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Focal ratio and imaging

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#1 danm

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Posted 27 July 2008 - 10:34 PM

Hi,
Total newbie here, I've heard offhand that a fast focal ratio is good for imaging - why, if true?

If this is true than why do many imaging setups have a long focal length (f/9 for the new AT RC scopes)

#2 blueman

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Posted 27 July 2008 - 11:14 PM

Fast is easier because it has a larger Field of View and the demands for a mount are much less. Slow long focal length scopes and the small pixel size associated with them, make it necessary to have very accurate tracking.
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#3 Rusty

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Posted 27 July 2008 - 11:49 PM

And faster FRs allow shorter exposures. Focal length doesn't affect exposure times, but as blueman mentioned, makes tracking more critical. Longer focal length (at the same FR) just provides larger images. The compromise is that longer focal lengths have a wider CFZ (Critical Focus Zone).

#4 Jeffkop

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Posted 28 July 2008 - 04:45 AM

My advise ... If you are new to this, get a small refractor. I needed this advise when I started but didnt get it ... So I chose poorly for my first scope (Cassegrain) ... and it was unworkable for imaging ... bought a refractor ... employed the same principals as the first scope .. but now get pretty reasonable results ... and it wasnt the first scope .. it was me .. dont put yourself thru it ... believe me .. there are many hurdles to clear ... dont make one you dont have to jump at this stage or you will either waste some money or lose interest in the hobby.
Anyway thats my 2cents worth.

Jeff

#5 danm

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Posted 28 July 2008 - 09:16 AM

Hi Jeff,
Thanks for the advice, but I'm a long way from anything. Yes if I actually was going to do some imaging I would get a cheap cam and put it on my AT66 probably, but now I'm just investigating.

Rusty, you're contradicting yourself "And faster FRs allow shorter exposures. Focal length doesn't affect exposure times ..." - can you explain further?

#6 yg1968

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Posted 28 July 2008 - 09:47 AM

A fast focal ratio allows for shorter exposure. For example an F5 200mm scope will allow for shorter exposures than an 100mm F10 scope despite the fact that they both have a focal lenght of 1000mm (F5 x 200mm = 1000mm and F10 x 100mm = 1000mm). That is why people like fast focal ratio scopes.

#7 danm

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Posted 28 July 2008 - 12:39 PM

OK, I understand now. But still not answered - why does a fast focal ratio make for a faster exposure? What's the mechanism?

And a little OT, does this have more of an effect than the aperture in terms of exposure time?

#8 Rick J

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Posted 28 July 2008 - 01:45 PM

There are a lot of ifs in the statement about a "fast" f ratio making for a shorter exposure. You must hold everything else the same to be sure that holds. Thus it does in ordinary photography when you set a lens for f/4 it will need only one forth the exposure as when it is set at f/8. In this case it is because the lens is "stopped down" to where it has only half the aperture at f/8 as at f/4.

In astronomy if you have a 6" f/8 scope and a 6" f/4 scope and use the same CCD on both then this too will be the case. The f/4 scope will need only one fourth the exposure IF the image is not severely undersampled in the f/4 shot. Undersampled stars will not expose 4 times faster.

What's going on in this case is you start with the same amount of light but focus it, at f/4, into one fourth the area. By the inverse square law it is now 4 times brighter. The size of nebula and stars is reduced to one fourth the area. Thus, each pixel of the CCD sees a 4 times brighter image but only if that star is still larger than the pixel. Once the star gets smaller than the CCD pixel then there's no more gain from shrinking the image into a smaller space. The inverse square law breaks down due to finite pixel size. Nebula though are nearly always (very tiny planetary nebula are a rare exception) larger than a pixel so they do continue to follow the inverse square law. Thus a fast scope with a CCD pixel size that undersamples stars will show nebula better than one that doesn't undersample stars as the stars no longer dominate the image. If you are shooting the nebula this is a good thing and a trick many of the better imagers sometimes employ. Though with today's digital processing you can suppress stars by digital means and to a greater extent if you wish. It was more commonly done back in film days.

