Dual rig speed calculation - meanigful or not???

[ollypenrice]

I'm writing a piece on dual rigs and had a thought which I'll put on the table. It may be meaningless!

We can safely say that using two parallel and 'identical' rigs will be almost exactly twice as fast as using one. (Identical is in inverted commas because the chip noise won't be identical but I don't think this is very importantfor our purposes here.)

Now suppose we take an F5.3 Tak 85 and put a second one alongside it.

- The lens area of one scope is 5674.5 square mm.

- The lens area of two is therefore 11349.0 sq mm.

- 11349.0 sq mm is the lens area of a single lens of 120.2mm diameter.

- The doubling of scopes leaves the FL unchanged. With/without reducer the Baby Q has a FL of 450/328mm.

- Considering the two lenses to be the equivalent of one at 120.2mm, this would give 'effective focal ratios' of F3.74/F2.73.

Setting aside the introduction of two sets of read noise (from the use of two cameras), what do you think of the concept of 'effective focal ratio' from a photon-collecting point of view? Is it a spurious concept for some reason that I haven't seen?

Olly

[vlaiv]

It will not be as twice as fast dough. In best case it will be 1.41.... (square root of 2) as fast.

Calculation should be fairly simple, just imagine that you had a single scope but managed to get twice as many subs. For identical setups, and using same sub length on both scopes it effectively amounts to using single scope on two nights. This means that for half of imaging time, by using two scopes you will get ~1.41 increase in SNR.

If you have any sort of calculator for SNR, you should be able to estimate how much faster would be to have two scopes at the same target by entering double the number of subs.

I've just run quick test on this, parameters being:

Target Mag24, LP Mag19, 2 hours of 1 minute exposure as base, RC8, ASI1600mm (binned x2 in software) and ratio of obtained SNR's is : ~1.41031

[Scooot]

Shouldn’t you also double the focal length before you do the sum? So 900/170?

edit

otherwise if you took two images at different times from the different scopes and stacked them, you could say the focal ratio of the combined stack has changed from 5.3 to 2.65

The shape of the light cone doesn’t change with two scopes, whereas it does if you doubled the aperture of a single scope.

[Jessun]

It will of course be twice as fast in layman's terms. 1 hour magically equals 2 hours. The equivalent necessary f-ratio of a one-scope-only setup would be one f-stop lower.

That's your 1.4 factor, for the f-ratio only. Still twice as fast.

Effective f-ratio is just as you calculated, Olly.

I crunched these numbers many times with my triple rig - and I liked what I saw.

AND you're lucky to even have to bother about read noise. Three sets don't necessarily make for a result that is three times worse looking at each stacked pixel. Might well work the opposite way to uniform the combined stacked noise.

Many of us work with sky glow as you know. Hours of exposure are slowly accumulating gold dust in that respect.

/Jesper

 

 

 

[ollypenrice]

1 hour ago, vlaiv said:

It will not be as twice as fast dough. In best case it will be 1.41.... (square root of 2) as fast.

Calculation should be fairly simple, just imagine that you had a single scope but managed to get twice as many subs. For identical setups, and using same sub length on both scopes it effectively amounts to using single scope on two nights. This means that for half of imaging time, by using two scopes you will get ~1.41 increase in SNR.

If you have any sort of calculator for SNR, you should be able to estimate how much faster would be to have two scopes at the same target by entering double the number of subs.

I've just run quick test on this, parameters being:

Target Mag24, LP Mag19, 2 hours of 1 minute exposure as base, RC8, ASI1600mm (binned x2 in software) and ratio of obtained SNR's is : ~1.41031

For a given result I'd still say a dual rig was twice as fast as a single, I think. That's to say, whatever result takes you 2 hours in a single scope will take you just 1 hour in a double. I can't see the flaw in this logic. (I'm not suggesting that doubling the exposure time doubles the signal in the S/N ratio.) I entirely agree that the doubling of the scope is, by definition, equivalent to coming down one F stop.

1 hour ago, Scooot said:

Shouldn’t you also double the focal length before you do the sum? So 900/170?

edit

otherwise if you took two images at different times from the different scopes and stacked them, you could say the focal ratio of the combined stack has changed from 5.3 to 2.65

The shape of the light cone doesn’t change with two scopes, whereas it does if you doubled the aperture of a single scope.

