[naskies (Dave)]

Hi Ray,

Originally Posted by Shiraz

A generally accepted rule for choosing the sub length is to make the subs long enough that shot noise in a sub (from the sky background) will overwhelm the read noise that is added at the end of the sub exposure. A widely used equation for determining an appropriate sub length is that from Starizona, which is:

Sub length = constant*(readnoise*readnoise)/skyflux

The key thing about this equation is that the sub length is proportional to the square of the read noise (for a given sky flux).

Rick posted this link in another discussion thread recently on this very topic:

http://www.cloudynights.com/item.php?item_id=1622

(One issue being that the sky-noise-dominating-read-noise equation ignores the target brightness and noise.)

To put some numbers on this, if a system using a camera with a read noise of 10 electrons requires 10 minute subs, a similar camera, but with a read noise of 5 electrons, would only require 2.5 minute subs for the same conditions (half the read noise, a quarter the sub length).

I'm not sure that this is correct... SNR = Signal / Noise for a single sub, i.e. it's a linear relationship. If you halve the noise, you can only halve the signal to keep the same SNR.

Adding n separate subs together gives you SNR = n * Signal / (Sqrt(n) * Noise), i.e. the "four times the integration time for half the noise" relationship that we're all familiar with.

You could use longer subs, but you wouldn’t gain anything practical in signal to noise ratio, since read noise has already been taken out of consideration once subs are longer than 2.5 minutes.

There's a zone where the SNR depends purely on total integration time, i.e. where the number of subs and the sub length are interchangeable provided that the total integration time remains constant.

However, the main reason for longer subs is to go deeper by avoiding quantisation errors. If your target is so dim that you're only getting 1 photon every 5 mins (e.g. a faint jet from a galaxy) - but you're taking 2.5 min subs - then it'll just be lost in the noise and you won't record a signal over the noise at all.

On the other hand, if you take 5 min subs you'd be able to detect a 1 photon brightening over the surrounding background with lots of stretching. However, with an average of 1 photon you won't be able to detect any surface detail - there's no zoom for contrast. With 30 min subs, you'd average 6 photons per sub... and there'd be enough room to have brighter (e.g. 8 photons) or darker (e.g. 4 photons) regions within the surface for detail.

This is also why long narrowband subexposures show more detail.

Don't forget the other source of noise: non-Poisson/non-random noise such as pixel defects, cosmic rays, planes, satellites, and so on. These will decrease only by dithering and stacking a larger number of subs (individual sub length has little effect).

The new breed of low read noise chips (eg from Sony) really can operate very effectively with short subs – the game is changing.

Absolutely - for bright regions where plenty of photons are coming in. However, even low noise sensors will still have quantisation issues.

The complete game changer will be if we get effectively *zero* noise sensors one day: stacking will be done by sum rather than average/median combine. This would also make lucky imaging possible - just take the sharp frames of a video and sum them over the subexposure time. Maybe we'll also have to carry tanks of liquid nitrogen or helium out to our dark sites one day?

The other thing to note from the equation is that the sub length is inversely proportional to sky flux – if the sky is bright, you can use shorter subs than if it is dark. Shorter subs do not help with sensitivity under bright sky, but they do not make it any worse - the shot noise from the sky is so high that it doesn’t matter if you add a bit more read noise.

The SNR is worse under bright skies. Although you don't have to expose for as long, the sky shot noise contribution is proportional to the square root of the brightness, i.e. 4x the sky brightness leads to 2x the sky shot noise. To cancel out 2x the sky shot noise, you'll have to increase the total integration time by 4x (but you can use shorter subexposures to do so). Intuitively, most of us have experienced this - shooting shorter subs from light pollution, but stacking a huge number of them to overcome the noise.

All this goes out the window with NB - the sky flux in the equation above will be very small and the basic rule is that subs should be as long as possible - low read noise chips will have better SNR, but even they can benefit from long subs in NB.

It's not technically just a NB thing - this applies whenever the target is *much* brighter the sky background, such as NB exposures or even say Orion Nebula under mag 22 dark skies.

This is a good zone to be in, because SNR increases linearly with sub duration (sky noise contribution is effectively zero)... which is why it's still worth shooting Orion Nebula under dark skies.

thanks for reading - discussion welcomed. regards ray

Thanks for the discussion. My comments above are based on my understanding of the maths/stats behind image sampling (e.g. the formulae in the Anstey article). Feel free to correct the inevitable mistakes that I've made