But pixel size and focal length are related. I image with a 14" f/10 scope. My seeing is normally about 3" so I use a 1" pixel size to properly sample and image, this is 18 microns at that focal length. If I were to use a 9 micron pixel then the pixel size would be 0.5" per pixel and each pixel would see one fourth the light. This is over sampling on all but the best of nights and for deep sky imaging something to avoid because it increases exposure time greatly without any increase in image quality. But on those rare nights of great seeing I am able to switch to 1x1 binning as I did for the NGC 7008 shot posted recently.

Here then is where the fast/slow debate often gets off track. By imaging at a 1" of arc pixel size in 3" of arc seeing it makes absolutely no difference what my focal length is if aperture is kept the same. If the scope is f/10 with a 18 micron pixel or f/5 with a 9 micron pixel or f/2.5 with a 4.5 micron pixel the scale is still 1" of arc per pixel and stars are still 3 pixels in diameter (all are using the same 14" of aperture) then each pixel sees the same number of photons per minute and the image is equally bright. The f/2.5 scope is no faster than the f/10 scope! So I can change my effective f ratio from f/10 to f/5 simply by binning the exposure from 1x1 binning for f/10 and thus 0.5" per pixel to f/5 at 1" per pixel when using 2x2 binning. 3x3 binning then makes the scope 1.5" per pixel and f/3.333 etc. But then the image would be close to undersampled so this would be the place to stop. Note you don't stop the lens down as you do in ordinary photography, you change the pixel size instead.

In ordinary photography going to a faster setting keeps image scale the same, in astro imaging it reduces the image scale.

When you properly match the CCD pixel size to the seeing conditions at your site f ratio has no real say in exposure time, it is aperture that rules. This is why 8 meter scopes are far "faster" than 8" scopes. The big guys do in a few seconds what takes the small scoope hours to do, not because they have a faster f ratio but because they pack far more photons into one large CCD "pixel".

Most beginners should start with a small scope such that they can use a rather large pixel size and not too severely undersample the image. This doesn't give the optimum image for the scope but it does give a good result without the tracking woes you'd have otherwise. Since a 3" star is pretty common across the country if you properly sample at 1" per pixel guiding accuracy needed is no greater for the 16" scope as for the 3" scope! But with less mass and lever arm it puts far less strain on the mount needed and thus makes it easier. Then too you can under sample with say a 3" pixel without much loss and further ease your tracking problems. Instead of focal ratio concentrate on focal length and pixel size, they are far more important in today's digital age.

A long answer to an apparently simple question.

Rick

#9 PhilG

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Posted 28 July 2008 - 01:50 PM

This can be confusing. You need to remember to only vary one thing at a time when making comparisons. yg1968 put it correctly. For the same focal length you will have the same image FOV. The faster scope will then have more aperture "funneling" light onto the same area of CCD. The signal-to-noise with the larger aperture scope will be greater by sqrt(A2/A1), the ratio of the areas, or D2/D1, the ratio of the apertures of the faster vs slower scope. So an 8" aperture refractor should get you the same signal-to-noise as the same fl 4" refractor in half the time.

If you're talking about the same aperture scope, then a faster scope doesn't buy you anything other than more potential FOV at the expense of resolution.

Hope this helps.

Phil

#10 danm

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Posted 28 July 2008 - 02:40 PM

Thanks so much guys! I probably should have put this in the beginners forum, I'll direct my questions there in the future.

#11 jay52

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Posted 28 July 2008 - 04:41 PM

LOL, here we go again.

It's all about aperture, not focal ratio. In CCD imaging, once your signal is well above the read noise, the aperture takes over from f-ratio as the dominant factor in signal/noise ratio.

It's not about photons per pixel, but rather photons per arc-sec^2 of the sky...and that depends on aperture.

Focal ratio affects pixel S/N...meaning that more photons get concentrated on each pixel, which makes data more certain on that pixel...and thus, you need less time to fill that pixel. This is important for widefield imaging, where you want silky smooth backgrounds and the objects themselves only cover relatively few pixels.

But when you image at longer focal lengths, you are placing emphasis on the OBJECT, not the pixels. This is where sampling comes into play. Regardless of focal ratio, when you want a good picture of that object (as opposed to widefield where it's one of many objects) then you really don't care about pixels, but rather about the photons recorded of the object. In other words, a 6" scope, whether f/5 or f/10, will still record an identical number of photons of the OBJECT. Only larger apertures will increase the number of photons in a given exposure time.

