OK, so before you write in the comments that the video is wrong, read this! It is 100% true that for a given amount of exposure time, the F/4 setup has 1/2 the SNR as the F/2. So... you could very reasonably make the argument that the F/4 scope is only half as fast (not 1/4 as fast) as the F/2. But, at the end there, when examining "average speed" measured in SNR per hour, it seems like the F/2 setup is 4x as fast! What the heck is going on?! This is why, I assume, Dr. Detail interjected himself at the end. It seems like there is a paradox! How can we resolve it? Feel free to comment on how the paradox can be resolved! 💛 Also, if you'd like to support the channel, you can at buymeacoffee.com/deepskydetail
I would say there is a mixing of context here. One context is your example of just doubling the objective giving you 4x more signal. If done with the same exposure time then there is no additional noise so you get 4x more SNR. This is how focal stops are used, f/4, f2.8, f/2. Each focal stop is a 2x or 1/2 change in light gathering presuming shutter speed is the same so the noise is consistent. But most doing AP aren't doing this which is the second scenario. They want to know with the same given setup how much more total integration time is needed to double the SNR. So, now noise is a factor. Noise is random and doubling the integration time only adds the square root of the noise. So with the same setup, taking 4x more integration time along with the square root of 4x the noise will yield a 2x increase in SNR (4x signal / sqrt of 4x noise = 2x SNR).
Thanks for the comment! All that makes sense to me. But, could you explain hour SNR per hour is still 4x faster for the faster setup? In other words, it seems like even considering the noise, it's still 4x faster.
@@deepskydetail I'm not sure I completely understand your question, but I'll try, though it's just going to be a reiteration of my comment. In my opinion, the only way noise wouldn't figure in is if the two SNR comparisons had the same noise either because the noise was completely discounted for both or they had the same noise due to equal integration times. In your example, you completely discounted the noise so you got full signal benefit by doubling the objective size. That should be the case also with noise as long as the noise was the same in the comparison as they would cancel each other out. In my experience, when I hear you need 4x the exposure to get 2x the SNR, they are talking about a single setup and just changing integration time so in that situation as you increase the integration time you get the increase in signal along with the increase in noise. In this case, the signal will increase linearly (coherent signal) while the noise will only increase by the square root (random signal, i.e. noise). In the previous example, you don't get that increase in noise. I'm definitely not an expert on this. Thanks Edit. When I say noise above, I'm talking about shot noise. If there is a meaningful amount of sky glow/light pollution then even if you keep the same amount of shot noise and increase only the objective, then I expect you will see also an increase in the amount of noise due to the sky glow/light pollution which would also be better gathered along with the signal which would reduce getting the full SNR increase.
Just to clarify: I didn't ignore noise for either setup. The SNR calculation takes into account the noise. So when I put in the signal measurements, the shot noise gets calculated too. The other types of noise were removed to make the example simpler, but we would still have the same "paradox."
Let me clarify, at the beginning the thing that is untrue is "4x the signal is 2x the speed." At the end of the video, this remains untrue. What is true is 4x the signal = 2x SNR. And SNR is not speed.
So, I was happy with your video until the bait & switch at the end. Come on now. You are normally the only channel that I can rely on to get the math correct. This is simple. Noise increases at the SQRT() of Signal. Why persist with the false equivalence of speed? Also, sticking with square numbers makes this topic a lot easier to understand: 4, 8, 16, 32, etc. With 16x180 sec frames, I have a great signal and 1/8th of the original noise, no calculator needed. Speed and focal length are the two characteristics that get mixed and confused. There you have it correct, with the pixels receiving more photons, so no issues. Maybe separate these topics to get a clearer message.
It's the pinned comment. The thing I want to dive into in the next video is the apparent contradiction where at any time comparing the f2 and f4 system, the f2 system has 2x the SNR. But (!!) using the average SNR per hour, it still seems like SNR is being gathered 4x as fast. It seems like a paradox, and next video I want to dive into it a bit deeper.