I don't think so. The field of view is identical in both scopes so the original focal length applies. You cannot say that you've changed the F ratio by adding a second night, you can only say that you've collected more light at that original F ratio. Your third point brings us to the crux of the dual rig. It retains the shallower and more tolerant light cone of the slower F ratio. Greater depth of field means easier focus and greater tolerance of other errors like tilt. That's what many dual rig owners like about their rigs. Very fast optics tend to be very difficult optics.

We can think about light intensity hitting the chip and, if we do, we can see that a larger aperture (therefore faster) single scope of the same FL and same lens area as the dual rig will concentrate twice as much light onto its chip as the single scopes do, but then, in processing, we combine the two chip surfaces into one. So there are two chips at the capture stage but, in effect, only one at the stacked stage.

Olly

[Scooot]

4 minutes ago, ollypenrice said:

I don't think so. The field of view is identical in both scopes so the original focal length applies. You cannot say that you've changed the F ratio by adding a second night, you can only say that you've collected more light at that original F ratio. Your third point brings us to the crux of the dual rig. It retains the shallower and more tolerant light cone of the slower F ratio. Greater depth of field means easier focus and greater tolerance of other errors like tilt. That's what many dual rig owners like about thier rigs. Very fast optics tend to be very difficult optics.

We can think about light intensity hitting the chip and, if we do, we can see that a larger aperture (therefore faster) single scope of the same FL and same lens area as the dual rig will concentrate twice as much light onto its chip as the single scopes do, but then, in processing, we combine the two chip surfaces into one. So there are two chips at the capture stage but, in effect, only one at the stacked stage.

Olly

I think I’ve misunderstood your point. I thought you were effectively asking whether two images taken with two scopes at f5.3 were the same as one image at f2.65. Ie the same as taking with a fast optic scope. Using two scopes, or two cameras, doubles the exposure, it doesn’t change the depth of field which is what would happen if the f ratio was altered on a camera.

[vlaiv]

14 minutes ago, ollypenrice said:

For a given result I'd still say a dual rig was twice as fast as a single, I think. That's to say, whatever result takes you 2 hours in a single scope will take you just 1 hour in a double. I can't see the flaw in this logic. (I'm not suggesting that doubling the exposure time doubles the signal in the S/N ratio.) I entirely agree that the doubling of the scope is, by definition, equivalent to coming down one F stop.

Yes, my bad, I never think in F stops, I always think in terms of SNR so I misunderstood your post. You are quite right, it will most certainly be at best - twice as fast (same SNR for x2 less time).

[Jessun]

Quote

Your third point brings us to the crux of the dual rig. It retains the shallower and more tolerant light cone of the slower F ratio. Greater depth of field means easier focus and greter tolerance of other errors like tilt. That's what many dual rig owners like about thier rigs. Very fast optics tend to be very difficult optics.

Precisely!

I won't argue this in detail as it would be embarrassing to pin down what you already know better that I do.

/Jesper

 

 

[The Admiral]

20 minutes ago, ollypenrice said:

For a given result I'd still say a dual rig was twice as fast as a single, I think. That's to say, whatever result takes you 2 hours in a single scope will take you just 1 hour in a double. I can't see the flaw in this logic. (I'm not suggesting that doubling the exposure time doubles the signal in the S/N ratio.)

This troubles me a bit and I'm not sure I can see why. Although in either case you are collecting the same total number of photons, isn't the issue that in effect you are performing two separate measurements with the dual rig, and as such the resultant SNR will be the quadrature sum of the two individual SNRs for each 'scope?

Or may be that just illustrates my lack of understanding of noise!

Ian

[vlaiv]

1 minute ago, The Admiral said:

This troubles me a bit and I'm not sure I can see why. Although in either case you are collecting the same total number of photons, isn't the issue that in effect you are performing two separate measurements with the dual rig, and as such the resultant SNR will be the quadrature sum of the two individual SNRs for each 'scope?

Ian

Key words being for a given result - meaning for given target SNR. Let say you obtain your given SNR with 60 subs using one scope for total of 4 hours imaging time (4 minute sub).

Now using two scopes to get same number of subs (hence same target SNR) will take you 2 hours - first will get 30 subs in 2 hours, second will take 30 subs in 2 hours - total will be 60 subs, each lasting 4 minutes - same as above, but time spend recording them will be 2 hours because they record subs at the same time.

So if you look at the time spent - definitively 2 times faster (x2 less time used to obtain given target SNR).

[Jessun]

S/N will go down as a function of the number of exposures. Doesn't matter what rig it comes from once combined.