If you don't believe me, then take a picture of an object at 530mm (f/5) and 2857mm (f/9) at the same exposure time. Then down-sample the f/9 image in Photoshop afterwards to match the image scale of the f/5 shot. Then, tell me which object looks better and cleaner.

That said, RCOS scopes are f/9 because we want to image at 2857mm, not 500mm. If we wanted 500mm, we'd get an Epsilon, or an FSQ. Only the larger aperture scope can deliver more photons for the area of sky we want to shoot...and that's why we shoot it, even at a "slow" f/9.

For a good technical read on the f/l issue, see these pages here...

http://www.stanmoore..._ratio_myth.htm
http://www.telescope...php?topic=102.0

#12 jay52

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Posted 28 July 2008 - 05:02 PM

Let me phrase this another way...

If I want to shoot a 4 arc degree swath of the sky with a given camera, then I would be better off shooting an Epsilon 180mm than I would an FSQ-106. This is not because the Epsilon has the faster f/ratio, but rather that is has more aperture.

If I want to shoot a .5 arc degree section of the sky, as for imaging close-up views of a galaxy, then I would also opt for the largest aperture possible at the focal length I need for that FOV. My 12.5" RCOS fits the bill perfectly with my SBIG STL cameras. However, I could certainly collect photons faster if I was using a 20" scope, as long as the focal length was still sufficient for yield the FOV I need.

So, the point is, the more you get into astroimaging, the more you actually CARE about FOV and composition. So, practically speaking, I'm not going to purchase an f/5 instrument just because it's "fast." If it doesn't yield the composition I need, then it doesn't really matter.

Sure, a fast, wide-field scope is great, especially to begin with as it allows you quicker images at an easier image scale. But when you start focusing on the objects themselves, you just want photons on the chip...anywhere on the chip...and that provides you with the best s/n and cleanest images. That means using as large an aperture scope as you can afford.

#13 yg1968

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Posted 28 July 2008 - 09:46 PM

Interesting thread. I knew there was a reason why I liked longer focal lenghts SCTs... Now I know why!

#14 danm

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Posted 28 July 2008 - 11:12 PM

Jay,
That makes a lot more sense. I have a physics background which is why I had trouble understanding how f/ratio could improve imaging time- all your collecting is photons. Thanks -

Dan

#15 jay52

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Posted 28 July 2008 - 11:24 PM

Dan:

Well, it does improve imaging time, in certain circumstances. The problem is that people want to make it a blanket statement and say that focal ratio always means "faster" images. It's not a "rule of thumb."

None of it is applicable when you deal with advanced astrophotography.

If focal ratio was indeed everything, then there wouldn't be a need for 10 meter telescopes. For that matter, we could all just use 1 inch telescopes at f/2.

The point is that we have certain priorities with our imaging...image scale and field of view are what it's about. It should NOT be imaging speed at the expense of all the other important criteria.

Now, as a beginner, we normally don't care. We are willing to get 4x more light on individual pixels, even though it means we get 4x the field of view. Honestly, we often don't need, nor wish for, such a big field of view. I mean, how much is enough? You go to shoot M81/M82 and they end up looking like ant droppings on black velvet...but, what the heck, you imaged them FAST, right? :)

In fact, this is why I generally tell newbies to go with a nice, small, cooled astro CCD for their first cameras. We just don't always need the big, full-sized chips.

#16 Rusty

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Posted 28 July 2008 - 11:34 PM

Rusty, you're contradicting yourself "And faster FRs allow shorter exposures. Focal length doesn't affect exposure times ..." - can you explain further?


A 500mm f/5 scope and a 4000mm f/5 scope will both require the same exposure times, but the image size on the 4000mm sope will be MUCH larger. Focal ratio is the key for exposure, while image size is a function of focal length. the image size on a 500mm f/5 scope will be the same as on a 500mm f/10 scope, but the former will have a wider field of view, showing more of what's around the central object.

#17 jay52

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Posted 29 July 2008 - 12:19 AM

...the image size on a 500mm f/5 scope will be the same as on a 500mm f/10 scope, but the former will have a wider field of view, showing more of what's around the central object.


No, the size of the object will not be the same. The object will be much more undersampled on the f/5 scope. The object of interest will appear much more defined in the f/10 instrument, and you will get equal object S/N for either scope.