OK, so before you write in the comments that the video is wrong, read this! It is 100% true that for a given amount of exposure time, the F/4 setup has 1/2 the SNR as the F/2. So... you could very reasonably make the argument that the F/4 scope is only half as fast (not 1/4 as fast) as the F/2. But, at the end there, when examining "average speed" measured in SNR per hour, it seems like the F/2 setup is 4x as fast! What the heck is going on?! This is why, I assume, Dr. Detail interjected himself at the end. It seems like there is a paradox! How can we resolve it? Feel free to comment on how the paradox can be resolved! 💛
Also, if you'd like to support the channel, you can at buymeacoffee.com/deepskydetail
Ok.. agree
As I understand, SNR measurements are only reference to noise( noise floor). Sometimes are in decibels.
I would say there is a mixing of context here. One context is your example of just doubling the objective giving you 4x more signal. If done with the same exposure time then there is no additional noise so you get 4x more SNR. This is how focal stops are used, f/4, f2.8, f/2. Each focal stop is a 2x or 1/2 change in light gathering presuming shutter speed is the same so the noise is consistent. But most doing AP aren't doing this which is the second scenario. They want to know with the same given setup how much more total integration time is needed to double the SNR. So, now noise is a factor. Noise is random and doubling the integration time only adds the square root of the noise. So with the same setup, taking 4x more integration time along with the square root of 4x the noise will yield a 2x increase in SNR (4x signal / sqrt of 4x noise = 2x SNR).
Thanks for the comment! All that makes sense to me. But, could you explain hour SNR per hour is still 4x faster for the faster setup? In other words, it seems like even considering the noise, it's still 4x faster.
@@deepskydetail I'm not sure I completely understand your question, but I'll try, though it's just going to be a reiteration of my comment. In my opinion, the only way noise wouldn't figure in is if the two SNR comparisons had the same noise either because the noise was completely discounted for both or they had the same noise due to equal integration times. In your example, you completely discounted the noise so you got full signal benefit by doubling the objective size. That should be the case also with noise as long as the noise was the same in the comparison as they would cancel each other out. In my experience, when I hear you need 4x the exposure to get 2x the SNR, they are talking about a single setup and just changing integration time so in that situation as you increase the integration time you get the increase in signal along with the increase in noise. In this case, the signal will increase linearly (coherent signal) while the noise will only increase by the square root (random signal, i.e. noise). In the previous example, you don't get that increase in noise. I'm definitely not an expert on this. Thanks
Edit. When I say noise above, I'm talking about shot noise. If there is a meaningful amount of sky glow/light pollution then even if you keep the same amount of shot noise and increase only the objective, then I expect you will see also an increase in the amount of noise due to the sky glow/light pollution which would also be better gathered along with the signal which would reduce getting the full SNR increase.
Just to clarify: I didn't ignore noise for either setup. The SNR calculation takes into account the noise. So when I put in the signal measurements, the shot noise gets calculated too. The other types of noise were removed to make the example simpler, but we would still have the same "paradox."
Says something is untrue and then proves it's true but in a very confusing and obtuse way...
You got that right!
Let me clarify, at the beginning the thing that is untrue is "4x the signal is 2x the speed." At the end of the video, this remains untrue. What is true is 4x the signal = 2x SNR. And SNR is not speed.
F2 is 4 times faster than F2, not double. F2.8 is the double for F4
I would agree with that: f2 is 4 times faster than f4, and roughly 2x faster for f2.8 :)
So, I was happy with your video until the bait & switch at the end. Come on now. You are normally the only channel that I can rely on to get the math correct. This is simple. Noise increases at the SQRT() of Signal. Why persist with the false equivalence of speed? Also, sticking with square numbers makes this topic a lot easier to understand: 4, 8, 16, 32, etc. With 16x180 sec frames, I have a great signal and 1/8th of the original noise, no calculator needed.
Speed and focal length are the two characteristics that get mixed and confused. There you have it correct, with the pixels receiving more photons, so no issues. Maybe separate these topics to get a clearer message.
It's the pinned comment. The thing I want to dive into in the next video is the apparent contradiction where at any time comparing the f2 and f4 system, the f2 system has 2x the SNR. But (!!) using the average SNR per hour, it still seems like SNR is being gathered 4x as fast. It seems like a paradox, and next video I want to dive into it a bit deeper.
In other words, I don't think the apparent contradiction is dealt with very well and needs more elaboration.