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Question About Dark Skies and SNR

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#1 rhart426

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Posted 06 July 2020 - 06:19 PM

Hello everyone,

 

I've recently made the leap from DSLR to an ASI1600-MM, and it's going great!  I've adapted my acquisition processes so that I'm now getting the best guiding, FWHM, and eccentricity values I've seen yet.  I even had a chance to take it up to Cherry Springs for some dark sky action and acquired some truly excellent data.  I'm curious about how to compare the data from each site though.

 

For reference, here are the relevant statistics for comparison.  Both images are of the Witch's Broom, S2 filter, 10 minutes, Gain 200, Offset 50, (Minimum) Target ADU (16-bit) = 1300.  Median ADU was measured from uncalibrated frames, while SNRWeight was measured (in PixInsight) on the same frames after calibration.

 

Backyard: SQM = 19.47, Median ADU = 1440, SNRWeight = 1.4359

 

Cherry Springs: SQM = 21.94, Median ADU = 1175 (I've read that 10 minute exposures are the maximum duration you should do with this camera, so I didn't increase the exposure even though this fell below 1300.), SNRWeight = 3.0615

 

So, the difference in sky brightness should be 2.512^(21.94-19.47) = 9.73, so an hour at the dark site should equal 9.73 hours in my backyard.  Comparing the SNRWeights in PixInsight shows a much more modest ratio of 2:1.  Am I looking at this the right way?  If so, what is causing the discrepancy? If not, where am I going wrong?

 

As always, thank you for considering my question!


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#2 ceteris_paribus

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Posted 06 July 2020 - 06:49 PM

It's been awhile since I did the maths on these kinds of things, but I think the discrepancy is appearing because the noise term should be a square root.  The full formula for SNR would be SNR = Signal / sqrt(signal + skyfog + Dark Noise + ... etc.).  The important term here is the skyfog, which is your light pollution in this case.  Given that this term will be far and away larger than the other terms under the square root, I'll use the simplified formula of SNR = signal / sqrt(skyfog).  So, if skyfog increases by a factor of 9, you'd see an SNR that is 1/3 of normal.  This is not exactly what you have, but there are always other variables such as seeing conditions and the way that Pixinsight calculates SNRWeight that might account for there being a 2x difference instead of a 3x.  Either way, numbers make a whole lot more sense if you calculate it with the square root.  I hope this helps.

 

Take care,

 

-John


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#3 AstroBrett

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Posted 06 July 2020 - 06:52 PM

If you refer to PI's documentation regarding SNRWeight, here is what is says:

 

The signal to noise ratio weight estimate for the subframe. SNRWeight equals MeanDeviation2 / Noise2. SNRWeight is unnormalized approximation to the current NoiseEvaluation weight used by the ImageIntegration process. In a subframe integration, the ratio between a subframe's SNRWeight and the reference subframe's SNRWeight approximately equals the NoiseEvaluation weight of the subframe.

The significance of the unnormalized SNRWeight and the normalized NoiseEvaluation weight is that a weighted subframe integration using these weights is an approximate maximum likelyhood estimator for pixel values that correspond to background limited targets, without requiring additional information such as exposure times or sensor parameters. See the ImageIntegration documentation for more information.

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.

 

As you can see, SNRWeight is not intended to be a measure of SNR and as Juan has stated in PI's forum "We cannot estimate the SNR directly because the noise introduces uncertainty in the data".


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#4 rhart426

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Posted 06 July 2020 - 07:33 PM

Thank you for that!  So, SNRWeight is a relative value and won't help me here, and SNR can't be found directly.  So, I should just stick to the sky brightness ratio when determining my relative exposure between sites?



#5 sn2006gy

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Posted 06 July 2020 - 09:22 PM

You can run sharpcap Smart Histogram to calculate optimal gain, exposure, number of exposures based on sky brightness.




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