Again, if you don't believe me, just downsample the f/10 shot later in Photoshop and you'll have the same image of that object.

However, this assumes you have an object of interest. If you just care about wide-fields, then the f/5 scope is for you. If you want details on the object, then the f/10 scope is for you.

Saying one is faster than the other without considering the goal of the image is just comparing apples and oranges...and it doesn't help anybody understand what's really happening when doing CCD imaging.

#18 stkoepke

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Posted 29 July 2008 - 12:41 AM

Thanks danm for asking this question, I was wondering about this myself and found that I was understanding only a little.

VERY interesting answers from everyone that finally make sense. (It's nice when the "light of understanding" suddenly turns on in your head.)

Rick, your answer may have been "long" as you put it, but it sure explained a great deal, at least to me...and in terms that I understand. :bow: :bow:

I'll have to keep up with this thread...

#19 nytecam

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Posted 29 July 2008 - 06:21 AM

Agreed :bow: a short focus refractor can record deep but places much less strain on the whole train of equipment and user skills ;)

My astrograph is only 70mm aperture and 350mm fl but does pretty good - see link below :rainbow:

#20 Jared

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Posted 29 July 2008 - 09:56 AM

There are lots of ways to look at this, but here's how I do it.

Most people, when discussing fast vs. slow scopes, want to know what the advantages and disadvantages are when looking at two scopes of the same aperture. This is different from terrestrial photography, where you keep the focal length constant and vary the aperture to get different focal ratios.

Let’s take an 8” f/6 scope vs. an 8” f/9 scope as an example. Let’s also assume that we are able to choose our camera to provide “optimum” sampling rates for either scope based on our typical seeing conditions. In other words, the pixels for the f/9 scope would be 1.5 times larger than the pixels for the f/6 scope. In both cases we will choose a pixel size that can just barely resolve the finest details the seeing conditions will allow. For 3 arc second seeing conditions, that would correspond to approximately 1 arc seconds per pixel (though some would argue a slightly higher or lower value would be “optimum”, and many sites would offer seeing conditions better than 3 arc seconds). For the f/9 scope we would need 9 micron pixels, and for the f/6 scope we would need 6 micron pixels. These are fairly typical values for the chips available to amateur imagers.

Field of view would be the same in both scopes since the faster scope would have a smaller, more densely packed chip.

Resolution would be the same in both scopes since the aperture is identical and we are limited by seeing conditions in any event. Typically, once you get above about 8” of aperture, resolution for long exposure imaging at visual wavelengths is limited by atmospheric conditions not by the telescope itself.

Signal to noise ratio would be nearly identical in both scopes. Shot noise would be the same—same amount of signal captured from your object right down to the pixel level, same amount of noise captured from sky glow (fixed aperture, remember--constant number of photons streaming in and equal per pixel intensity levels since the faster scope has smaller pixels), same amount of thermal noise if the chips were using the same technology, and same amount of read noise. The larger full well capacity of the physically larger chip might allow slightly longer subexposures before dynamic range becomes eroded by sky glow and thermal noise, but this difference is likely to be minor.

Photographic limiting magnitude would be the same for both scopes—it is determined purely by aperture, quantum efficiency of the camera, and sky glow. Either setup should go just as “deep” from a given location on a given night. This is true for both point sources and extended objects.

So if signal to noise is the same, resolution is the same, and field of view is the same when you choose the camera to match the scope’s focal length (optimum sampling), are there any advantages or disadvantages to a faster or slower scope?

  • Faster scopes are usually (but not always) more compact.
  • Faster scopes may pose less of a challenge for your mount since they will typically be smaller and lighter. The shorter focal length won’t help, though, since you compensated for that by using smaller pixels.
  • Slower scopes will be easier to focus.
  • Slower scopes are generally easier to make to a given level of quality.
  • In an obstructed optical tube, slower scopes usually have a smaller central obstruction and will therefore have higher contrast.
  • Larger CCD’s of a given resolution are usually more expensive than smaller CCD’s, but this will be counterbalanced by the fact that faster scopes are usually more expensive for a given level of quality.
  • Most optical designs have a “sweet spot” in terms of optimum image quality—balancing various aberrations, field curvature, etc., so the range of focal ratios for a given scope design is usually fairly narrow.
You can build a good imaging rig with an f/6 scope. You can also build one with an f/9 scope. Or an f/4 scope. Or an f/12 scope. If the camera is matched to the scope, any focal ratio should be able to provide essentially the same image quality, the same resolution, and the same field of view.