/Jesper

[The Admiral]

5 minutes ago, vlaiv said:

Key words being for a given result - meaning for given target SNR. Let say you obtain your given SNR with 60 subs using one scope for total of 4 hours imaging time (4 minute sub).

Now using two scopes to get same number of subs (hence same target SNR) will take you 2 hours - first will get 30 subs in 2 hours, second will take 30 subs in 2 hours - total will be 60 subs, each lasting 4 minutes - same as above, but time spend recording them will be 2 hours because they record subs at the same time.

So if you look at the time spent - definitively 2 times faster (x2 less time used to obtain given target SNR).

 

4 minutes ago, Jessun said:

S/N will go down as a function of the number of exposures. Doesn't matter what rig it comes from once combined.

/Jesper

Thanks for input chaps, but would I be correct in assuming that this will only be true if the subs from both 'scopes are stacked together?

Ian

[vlaiv]

6 minutes ago, The Admiral said:

 

Thanks for input chaps, but would I be correct in assuming that this will only be true if the subs from both 'scopes are stacked together?

Ian

Quite so. Or there are other ways to half ones "time under stars". Use one scope to shoot L while other captures color / ha / whatever.

[Jessun]

True of course Ian.

/Jesper

[ollypenrice]

57 minutes ago, The Admiral said:

This troubles me a bit and I'm not sure I can see why. Although in either case you are collecting the same total number of photons, isn't the issue that in effect you are performing two separate measurements with the dual rig, and as such the resultant SNR will be the quadrature sum of the two individual SNRs for each 'scope?

Or may be that just illustrates my lack of understanding of noise!

Ian

I think that what might lie in the back of your mind could be the issue of photons failing to make it above the read noise of the chip. This is where the dual rig is not, I think, equivalent to a single scope of the same lens area and focal length. That's what I had in mind when I included the following caveat in my original question.

2 hours ago, ollypenrice said:

Setting aside the introduction of two sets of read noise (from the use of two cameras), what do you think of the concept of 'effective focal ratio' from a photon-collecting point of view?

A failed attempt to beat the read noise, when repeated in a second scope, remains a failed attempt.

 

1 hour ago, Scooot said:

I think I’ve misunderstood your point. I thought you were effectively asking whether two images taken with two scopes at f5.3 were the same as one image at f2.65. Ie the same as taking with a fast optic scope. Using two scopes, or two cameras, doubles the exposure, it doesn’t change the depth of field which is what would happen if the f ratio was altered on a camera.

Does my point above address this point of yours, Scoot? Essentially I'm saying that the signal which beats the read noise is doubled in a dual rig but that which doesn't remains lost.

Does this imply that the dual rig would be even more effective for CMOS cameras than for CCD?

Olly

[vlaiv]

@ollypenrice

Could you please explain the notion of signal being lost if it is below read noise level. I've encountered this claim couple of times now, and I can't wrap my head around it.

[Scooot]

37 minutes ago, ollypenrice said:

I think that what might lie in the back of your mind could be the issue of photons failing to make it above the read noise of the chip. This is where the dual rig is not, I think, equivalent to a single scope of the same lens area and focal length. That's what I had in mind when I included the following caveat in my original question.

A failed attempt to beat the read noise, when repeated in a second scope, remains a failed attempt.

 

Does my point above address this point of yours, Scoot? Essentially I'm saying that the signal which beats the read noise is doubled in a dual rig but that which doesn't remains lost.

Does this imply that the dual rig would be even more effective for CMOS cameras than for CCD?

Olly

Yes I think I understand you now. You’re referring to the noise & signal generated in images taken on a duel rig with two cameras in comparison to those taken with one camera on a single rig?

[ollypenrice]

32 minutes ago, vlaiv said:

@ollypenrice

Could you please explain the notion of signal being lost if it is below read noise level. I've encountered this claim couple of times now, and I can't wrap my head around it.

I can't explain it! My understandng, which may be false, is that if the signal doesn't beat the read noise it won't be possible to separate it from the background in processing so it cannot 'participate' in the image. I don't insist that this is true, it is just what I've assumed.

Olly

[ollypenrice]

6 minutes ago, Scooot said:

Yes I think I understand you now. You’re referring to the noise & signal generated in images taken on a duel rig with two cameras in comparison to those taken with one camera on a single rig?

Yes, that's what I mean. If I'm right that signal below the read noise can't be exploited in the image then there is a difference between photons caught on two chips and the same number of photons caught on a single chip.

But am I right? Vliav seems to doubt it.

Olly

PS Thanks for all the contributions. It's an interesting ball to kick around.

