86 replies to this topic

[pvdv]

if one stacks in groups of N (e.g. 6x10s or 9x10s).

I don't think stacking is needed, if you have 3600 measurements and stack them by 9 you'll get 400 "better" measurements. If you measure 3600 times and bin the measure by 9, the result is identical (if you maintain numerical accuracy of course in order to avoid quantization which may matter with very low ADU counts)

Edited by pvdv, 04 April 2025 - 07:12 AM.

[terrain_inconnu]

I don't think stacking is needed, if you have 3600 measurements and stack them by 9 you'll get 400 "better" measurements. If you measure 3600 times and bin the measure by 9, the result is identical (if you maintain numerical accuracy of course in order to avoid quantization which may matter with very low ADU counts)

I don't know enough about binning but I do occasionally stack because otherwise the photometry on 13-14 mag stars will fail. At least that was my experience with Seestar data and ASTAP so far.

[pvdv]

Just to be clear, I am talking about binning the measurements (not the sensor) by 9 as opposed to stacking the images by 9 - it is mathematically identical and in practice that can save time because you don't need to split your data and stack it. On top of that, stacking may have implementation issues (as in Pixinsight using defaults) but Astap should be OK

 

[Xilman]

I don't think stacking is needed, if you have 3600 measurements and stack them by 9 you'll get 400 "better" measurements. If you measure 3600 times and bin the measure by 9, the result is identical (if you maintain numerical accuracy of course in order to avoid quantization which may matter with very low ADU counts)

That assumes that all 3600 targets of interest are bright enough to be measured individually.  That is they are at least several times brighter than the sky background.

 

If the images are stacked and the result measured, the sky background can be subtracted more accurately from the much greater intensity of (sky+object) resulting in an adequate SNR for the object itself.

 

For example: with stacking I have detected with a SNR of 3-5 objects which are only 1% the brightness of the sky. Useful photometry (SNR 10-100) can be done on objects 10% - 100% of the sky brightness. They are completely invisible on each sub.

 

An example can be found here: http://www.astropalm.../praxidike.html where the object was catalogued at mag 21.7 and the sky brightness at 21.0 mag/arcsec^2.  The seeing disk is around 2.5 arcsec in diameter, or 4.9 arcsec^2 in area.  A factor of 4.9 corresponds to 1.7 magnitudes, so the sky flux from the seeing disk is (21-1.7) =19.3 magnitudes, which is 2.4 magnitudes brighter than the target. A magnitude difference of 2.4 corresponds to a brightness ratio of 9.2.  In other words, the object is only 11% as bright as the sky background.

 

 

(Edited to fix a small but important error in the calculation. I had assumed an area of sky which was a 2.5 arcsec square, not a circle.)

Edited by Xilman, 04 April 2025 - 09:05 AM.

[Xilman]

On top of that, stacking may have implementation issues (as in Pixinsight using defaults) but Astap should be OK

My approach to stacking uses SWarp to put a WCS (world coordinate system) on each sub and then astronomy.net, which uses the WCS, to stack the results.  Has worked very well indeed for tens of thousands of images taken over six years. YMMV.

[pvdv]

Yes, I saw that one when you mentioned it earlier. Very impressive result!

Still, as long as numerical accuracy is conserved, I just don't see, mathematically, how the difference arises. 9 times 10 seconds of average stacked sky backgrounds are equivalent to 9 individual measurements average binned.  That being said, "numerical accuracy being preserved" is one of the issues with different stackers.

Very accurate WCS and plate distortion coefficients also certainly help (as opposed to some stackers who will just align on psf peaks without any care for plate distortions).

I was surprised a few times myself, for example with Tycho synthetic tracker identifying with high confidence a 22 ish mag asteroid, in the haze of Pleiads no less, while my SQM reported 21.4 at the zenith. In that case there is however a possible explanation: the asteroid is rotating and one of its side is more reflective and it was higher than mag 22. It is not as if we have detailed light curves for all those small faint bodies.

[Xilman]

Yes, I saw that one when you mentioned it earlier. Very impressive result!

