanity

[rogerg]

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 :lol:

But... just checking?!??? :)

Thanks,
Roger.

[multiweb]

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".



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]

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 :screwy:

[multiweb]

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



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]

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]

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]

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]

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]

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]

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 :lol:

[bird]

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]

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

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 (http://www.astromart.com/articles/article.asp?article_id=73)

[AstroJunk]

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]

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]

:lol:

... 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 :)




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.



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 :)


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" :lol:

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



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]

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 - :thanx:

[mithrandir]

You might want to check on http://occsec.wellington.net.nz/planet/2010/predict/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.

[rogerg]

I'd really rather keep the thread to observations in general, not specific to occultations or a particular occlation. My original clarification was only simplifiedto "a star" because I thought there wouldn't be any difference as to how a star vs a larger object made up of billions of stars would be treated. Still a little confused on that one :rolleyes:

To my way of reading there are 4 TNO's going directly over our locations in the next month, and another 3 or so which are worth observing because the path is close enough that an outside observation would be of use. And I'm aiming for time to observe one or two :)

:thumbsup:

[Blue Skies]

The last one that was attempted that I know of the track shifted quite a few hundred km north, and Perth ended up being on the edge. Even a miss is a positive result in this game!

[StellariuS]

Does this dodgy image work? it might put us back on track.

All stars are the same size no matter the aperture or focal length, just brightness and scales change.

This is how I've come to understand the works of it. but i have only seen through one telescope. I'm fairly new to starwatching so please correct me if I'm wrong.

Go paint lol :P

[rogerg]

Thanks for your effrots to help :) it might help I'm not sure :)

Image scale: I don't have any problem there, I think we're all in agreeance that longer focal length = smaller FOV = smaller area of sky = larger view of an object = smaller scale (each pixel covers fewer arc seconds of sky).

Star brightness: Your graphic doesn't indicate if 12" F/7 or 6" F/3 is brighter, and that's really the critical question I'm getting at :)

Also just to clarify again I'm only interested in photographically thinking - not visual.

:shrug:
Roger.

[Terry B]

The graphic isn't really true. The 12" f7 and the 12" f3 should have the stars at the same brightness. This holds for all except the very bright stars that will saturate the sensor and spread out over lots of pixels. The 12" scope will also show dim stars that won't be visible in the 6" scope.
For my scope I have taken images of stars for photometry with and without a reducer. The limiting magnitude I can detect with a 5 minute exposure is the same at f8 and f6.4. To improve my ability to measure dimmer stars I need a bigger scope not a bigger focal reducer.

[tonybarry]

Hello Jacqui,

I also have an 8" scope (LX90) and a GStar which I can use to observe the occultation. What do the knowledgeable people say about this combination? Will it suffice? Or is the limiting magnitude of the optical / CCD system too great?

One thing is that the GStar will need to integrate to some extent to obtain the necessary light collection. This will reduce the time accuracy. Will this allow the observations to be still useful?

Regards,
Tony Barry

[Blue Skies]

Sorry, Tony, only just noticed your questions.

I'm a beginner in this game as well (hence the questions in this thread) and can't tell you much more until I can get together with Roger to do some tests. But I'm told that only one or two integrations is enough - you need to have a frame rate of 25/sec being recorded, so as long as you can achieve that and see the target star it should be right.

[AstroJunk]

Tony, I happen to have the rather pointless and unofficial world record for observing the faintest ever asteroidal occultation of a 14.5th mag star. I mention this because your 8" and GSTAR combo could have made this observation too.

Yes, you would have had to use a higher level of integration which would have reduced your acuracy. But would this have still be useful? Yes, absolutely. There is an enourmous scientific payload of every extra observation, no matter how inacurate. Just getting the duration of an event with a stopwatch is massively helpful.

Hope you get involved,

Jonathan

[DaveGee]

Hi Jacqui,

Short answer... YES!

Slightly longer answer... Yes, an 8" f10 SCT with a f3.3 focal reducer and a Gstar camera is enough for you to detect the mag. 15 target star and mag. 14 Pluto.

Longer answer... Yes, an 8"... blar blar blar... I use my 8" LX90 and WAT-120N to observe asteroid occultations of faint stars. I prefer my 10" newtonian as it's already set up and lives in my skyshed ready to go with the minimum of fuss, but the 8" SCT is good enough. The 10" gives a slightly better Signal to Noise video but not by much. A 12" 14" or 20" will give you even better S/N @ a faster frame rate but in the end, if you use what you have to the best of your ability, you can't go wrong.

Remember, the mag. 14.0 Pluto will merge with the mag. 15.2 target star and the pair will brighten to mag. 13.7 and if/when the star disappears you will see a mag. 0.3 drop in brightness.

Bottom line. In the days before the event, practise observing Pluto appulsing (approaching) the star to determine the fastest frame rate you can achieve to "only just" detect the target star. This is best done at a similar time of the event so that the targets are at a similar altitude and so atmospheric extinction will be the same as that on event night. This, in the trade is called a mocultation... mock-occultation.... get it...:rofl:

[Blue Skies]

Now this is exactly the info I was looking for. I'm still trying to get my head around combined magnitudes, though. I had been wondering what rate of integration was needed but you've answered that - it varies with each situation. I really should have asked you first...




...mocultation...! :lol: Its hard to find jokes in astronomy but that's a good one!

P.S. pm coming your way!

[tonybarry]

Hello Dave,

Many thanks for this answer, which is exactly what I was hoping for.

I have both an f/6.3 and an f/3.3 focal reducer for my LX90-8" - which would be better for this purpose?

From Massey & Quirk's book (Deep Sky Video Astronomy, p14) I have the native (f/10) field of view of an 8" SCT with a GStar at prime focus as 11' x 8' and a limiting magnitude of 15.5 at 128x accumulation (2.56 seconds per frame).

Putting a f/6.3 reducer on the scope should increase the field of view (helpful in the case of locating an object with few distinguishing features).
If I understand things correctly, this will make the apparent disc of the planet on the CCD occupy fewer pixels, dumping a little more light on each pixel, which for Pluto (at mag 14.0) is probably a good thing.

Now the less pleasant thoughts I have. According to your web page, the apparent diameter of Pluto is about 0.1", but I understand that the seeing in average conditions blurs starlike objects out to about 2". The resolving power of an 8" SCT (Dawes limit) is about 0.6" and the GStar has about 0.87" / pixel at f/10 of 2000mm.

So at f/10, the 8" SCT / GStar combination should produce an image of Pluto of about 2.3 pixels diameter (due entirely to the seeing conditions). Putting the f/6.3 reducer in the imaging train should reduce the image down to 1.4 pixels diameter. The f/3.3 reducer lowers that to less than one pixel on the CCD ... which for me is a little problematic. Would you prefer the f/3.3 over the f/6.3 reducer?

The next question is regarding hot pixels, which the GStar has plenty of (at 128x accumulation). They are not obvious at 1x accumulation. How did you deal with hot pixels?

Regards,
Tony Barry

[DaveGee]

Hi Tony,
Sorry for the delay in answering... I must check the forums more often...:P

I always use a f3.3 reducer with my 8"LX90 for asteroid events. I'm always seeking a larger FOV to help IDing the field and to make sure I have enough comparison stars. I've never had the conditions good enough to get star images on one pixel, and if that were to happen, I'd simply defocus a little to smear the light onto more pixels.

I have plenty of hot pixels on my WAT120N. I've been tempted to use black paint on the monitor to see if that helps...:rofl::rofl::rofl:. Sadly there is not much you can do except to move the target to avoid them, or chill the camera...:shrug:

Good luck!