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Originally Posted by Peter.M
And this is where the "you need more exposure for narrower bandpasses" statement comes from. If you are saying that the shot noise is reduced by a factor of 2.8 (signal surely isnt going up by changing a filter) then it stands to reason that to make a single sub shot noise limited, the 3nm filter will need each sub to be 2.8 times longer than the 5nm.
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Ahhh... no.
The point I was trying to get across was that (assuming the signal was identical in each filter) and that the background noise in the 5nm filter is 5/3 greater. Then to achieve the same signal to noise ratio
of faint features using the 5nm filter you would need to increase the exposure by the ratio of 5^2/3^2 = 25/9 = 2.7777
If you were to compare an exposure through a 3nm filter that had a duration 2.7777 times the length of one taken through the 5nm filter then it would have 2.7777^0.5 x (5/3)^2 = 4.63 times the signal to noise... for faint features. However, when the nebula is bright enough to dominate the background noise, the difference between 3 & 5nm filters completely evaporates.
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I think the thing that trips people up is that the 3nm filter image will be read noise limited, which will still be lower than the total noise in the 5nm image, even if they are exposed for the same duration.
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The focal ratio, camera noise, sky background and signal intensity are variable to the extent that you cannot use this as an accurate premise.
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So the statement that it "needs" more exposure is not valid, the 3nm filter would benefit from more exposure, where the 5nm would not.
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More exposure than what?
The fact of the matter is that there is an optimum exposure which can be derived from sky background, camera read noise, filter bandwidth, focal ratio and signal intensity. When the signal is bright, you can get away with a lot. For the faintest nebula, the formula is simple:
Narrow bandwidth
Fastest focal ratio (up to a point)
Darkest sky.
Optimum exposure.
When you align those ducks, the 3nm filter will record the faintest details 2.7777 times faster than through the 5nm filter.
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