Still, as long as numerical accuracy is conserved, I just don't see, mathematically, how the difference arises. 9 times 10 seconds of average stacked sky backgrounds are equivalent to 9 individual measurements average binned.  That being said, "numerical accuracy being preserved" is one of the issues with different stackers.

The fly in the ointment is noise.

 

Here's a quick OOM calculation to show the problem.

 

Assume the average sky background is 900 counts and the object is 10 times fainter than the sky, so 990 counts come from object+sky. One sigma noise in the sky (assuming ideal statristics) is then sqrt(900)=30.  (That's why I chose 900: to make the numbers simpler.) The noise in object+sky is then sqrt(990) = 31.5.  Now subtract the average sky background to find a point source containing 90 counts. However, in subtraction the noise adds in quadrature. sqrt (30*30 +31.5*31.5) = sqrt (1890) = 43.5. As the signal is 90 counts, the SNR is 90/43.5 = 2.1.  An object in an image like that is barely detectable --- even with the aid of extreme contrast enhancement, a good catalogue, and the eye of faith. It certainly isn't measurable photometrically.

 

Now add 100 subs. The sky background now contributes 900*100 = 90000 counts with noise of 300 and the sky + object comes to 99000 with noise 315.  The noise in the combined measurement is 435. Now the object contributes 9000 (i.e. 90 * 100) counts and the SNR is now 9000/435 = 21.  That is very easily measurable and will give a precision of about 0.05 magnitudes.

 

TL;DR.  Adding N subs lets you detect and measure objects which are sqrt(N) times fainter. In this sentence, the important word is measure.

 

 

(Thinking about my earlier post: the sky brightness could well have been significantly brighter than the 21.0 m/arcsec^2 assumed. Jupiter was close to the FOV and scattered light from the planet is readily visible in the image.  If this was the case, Praxidike may have ten times or more fainter than the sky.)

[pvdv]

Yeah, I understand how stacking increases SNR - that's the most very basic thing there is to know tbh .

 

But that's not my point at all...My point is that if you take those 100 poor measurements and average them, you get the same result as a single measurement on a stack.
Which means that in practice there is no need to go to the trouble of doing partial stacks of a large data set.

 

(provided of course you maintain numerical accuracy if the measurements are extremely small)

[robin_astro]

Making individual measurements and combining them after also allows any outliers to be spotted and removed without contaminating the combined measurement and you can use the statistics of the individual measurements to give a robust estimate of the SNR. (This assumes read noise is not a limiting factor, in which case longer exposures are better as long as you can still get the required temporal resolution)

Edited by robin_astro, 04 April 2025 - 01:51 PM.

[Xilman]

Yeah, I understand how stacking increases SNR - that's the most very basic thing there is to know tbh .

 

But that's not my point at all...My point is that if you take those 100 poor measurements and average them, you get the same result as a single measurement on a stack.
Which means that in practice there is no need to go to the trouble of doing partial stacks of a large data set.

 

(provided of course you maintain numerical accuracy if the measurements are extremely small)

If you can measure them at all.  That is my point.

[robin_astro]

If you can measure them at all.  That is my point.

It certainly helps to be able to see the target in the sub exposures! Even then if you plate solve and know where the target is you could do forced photometry on the individual images and still combine the the data. At the end of the day you are working with the same numerical pixel values. Tycho tracker though for example appears to shift and stack the images to find faint moving objects.  Perhaps it is  computationally faster using GPU hardware. On a single fixed target though measuring the target area in each image is probably quicker as you are only interested in a small number of pixels in each image.

[pvdv]

On the topic of faint moving objects, background noise synthetic tracking, here's an excellent paper

https://arxiv.org/pdf/2401.03255

Some things surprised me a bit, for example, talking about IMX 455 based cameras and RASAs

"Such a low read noise means even during dark times near the new moon, taking

frames at 1 Hz, the read noise is still lower than the sky background noise for an 11-inch telescope." 

Intuitively, I would have thought this was a significant issue.

The appendix is intesting as well, even if it goes a bit beyong stacking increases SNR