[Scooot]

10 minutes ago, ollypenrice said:

Yes, that's what I mean. If I'm right that signal below the read noise can't be exploited in the image then there is a difference between photons caught on two chips and the same number of photons caught on a single chip.

But am I right? Vliav seems to doubt it.

Olly

I don’t know the answer but if you use two cameras there is double the camera noise for the same number of photons. So unless you can remove the additional noise, ceteris parisbas, I would have thought using one camera is better? I don’t understand why you would be able to exploit the signal below the read noise any more in one situation rather than the other.

[Jessun]

Quote

I don’t know the answer but if you use two cameras there is double the camera noise for the same number of photons.

No, not at all. The combined noise will be doubled worst case per pixel, or cancelled out totally best case, but for the majority of the millions of pixels it will be a naturally averaged mix. Even before software routines.

There's also of course the possibility to run two different filters in the two scopes, gathering two completely different sets of data. No need to combine. Just plain time saving.

/Jesper

[ollypenrice]

1 hour ago, Scooot said:

I don’t know the answer but if you use two cameras there is double the camera noise for the same number of photons. So unless you can remove the additional noise, ceteris parisbas, I would have thought using one camera is better? I don’t understand why you would be able to exploit the signal below the read noise any more in one situation rather than the other.

After calibration I would have thought that there would be double the residual noise which would then behave as Jessun suggests.

I don't think I would be able to exploit the signal below the read noise any more in one situation rather than the other. What I think is that in the 'lens area equivalent' single fast astrograph there would be a higher photon flux per pixel and so more of the faint signal would exceed the noise floor. But this assumes signal below the noise floor in any one exposure is lost. Maybe it isn't? I don't know.

Olly

[vlaiv]

1 hour ago, ollypenrice said:

I can't explain it! My understandng, which may be false, is that if the signal doesn't beat the read noise it won't be possible to separate it from the background in processing so it cannot 'participate' in the image. I don't insist that this is true, it is just what I've assumed.

Olly

That is quite correct for stack of calibrated subs, signal needs to "beat" all noise sources by about 3:1 (I've done some tests, 3:1 is recognizable but noisy, 5:1 can be processed out so that almost no noise is visible) in order to participate in the image in the meaningful way.

But this has nothing to do with signal beating noise in single sub. This is exactly why we take multiple subs. For me for example, dominating noise term is LP rather then read noise. So much of signal in my subs is buried in LP noise, and some is indeed below read noise but when stacked if 3:1 or above is achieved - signal is there to participate in the image, regardless of the fact that in single sub both read noise and LP noise beat it.

Take for example these two - one single sub and one stack of many subs - stretched the same. Small galaxy and surrounding faint stars are in noise level or below in left image - but show clearly in right.

(images are just linearly stretched)

[ollypenrice]

30 minutes ago, vlaiv said:

That is quite correct for stack of calibrated subs, signal needs to "beat" all noise sources by about 3:1 (I've done some tests, 3:1 is recognizable but noisy, 5:1 can be processed out so that almost no noise is visible) in order to participate in the image in the meaningful way.

But this has nothing to do with signal beating noise in single sub. This is exactly why we take multiple subs. For me for example, dominating noise term is LP rather then read noise. So much of signal in my subs is buried in LP noise, and some is indeed below read noise but when stacked if 3:1 or above is achieved - signal is there to participate in the image, regardless of the fact that in single sub both read noise and LP noise beat it.

Take for example these two - one single sub and one stack of many subs - stretched the same. Small galaxy and surrounding faint stars are in noise level or below in left image - but show clearly in right.

(images are just linearly stretched)

I see. For me, imaging at a dark site, I can expose for as long as I like, to all intents and purposes. I often do 30 minute L subs, for instance, and I find that these are advantageous for finding the very faint signal but that twice as many 15 minute ones probably give a smoother result on the less faint signal. I've always understood that the read noise prevents multiple short subs matching fewer longer ones in CCD imaging (at a dark site) but that the low read noise of CMOS makes multiple shorter subs attractive.

Olly

[gorann]

This is probably besides the point, but my thought is that if I ever get a dual rig (assuming it means having two identical scopes side by side, and not a refractor and a telephoto lens side by side as I now have) I would equip one with a mono and one with a colour camera with the same chip (like ASI1600MM and MC) and then collect RGB with one and Lum and possibly Ha with the other. That would save having a filter wheel on one of them and it just seems a bit dull to me to let the two scopes do the same thing.