Signal to Noise Ratio

[Scooot]

I took a 120 subs of the Double Cluster the other evening with my Canon 450D and 135mm lens. I've begun to process them and used Pixinsights subframe selector  to analyse and pick the best subs.

I've noticed that as the evening drew on and the cluster sunk towards the horizon, the SNR on the subs begun to improve, so the best subs according to this measure are the latest, which doesn't make sense to me.

EG stats are

	Median	Median Deviation	Noise	SNR
Late Sub	73.948	8.215	3.511	5.4738
Early Sub	60.075	6.023	3.253	3.4277

I'd be interested in any thoughts on this. There is obviously a lot more light pollution lower down which is probably the increase in signal.

 

Edited February 19, 2020 by Scooot

[vlaiv]

I'm very skeptical of any tool that takes an image and reports single SNR value.

Such thing does not make any sense at all. Every single pixel has its own signal and its own noise and every signal in the image has SNR value associated with it. In principle there is no way to find out SNR value of any pixel in the image.

There is a way to get good SNR approximation if there is no much change in the conditions when image is shot - meaning SNR remains roughly the same over the course of the evening. In this case - you can take average of values for each pixel to be signal - that is what regular stacking does, and then take standard deviation of the stack for each pixel and divide with square root of number of subs to get the final noise of the stack (or just standard deviation without dividing with square root of number of subs to get noise per sub).

This works if subs are the same - but they almost never are. As target moves across the sky during the course of the evening it will be both in parts of the sky with different levels of LP and will be at different air-mass meaning it will be attenuated by different amount - more or less bright. First changes total amount of noise, second changes both signal and noise parts - thus each sub will have different level of noise once we equalize signal.

There are methods to actually both equalize the signal and measure noise - but not for single sub, rather for intensity range and sub as part of ensemble of subs.

Back to original question and why there is no single SNR in the image. Imagine you have two galaxies in the image - one bright with signal 100 and other faint with signal 10, and background noise with value of 2. SNR of first galaxy will be 100/2 = 50, SNR of second galaxy will be 10/2 = 5 and SNR of background sky will be 0/2 = 0

Which one is SNR of the image? 50, 5 or 0?

Imagine if you have background LP, so there is component of the signal that is unwanted over the whole image - let it be 2 as well. Now we have signal in bright galaxy to be 102 and noise 2 so SNR now is 51, similarly for faint galaxy SNR will now be 6 and for background SNR will be 1.

But we did not change signals of galaxies, nor did we change level of noise (although background LP will change the level of noise - I'm just making a point here) - suddenly we now have different SNR values because there is some offset in values in the image.

True SNR value can only be associated with each pixel and can be approximately calculated once you take into account:

- that each sub is part of ensemble of subs

- equalize signal levels in each sub

- account for different level of noise in different subs (this is really hard part)

- remove background LP signal (this part is also quite hard).

Weighted stacking by single SNR value is not really the best approach to handle things.

[Scooot]

Thanks very much for your detailed response Vlaiv.

I won’t use their SNR in this tool from now on. It certainly doesn’t seem to very useful with this set of subs.  

[vlaiv]

44 minutes ago, Scooot said:

Thanks very much for your detailed response Vlaiv.

I won’t use their SNR in this tool from now on. It certainly doesn’t seem to very useful with this set of subs.  

Do you by any chance know how is it calculated? That might shed some light if it is useful and under what circumstances.

For example - it could be calculated like this:

Take all pixels that are dark enough (sigma reject all bright pixels) and calculate standard deviation of such pixels - that is good approximation of background noise if there is enough empty background - it will not work well if much of the image is covered by nebulosity.

Take all other pixels and calculate average pixel value - subtract average pixel value from first group of pixels (LP level) - this gets you "average" signal.

So you conclude that SNR is average signal / background noise for example or something similar.

[Scooot]

33 minutes ago, vlaiv said:

Do you by any chance know how is it calculated? That might shed some light if it is useful and under what circumstances.

For example - it could be calculated like this:

Take all pixels that are dark enough (sigma reject all bright pixels) and calculate standard deviation of such pixels - that is good approximation of background noise if there is enough empty background - it will not work well if much of the image is covered by nebulosity.

Take all other pixels and calculate average pixel value - subtract average pixel value from first group of pixels (LP level) - this gets you "average" signal.

So you conclude that SNR is average signal / background noise for example or something similar.

Yes on the table in my original post, it’s the Median Deviation squared / noise squared.

The median is the median of the subframe in electrons or Data Numbers.

In circumstances when the light pollution doesn’t alter much over the image run the differences in SNR might be more useful. I don’t think they’re meant to be an accurate measure of the SNR in each image but more as a comparison between images.

Edited February 19, 2020 by Scooot

[Aramcheck]

20 minutes ago, vlaiv said:

Do you by any chance know how is it calculated? That might shed some light if it is useful and under what circumstances.

This might help:- https://pixinsight.com/doc/scripts/SubframeSelector/SubframeSelector.html#subframe_property_SNRWeight

 

[Scooot]

1 hour ago, Aramcheck said:

This might help:- https://pixinsight.com/doc/scripts/SubframeSelector/SubframeSelector.html#subframe_property_SNRWeight

 

Yes thanks,

this is the crux of the matter in this case.

“Note that SNRWeight and NoiseEvaluation weight are relative and not absolute measures of signal to noise ratio. Their formulation assumes that the subframes represent observations of the same target and that the subframes have similar background gradients.”