So what’s wrong with the above argument? There’s got to be a catch, right? Yes, there is a catch—it’s my assumption that you can match the CCD to the telescope to achieve optimum resolution. In the real world, the range of pixel sizes available to imagers is somewhat limited, so you may not be able to get “optimum” sampling rates. So what happens if you take an optimally sampled scope/camera combination and suddenly make the scope faster without changing the CCD camera? What happens if you shorten the focal length without affecting the aperture? Well, you are obviously going to lose some spatial resolution--you have lost your "optimum" sampling rate. That doesn’t mean that pictures are going to look any less sharp, by the way—a given object in the field of view will have less detail apparent, but the wider field of view will include more objects so the perceived “sharpness” of the entire frame may well remain constant or even increase. You will only notice the decrease in spatial resolution if you crop your image to provide the same field of view as you had with the slower scope. Then you will, indeed, lose resolution and image sharpness.

What else happens when you make your scope faster but keep the camera constant? To some extent, the signal to noise ratio in the image will improve. The object SNR—created by shot noise—will remain constant, but the read noise and thermal noise will be proportionately lower. Of course, you can compensate for this simply by increasing exposure duration to the point that shot noise overwhelms read noise and thermal noise, but larger pixels will always have at least some advantage with respect to SNR.

Doesn’t sound like much a very good idea—trading resolution for some small improvements in SNR. So why would you ever build an undersampled system? What good is an 8” f/4 scope if nobody manufactures 3 micron pixel cameras (optimum sampling rate)? For many subjects, you don’t want “optimum” sampling. You may want a wider field of view to capture a larger subject. Particularly if you are imaging with a smaller chip, many astronomical objects won’t fit in the field of view of an “optimally” sampled image. That’s why many imagers own more than one optical tube for imaging. A fast 4” refractor, for example, will make a fine widefield scope when partnered with a larger scope for higher resolution imaging. Most advanced imagers end up owning one CCD camera and multiple optical tubes in order to provide the range of spatial resolution and fields of view desired. That's why there is still a market for small, fast scopes like the TV NP127 or the Takahashi Q's even though an imaging rig based on these tubes will never be able to achieve high spatial resolution. For wide fields of view you need a short focal length, and the only way to achieve a short focal length is with a small (aperture), fast telescope.

#21 jay52

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Posted 29 July 2008 - 10:52 AM

That's a pretty good write up, Jared. I believe I'm in agreement with everything you've said.

For me, the central point is that there are too many factors involved...you just can't say, for the sake of simplicity, that's fast focal ratios are better, or even "faster."

#22 Dan G

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Posted 29 July 2008 - 12:02 PM

Very good post Jared. You raise all the right points. The reason I purchased the NP127 is solely for widefield imaging which I enjoy. The jet stream frequently parks over my house so hi res shots are often frustrating to obtain. However - I do have the 8" for those nights I do have steady seeing.

Dan in NY

#23 Jared

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Posted 29 July 2008 - 01:26 PM

That's a pretty good write up, Jared. I believe I'm in agreement with everything you've said.

For me, the central point is that there are too many factors involved...you just can't say, for the sake of simplicity, that's fast focal ratios are better, or even "faster."


Absolutely correct. Faster is neither better nor worse. It is simply one more variable to put into the equation.

#24 imhotep

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Posted 29 July 2008 - 01:32 PM

Does anyone have any popcorn?

#25 Jared

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Posted 29 July 2008 - 01:32 PM

I'll add two more points. The first is similar to what Blueman said earlier in this thread. For beginning imagers, a short focal length is often recommended. It isn't that a faster scope is better in its own right, but shorter focal lengths are usually significantly undersampled. This poses less of a challenge for the mount, so it makes achieving "sharp" results easier. Second, faster focal ratios at a given aperture will result in better signal to noise ratio if you are taking very short exposures. Beginning imagers often don't autoguide, so they are often not able to get shot noise to swamp read noise and thermal noise--the exposures are, of necessity, too short. As a result, with short exposures you will often achieve better results with a faster focal ratio.






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